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cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/series/tests/test_limits.py
|
from itertools import product as cartes
from sympy import (
limit, exp, oo, log, sqrt, Limit, sin, floor, cos, ceiling,
atan, gamma, Symbol, S, pi, Integral, Rational, I, EulerGamma,
tan, cot, integrate, Sum, sign, Function, subfactorial, symbols,
binomial, simplify, frac, Float)
from sympy.calculus.util import AccumBounds
from sympy.core.add import Add
from sympy.core.mul import Mul
from sympy.series.limits import heuristics
from sympy.series.order import Order
from sympy.utilities.pytest import XFAIL, raises
from sympy.core.numbers import GoldenRatio
from sympy.functions.combinatorial.numbers import fibonacci
from sympy.abc import x, y, z, k
n = Symbol('n', integer=True, positive=True)
def test_basic1():
assert limit(x, x, oo) == oo
assert limit(x, x, -oo) == -oo
assert limit(-x, x, oo) == -oo
assert limit(x**2, x, -oo) == oo
assert limit(-x**2, x, oo) == -oo
assert limit(x*log(x), x, 0, dir="+") == 0
assert limit(1/x, x, oo) == 0
assert limit(exp(x), x, oo) == oo
assert limit(-exp(x), x, oo) == -oo
assert limit(exp(x)/x, x, oo) == oo
assert limit(1/x - exp(-x), x, oo) == 0
assert limit(x + 1/x, x, oo) == oo
assert limit(x - x**2, x, oo) == -oo
assert limit((1 + x)**(1 + sqrt(2)), x, 0) == 1
assert limit((1 + x)**oo, x, 0) == oo
assert limit((1 + x)**oo, x, 0, dir='-') == 0
assert limit((1 + x + y)**oo, x, 0, dir='-') == (1 + y)**(oo)
assert limit(y/x/log(x), x, 0) == -oo*sign(y)
assert limit(cos(x + y)/x, x, 0) == sign(cos(y))*oo
assert limit(gamma(1/x + 3), x, oo) == 2
assert limit(S.NaN, x, -oo) == S.NaN
assert limit(Order(2)*x, x, S.NaN) == S.NaN
assert limit(1/(x - 1), x, 1, dir="+") == oo
assert limit(1/(x - 1), x, 1, dir="-") == -oo
assert limit(1/(5 - x)**3, x, 5, dir="+") == -oo
assert limit(1/(5 - x)**3, x, 5, dir="-") == oo
assert limit(1/sin(x), x, pi, dir="+") == -oo
assert limit(1/sin(x), x, pi, dir="-") == oo
assert limit(1/cos(x), x, pi/2, dir="+") == -oo
assert limit(1/cos(x), x, pi/2, dir="-") == oo
assert limit(1/tan(x**3), x, (2*pi)**(S(1)/3), dir="+") == oo
assert limit(1/tan(x**3), x, (2*pi)**(S(1)/3), dir="-") == -oo
assert limit(1/cot(x)**3, x, (3*pi/2), dir="+") == -oo
assert limit(1/cot(x)**3, x, (3*pi/2), dir="-") == oo
# approaching 0
# from dir="+"
assert limit(1 + 1/x, x, 0) == oo
# from dir='-'
# Add
assert limit(1 + 1/x, x, 0, dir='-') == -oo
# Pow
assert limit(x**(-2), x, 0, dir='-') == oo
assert limit(x**(-3), x, 0, dir='-') == -oo
assert limit(1/sqrt(x), x, 0, dir='-') == (-oo)*I
assert limit(x**2, x, 0, dir='-') == 0
assert limit(sqrt(x), x, 0, dir='-') == 0
assert limit(x**-pi, x, 0, dir='-') == oo*sign((-1)**(-pi))
assert limit((1 + cos(x))**oo, x, 0) == oo
def test_basic2():
assert limit(x**x, x, 0, dir="+") == 1
assert limit((exp(x) - 1)/x, x, 0) == 1
assert limit(1 + 1/x, x, oo) == 1
assert limit(-exp(1/x), x, oo) == -1
assert limit(x + exp(-x), x, oo) == oo
assert limit(x + exp(-x**2), x, oo) == oo
assert limit(x + exp(-exp(x)), x, oo) == oo
assert limit(13 + 1/x - exp(-x), x, oo) == 13
def test_basic3():
assert limit(1/x, x, 0, dir="+") == oo
assert limit(1/x, x, 0, dir="-") == -oo
def test_basic4():
assert limit(2*x + y*x, x, 0) == 0
assert limit(2*x + y*x, x, 1) == 2 + y
assert limit(2*x**8 + y*x**(-3), x, -2) == 512 - y/8
assert limit(sqrt(x + 1) - sqrt(x), x, oo) == 0
assert integrate(1/(x**3 + 1), (x, 0, oo)) == 2*pi*sqrt(3)/9
def test_basic5():
class my(Function):
@classmethod
def eval(cls, arg):
if arg is S.Infinity:
return S.NaN
assert limit(my(x), x, oo) == Limit(my(x), x, oo)
def test_issue_3885():
assert limit(x*y + x*z, z, 2) == x*y + 2*x
def test_issue_10382():
n = Symbol('n', integer=True)
assert limit(fibonacci(n+1)/fibonacci(n), n, oo) == S.GoldenRatio
def test_Limit():
assert Limit(sin(x)/x, x, 0) != 1
assert Limit(sin(x)/x, x, 0).doit() == 1
def test_floor():
assert limit(floor(x), x, -2, "+") == -2
assert limit(floor(x), x, -2, "-") == -3
assert limit(floor(x), x, -1, "+") == -1
assert limit(floor(x), x, -1, "-") == -2
assert limit(floor(x), x, 0, "+") == 0
assert limit(floor(x), x, 0, "-") == -1
assert limit(floor(x), x, 1, "+") == 1
assert limit(floor(x), x, 1, "-") == 0
assert limit(floor(x), x, 2, "+") == 2
assert limit(floor(x), x, 2, "-") == 1
assert limit(floor(x), x, 248, "+") == 248
assert limit(floor(x), x, 248, "-") == 247
def test_floor_requires_robust_assumptions():
assert limit(floor(sin(x)), x, 0, "+") == 0
assert limit(floor(sin(x)), x, 0, "-") == -1
assert limit(floor(cos(x)), x, 0, "+") == 0
assert limit(floor(cos(x)), x, 0, "-") == 0
assert limit(floor(5 + sin(x)), x, 0, "+") == 5
assert limit(floor(5 + sin(x)), x, 0, "-") == 4
assert limit(floor(5 + cos(x)), x, 0, "+") == 5
assert limit(floor(5 + cos(x)), x, 0, "-") == 5
def test_ceiling():
assert limit(ceiling(x), x, -2, "+") == -1
assert limit(ceiling(x), x, -2, "-") == -2
assert limit(ceiling(x), x, -1, "+") == 0
assert limit(ceiling(x), x, -1, "-") == -1
assert limit(ceiling(x), x, 0, "+") == 1
assert limit(ceiling(x), x, 0, "-") == 0
assert limit(ceiling(x), x, 1, "+") == 2
assert limit(ceiling(x), x, 1, "-") == 1
assert limit(ceiling(x), x, 2, "+") == 3
assert limit(ceiling(x), x, 2, "-") == 2
assert limit(ceiling(x), x, 248, "+") == 249
assert limit(ceiling(x), x, 248, "-") == 248
def test_ceiling_requires_robust_assumptions():
assert limit(ceiling(sin(x)), x, 0, "+") == 1
assert limit(ceiling(sin(x)), x, 0, "-") == 0
assert limit(ceiling(cos(x)), x, 0, "+") == 1
assert limit(ceiling(cos(x)), x, 0, "-") == 1
assert limit(ceiling(5 + sin(x)), x, 0, "+") == 6
assert limit(ceiling(5 + sin(x)), x, 0, "-") == 5
assert limit(ceiling(5 + cos(x)), x, 0, "+") == 6
assert limit(ceiling(5 + cos(x)), x, 0, "-") == 6
def test_atan():
x = Symbol("x", real=True)
assert limit(atan(x)*sin(1/x), x, 0) == 0
assert limit(atan(x) + sqrt(x + 1) - sqrt(x), x, oo) == pi/2
def test_abs():
assert limit(abs(x), x, 0) == 0
assert limit(abs(sin(x)), x, 0) == 0
assert limit(abs(cos(x)), x, 0) == 1
assert limit(abs(sin(x + 1)), x, 0) == sin(1)
def test_heuristic():
x = Symbol("x", real=True)
assert heuristics(sin(1/x) + atan(x), x, 0, '+') == AccumBounds(-1, 1)
assert limit(log(2 + sqrt(atan(x))*sqrt(sin(1/x))), x, 0) == log(2)
def test_issue_3871():
z = Symbol("z", positive=True)
f = -1/z*exp(-z*x)
assert limit(f, x, oo) == 0
assert f.limit(x, oo) == 0
def test_exponential():
n = Symbol('n')
x = Symbol('x', real=True)
assert limit((1 + x/n)**n, n, oo) == exp(x)
assert limit((1 + x/(2*n))**n, n, oo) == exp(x/2)
assert limit((1 + x/(2*n + 1))**n, n, oo) == exp(x/2)
assert limit(((x - 1)/(x + 1))**x, x, oo) == exp(-2)
assert limit(1 + (1 + 1/x)**x, x, oo) == 1 + S.Exp1
@XFAIL
def test_exponential2():
n = Symbol('n')
assert limit((1 + x/(n + sin(n)))**n, n, oo) == exp(x)
def test_doit():
f = Integral(2 * x, x)
l = Limit(f, x, oo)
assert l.doit() == oo
def test_AccumBounds():
assert limit(sin(k) - sin(k + 1), k, oo) == AccumBounds(-2, 2)
assert limit(cos(k) - cos(k + 1) + 1, k, oo) == AccumBounds(-1, 3)
# not the exact bound
assert limit(sin(k) - sin(k)*cos(k), k, oo) == AccumBounds(-2, 2)
# test for issue #9934
t1 = Mul(S(1)/2, 1/(-1 + cos(1)), Add(AccumBounds(-3, 1), cos(1)))
assert limit(simplify(Sum(cos(n).rewrite(exp), (n, 0, k)).doit().rewrite(sin)), k, oo) == t1
t2 = Mul(S(1)/2, Add(AccumBounds(-2, 2), sin(1)), 1/(-cos(1) + 1))
assert limit(simplify(Sum(sin(n).rewrite(exp), (n, 0, k)).doit().rewrite(sin)), k, oo) == t2
assert limit(frac(x)**x, x, oo) == AccumBounds(0, oo)
assert limit(((sin(x) + 1)/2)**x, x, oo) == AccumBounds(0, oo)
# Possible improvement: AccumBounds(0, 1)
@XFAIL
def test_doit2():
f = Integral(2 * x, x)
l = Limit(f, x, oo)
# limit() breaks on the contained Integral.
assert l.doit(deep=False) == l
def test_issue_3792():
assert limit((1 - cos(x))/x**2, x, S(1)/2) == 4 - 4*cos(S(1)/2)
assert limit(sin(sin(x + 1) + 1), x, 0) == sin(1 + sin(1))
assert limit(abs(sin(x + 1) + 1), x, 0) == 1 + sin(1)
def test_issue_4090():
assert limit(1/(x + 3), x, 2) == S(1)/5
assert limit(1/(x + pi), x, 2) == S(1)/(2 + pi)
assert limit(log(x)/(x**2 + 3), x, 2) == log(2)/7
assert limit(log(x)/(x**2 + pi), x, 2) == log(2)/(4 + pi)
def test_issue_4547():
assert limit(cot(x), x, 0, dir='+') == oo
assert limit(cot(x), x, pi/2, dir='+') == 0
def test_issue_5164():
assert limit(x**0.5, x, oo) == oo**0.5 == oo
assert limit(x**0.5, x, 16) == S(16)**0.5
assert limit(x**0.5, x, 0) == 0
assert limit(x**(-0.5), x, oo) == 0
assert limit(x**(-0.5), x, 4) == S(4)**(-0.5)
def test_issue_5183():
# using list(...) so py.test can recalculate values
tests = list(cartes([x, -x],
[-1, 1],
[2, 3, Rational(1, 2), Rational(2, 3)],
['-', '+']))
results = (oo, oo, -oo, oo, -oo*I, oo, -oo*(-1)**Rational(1, 3), oo,
0, 0, 0, 0, 0, 0, 0, 0,
oo, oo, oo, -oo, oo, -oo*I, oo, -oo*(-1)**Rational(1, 3),
0, 0, 0, 0, 0, 0, 0, 0)
assert len(tests) == len(results)
for i, (args, res) in enumerate(zip(tests, results)):
y, s, e, d = args
eq = y**(s*e)
try:
assert limit(eq, x, 0, dir=d) == res
except AssertionError:
if 0: # change to 1 if you want to see the failing tests
print()
print(i, res, eq, d, limit(eq, x, 0, dir=d))
else:
assert None
def test_issue_5184():
assert limit(sin(x)/x, x, oo) == 0
assert limit(atan(x), x, oo) == pi/2
assert limit(gamma(x), x, oo) == oo
assert limit(cos(x)/x, x, oo) == 0
assert limit(gamma(x), x, Rational(1, 2)) == sqrt(pi)
r = Symbol('r', real=True, finite=True)
assert limit(r*sin(1/r), r, 0) == 0
def test_issue_5229():
assert limit((1 + y)**(1/y) - S.Exp1, y, 0) == 0
def test_issue_4546():
# using list(...) so py.test can recalculate values
tests = list(cartes([cot, tan],
[-pi/2, 0, pi/2, pi, 3*pi/2],
['-', '+']))
results = (0, 0, -oo, oo, 0, 0, -oo, oo, 0, 0,
oo, -oo, 0, 0, oo, -oo, 0, 0, oo, -oo)
assert len(tests) == len(results)
for i, (args, res) in enumerate(zip(tests, results)):
f, l, d = args
eq = f(x)
try:
assert limit(eq, x, l, dir=d) == res
except AssertionError:
if 0: # change to 1 if you want to see the failing tests
print()
print(i, res, eq, l, d, limit(eq, x, l, dir=d))
else:
assert None
def test_issue_3934():
assert limit((1 + x**log(3))**(1/x), x, 0) == 1
assert limit((5**(1/x) + 3**(1/x))**x, x, 0) == 5
def test_calculate_series():
# needs gruntz calculate_series to go to n = 32
assert limit(x**(S(77)/3)/(1 + x**(S(77)/3)), x, oo) == 1
# needs gruntz calculate_series to go to n = 128
assert limit(x**101.1/(1 + x**101.1), x, oo) == 1
def test_issue_5955():
assert limit((x**16)/(1 + x**16), x, oo) == 1
assert limit((x**100)/(1 + x**100), x, oo) == 1
assert limit((x**1885)/(1 + x**1885), x, oo) == 1
assert limit((x**1000/((x + 1)**1000 + exp(-x))), x, oo) == 1
def test_newissue():
assert limit(exp(1/sin(x))/exp(cot(x)), x, 0) == 1
def test_extended_real_line():
assert limit(x - oo, x, oo) == -oo
assert limit(oo - x, x, -oo) == oo
assert limit(x**2/(x - 5) - oo, x, oo) == -oo
assert limit(1/(x + sin(x)) - oo, x, 0) == -oo
assert limit(oo/x, x, oo) == oo
assert limit(x - oo + 1/x, x, oo) == -oo
assert limit(x - oo + 1/x, x, 0) == -oo
@XFAIL
def test_order_oo():
x = Symbol('x', positive=True, finite=True)
assert Order(x)*oo != Order(1, x)
assert limit(oo/(x**2 - 4), x, oo) == oo
def test_issue_5436():
raises(NotImplementedError, lambda: limit(exp(x*y), x, oo))
raises(NotImplementedError, lambda: limit(exp(-x*y), x, oo))
def test_Limit_dir():
raises(TypeError, lambda: Limit(x, x, 0, dir=0))
raises(ValueError, lambda: Limit(x, x, 0, dir='0'))
def test_polynomial():
assert limit((x + 1)**1000/((x + 1)**1000 + 1), x, oo) == 1
assert limit((x + 1)**1000/((x + 1)**1000 + 1), x, -oo) == 1
def test_rational():
assert limit(1/y - (1/(y + x) + x/(y + x)/y)/z, x, oo) == (z - 1)/(y*z)
assert limit(1/y - (1/(y + x) + x/(y + x)/y)/z, x, -oo) == (z - 1)/(y*z)
def test_issue_5740():
assert limit(log(x)*z - log(2*x)*y, x, 0) == oo*sign(y - z)
def test_issue_6366():
n = Symbol('n', integer=True, positive=True)
r = (n + 1)*x**(n + 1)/(x**(n + 1) - 1) - x/(x - 1)
assert limit(r, x, 1).simplify() == n/2
def test_factorial():
from sympy import factorial, E
f = factorial(x)
assert limit(f, x, oo) == oo
assert limit(x/f, x, oo) == 0
# see Stirling's approximation:
# http://en.wikipedia.org/wiki/Stirling's_approximation
assert limit(f/(sqrt(2*pi*x)*(x/E)**x), x, oo) == 1
assert limit(f, x, -oo) == factorial(-oo)
assert limit(f, x, x**2) == factorial(x**2)
assert limit(f, x, -x**2) == factorial(-x**2)
def test_issue_6560():
e = (5*x**3/4 - 3*x/4 + (y*(3*x**2/2 - S(1)/2) +
35*x**4/8 - 15*x**2/4 + S(3)/8)/(2*(y + 1)))
assert limit(e, y, oo) == (5*x**3 + 3*x**2 - 3*x - 1)/4
def test_issue_5172():
n = Symbol('n')
r = Symbol('r', positive=True)
c = Symbol('c')
p = Symbol('p', positive=True)
m = Symbol('m', negative=True)
expr = ((2*n*(n - r + 1)/(n + r*(n - r + 1)))**c +
(r - 1)*(n*(n - r + 2)/(n + r*(n - r + 1)))**c - n)/(n**c - n)
expr = expr.subs(c, c + 1)
raises(NotImplementedError, lambda: limit(expr, n, oo))
assert limit(expr.subs(c, m), n, oo) == 1
assert limit(expr.subs(c, p), n, oo).simplify() == \
(2**(p + 1) + r - 1)/(r + 1)**(p + 1)
def test_issue_7088():
a = Symbol('a')
assert limit(sqrt(x/(x + a)), x, oo) == 1
def test_issue_6364():
a = Symbol('a')
e = z/(1 - sqrt(1 + z)*sin(a)**2 - sqrt(1 - z)*cos(a)**2)
assert limit(e, z, 0).simplify() == 2/cos(2*a)
def test_issue_4099():
a = Symbol('a')
assert limit(a/x, x, 0) == oo*sign(a)
assert limit(-a/x, x, 0) == -oo*sign(a)
assert limit(-a*x, x, oo) == -oo*sign(a)
assert limit(a*x, x, oo) == oo*sign(a)
def test_issue_4503():
dx = Symbol('dx')
assert limit((sqrt(1 + exp(x + dx)) - sqrt(1 + exp(x)))/dx, dx, 0) == \
exp(x)/(2*sqrt(exp(x) + 1))
def test_issue_8730():
assert limit(subfactorial(x), x, oo) == oo
def test_issue_10801():
# make sure limits work with binomial
assert limit(16**k / (k * binomial(2*k, k)**2), k, oo) == pi
def test_issue_9205():
x, y, a = symbols('x, y, a')
assert Limit(x, x, a).free_symbols == {a}
assert Limit(x, x, a, '-').free_symbols == {a}
assert Limit(x + y, x + y, a).free_symbols == {a}
assert Limit(-x**2 + y, x**2, a).free_symbols == {y, a}
def test_limit_seq():
assert limit(Sum(1/x, (x, 1, y)) - log(y), y, oo) == EulerGamma
assert limit(Sum(1/x, (x, 1, y)) - 1/y, y, oo) == S.Infinity
assert (limit(binomial(2*x, x) / Sum(binomial(2*y, y), (y, 1, x)), x, oo) ==
S(3) / 4)
assert (limit(Sum(y**2 * Sum(2**z/z, (z, 1, y)), (y, 1, x)) /
(2**x*x), x, oo) == 4)
def test_issue_11879():
assert simplify(limit(((x+y)**n-x**n)/y, y, 0)) == n*x**(n-1)
def test_limit_with_Float():
k = symbols("k")
assert limit(1.0 ** k, k, oo) == 1
assert limit(0.3*1.0**k, k, oo) == Float(0.3)
def test_issue_10610():
assert limit(3**x*3**(-x - 1)*(x + 1)**2/x**2, x, oo) == S(1)/3
def test_issue_6599():
assert limit((n + cos(n))/n, n, oo) == 1
def test_issue_12555():
assert limit((3**x + 2* x**10) / (x**10 + exp(x)), x, -oo) == 2
assert limit((3**x + 2* x**10) / (x**10 + exp(x)), x, oo) == oo
| 16,575 | 31.629921 | 96 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/series/tests/test_nseries.py
|
from sympy import (Symbol, Rational, ln, exp, log, sqrt, E, O, pi, I, sinh,
sin, cosh, cos, tanh, coth, asinh, acosh, atanh, acoth, tan, cot, Integer,
PoleError, floor, ceiling, asin, symbols, limit, Piecewise, Eq, sign,
Derivative)
from sympy.abc import x, y, z
from sympy.utilities.pytest import raises, XFAIL
def test_simple_1():
assert x.nseries(x, n=5) == x
assert y.nseries(x, n=5) == y
assert (1/(x*y)).nseries(y, n=5) == 1/(x*y)
assert Rational(3, 4).nseries(x, n=5) == Rational(3, 4)
assert x.nseries() == x
def test_mul_0():
assert (x*ln(x)).nseries(x, n=5) == x*ln(x)
def test_mul_1():
assert (x*ln(2 + x)).nseries(x, n=5) == x*log(2) + x**2/2 - x**3/8 + \
x**4/24 + O(x**5)
assert (x*ln(1 + x)).nseries(
x, n=5) == x**2 - x**3/2 + x**4/3 + O(x**5)
def test_pow_0():
assert (x**2).nseries(x, n=5) == x**2
assert (1/x).nseries(x, n=5) == 1/x
assert (1/x**2).nseries(x, n=5) == 1/x**2
assert (x**Rational(2, 3)).nseries(x, n=5) == (x**Rational(2, 3))
assert (sqrt(x)**3).nseries(x, n=5) == (sqrt(x)**3)
def test_pow_1():
assert ((1 + x)**2).nseries(x, n=5) == 1 + 2*x + x**2
def test_geometric_1():
assert (1/(1 - x)).nseries(x, n=5) == 1 + x + x**2 + x**3 + x**4 + O(x**5)
assert (x/(1 - x)).nseries(x, n=6) == x + x**2 + x**3 + x**4 + x**5 + O(x**6)
assert (x**3/(1 - x)).nseries(x, n=8) == x**3 + x**4 + x**5 + x**6 + \
x**7 + O(x**8)
def test_sqrt_1():
assert sqrt(1 + x).nseries(x, n=5) == 1 + x/2 - x**2/8 + x**3/16 - 5*x**4/128 + O(x**5)
def test_exp_1():
assert exp(x).nseries(x, n=5) == 1 + x + x**2/2 + x**3/6 + x**4/24 + O(x**5)
assert exp(x).nseries(x, n=12) == 1 + x + x**2/2 + x**3/6 + x**4/24 + x**5/120 + \
x**6/720 + x**7/5040 + x**8/40320 + x**9/362880 + x**10/3628800 + \
x**11/39916800 + O(x**12)
assert exp(1/x).nseries(x, n=5) == exp(1/x)
assert exp(1/(1 + x)).nseries(x, n=4) == \
(E*(1 - x - 13*x**3/6 + 3*x**2/2)).expand() + O(x**4)
assert exp(2 + x).nseries(x, n=5) == \
(exp(2)*(1 + x + x**2/2 + x**3/6 + x**4/24)).expand() + O(x**5)
def test_exp_sqrt_1():
assert exp(1 + sqrt(x)).nseries(x, n=3) == \
(exp(1)*(1 + sqrt(x) + x/2 + sqrt(x)*x/6)).expand() + O(sqrt(x)**3)
def test_power_x_x1():
assert (exp(x*ln(x))).nseries(x, n=4) == \
1 + x*log(x) + x**2*log(x)**2/2 + x**3*log(x)**3/6 + O(x**4*log(x)**4)
def test_power_x_x2():
assert (x**x).nseries(x, n=4) == \
1 + x*log(x) + x**2*log(x)**2/2 + x**3*log(x)**3/6 + O(x**4*log(x)**4)
def test_log_singular1():
assert log(1 + 1/x).nseries(x, n=5) == x - log(x) - x**2/2 + x**3/3 - \
x**4/4 + O(x**5)
def test_log_power1():
e = 1 / (1/x + x ** (log(3)/log(2)))
assert e.nseries(x, n=5) == x - x**(2 + log(3)/log(2)) + O(x**5)
def test_log_series():
l = Symbol('l')
e = 1/(1 - log(x))
assert e.nseries(x, n=5, logx=l) == 1/(1 - l)
def test_log2():
e = log(-1/x)
assert e.nseries(x, n=5) == -log(x) + log(-1)
def test_log3():
l = Symbol('l')
e = 1/log(-1/x)
assert e.nseries(x, n=4, logx=l) == 1/(-l + log(-1))
def test_series1():
e = sin(x)
assert e.nseries(x, 0, 0) != 0
assert e.nseries(x, 0, 0) == O(1, x)
assert e.nseries(x, 0, 1) == O(x, x)
assert e.nseries(x, 0, 2) == x + O(x**2, x)
assert e.nseries(x, 0, 3) == x + O(x**3, x)
assert e.nseries(x, 0, 4) == x - x**3/6 + O(x**4, x)
e = (exp(x) - 1)/x
assert e.nseries(x, 0, 3) == 1 + x/2 + O(x**2, x)
assert x.nseries(x, 0, 2) == x
@XFAIL
def test_series1_failing():
assert x.nseries(x, 0, 0) == O(1, x)
assert x.nseries(x, 0, 1) == O(x, x)
def test_seriesbug1():
assert (1/x).nseries(x, 0, 3) == 1/x
assert (x + 1/x).nseries(x, 0, 3) == x + 1/x
def test_series2x():
assert ((x + 1)**(-2)).nseries(x, 0, 4) == 1 - 2*x + 3*x**2 - 4*x**3 + O(x**4, x)
assert ((x + 1)**(-1)).nseries(x, 0, 4) == 1 - x + x**2 - x**3 + O(x**4, x)
assert ((x + 1)**0).nseries(x, 0, 3) == 1
assert ((x + 1)**1).nseries(x, 0, 3) == 1 + x
assert ((x + 1)**2).nseries(x, 0, 3) == 1 + 2*x + x**2
assert ((x + 1)**3).nseries(
x, 0, 3) == 1 + 3*x + 3*x**2 + x**3 # 1+3*x+3*x**2+O(x**3)
assert (1/(1 + x)).nseries(x, 0, 4) == 1 - x + x**2 - x**3 + O(x**4, x)
assert (x + 3/(1 + 2*x)).nseries(x, 0, 4) == 3 - 5*x + 12*x**2 - 24*x**3 + O(x**4, x)
assert ((1/x + 1)**3).nseries(x, 0, 3) == 1 + x**(-3) + 3*x**(-2) + 3/x
assert (1/(1 + 1/x)).nseries(x, 0, 4) == x - x**2 + x**3 - O(x**4, x)
assert (1/(1 + 1/x**2)).nseries(x, 0, 6) == x**2 - x**4 + O(x**6, x)
def test_bug2(): # 1/log(0) * log(0) problem
w = Symbol("w")
e = (w**(-1) + w**(
-log(3)*log(2)**(-1)))**(-1)*(3*w**(-log(3)*log(2)**(-1)) + 2*w**(-1))
e = e.expand()
assert e.nseries(w, 0, 4).subs(w, 0) == 3
def test_exp():
e = (1 + x)**(1/x)
assert e.nseries(x, n=3) == exp(1) - x*exp(1)/2 + O(x**2, x)
def test_exp2():
w = Symbol("w")
e = w**(1 - log(x)/(log(2) + log(x)))
logw = Symbol("logw")
assert e.nseries(
w, 0, 1, logx=logw) == exp(logw - logw*log(x)/(log(2) + log(x)))
def test_bug3():
e = (2/x + 3/x**2)/(1/x + 1/x**2)
assert e.nseries(x, n=3) == 3 + O(x)
def test_generalexponent():
p = 2
e = (2/x + 3/x**p)/(1/x + 1/x**p)
assert e.nseries(x, 0, 3) == 3 + O(x)
p = Rational(1, 2)
e = (2/x + 3/x**p)/(1/x + 1/x**p)
assert e.nseries(x, 0, 2) == 2 + sqrt(x) + O(x)
e = 1 + sqrt(x)
assert e.nseries(x, 0, 4) == 1 + sqrt(x)
# more complicated example
def test_genexp_x():
e = 1/(1 + sqrt(x))
assert e.nseries(x, 0, 2) == \
1 + x - sqrt(x) - sqrt(x)**3 + O(x**2, x)
# more complicated example
def test_genexp_x2():
p = Rational(3, 2)
e = (2/x + 3/x**p)/(1/x + 1/x**p)
assert e.nseries(x, 0, 3) == 3 - sqrt(x) + x + O(sqrt(x)**3)
def test_seriesbug2():
w = Symbol("w")
#simple case (1):
e = ((2*w)/w)**(1 + w)
assert e.nseries(w, 0, 1) == 2 + O(w, w)
assert e.nseries(w, 0, 1).subs(w, 0) == 2
def test_seriesbug2b():
w = Symbol("w")
#test sin
e = sin(2*w)/w
assert e.nseries(w, 0, 3) == 2 + O(w**2, w)
def test_seriesbug2d():
w = Symbol("w", real=True)
e = log(sin(2*w)/w)
assert e.series(w, n=5) == log(2) - 2*w**2/3 - 4*w**4/45 + O(w**5)
def test_seriesbug2c():
w = Symbol("w", real=True)
#more complicated case, but sin(x)~x, so the result is the same as in (1)
e = (sin(2*w)/w)**(1 + w)
assert e.series(w, 0, 1) == 2 + O(w)
assert e.series(w, 0, 3) == 2 + 2*w*log(2) + \
w**2*(-Rational(4, 3) + log(2)**2) + O(w**3)
assert e.series(w, 0, 2).subs(w, 0) == 2
def test_expbug4():
x = Symbol("x", real=True)
assert (log(
sin(2*x)/x)*(1 + x)).series(x, 0, 2) == log(2) + x*log(2) + O(x**2, x)
assert exp(
log(sin(2*x)/x)*(1 + x)).series(x, 0, 2) == 2 + 2*x*log(2) + O(x**2)
assert exp(log(2) + O(x)).nseries(x, 0, 2) == 2 + O(x)
assert ((2 + O(x))**(1 + x)).nseries(x, 0, 2) == 2 + O(x)
def test_logbug4():
assert log(2 + O(x)).nseries(x, 0, 2) == log(2) + O(x, x)
def test_expbug5():
assert exp(log(1 + x)/x).nseries(x, n=3) == exp(1) + -exp(1)*x/2 + O(x**2)
assert exp(O(x)).nseries(x, 0, 2) == 1 + O(x)
def test_sinsinbug():
assert sin(sin(x)).nseries(x, 0, 8) == x - x**3/3 + x**5/10 - 8*x**7/315 + O(x**8)
def test_issue_3258():
a = x/(exp(x) - 1)
assert a.nseries(x, 0, 5) == 1 - x/2 - x**4/720 + x**2/12 + O(x**5)
def test_issue_3204():
x = Symbol("x", nonnegative=True)
f = sin(x**3)**Rational(1, 3)
assert f.nseries(x, 0, 17) == x - x**7/18 - x**13/3240 + O(x**17)
def test_issue_3224():
f = sqrt(1 - sqrt(y))
assert f.nseries(y, 0, 2) == 1 - sqrt(y)/2 - y/8 - sqrt(y)**3/16 + O(y**2)
def test_issue_3463():
from sympy import symbols
w, i = symbols('w,i')
r = log(5)/log(3)
p = w**(-1 + r)
e = 1/x*(-log(w**(1 + r)) + log(w + w**r))
e_ser = -r*log(w)/x + p/x - p**2/(2*x) + O(p**3)
assert e.nseries(w, n=3) == e_ser
def test_sin():
assert sin(8*x).nseries(x, n=4) == 8*x - 256*x**3/3 + O(x**4)
assert sin(x + y).nseries(x, n=1) == sin(y) + O(x)
assert sin(x + y).nseries(x, n=2) == sin(y) + cos(y)*x + O(x**2)
assert sin(x + y).nseries(x, n=5) == sin(y) + cos(y)*x - sin(y)*x**2/2 - \
cos(y)*x**3/6 + sin(y)*x**4/24 + O(x**5)
def test_issue_3515():
e = sin(8*x)/x
assert e.nseries(x, n=6) == 8 - 256*x**2/3 + 4096*x**4/15 + O(x**5)
def test_issue_3505():
e = sin(x)**(-4)*(sqrt(cos(x))*sin(x)**2 -
cos(x)**Rational(1, 3)*sin(x)**2)
assert e.nseries(x, n=9) == -Rational(1)/12 - 7*x**2/288 - \
43*x**4/10368 + O(x**5)
def test_issue_3501():
a = Symbol("a")
e = x**(-2)*(x*sin(a + x) - x*sin(a))
assert e.nseries(x, n=6) == cos(a) - sin(a)*x/2 - cos(a)*x**2/6 + \
sin(a)*x**3/24 + O(x**4)
e = x**(-2)*(x*cos(a + x) - x*cos(a))
assert e.nseries(x, n=6) == -sin(a) - cos(a)*x/2 + sin(a)*x**2/6 + \
cos(a)*x**3/24 + O(x**4)
def test_issue_3502():
e = sin(5*x)/sin(2*x)
assert e.nseries(x, n=2) == Rational(5, 2) + O(x)
assert e.nseries(x, n=6) == \
Rational(5, 2) - 35*x**2/4 + 329*x**4/48 + O(x**5)
def test_issue_3503():
e = sin(2 + x)/(2 + x)
assert e.nseries(x, n=2) == sin(2)/2 + x*cos(2)/2 - x*sin(2)/4 + O(x**2)
def test_issue_3506():
e = (x + sin(3*x))**(-2)*(x*(x + sin(3*x)) - (x + sin(3*x))*sin(2*x))
assert e.nseries(x, n=7) == \
-Rational(1, 4) + 5*x**2/96 + 91*x**4/768 + O(x**5)
def test_issue_3508():
x = Symbol("x", real=True)
assert log(sin(x)).series(x, n=5) == log(x) - x**2/6 - x**4/180 + O(x**5)
e = -log(x) + x*(-log(x) + log(sin(2*x))) + log(sin(2*x))
assert e.series(x, n=5) == \
log(2) + log(2)*x - 2*x**2/3 - 2*x**3/3 - 4*x**4/45 + O(x**5)
def test_issue_3507():
e = x**(-4)*(x**2 - x**2*sqrt(cos(x)))
assert e.nseries(x, n=9) == \
Rational(1, 4) + x**2/96 + 19*x**4/5760 + O(x**5)
def test_issue_3639():
assert sin(cos(x)).nseries(x, n=5) == \
sin(1) - x**2*cos(1)/2 - x**4*sin(1)/8 + x**4*cos(1)/24 + O(x**5)
def test_hyperbolic():
assert sinh(x).nseries(x, n=6) == x + x**3/6 + x**5/120 + O(x**6)
assert cosh(x).nseries(x, n=5) == 1 + x**2/2 + x**4/24 + O(x**5)
assert tanh(x).nseries(x, n=6) == x - x**3/3 + 2*x**5/15 + O(x**6)
assert coth(x).nseries(x, n=6) == \
1/x - x**3/45 + x/3 + 2*x**5/945 + O(x**6)
assert asinh(x).nseries(x, n=6) == x - x**3/6 + 3*x**5/40 + O(x**6)
assert acosh(x).nseries(x, n=6) == \
pi*I/2 - I*x - 3*I*x**5/40 - I*x**3/6 + O(x**6)
assert atanh(x).nseries(x, n=6) == x + x**3/3 + x**5/5 + O(x**6)
assert acoth(x).nseries(x, n=6) == x + x**3/3 + x**5/5 + pi*I/2 + O(x**6)
def test_series2():
w = Symbol("w", real=True)
x = Symbol("x", real=True)
e = w**(-2)*(w*exp(1/x - w) - w*exp(1/x))
assert e.nseries(w, n=4) == -exp(1/x) + w * exp(1/x) / 2 + O(w**2)
def test_series3():
w = Symbol("w", real=True)
x = Symbol("x", real=True)
e = w**(-6)*(w**3*tan(w) - w**3*sin(w))
assert e.nseries(w, n=8) == Integer(1)/2 + O(w**2)
def test_bug4():
w = Symbol("w")
e = x/(w**4 + x**2*w**4 + 2*x*w**4)*w**4
assert e.nseries(w, n=2) in [x/(1 + 2*x + x**2),
1/(1 + x/2 + 1/x/2)/2, 1/x/(1 + 2/x + x**(-2))]
def test_bug5():
w = Symbol("w")
l = Symbol('l')
e = (-log(w) + log(1 + w*log(x)))**(-2)*w**(-2)*((-log(w) +
log(1 + x*w))*(-log(w) + log(1 + w*log(x)))*w - x*(-log(w) +
log(1 + w*log(x)))*w)
assert e.nseries(w, n=2, logx=l) == x/w/l + 1/w + O(1, w)
assert e.nseries(w, n=3, logx=l) == x/w/l + 1/w - x/l + 1/l*log(x) \
+ x*log(x)/l**2 + O(w)
def test_issue_4115():
assert (sin(x)/(1 - cos(x))).nseries(x, n=1) == O(1/x)
assert (sin(x)**2/(1 - cos(x))).nseries(x, n=1) == O(1, x)
def test_pole():
raises(PoleError, lambda: sin(1/x).series(x, 0, 5))
raises(PoleError, lambda: sin(1 + 1/x).series(x, 0, 5))
raises(PoleError, lambda: (x*sin(1/x)).series(x, 0, 5))
def test_expsinbug():
assert exp(sin(x)).series(x, 0, 0) == O(1, x)
assert exp(sin(x)).series(x, 0, 1) == 1 + O(x)
assert exp(sin(x)).series(x, 0, 2) == 1 + x + O(x**2)
assert exp(sin(x)).series(x, 0, 3) == 1 + x + x**2/2 + O(x**3)
assert exp(sin(x)).series(x, 0, 4) == 1 + x + x**2/2 + O(x**4)
assert exp(sin(x)).series(x, 0, 5) == 1 + x + x**2/2 - x**4/8 + O(x**5)
def test_floor():
x = Symbol('x')
assert floor(x).series(x) == 0
assert floor(-x).series(x) == -1
assert floor(sin(x)).series(x) == 0
assert floor(sin(-x)).series(x) == -1
assert floor(x**3).series(x) == 0
assert floor(-x**3).series(x) == -1
assert floor(cos(x)).series(x) == 0
assert floor(cos(-x)).series(x) == 0
assert floor(5 + sin(x)).series(x) == 5
assert floor(5 + sin(-x)).series(x) == 4
assert floor(x).series(x, 2) == 2
assert floor(-x).series(x, 2) == -3
x = Symbol('x', negative=True)
assert floor(x + 1.5).series(x) == 1
def test_ceiling():
assert ceiling(x).series(x) == 1
assert ceiling(-x).series(x) == 0
assert ceiling(sin(x)).series(x) == 1
assert ceiling(sin(-x)).series(x) == 0
assert ceiling(1 - cos(x)).series(x) == 1
assert ceiling(1 - cos(-x)).series(x) == 1
assert ceiling(x).series(x, 2) == 3
assert ceiling(-x).series(x, 2) == -2
def test_abs():
a = Symbol('a')
assert abs(x).nseries(x, n=4) == x
assert abs(-x).nseries(x, n=4) == x
assert abs(x + 1).nseries(x, n=4) == x + 1
assert abs(sin(x)).nseries(x, n=4) == x - Rational(1, 6)*x**3 + O(x**4)
assert abs(sin(-x)).nseries(x, n=4) == x - Rational(1, 6)*x**3 + O(x**4)
assert abs(x - a).nseries(x, 1) == Piecewise((x - 1, Eq(1 - a, 0)),
((x - a)*sign(1 - a), True))
def test_dir():
assert abs(x).series(x, 0, dir="+") == x
assert abs(x).series(x, 0, dir="-") == -x
assert floor(x + 2).series(x, 0, dir='+') == 2
assert floor(x + 2).series(x, 0, dir='-') == 1
assert floor(x + 2.2).series(x, 0, dir='-') == 2
assert ceiling(x + 2.2).series(x, 0, dir='-') == 3
assert sin(x + y).series(x, 0, dir='-') == sin(x + y).series(x, 0, dir='+')
def test_issue_3504():
a = Symbol("a")
e = asin(a*x)/x
assert e.series(x, 4, n=2).removeO() == \
(x - 4)*(a/(4*sqrt(-16*a**2 + 1)) - asin(4*a)/16) + asin(4*a)/4
def test_issue_4441():
a, b = symbols('a,b')
f = 1/(1 + a*x)
assert f.series(x, 0, 5) == 1 - a*x + a**2*x**2 - a**3*x**3 + \
a**4*x**4 + O(x**5)
f = 1/(1 + (a + b)*x)
assert f.series(x, 0, 3) == 1 + x*(-a - b) + \
x**2*(a**2 + 2*a*b + b**2) + O(x**3)
def test_issue_4329():
assert tan(x).series(x, pi/2, n=3).removeO() == \
-pi/6 + x/3 - 1/(x - pi/2)
assert cot(x).series(x, pi, n=3).removeO() == \
-x/3 + pi/3 + 1/(x - pi)
assert limit(tan(x)**tan(2*x), x, pi/4) == exp(-1)
def test_issue_5183():
assert abs(x + x**2).series(n=1) == O(x)
assert abs(x + x**2).series(n=2) == x + O(x**2)
assert ((1 + x)**2).series(x, n=6) == 1 + 2*x + x**2
assert (1 + 1/x).series() == 1 + 1/x
assert Derivative(exp(x).series(), x).doit() == \
1 + x + x**2/2 + x**3/6 + x**4/24 + O(x**5)
def test_issue_5654():
a = Symbol('a')
assert (1/(x**2+a**2)**2).nseries(x, x0=I*a, n=0) == \
-I/(4*a**3*(-I*a + x)) - 1/(4*a**2*(-I*a + x)**2) + O(1, (x, I*a))
assert (1/(x**2+a**2)**2).nseries(x, x0=I*a, n=1) == 3/(16*a**4) \
-I/(4*a**3*(-I*a + x)) - 1/(4*a**2*(-I*a + x)**2) + O(-I*a + x, (x, I*a))
def test_issue_5925():
sx = sqrt(x + z).series(z, 0, 1)
sxy = sqrt(x + y + z).series(z, 0, 1)
s1, s2 = sx.subs(x, x + y), sxy
assert (s1 - s2).expand().removeO().simplify() == 0
sx = sqrt(x + z).series(z, 0, 1)
sxy = sqrt(x + y + z).series(z, 0, 1)
assert sxy.subs({x:1, y:2}) == sx.subs(x, 3)
| 16,155 | 30.069231 | 91 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/series/tests/test_approximants.py
|
from sympy.core.compatibility import range
from sympy.series import approximants
from sympy import lucas, fibonacci, symbols, binomial
def test_approximants():
x, t = symbols("x,t")
g = [lucas(k) for k in range(16)]
assert [e for e in approximants(g)] == (
[2, -4/(x - 2), (5*x - 2)/(3*x - 1), (x - 2)/(x**2 + x - 1)] )
g = [lucas(k)+fibonacci(k+2) for k in range(16)]
assert [e for e in approximants(g)] == (
[3, -3/(x - 1), (3*x - 3)/(2*x - 1), -3/(x**2 + x - 1)] )
g = [lucas(k)**2 for k in range(16)]
assert [e for e in approximants(g)] == (
[4, -16/(x - 4), (35*x - 4)/(9*x - 1), (37*x - 28)/(13*x**2 + 11*x - 7),
(50*x**2 + 63*x - 52)/(37*x**2 + 19*x - 13),
(-x**2 - 7*x + 4)/(x**3 - 2*x**2 - 2*x + 1)] )
p = [sum(binomial(k,i)*x**i for i in range(k+1)) for k in range(16)]
y = approximants(p, t, simplify=True)
assert next(y) == 1
assert next(y) == -1/(t*(x + 1) - 1)
| 962 | 39.125 | 80 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/series/tests/test_series.py
|
from sympy import sin, cos, exp, E, series, oo, S, Derivative, O, Integral, \
Function, log, sqrt, Symbol, Subs, pi, symbols, IndexedBase
from sympy.abc import x, y, n, k
from sympy.utilities.pytest import raises
from sympy.core.compatibility import range
from sympy.series.gruntz import calculate_series
def test_sin():
e1 = sin(x).series(x, 0)
e2 = series(sin(x), x, 0)
assert e1 == e2
def test_cos():
e1 = cos(x).series(x, 0)
e2 = series(cos(x), x, 0)
assert e1 == e2
def test_exp():
e1 = exp(x).series(x, 0)
e2 = series(exp(x), x, 0)
assert e1 == e2
def test_exp2():
e1 = exp(cos(x)).series(x, 0)
e2 = series(exp(cos(x)), x, 0)
assert e1 == e2
def test_issue_5223():
assert series(1, x) == 1
assert next(S(0).lseries(x)) == 0
assert cos(x).series() == cos(x).series(x)
raises(ValueError, lambda: cos(x + y).series())
raises(ValueError, lambda: x.series(dir=""))
assert (cos(x).series(x, 1) -
cos(x + 1).series(x).subs(x, x - 1)).removeO() == 0
e = cos(x).series(x, 1, n=None)
assert [next(e) for i in range(2)] == [cos(1), -((x - 1)*sin(1))]
e = cos(x).series(x, 1, n=None, dir='-')
assert [next(e) for i in range(2)] == [cos(1), (1 - x)*sin(1)]
# the following test is exact so no need for x -> x - 1 replacement
assert abs(x).series(x, 1, dir='-') == x
assert exp(x).series(x, 1, dir='-', n=3).removeO() == \
E - E*(-x + 1) + E*(-x + 1)**2/2
D = Derivative
assert D(x**2 + x**3*y**2, x, 2, y, 1).series(x).doit() == 12*x*y
assert next(D(cos(x), x).lseries()) == D(1, x)
assert D(
exp(x), x).series(n=3) == D(1, x) + D(x, x) + D(x**2/2, x) + D(x**3/6, x) + O(x**3)
assert Integral(x, (x, 1, 3), (y, 1, x)).series(x) == -4 + 4*x
assert (1 + x + O(x**2)).getn() == 2
assert (1 + x).getn() is None
assert ((1/sin(x))**oo).series() == oo
logx = Symbol('logx')
assert ((sin(x))**y).nseries(x, n=1, logx=logx) == \
exp(y*logx) + O(x*exp(y*logx), x)
assert sin(1/x).series(x, oo, n=5) == 1/x - 1/(6*x**3) + O(x**(-5), (x, oo))
assert abs(x).series(x, oo, n=5, dir='+') == x
assert abs(x).series(x, -oo, n=5, dir='-') == -x
assert abs(-x).series(x, oo, n=5, dir='+') == x
assert abs(-x).series(x, -oo, n=5, dir='-') == -x
assert exp(x*log(x)).series(n=3) == \
1 + x*log(x) + x**2*log(x)**2/2 + O(x**3*log(x)**3)
# XXX is this right? If not, fix "ngot > n" handling in expr.
p = Symbol('p', positive=True)
assert exp(sqrt(p)**3*log(p)).series(n=3) == \
1 + p**S('3/2')*log(p) + O(p**3*log(p)**3)
assert exp(sin(x)*log(x)).series(n=2) == 1 + x*log(x) + O(x**2*log(x)**2)
def test_issue_11313():
assert Integral(cos(x), x).series(x) == sin(x).series(x)
assert Derivative(sin(x), x).series(x, n=3).doit() == cos(x).series(x, n=3)
assert Derivative(x**3, x).as_leading_term(x) == 3*x**2
assert Derivative(x**3, y).as_leading_term(x) == 0
assert Derivative(sin(x), x).as_leading_term(x) == 1
assert Derivative(cos(x), x).as_leading_term(x) == -x
# This result is equivalent to zero, zero is not return because
# `Expr.series` doesn't currently detect an `x` in its `free_symbol`s.
assert Derivative(1, x).as_leading_term(x) == Derivative(1, x)
assert Derivative(exp(x), x).series(x).doit() == exp(x).series(x)
assert 1 + Integral(exp(x), x).series(x) == exp(x).series(x)
assert Derivative(log(x), x).series(x).doit() == (1/x).series(x)
assert Integral(log(x), x).series(x) == Integral(log(x), x).doit().series(x)
def test_series_of_Subs():
from sympy.abc import x, y, z
subs1 = Subs(sin(x), (x,), (y,))
subs2 = Subs(sin(x) * cos(z), (x,), (y,))
subs3 = Subs(sin(x * z), (x, z), (y, x))
assert subs1.series(x) == subs1
assert subs1.series(y) == Subs(x, (x,), (y,)) + Subs(-x**3/6, (x,), (y,)) + Subs(x**5/120, (x,), (y,)) + O(y**6)
assert subs1.series(z) == subs1
assert subs2.series(z) == Subs(z**4*sin(x)/24, (x,), (y,)) + Subs(-z**2*sin(x)/2, (x,), (y,)) + Subs(sin(x), (x,), (y,)) + O(z**6)
assert subs3.series(x).doit() == subs3.doit().series(x)
assert subs3.series(z).doit() == sin(x*y)
def test_issue_3978():
f = Function('f')
assert f(x).series(x, 0, 3, dir='-') == \
f(0) + x*Subs(Derivative(f(x), x), (x,), (0,)) + \
x**2*Subs(Derivative(f(x), x, x), (x,), (0,))/2 + O(x**3)
assert f(x).series(x, 0, 3) == \
f(0) + x*Subs(Derivative(f(x), x), (x,), (0,)) + \
x**2*Subs(Derivative(f(x), x, x), (x,), (0,))/2 + O(x**3)
assert f(x**2).series(x, 0, 3) == \
f(0) + x**2*Subs(Derivative(f(x), x), (x,), (0,)) + O(x**3)
assert f(x**2+1).series(x, 0, 3) == \
f(1) + x**2*Subs(Derivative(f(x), x), (x,), (1,)) + O(x**3)
class TestF(Function):
pass
assert TestF(x).series(x, 0, 3) == TestF(0) + \
x*Subs(Derivative(TestF(x), x), (x,), (0,)) + \
x**2*Subs(Derivative(TestF(x), x, x), (x,), (0,))/2 + O(x**3)
from sympy.series.acceleration import richardson, shanks
from sympy import Sum, Integer
def test_acceleration():
e = (1 + 1/n)**n
assert round(richardson(e, n, 10, 20).evalf(), 10) == round(E.evalf(), 10)
A = Sum(Integer(-1)**(k + 1) / k, (k, 1, n))
assert round(shanks(A, n, 25).evalf(), 4) == round(log(2).evalf(), 4)
assert round(shanks(A, n, 25, 5).evalf(), 10) == round(log(2).evalf(), 10)
def test_issue_5852():
assert series(1/cos(x/log(x)), x, 0) == 1 + x**2/(2*log(x)**2) + \
5*x**4/(24*log(x)**4) + O(x**6)
def test_issue_4583():
assert cos(1 + x + x**2).series(x, 0, 5) == cos(1) - x*sin(1) + \
x**2*(-sin(1) - cos(1)/2) + x**3*(-cos(1) + sin(1)/6) + \
x**4*(-11*cos(1)/24 + sin(1)/2) + O(x**5)
def test_issue_6318():
eq = (1/x)**(S(2)/3)
assert (eq + 1).as_leading_term(x) == eq
def test_x_is_base_detection():
eq = (x**2)**(S(2)/3)
assert eq.series() == x**(S(4)/3)
def test_sin_power():
e = sin(x)**1.2
assert calculate_series(e, x) == x**1.2
def test_issue_7203():
assert series(cos(x), x, pi, 3) == \
-1 + (x - pi)**2/2 + O((x - pi)**3, (x, pi))
def test_exp_product_positive_factors():
a, b = symbols('a, b', positive=True)
x = a * b
assert series(exp(x), x, n=8) == 1 + a*b + a**2*b**2/2 + \
a**3*b**3/6 + a**4*b**4/24 + a**5*b**5/120 + a**6*b**6/720 + \
a**7*b**7/5040 + O(a**8*b**8, a, b)
def test_issue_8805():
assert series(1, n=8) == 1
def test_issue_10761():
assert series(1/(x**-2 + x**-3), x, 0) == x**3 - x**4 + x**5 + O(x**6)
| 6,689 | 33.307692 | 134 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/series/tests/test_sequences.py
|
from sympy import (S, Tuple, symbols, Interval, EmptySequence, oo, SeqPer,
SeqFormula, sequence, SeqAdd, SeqMul, Indexed, Idx, sqrt,
fibonacci)
from sympy.series.sequences import SeqExpr, SeqExprOp
from sympy.utilities.pytest import raises
x, y, z = symbols('x y z')
n, m = symbols('n m')
def test_EmptySequence():
assert isinstance(S.EmptySequence, EmptySequence)
assert S.EmptySequence.interval is S.EmptySet
assert S.EmptySequence.length is S.Zero
assert list(S.EmptySequence) == []
def test_SeqExpr():
s = SeqExpr((1, n, y), (x, 0, 10))
assert isinstance(s, SeqExpr)
assert s.gen == (1, n, y)
assert s.interval == Interval(0, 10)
assert s.start == 0
assert s.stop == 10
assert s.length == 11
assert s.variables == (x,)
assert SeqExpr((1, 2, 3), (x, 0, oo)).length is oo
def test_SeqPer():
s = SeqPer((1, n, 3), (x, 0, 5))
assert isinstance(s, SeqPer)
assert s.periodical == Tuple(1, n, 3)
assert s.period == 3
assert s.coeff(3) == 1
assert s.free_symbols == {n}
assert list(s) == [1, n, 3, 1, n, 3]
assert s[:] == [1, n, 3, 1, n, 3]
assert SeqPer((1, n, 3), (x, -oo, 0))[0:6] == [1, n, 3, 1, n, 3]
raises(ValueError, lambda: SeqPer((1, 2, 3), (0, 1, 2)))
raises(ValueError, lambda: SeqPer((1, 2, 3), (x, -oo, oo)))
raises(ValueError, lambda: SeqPer(n**2, (0, oo)))
assert SeqPer((n, n**2, n**3), (m, 0, oo))[:6] == \
[n, n**2, n**3, n, n**2, n**3]
assert SeqPer((n, n**2, n**3), (n, 0, oo))[:6] == [0, 1, 8, 3, 16, 125]
assert SeqPer((n, m), (n, 0, oo))[:6] == [0, m, 2, m, 4, m]
def test_SeqFormula():
s = SeqFormula(n**2, (n, 0, 5))
assert isinstance(s, SeqFormula)
assert s.formula == n**2
assert s.coeff(3) == 9
assert list(s) == [i**2 for i in range(6)]
assert s[:] == [i**2 for i in range(6)]
assert SeqFormula(n**2, (n, -oo, 0))[0:6] == [i**2 for i in range(6)]
assert SeqFormula(n**2, (0, oo)) == SeqFormula(n**2, (n, 0, oo))
assert SeqFormula(n**2, (0, m)).subs(m, x) == SeqFormula(n**2, (0, x))
assert SeqFormula(m*n**2, (n, 0, oo)).subs(m, x) == \
SeqFormula(x*n**2, (n, 0, oo))
raises(ValueError, lambda: SeqFormula(n**2, (0, 1, 2)))
raises(ValueError, lambda: SeqFormula(n**2, (n, -oo, oo)))
raises(ValueError, lambda: SeqFormula(m*n**2, (0, oo)))
def test_sequence():
form = SeqFormula(n**2, (n, 0, 5))
per = SeqPer((1, 2, 3), (n, 0, 5))
inter = SeqFormula(n**2)
assert sequence(n**2, (n, 0, 5)) == form
assert sequence((1, 2, 3), (n, 0, 5)) == per
assert sequence(n**2) == inter
def test_SeqExprOp():
form = SeqFormula(n**2, (n, 0, 10))
per = SeqPer((1, 2, 3), (m, 5, 10))
s = SeqExprOp(form, per)
assert s.gen == (n**2, (1, 2, 3))
assert s.interval == Interval(5, 10)
assert s.start == 5
assert s.stop == 10
assert s.length == 6
assert s.variables == (n, m)
def test_SeqAdd():
per = SeqPer((1, 2, 3), (n, 0, oo))
form = SeqFormula(n**2)
per_bou = SeqPer((1, 2), (n, 1, 5))
form_bou = SeqFormula(n**2, (6, 10))
form_bou2 = SeqFormula(n**2, (1, 5))
assert SeqAdd() == S.EmptySequence
assert SeqAdd(S.EmptySequence) == S.EmptySequence
assert SeqAdd(per) == per
assert SeqAdd(per, S.EmptySequence) == per
assert SeqAdd(per_bou, form_bou) == S.EmptySequence
s = SeqAdd(per_bou, form_bou2, evaluate=False)
assert s.args == (form_bou2, per_bou)
assert s[:] == [2, 6, 10, 18, 26]
assert list(s) == [2, 6, 10, 18, 26]
assert isinstance(SeqAdd(per, per_bou, evaluate=False), SeqAdd)
s1 = SeqAdd(per, per_bou)
assert isinstance(s1, SeqPer)
assert s1 == SeqPer((2, 4, 4, 3, 3, 5), (n, 1, 5))
s2 = SeqAdd(form, form_bou)
assert isinstance(s2, SeqFormula)
assert s2 == SeqFormula(2*n**2, (6, 10))
assert SeqAdd(form, form_bou, per) == \
SeqAdd(per, SeqFormula(2*n**2, (6, 10)))
assert SeqAdd(form, SeqAdd(form_bou, per)) == \
SeqAdd(per, SeqFormula(2*n**2, (6, 10)))
assert SeqAdd(per, SeqAdd(form, form_bou), evaluate=False) == \
SeqAdd(per, SeqFormula(2*n**2, (6, 10)))
assert SeqAdd(SeqPer((1, 2), (n, 0, oo)), SeqPer((1, 2), (m, 0, oo))) == \
SeqPer((2, 4), (n, 0, oo))
def test_SeqMul():
per = SeqPer((1, 2, 3), (n, 0, oo))
form = SeqFormula(n**2)
per_bou = SeqPer((1, 2), (n, 1, 5))
form_bou = SeqFormula(n**2, (n, 6, 10))
form_bou2 = SeqFormula(n**2, (1, 5))
assert SeqMul() == S.EmptySequence
assert SeqMul(S.EmptySequence) == S.EmptySequence
assert SeqMul(per) == per
assert SeqMul(per, S.EmptySequence) == S.EmptySequence
assert SeqMul(per_bou, form_bou) == S.EmptySequence
s = SeqMul(per_bou, form_bou2, evaluate=False)
assert s.args == (form_bou2, per_bou)
assert s[:] == [1, 8, 9, 32, 25]
assert list(s) == [1, 8, 9, 32, 25]
assert isinstance(SeqMul(per, per_bou, evaluate=False), SeqMul)
s1 = SeqMul(per, per_bou)
assert isinstance(s1, SeqPer)
assert s1 == SeqPer((1, 4, 3, 2, 2, 6), (n, 1, 5))
s2 = SeqMul(form, form_bou)
assert isinstance(s2, SeqFormula)
assert s2 == SeqFormula(n**4, (6, 10))
assert SeqMul(form, form_bou, per) == \
SeqMul(per, SeqFormula(n**4, (6, 10)))
assert SeqMul(form, SeqMul(form_bou, per)) == \
SeqMul(per, SeqFormula(n**4, (6, 10)))
assert SeqMul(per, SeqMul(form, form_bou2,
evaluate=False), evaluate=False) == \
SeqMul(form, per, form_bou2, evaluate=False)
assert SeqMul(SeqPer((1, 2), (n, 0, oo)), SeqPer((1, 2), (n, 0, oo))) == \
SeqPer((1, 4), (n, 0, oo))
def test_add():
per = SeqPer((1, 2), (n, 0, oo))
form = SeqFormula(n**2)
assert per + (SeqPer((2, 3))) == SeqPer((3, 5), (n, 0, oo))
assert form + SeqFormula(n**3) == SeqFormula(n**2 + n**3)
assert per + form == SeqAdd(per, form)
raises(TypeError, lambda: per + n)
raises(TypeError, lambda: n + per)
def test_sub():
per = SeqPer((1, 2), (n, 0, oo))
form = SeqFormula(n**2)
assert per - (SeqPer((2, 3))) == SeqPer((-1, -1), (n, 0, oo))
assert form - (SeqFormula(n**3)) == SeqFormula(n**2 - n**3)
assert per - form == SeqAdd(per, -form)
raises(TypeError, lambda: per - n)
raises(TypeError, lambda: n - per)
def test_mul__coeff_mul():
assert SeqPer((1, 2), (n, 0, oo)).coeff_mul(2) == SeqPer((2, 4), (n, 0, oo))
assert SeqFormula(n**2).coeff_mul(2) == SeqFormula(2*n**2)
assert S.EmptySequence.coeff_mul(100) == S.EmptySequence
assert SeqPer((1, 2), (n, 0, oo)) * (SeqPer((2, 3))) == \
SeqPer((2, 6), (n, 0, oo))
assert SeqFormula(n**2) * SeqFormula(n**3) == SeqFormula(n**5)
assert S.EmptySequence * SeqFormula(n**2) == S.EmptySequence
assert SeqFormula(n**2) * S.EmptySequence == S.EmptySequence
raises(TypeError, lambda: sequence(n**2) * n)
raises(TypeError, lambda: n * sequence(n**2))
def test_neg():
assert -SeqPer((1, -2), (n, 0, oo)) == SeqPer((-1, 2), (n, 0, oo))
assert -SeqFormula(n**2) == SeqFormula(-n**2)
def test_operations():
per = SeqPer((1, 2), (n, 0, oo))
per2 = SeqPer((2, 4), (n, 0, oo))
form = SeqFormula(n**2)
form2 = SeqFormula(n**3)
assert per + form + form2 == SeqAdd(per, form, form2)
assert per + form - form2 == SeqAdd(per, form, -form2)
assert per + form - S.EmptySequence == SeqAdd(per, form)
assert per + per2 + form == SeqAdd(SeqPer((3, 6), (n, 0, oo)), form)
assert S.EmptySequence - per == -per
assert form + form == SeqFormula(2*n**2)
assert per * form * form2 == SeqMul(per, form, form2)
assert form * form == SeqFormula(n**4)
assert form * -form == SeqFormula(-n**4)
assert form * (per + form2) == SeqMul(form, SeqAdd(per, form2))
assert form * (per + per) == SeqMul(form, per2)
assert form.coeff_mul(m) == SeqFormula(m*n**2, (n, 0, oo))
assert per.coeff_mul(m) == SeqPer((m, 2*m), (n, 0, oo))
def test_Idx_limits():
i = symbols('i', cls=Idx)
r = Indexed('r', i)
assert SeqFormula(r, (i, 0, 5))[:] == [r.subs(i, j) for j in range(6)]
assert SeqPer((1, 2), (i, 0, 5))[:] == [1, 2, 1, 2, 1, 2]
def test_find_linear_recurrence():
assert sequence((0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55), \
(n, 0, 10)).find_linear_recurrence(11) == [1, 1]
assert sequence((1, 2, 4, 7, 28, 128, 582, 2745, 13021, 61699, 292521, \
1387138), (n, 0, 11)).find_linear_recurrence(12) == [5, -2, 6, -11]
assert sequence(x*n**3+y*n, (n, 0, oo)).find_linear_recurrence(10) \
== [4, -6, 4, -1]
assert sequence(x**n, (n,0,20)).find_linear_recurrence(21) == [x]
assert sequence((1,2,3)).find_linear_recurrence(10, 5) == [0, 0, 1]
assert sequence(((1 + sqrt(5))/2)**n + \
(-(1 + sqrt(5))/2)**(-n)).find_linear_recurrence(10) == [1, 1]
assert sequence(x*((1 + sqrt(5))/2)**n + y*(-(1 + sqrt(5))/2)**(-n), \
(n,0,oo)).find_linear_recurrence(10) == [1, 1]
assert sequence((1,2,3,4,6),(n, 0, 4)).find_linear_recurrence(5) == []
assert sequence((2,3,4,5,6,79),(n, 0, 5)).find_linear_recurrence(6,gfvar=x) \
== ([], None)
assert sequence((2,3,4,5,8,30),(n, 0, 5)).find_linear_recurrence(6,gfvar=x) \
== ([19/2, -20, 27/2], (-31*x**2 + 32*x - 4)/(27*x**3 - 40*x**2 + 19*x -2))
assert sequence(fibonacci(n)).find_linear_recurrence(30,gfvar=x) \
== ([1, 1], -x/(x**2 + x - 1))
| 9,490 | 33.017921 | 81 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/series/tests/test_kauers.py
|
from sympy.series.kauers import finite_diff
from sympy.series.kauers import finite_diff_kauers
from sympy.abc import x, y, z, m, n, w
from sympy import sin, cos
from sympy import pi
from sympy import Sum
def test_finite_diff():
assert finite_diff(x**2 + 2*x + 1, x) == 2*x + 3
assert finite_diff(y**3 + 2*y**2 + 3*y + 5, y) == 3*y**2 + 7*y + 6
assert finite_diff(z**2 - 2*z + 3, z) == 2*z - 1
assert finite_diff(w**2 + 3*w - 2, w) == 2*w + 4
assert finite_diff(sin(x), x, pi/6) == -sin(x) + sin(x + pi/6)
assert finite_diff(cos(y), y, pi/3) == -cos(y) + cos(y + pi/3)
assert finite_diff(x**2 - 2*x + 3, x, 2) == 4*x
assert finite_diff(n**2 - 2*n + 3, n, 3) == 6*n + 3
def test_finite_diff_kauers():
assert finite_diff_kauers(Sum(x**2, (x, 1, n))) == (n + 1)**2
assert finite_diff_kauers(Sum(y, (y, 1, m))) == (m + 1)
assert finite_diff_kauers(Sum((x*y), (x, 1, m), (y, 1, n))) == (m + 1)*(n + 1)
assert finite_diff_kauers(Sum((x*y**2), (x, 1, m), (y, 1, n))) == (n + 1)**2*(m + 1)
| 1,032 | 42.041667 | 88 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/series/tests/test_limitseq.py
|
from sympy import symbols, oo, Sum, harmonic, Add, S, binomial, factorial
from sympy.series.limitseq import limit_seq
from sympy.series.limitseq import difference_delta as dd
from sympy.utilities.pytest import raises, XFAIL
n, m, k = symbols('n m k', integer=True)
def test_difference_delta():
e = n*(n + 1)
e2 = e * k
assert dd(e) == 2*n + 2
assert dd(e2, n, 2) == k*(4*n + 6)
raises(ValueError, lambda: dd(e2))
raises(ValueError, lambda: dd(e2, n, oo))
def test_difference_delta__Sum():
e = Sum(1/k, (k, 1, n))
assert dd(e, n) == 1/(n + 1)
assert dd(e, n, 5) == Add(*[1/(i + n + 1) for i in range(5)])
e = Sum(1/k, (k, 1, 3*n))
assert dd(e, n) == Add(*[1/(i + 3*n + 1) for i in range(3)])
e = n * Sum(1/k, (k, 1, n))
assert dd(e, n) == 1 + Sum(1/k, (k, 1, n))
e = Sum(1/k, (k, 1, n), (m, 1, n))
assert dd(e, n) == harmonic(n)
def test_difference_delta__Add():
e = n + n*(n + 1)
assert dd(e, n) == 2*n + 3
assert dd(e, n, 2) == 4*n + 8
e = n + Sum(1/k, (k, 1, n))
assert dd(e, n) == 1 + 1/(n + 1)
assert dd(e, n, 5) == 5 + Add(*[1/(i + n + 1) for i in range(5)])
def test_difference_delta__Pow():
e = 4**n
assert dd(e, n) == 3*4**n
assert dd(e, n, 2) == 15*4**n
e = 4**(2*n)
assert dd(e, n) == 15*4**(2*n)
assert dd(e, n, 2) == 255*4**(2*n)
e = n**4
assert dd(e, n) == (n + 1)**4 - n**4
e = n**n
assert dd(e, n) == (n + 1)**(n + 1) - n**n
def test_limit_seq():
e = binomial(2*n, n) / Sum(binomial(2*k, k), (k, 1, n))
assert limit_seq(e) == S(3) / 4
assert limit_seq(e, m) == e
e = (5*n**3 + 3*n**2 + 4) / (3*n**3 + 4*n - 5)
assert limit_seq(e, n) == S(5) / 3
e = (harmonic(n) * Sum(harmonic(k), (k, 1, n))) / (n * harmonic(2*n)**2)
assert limit_seq(e, n) == 1
e = Sum(k**2 * Sum(2**m/m, (m, 1, k)), (k, 1, n)) / (2**n*n)
assert limit_seq(e, n) == 4
e = (Sum(binomial(3*k, k) * binomial(5*k, k), (k, 1, n)) /
(binomial(3*n, n) * binomial(5*n, n)))
assert limit_seq(e, n) == S(84375) / 83351
e = Sum(harmonic(k)**2/k, (k, 1, 2*n)) / harmonic(n)**3
assert limit_seq(e, n) == S(1) / 3
raises(ValueError, lambda: limit_seq(e * m))
@XFAIL
def test_limit_seq_fail():
# improve Summation algorithm or add ad-hoc criteria
e = (harmonic(n)**3 * Sum(1/harmonic(k), (k, 1, n)) /
(n * Sum(harmonic(k)/k, (k, 1, n))))
assert limit_seq(e, n) == 2
# No unique dominant term
e = (Sum(2**k * binomial(2*k, k) / k**2, (k, 1, n)) /
(Sum(2**k/k*2, (k, 1, n)) * Sum(binomial(2*k, k), (k, 1, n))))
assert limit_seq(e, n) == S(3) / 7
# Simplifications of summations needs to be improved.
e = n**3*Sum(2**k/k**2, (k, 1, n))**2 / (2**n * Sum(2**k/k, (k, 1, n)))
assert limit_seq(e, n) == 2
e = (harmonic(n) * Sum(2**k/k, (k, 1, n)) /
(n * Sum(2**k*harmonic(k)/k**2, (k, 1, n))))
assert limit_seq(e, n) == 1
e = (Sum(2**k*factorial(k) / k**2, (k, 1, 2*n)) /
(Sum(4**k/k**2, (k, 1, n)) * Sum(factorial(k), (k, 1, 2*n))))
assert limit_seq(e, n) == S(3) / 16
| 3,139 | 28.074074 | 76 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/series/tests/test_fourier.py
|
from sympy import (symbols, pi, Piecewise, sin, cos, sinc, Rational,
oo, fourier_series, Add)
from sympy.series.fourier import FourierSeries
from sympy.utilities.pytest import raises
x, y, z = symbols('x y z')
fo = fourier_series(x, (x, -pi, pi))
fe = fourier_series(x**2, (-pi, pi))
fp = fourier_series(Piecewise((0, x < 0), (pi, True)), (x, -pi, pi))
def test_FourierSeries():
assert fourier_series(1, (-pi, pi)) == 1
assert (Piecewise((0, x < 0), (pi, True)).
fourier_series((x, -pi, pi)).truncate()) == fp.truncate()
assert isinstance(fo, FourierSeries)
assert fo.function == x
assert fo.x == x
assert fo.period == (-pi, pi)
assert fo.term(3) == 2*sin(3*x) / 3
assert fe.term(3) == -4*cos(3*x) / 9
assert fp.term(3) == 2*sin(3*x) / 3
assert fo.as_leading_term(x) == 2*sin(x)
assert fe.as_leading_term(x) == pi**2 / 3
assert fp.as_leading_term(x) == pi / 2
assert fo.truncate() == 2*sin(x) - sin(2*x) + (2*sin(3*x) / 3)
assert fe.truncate() == -4*cos(x) + cos(2*x) + pi**2 / 3
assert fp.truncate() == 2*sin(x) + (2*sin(3*x) / 3) + pi / 2
fot = fo.truncate(n=None)
s = [0, 2*sin(x), -sin(2*x)]
for i, t in enumerate(fot):
if i == 3:
break
assert s[i] == t
def _check_iter(f, i):
for ind, t in enumerate(f):
assert t == f[ind]
if ind == i:
break
_check_iter(fo, 3)
_check_iter(fe, 3)
_check_iter(fp, 3)
assert fo.subs(x, x**2) == fo
raises(ValueError, lambda: fourier_series(x, (0, 1, 2)))
raises(ValueError, lambda: fourier_series(x, (x, 0, oo)))
raises(ValueError, lambda: fourier_series(x*y, (0, oo)))
def test_FourierSeries_2():
p = Piecewise((0, x < 0), (x, True))
f = fourier_series(p, (x, -2, 2))
assert f.term(3) == (2*sin(3*pi*x / 2) / (3*pi) -
4*cos(3*pi*x / 2) / (9*pi**2))
assert f.truncate() == (2*sin(pi*x / 2) / pi - sin(pi*x) / pi -
4*cos(pi*x / 2) / pi**2 + Rational(1, 2))
def test_fourier_series_square_wave():
"""Test if fourier_series approximates discontinuous function correctly."""
square_wave = Piecewise((1, x < pi), (-1, True))
s = fourier_series(square_wave, (x, 0, 2*pi))
assert s.truncate(3) == 4 / pi * sin(x) + 4 / (3 * pi) * sin(3 * x) + \
4 / (5 * pi) * sin(5 * x)
assert s.sigma_approximation(4) == 4 / pi * sin(x) * sinc(pi / 4) + \
4 / (3 * pi) * sin(3 * x) * sinc(3 * pi / 4)
def test_FourierSeries__operations():
fes = fe.scale(-1).shift(pi**2)
assert fes.truncate() == 4*cos(x) - cos(2*x) + 2*pi**2 / 3
assert fp.shift(-pi/2).truncate() == (2*sin(x) + (2*sin(3*x) / 3) +
(2*sin(5*x) / 5))
fos = fo.scale(3)
assert fos.truncate() == 6*sin(x) - 3*sin(2*x) + 2*sin(3*x)
fx = fe.scalex(2).shiftx(1)
assert fx.truncate() == -4*cos(2*x + 2) + cos(4*x + 4) + pi**2 / 3
fl = fe.scalex(3).shift(-pi).scalex(2).shiftx(1).scale(4)
assert fl.truncate() == (-16*cos(6*x + 6) + 4*cos(12*x + 12) -
4*pi + 4*pi**2 / 3)
raises(ValueError, lambda: fo.shift(x))
raises(ValueError, lambda: fo.shiftx(sin(x)))
raises(ValueError, lambda: fo.scale(x*y))
raises(ValueError, lambda: fo.scalex(x**2))
def test_FourierSeries__neg():
assert (-fo).truncate() == -2*sin(x) + sin(2*x) - (2*sin(3*x) / 3)
assert (-fe).truncate() == +4*cos(x) - cos(2*x) - pi**2 / 3
def test_FourierSeries__add__sub():
assert fo + fo == fo.scale(2)
assert fo - fo == 0
assert -fe - fe == fe.scale(-2)
assert (fo + fe).truncate() == 2*sin(x) - sin(2*x) - 4*cos(x) + cos(2*x) \
+ pi**2 / 3
assert (fo - fe).truncate() == 2*sin(x) - sin(2*x) + 4*cos(x) - cos(2*x) \
- pi**2 / 3
assert isinstance(fo + 1, Add)
raises(ValueError, lambda: fo + fourier_series(x, (x, 0, 2)))
| 3,982 | 32.191667 | 79 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/series/tests/test_lseries.py
|
from sympy import sin, cos, exp, tanh, E, S, Order
from sympy.abc import x, y
def test_sin():
e = sin(x).lseries(x)
assert next(e) == x
assert next(e) == -x**3/6
assert next(e) == x**5/120
def test_cos():
e = cos(x).lseries(x)
assert next(e) == 1
assert next(e) == -x**2/2
assert next(e) == x**4/24
def test_exp():
e = exp(x).lseries(x)
assert next(e) == 1
assert next(e) == x
assert next(e) == x**2/2
assert next(e) == x**3/6
def test_exp2():
e = exp(cos(x)).lseries(x)
assert next(e) == E
assert next(e) == -E*x**2/2
assert next(e) == E*x**4/6
assert next(e) == -31*E*x**6/720
def test_simple():
assert [t for t in x.lseries()] == [x]
assert [t for t in S.One.lseries(x)] == [1]
assert not next((x/(x + y)).lseries(y)).has(Order)
def test_issue_5183():
s = (x + 1/x).lseries()
assert [si for si in s] == [1/x, x]
assert next((x + x**2).lseries()) == x
assert next(((1 + x)**7).lseries(x)) == 1
assert next((sin(x + y)).series(x, n=3).lseries(y)) == x
# it would be nice if all terms were grouped, but in the
# following case that would mean that all the terms would have
# to be known since, for example, every term has a constant in it.
s = ((1 + x)**7).series(x, 1, n=None)
assert [next(s) for i in range(2)] == [128, -448 + 448*x]
def test_issue_6999():
s = tanh(x).lseries(x, 1)
assert next(s) == tanh(1)
assert next(s) == x - (x - 1)*tanh(1)**2 - 1
assert next(s) == -(x - 1)**2*tanh(1) + (x - 1)**2*tanh(1)**3
assert next(s) == -(x - 1)**3*tanh(1)**4 - (x - 1)**3/3 + \
4*(x - 1)**3*tanh(1)**2/3
| 1,670 | 26.393443 | 70 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/series/tests/__init__.py
| 0 | 0 | 0 |
py
|
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/series/tests/test_order.py
|
from sympy import (Symbol, Rational, Order, exp, ln, log, nan, oo, O, pi, I,
S, Integral, sin, cos, sqrt, conjugate, expand, transpose, symbols,
Function, Add)
from sympy.utilities.pytest import raises
from sympy.abc import w, x, y, z
def test_caching_bug():
#needs to be a first test, so that all caches are clean
#cache it
e = O(w)
#and test that this won't raise an exception
O(w**(-1/x/log(3)*log(5)), w)
def test_free_symbols():
assert Order(1).free_symbols == set()
assert Order(x).free_symbols == {x}
assert Order(1, x).free_symbols == {x}
assert Order(x*y).free_symbols == {x, y}
assert Order(x, x, y).free_symbols == {x, y}
def test_simple_1():
o = Rational(0)
assert Order(2*x) == Order(x)
assert Order(x)*3 == Order(x)
assert -28*Order(x) == Order(x)
assert Order(Order(x)) == Order(x)
assert Order(Order(x), y) == Order(Order(x), x, y)
assert Order(-23) == Order(1)
assert Order(exp(x)) == Order(1, x)
assert Order(exp(1/x)).expr == exp(1/x)
assert Order(x*exp(1/x)).expr == x*exp(1/x)
assert Order(x**(o/3)).expr == x**(o/3)
assert Order(x**(5*o/3)).expr == x**(5*o/3)
assert Order(x**2 + x + y, x) == O(1, x)
assert Order(x**2 + x + y, y) == O(1, y)
raises(ValueError, lambda: Order(exp(x), x, x))
raises(TypeError, lambda: Order(x, 2 - x))
def test_simple_2():
assert Order(2*x)*x == Order(x**2)
assert Order(2*x)/x == Order(1, x)
assert Order(2*x)*x*exp(1/x) == Order(x**2*exp(1/x))
assert (Order(2*x)*x*exp(1/x)/ln(x)**3).expr == x**2*exp(1/x)*ln(x)**-3
def test_simple_3():
assert Order(x) + x == Order(x)
assert Order(x) + 2 == 2 + Order(x)
assert Order(x) + x**2 == Order(x)
assert Order(x) + 1/x == 1/x + Order(x)
assert Order(1/x) + 1/x**2 == 1/x**2 + Order(1/x)
assert Order(x) + exp(1/x) == Order(x) + exp(1/x)
def test_simple_4():
assert Order(x)**2 == Order(x**2)
def test_simple_5():
assert Order(x) + Order(x**2) == Order(x)
assert Order(x) + Order(x**-2) == Order(x**-2)
assert Order(x) + Order(1/x) == Order(1/x)
def test_simple_6():
assert Order(x) - Order(x) == Order(x)
assert Order(x) + Order(1) == Order(1)
assert Order(x) + Order(x**2) == Order(x)
assert Order(1/x) + Order(1) == Order(1/x)
assert Order(x) + Order(exp(1/x)) == Order(exp(1/x))
assert Order(x**3) + Order(exp(2/x)) == Order(exp(2/x))
assert Order(x**-3) + Order(exp(2/x)) == Order(exp(2/x))
def test_simple_7():
assert 1 + O(1) == O(1)
assert 2 + O(1) == O(1)
assert x + O(1) == O(1)
assert 1/x + O(1) == 1/x + O(1)
def test_simple_8():
assert O(sqrt(-x)) == O(sqrt(x))
assert O(x**2*sqrt(x)) == O(x**(S(5)/2))
assert O(x**3*sqrt(-(-x)**3)) == O(x**(S(9)/2))
assert O(x**(S(3)/2)*sqrt((-x)**3)) == O(x**3)
assert O(x*(-2*x)**(I/2)) == O(x*(-x)**(I/2))
def test_as_expr_variables():
assert Order(x).as_expr_variables(None) == (x, ((x, 0),))
assert Order(x).as_expr_variables((((x, 0),))) == (x, ((x, 0),))
assert Order(y).as_expr_variables(((x, 0),)) == (y, ((x, 0), (y, 0)))
assert Order(y).as_expr_variables(((x, 0), (y, 0))) == (y, ((x, 0), (y, 0)))
def test_contains_0():
assert Order(1, x).contains(Order(1, x))
assert Order(1, x).contains(Order(1))
assert Order(1).contains(Order(1, x)) is False
def test_contains_1():
assert Order(x).contains(Order(x))
assert Order(x).contains(Order(x**2))
assert not Order(x**2).contains(Order(x))
assert not Order(x).contains(Order(1/x))
assert not Order(1/x).contains(Order(exp(1/x)))
assert not Order(x).contains(Order(exp(1/x)))
assert Order(1/x).contains(Order(x))
assert Order(exp(1/x)).contains(Order(x))
assert Order(exp(1/x)).contains(Order(1/x))
assert Order(exp(1/x)).contains(Order(exp(1/x)))
assert Order(exp(2/x)).contains(Order(exp(1/x)))
assert not Order(exp(1/x)).contains(Order(exp(2/x)))
def test_contains_2():
assert Order(x).contains(Order(y)) is None
assert Order(x).contains(Order(y*x))
assert Order(y*x).contains(Order(x))
assert Order(y).contains(Order(x*y))
assert Order(x).contains(Order(y**2*x))
def test_contains_3():
assert Order(x*y**2).contains(Order(x**2*y)) is None
assert Order(x**2*y).contains(Order(x*y**2)) is None
def test_contains_4():
assert Order(sin(1/x**2)).contains(Order(cos(1/x**2))) is None
assert Order(cos(1/x**2)).contains(Order(sin(1/x**2))) is None
def test_contains():
assert Order(1, x) not in Order(1)
assert Order(1) in Order(1, x)
raises(TypeError, lambda: Order(x*y**2) in Order(x**2*y))
def test_add_1():
assert Order(x + x) == Order(x)
assert Order(3*x - 2*x**2) == Order(x)
assert Order(1 + x) == Order(1, x)
assert Order(1 + 1/x) == Order(1/x)
assert Order(ln(x) + 1/ln(x)) == Order(ln(x))
assert Order(exp(1/x) + x) == Order(exp(1/x))
assert Order(exp(1/x) + 1/x**20) == Order(exp(1/x))
def test_ln_args():
assert O(log(x)) + O(log(2*x)) == O(log(x))
assert O(log(x)) + O(log(x**3)) == O(log(x))
assert O(log(x*y)) + O(log(x) + log(y)) == O(log(x*y))
def test_multivar_0():
assert Order(x*y).expr == x*y
assert Order(x*y**2).expr == x*y**2
assert Order(x*y, x).expr == x
assert Order(x*y**2, y).expr == y**2
assert Order(x*y*z).expr == x*y*z
assert Order(x/y).expr == x/y
assert Order(x*exp(1/y)).expr == x*exp(1/y)
assert Order(exp(x)*exp(1/y)).expr == exp(1/y)
def test_multivar_0a():
assert Order(exp(1/x)*exp(1/y)).expr == exp(1/x + 1/y)
def test_multivar_1():
assert Order(x + y).expr == x + y
assert Order(x + 2*y).expr == x + y
assert (Order(x + y) + x).expr == (x + y)
assert (Order(x + y) + x**2) == Order(x + y)
assert (Order(x + y) + 1/x) == 1/x + Order(x + y)
assert Order(x**2 + y*x).expr == x**2 + y*x
def test_multivar_2():
assert Order(x**2*y + y**2*x, x, y).expr == x**2*y + y**2*x
def test_multivar_mul_1():
assert Order(x + y)*x == Order(x**2 + y*x, x, y)
def test_multivar_3():
assert (Order(x) + Order(y)).args in [
(Order(x), Order(y)),
(Order(y), Order(x))]
assert Order(x) + Order(y) + Order(x + y) == Order(x + y)
assert (Order(x**2*y) + Order(y**2*x)).args in [
(Order(x*y**2), Order(y*x**2)),
(Order(y*x**2), Order(x*y**2))]
assert (Order(x**2*y) + Order(y*x)) == Order(x*y)
def test_issue_3468():
y = Symbol('y', negative=True)
z = Symbol('z', complex=True)
# check that Order does not modify assumptions about symbols
Order(x)
Order(y)
Order(z)
assert x.is_positive is None
assert y.is_positive is False
assert z.is_positive is None
def test_leading_order():
assert (x + 1 + 1/x**5).extract_leading_order(x) == ((1/x**5, O(1/x**5)),)
assert (1 + 1/x).extract_leading_order(x) == ((1/x, O(1/x)),)
assert (1 + x).extract_leading_order(x) == ((1, O(1, x)),)
assert (1 + x**2).extract_leading_order(x) == ((1, O(1, x)),)
assert (2 + x**2).extract_leading_order(x) == ((2, O(1, x)),)
assert (x + x**2).extract_leading_order(x) == ((x, O(x)),)
def test_leading_order2():
assert set((2 + pi + x**2).extract_leading_order(x)) == set(((pi, O(1, x)),
(S(2), O(1, x))))
assert set((2*x + pi*x + x**2).extract_leading_order(x)) == set(((2*x, O(x)),
(x*pi, O(x))))
def test_order_leadterm():
assert O(x**2)._eval_as_leading_term(x) == O(x**2)
def test_order_symbols():
e = x*y*sin(x)*Integral(x, (x, 1, 2))
assert O(e) == O(x**2*y, x, y)
assert O(e, x) == O(x**2)
def test_nan():
assert O(nan) == nan
assert not O(x).contains(nan)
def test_O1():
assert O(1, x) * x == O(x)
assert O(1, y) * x == O(1, y)
def test_getn():
# other lines are tested incidentally by the suite
assert O(x).getn() == 1
assert O(x/log(x)).getn() == 1
assert O(x**2/log(x)**2).getn() == 2
assert O(x*log(x)).getn() == 1
raises(NotImplementedError, lambda: (O(x) + O(y)).getn())
def test_diff():
assert O(x**2).diff(x) == O(x)
def test_getO():
assert (x).getO() is None
assert (x).removeO() == x
assert (O(x)).getO() == O(x)
assert (O(x)).removeO() == 0
assert (z + O(x) + O(y)).getO() == O(x) + O(y)
assert (z + O(x) + O(y)).removeO() == z
raises(NotImplementedError, lambda: (O(x) + O(y)).getn())
def test_leading_term():
from sympy import digamma
assert O(1/digamma(1/x)) == O(1/log(x))
def test_eval():
assert Order(x).subs(Order(x), 1) == 1
assert Order(x).subs(x, y) == Order(y)
assert Order(x).subs(y, x) == Order(x)
assert Order(x).subs(x, x + y) == Order(x + y, (x, -y))
assert (O(1)**x).is_Pow
def test_issue_4279():
a, b = symbols('a b')
assert O(a, a, b) + O(1, a, b) == O(1, a, b)
assert O(b, a, b) + O(1, a, b) == O(1, a, b)
assert O(a + b, a, b) + O(1, a, b) == O(1, a, b)
assert O(1, a, b) + O(a, a, b) == O(1, a, b)
assert O(1, a, b) + O(b, a, b) == O(1, a, b)
assert O(1, a, b) + O(a + b, a, b) == O(1, a, b)
def test_issue_4855():
assert 1/O(1) != O(1)
assert 1/O(x) != O(1/x)
assert 1/O(x, (x, oo)) != O(1/x, (x, oo))
f = Function('f')
assert 1/O(f(x)) != O(1/x)
def test_order_conjugate_transpose():
x = Symbol('x', real=True)
y = Symbol('y', imaginary=True)
assert conjugate(Order(x)) == Order(conjugate(x))
assert conjugate(Order(y)) == Order(conjugate(y))
assert conjugate(Order(x**2)) == Order(conjugate(x)**2)
assert conjugate(Order(y**2)) == Order(conjugate(y)**2)
assert transpose(Order(x)) == Order(transpose(x))
assert transpose(Order(y)) == Order(transpose(y))
assert transpose(Order(x**2)) == Order(transpose(x)**2)
assert transpose(Order(y**2)) == Order(transpose(y)**2)
def test_order_noncommutative():
A = Symbol('A', commutative=False)
assert Order(A + A*x, x) == Order(1, x)
assert (A + A*x)*Order(x) == Order(x)
assert (A*x)*Order(x) == Order(x**2, x)
assert expand((1 + Order(x))*A*A*x) == A*A*x + Order(x**2, x)
assert expand((A*A + Order(x))*x) == A*A*x + Order(x**2, x)
assert expand((A + Order(x))*A*x) == A*A*x + Order(x**2, x)
def test_issue_6753():
assert (1 + x**2)**10000*O(x) == O(x)
def test_order_at_infinity():
assert Order(1 + x, (x, oo)) == Order(x, (x, oo))
assert Order(3*x, (x, oo)) == Order(x, (x, oo))
assert Order(x, (x, oo))*3 == Order(x, (x, oo))
assert -28*Order(x, (x, oo)) == Order(x, (x, oo))
assert Order(Order(x, (x, oo)), (x, oo)) == Order(x, (x, oo))
assert Order(Order(x, (x, oo)), (y, oo)) == Order(x, (x, oo), (y, oo))
assert Order(3, (x, oo)) == Order(1, (x, oo))
assert Order(x**2 + x + y, (x, oo)) == O(x**2, (x, oo))
assert Order(x**2 + x + y, (y, oo)) == O(y, (y, oo))
assert Order(2*x, (x, oo))*x == Order(x**2, (x, oo))
assert Order(2*x, (x, oo))/x == Order(1, (x, oo))
assert Order(2*x, (x, oo))*x*exp(1/x) == Order(x**2*exp(1/x), (x, oo))
assert Order(2*x, (x, oo))*x*exp(1/x)/ln(x)**3 == Order(x**2*exp(1/x)*ln(x)**-3, (x, oo))
assert Order(x, (x, oo)) + 1/x == 1/x + Order(x, (x, oo)) == Order(x, (x, oo))
assert Order(x, (x, oo)) + 1 == 1 + Order(x, (x, oo)) == Order(x, (x, oo))
assert Order(x, (x, oo)) + x == x + Order(x, (x, oo)) == Order(x, (x, oo))
assert Order(x, (x, oo)) + x**2 == x**2 + Order(x, (x, oo))
assert Order(1/x, (x, oo)) + 1/x**2 == 1/x**2 + Order(1/x, (x, oo)) == Order(1/x, (x, oo))
assert Order(x, (x, oo)) + exp(1/x) == exp(1/x) + Order(x, (x, oo))
assert Order(x, (x, oo))**2 == Order(x**2, (x, oo))
assert Order(x, (x, oo)) + Order(x**2, (x, oo)) == Order(x**2, (x, oo))
assert Order(x, (x, oo)) + Order(x**-2, (x, oo)) == Order(x, (x, oo))
assert Order(x, (x, oo)) + Order(1/x, (x, oo)) == Order(x, (x, oo))
assert Order(x, (x, oo)) - Order(x, (x, oo)) == Order(x, (x, oo))
assert Order(x, (x, oo)) + Order(1, (x, oo)) == Order(x, (x, oo))
assert Order(x, (x, oo)) + Order(x**2, (x, oo)) == Order(x**2, (x, oo))
assert Order(1/x, (x, oo)) + Order(1, (x, oo)) == Order(1, (x, oo))
assert Order(x, (x, oo)) + Order(exp(1/x), (x, oo)) == Order(x, (x, oo))
assert Order(x**3, (x, oo)) + Order(exp(2/x), (x, oo)) == Order(x**3, (x, oo))
assert Order(x**-3, (x, oo)) + Order(exp(2/x), (x, oo)) == Order(exp(2/x), (x, oo))
# issue 7207
assert Order(exp(x), (x, oo)).expr == Order(2*exp(x), (x, oo)).expr == exp(x)
assert Order(y**x, (x, oo)).expr == Order(2*y**x, (x, oo)).expr == exp(log(y)*x)
def test_mixing_order_at_zero_and_infinity():
assert (Order(x, (x, 0)) + Order(x, (x, oo))).is_Add
assert Order(x, (x, 0)) + Order(x, (x, oo)) == Order(x, (x, oo)) + Order(x, (x, 0))
assert Order(Order(x, (x, oo))) == Order(x, (x, oo))
# not supported (yet)
raises(NotImplementedError, lambda: Order(x, (x, 0))*Order(x, (x, oo)))
raises(NotImplementedError, lambda: Order(x, (x, oo))*Order(x, (x, 0)))
raises(NotImplementedError, lambda: Order(Order(x, (x, oo)), y))
raises(NotImplementedError, lambda: Order(Order(x), (x, oo)))
def test_order_at_some_point():
assert Order(x, (x, 1)) == Order(1, (x, 1))
assert Order(2*x - 2, (x, 1)) == Order(x - 1, (x, 1))
assert Order(-x + 1, (x, 1)) == Order(x - 1, (x, 1))
assert Order(x - 1, (x, 1))**2 == Order((x - 1)**2, (x, 1))
assert Order(x - 2, (x, 2)) - O(x - 2, (x, 2)) == Order(x - 2, (x, 2))
def test_order_subs_limits():
# issue 3333
assert (1 + Order(x)).subs(x, 1/x) == 1 + Order(1/x, (x, oo))
assert (1 + Order(x)).limit(x, 0) == 1
# issue 5769
assert ((x + Order(x**2))/x).limit(x, 0) == 1
assert Order(x**2).subs(x, y - 1) == Order((y - 1)**2, (y, 1))
assert Order(10*x**2, (x, 2)).subs(x, y - 1) == Order(1, (y, 3))
def test_issue_9351():
assert exp(x).series(x, 10, 1) == exp(10) + Order(x - 10, (x, 10))
def test_issue_9192():
assert O(1)*O(1) == O(1)
assert O(1)**O(1) == O(1)
def test_performance_of_adding_order():
l = list(x**i for i in range(1000))
l.append(O(x**1001))
assert Add(*l).subs(x,1) == O(1)
| 14,249 | 32.767773 | 94 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/series/tests/test_formal.py
|
from sympy import (symbols, factorial, sqrt, Rational, atan, I, log, fps, O,
Sum, oo, S, pi, cos, sin, Function, exp, Derivative, asin,
airyai, acos, acosh, gamma, erf, asech, Add, Integral, Mul)
from sympy.series.formal import (rational_algorithm, FormalPowerSeries,
rational_independent, simpleDE, exp_re,
hyper_re)
from sympy.utilities.pytest import raises, XFAIL, slow
x, y, z = symbols('x y z')
n, m, k = symbols('n m k', integer=True)
f, r = Function('f'), Function('r')
def test_rational_algorithm():
f = 1 / ((x - 1)**2 * (x - 2))
assert rational_algorithm(f, x, k) == \
(-2**(-k - 1) + 1 - (factorial(k + 1) / factorial(k)), 0, 0)
f = (1 + x + x**2 + x**3) / ((x - 1) * (x - 2))
assert rational_algorithm(f, x, k) == \
(-15*2**(-k - 1) + 4, x + 4, 0)
f = z / (y*m - m*x - y*x + x**2)
assert rational_algorithm(f, x, k) == \
(((-y**(-k - 1)*z) / (y - m)) + ((m**(-k - 1)*z) / (y - m)), 0, 0)
f = x / (1 - x - x**2)
assert rational_algorithm(f, x, k) is None
assert rational_algorithm(f, x, k, full=True) == \
(((-Rational(1, 2) + sqrt(5)/2)**(-k - 1) *
(-sqrt(5)/10 + Rational(1, 2))) +
((-sqrt(5)/2 - Rational(1, 2))**(-k - 1) *
(sqrt(5)/10 + Rational(1, 2))), 0, 0)
f = 1 / (x**2 + 2*x + 2)
assert rational_algorithm(f, x, k) is None
assert rational_algorithm(f, x, k, full=True) == \
((I*(-1 + I)**(-k - 1)) / 2 - (I*(-1 - I)**(-k - 1)) / 2, 0, 0)
f = log(1 + x)
assert rational_algorithm(f, x, k) == \
(-(-1)**(-k) / k, 0, 1)
f = atan(x)
assert rational_algorithm(f, x, k) is None
assert rational_algorithm(f, x, k, full=True) == \
(((I*I**(-k)) / 2 - (I*(-I)**(-k)) / 2) / k, 0, 1)
f = x*atan(x) - log(1 + x**2) / 2
assert rational_algorithm(f, x, k) is None
assert rational_algorithm(f, x, k, full=True) == \
(((I*I**(-k + 1)) / 2 - (I*(-I)**(-k + 1)) / 2) /
(k*(k - 1)), 0, 2)
f = log((1 + x) / (1 - x)) / 2 - atan(x)
assert rational_algorithm(f, x, k) is None
assert rational_algorithm(f, x, k, full=True) == \
((-(-1)**(-k) / 2 - (I*I**(-k)) / 2 + (I*(-I)**(-k)) / 2 +
Rational(1, 2)) / k, 0, 1)
assert rational_algorithm(cos(x), x, k) is None
def test_rational_independent():
ri = rational_independent
assert ri([], x) == []
assert ri([cos(x), sin(x)], x) == [cos(x), sin(x)]
assert ri([x**2, sin(x), x*sin(x), x**3], x) == \
[x**3 + x**2, x*sin(x) + sin(x)]
assert ri([S.One, x*log(x), log(x), sin(x)/x, cos(x), sin(x), x], x) == \
[x + 1, x*log(x) + log(x), sin(x)/x + sin(x), cos(x)]
def test_simpleDE():
# Tests just the first valid DE
for DE in simpleDE(exp(x), x, f):
assert DE == (-f(x) + Derivative(f(x), x), 1)
break
for DE in simpleDE(sin(x), x, f):
assert DE == (f(x) + Derivative(f(x), x, x), 2)
break
for DE in simpleDE(log(1 + x), x, f):
assert DE == ((x + 1)*Derivative(f(x), x, 2) + Derivative(f(x), x), 2)
break
for DE in simpleDE(asin(x), x, f):
assert DE == (x*Derivative(f(x), x) + (x**2 - 1)*Derivative(f(x), x, x),
2)
break
for DE in simpleDE(exp(x)*sin(x), x, f):
assert DE == (2*f(x) - 2*Derivative(f(x)) + Derivative(f(x), x, x), 2)
break
for DE in simpleDE(((1 + x)/(1 - x))**n, x, f):
assert DE == (2*n*f(x) + (x**2 - 1)*Derivative(f(x), x), 1)
break
for DE in simpleDE(airyai(x), x, f):
assert DE == (-x*f(x) + Derivative(f(x), x, x), 2)
break
def test_exp_re():
d = -f(x) + Derivative(f(x), x)
assert exp_re(d, r, k) == -r(k) + r(k + 1)
d = f(x) + Derivative(f(x), x, x)
assert exp_re(d, r, k) == r(k) + r(k + 2)
d = f(x) + Derivative(f(x), x) + Derivative(f(x), x, x)
assert exp_re(d, r, k) == r(k) + r(k + 1) + r(k + 2)
d = Derivative(f(x), x) + Derivative(f(x), x, x)
assert exp_re(d, r, k) == r(k) + r(k + 1)
d = Derivative(f(x), x, 3) + Derivative(f(x), x, 4) + Derivative(f(x))
assert exp_re(d, r, k) == r(k) + r(k + 2) + r(k + 3)
def test_hyper_re():
d = f(x) + Derivative(f(x), x, x)
assert hyper_re(d, r, k) == r(k) + (k+1)*(k+2)*r(k + 2)
d = -x*f(x) + Derivative(f(x), x, x)
assert hyper_re(d, r, k) == (k + 2)*(k + 3)*r(k + 3) - r(k)
d = 2*f(x) - 2*Derivative(f(x), x) + Derivative(f(x), x, x)
assert hyper_re(d, r, k) == \
(-2*k - 2)*r(k + 1) + (k + 1)*(k + 2)*r(k + 2) + 2*r(k)
d = 2*n*f(x) + (x**2 - 1)*Derivative(f(x), x)
assert hyper_re(d, r, k) == \
k*r(k) + 2*n*r(k + 1) + (-k - 2)*r(k + 2)
d = (x**10 + 4)*Derivative(f(x), x) + x*(x**10 - 1)*Derivative(f(x), x, x)
assert hyper_re(d, r, k) == \
(k*(k - 1) + k)*r(k) + (4*k - (k + 9)*(k + 10) + 40)*r(k + 10)
d = ((x**2 - 1)*Derivative(f(x), x, 3) + 3*x*Derivative(f(x), x, x) +
Derivative(f(x), x))
assert hyper_re(d, r, k) == \
((k*(k - 2)*(k - 1) + 3*k*(k - 1) + k)*r(k) +
(-k*(k + 1)*(k + 2))*r(k + 2))
def test_fps():
assert fps(1) == 1
assert fps(2, x) == 2
assert fps(2, x, dir='+') == 2
assert fps(2, x, dir='-') == 2
assert fps(x**2 + x + 1) == x**2 + x + 1
assert fps(1/x + 1/x**2) == 1/x + 1/x**2
assert fps(log(1 + x), hyper=False, rational=False) == log(1 + x)
f = fps(log(1 + x))
assert isinstance(f, FormalPowerSeries)
assert f.function == log(1 + x)
assert f.subs(x, y) == f
assert f[:5] == [0, x, -x**2/2, x**3/3, -x**4/4]
assert f.as_leading_term(x) == x
assert f.polynomial(6) == x - x**2/2 + x**3/3 - x**4/4 + x**5/5
k = f.ak.variables[0]
assert f.infinite == Sum((-(-1)**(-k)*x**k)/k, (k, 1, oo))
ft, s = f.truncate(n=None), f[:5]
for i, t in enumerate(ft):
if i == 5:
break
assert s[i] == t
f = sin(x).fps(x)
assert isinstance(f, FormalPowerSeries)
assert f.truncate() == x - x**3/6 + x**5/120 + O(x**6)
raises(NotImplementedError, lambda: fps(y*x))
raises(ValueError, lambda: fps(x, dir=0))
def test_fps__rational():
assert fps(1/x) == (1/x)
assert fps((x**2 + x + 1) / x**3, dir=-1) == (x**2 + x + 1) / x**3
f = 1 / ((x - 1)**2 * (x - 2))
assert fps(f, x).truncate() == \
(-Rational(1, 2) - 5*x/4 - 17*x**2/8 - 49*x**3/16 - 129*x**4/32 -
321*x**5/64 + O(x**6))
f = (1 + x + x**2 + x**3) / ((x - 1) * (x - 2))
assert fps(f, x).truncate() == \
(Rational(1, 2) + 5*x/4 + 17*x**2/8 + 49*x**3/16 + 113*x**4/32 +
241*x**5/64 + O(x**6))
f = x / (1 - x - x**2)
assert fps(f, x, full=True).truncate() == \
x + x**2 + 2*x**3 + 3*x**4 + 5*x**5 + O(x**6)
f = 1 / (x**2 + 2*x + 2)
assert fps(f, x, full=True).truncate() == \
Rational(1, 2) - x/2 + x**2/4 - x**4/8 + x**5/8 + O(x**6)
f = log(1 + x)
assert fps(f, x).truncate() == \
x - x**2/2 + x**3/3 - x**4/4 + x**5/5 + O(x**6)
assert fps(f, x, dir=1).truncate() == fps(f, x, dir=-1).truncate()
assert fps(f, x, 2).truncate() == \
(log(3) - Rational(2, 3) - (x - 2)**2/18 + (x - 2)**3/81 -
(x - 2)**4/324 + (x - 2)**5/1215 + x/3 + O((x - 2)**6, (x, 2)))
assert fps(f, x, 2, dir=-1).truncate() == \
(log(3) - Rational(2, 3) - (-x + 2)**2/18 - (-x + 2)**3/81 -
(-x + 2)**4/324 - (-x + 2)**5/1215 + x/3 + O((x - 2)**6, (x, 2)))
f = atan(x)
assert fps(f, x, full=True).truncate() == x - x**3/3 + x**5/5 + O(x**6)
assert fps(f, x, full=True, dir=1).truncate() == \
fps(f, x, full=True, dir=-1).truncate()
assert fps(f, x, 2, full=True).truncate() == \
(atan(2) - Rational(2, 5) - 2*(x - 2)**2/25 + 11*(x - 2)**3/375 -
6*(x - 2)**4/625 + 41*(x - 2)**5/15625 + x/5 + O((x - 2)**6, (x, 2)))
assert fps(f, x, 2, full=True, dir=-1).truncate() == \
(atan(2) - Rational(2, 5) - 2*(-x + 2)**2/25 - 11*(-x + 2)**3/375 -
6*(-x + 2)**4/625 - 41*(-x + 2)**5/15625 + x/5 + O((x - 2)**6, (x, 2)))
f = x*atan(x) - log(1 + x**2) / 2
assert fps(f, x, full=True).truncate() == x**2/2 - x**4/12 + O(x**6)
f = log((1 + x) / (1 - x)) / 2 - atan(x)
assert fps(f, x, full=True).truncate(n=10) == 2*x**3/3 + 2*x**7/7 + O(x**10)
def test_fps__hyper():
f = sin(x)
assert fps(f, x).truncate() == x - x**3/6 + x**5/120 + O(x**6)
f = cos(x)
assert fps(f, x).truncate() == 1 - x**2/2 + x**4/24 + O(x**6)
f = exp(x)
assert fps(f, x).truncate() == \
1 + x + x**2/2 + x**3/6 + x**4/24 + x**5/120 + O(x**6)
f = atan(x)
assert fps(f, x).truncate() == x - x**3/3 + x**5/5 + O(x**6)
f = exp(acos(x))
assert fps(f, x).truncate() == \
(exp(pi/2) - x*exp(pi/2) + x**2*exp(pi/2)/2 - x**3*exp(pi/2)/3 +
5*x**4*exp(pi/2)/24 - x**5*exp(pi/2)/6 + O(x**6))
f = exp(acosh(x))
assert fps(f, x).truncate() == I + x - I*x**2/2 - I*x**4/8 + O(x**6)
f = atan(1/x)
assert fps(f, x).truncate() == pi/2 - x + x**3/3 - x**5/5 + O(x**6)
f = x*atan(x) - log(1 + x**2) / 2
assert fps(f, x, rational=False).truncate() == x**2/2 - x**4/12 + O(x**6)
f = log(1 + x)
assert fps(f, x, rational=False).truncate() == \
x - x**2/2 + x**3/3 - x**4/4 + x**5/5 + O(x**6)
f = airyai(x**2)
assert fps(f, x).truncate() == \
(3**Rational(5, 6)*gamma(Rational(1, 3))/(6*pi) -
3**Rational(2, 3)*x**2/(3*gamma(Rational(1, 3))) + O(x**6))
f = exp(x)*sin(x)
assert fps(f, x).truncate() == x + x**2 + x**3/3 - x**5/30 + O(x**6)
f = exp(x)*sin(x)/x
assert fps(f, x).truncate() == 1 + x + x**2/3 - x**4/30 - x**5/90 + O(x**6)
f = sin(x) * cos(x)
assert fps(f, x).truncate() == x - 2*x**3/3 + 2*x**5/15 + O(x**6)
def test_fps_shift():
f = x**-5*sin(x)
assert fps(f, x).truncate() == \
1/x**4 - 1/(6*x**2) + S.One/120 - x**2/5040 + x**4/362880 + O(x**6)
f = x**2*atan(x)
assert fps(f, x, rational=False).truncate() == \
x**3 - x**5/3 + O(x**6)
f = cos(sqrt(x))*x
assert fps(f, x).truncate() == \
x - x**2/2 + x**3/24 - x**4/720 + x**5/40320 + O(x**6)
f = x**2*cos(sqrt(x))
assert fps(f, x).truncate() == \
x**2 - x**3/2 + x**4/24 - x**5/720 + O(x**6)
def test_fps__Add_expr():
f = x*atan(x) - log(1 + x**2) / 2
assert fps(f, x).truncate() == x**2/2 - x**4/12 + O(x**6)
f = sin(x) + cos(x) - exp(x) + log(1 + x)
assert fps(f, x).truncate() == x - 3*x**2/2 - x**4/4 + x**5/5 + O(x**6)
f = 1/x + sin(x)
assert fps(f, x).truncate() == 1/x + x - x**3/6 + x**5/120 + O(x**6)
f = sin(x) - cos(x) + 1/(x - 1)
assert fps(f, x).truncate() == \
-2 - x**2/2 - 7*x**3/6 - 25*x**4/24 - 119*x**5/120 + O(x**6)
def test_fps__asymptotic():
f = exp(x)
assert fps(f, x, oo) == f
assert fps(f, x, -oo).truncate() == O(1/x**6, (x, oo))
f = erf(x)
assert fps(f, x, oo).truncate() == 1 + O(1/x**6, (x, oo))
assert fps(f, x, -oo).truncate() == -1 + O(1/x**6, (x, oo))
f = atan(x)
assert fps(f, x, oo, full=True).truncate() == \
-1/(5*x**5) + 1/(3*x**3) - 1/x + pi/2 + O(1/x**6, (x, oo))
assert fps(f, x, -oo, full=True).truncate() == \
-1/(5*x**5) + 1/(3*x**3) - 1/x - pi/2 + O(1/x**6, (x, oo))
f = log(1 + x)
assert fps(f, x, oo) != \
(-1/(5*x**5) - 1/(4*x**4) + 1/(3*x**3) - 1/(2*x**2) + 1/x - log(1/x) +
O(1/x**6, (x, oo)))
assert fps(f, x, -oo) != \
(-1/(5*x**5) - 1/(4*x**4) + 1/(3*x**3) - 1/(2*x**2) + 1/x + I*pi -
log(-1/x) + O(1/x**6, (x, oo)))
def test_fps__fractional():
f = sin(sqrt(x)) / x
assert fps(f, x).truncate() == \
(1/sqrt(x) - sqrt(x)/6 + x**Rational(3, 2)/120 -
x**Rational(5, 2)/5040 + x**Rational(7, 2)/362880 -
x**Rational(9, 2)/39916800 + x**Rational(11, 2)/6227020800 + O(x**6))
f = sin(sqrt(x)) * x
assert fps(f, x).truncate() == \
(x**Rational(3, 2) - x**Rational(5, 2)/6 + x**Rational(7, 2)/120 -
x**Rational(9, 2)/5040 + x**Rational(11, 2)/362880 + O(x**6))
f = atan(sqrt(x)) / x**2
assert fps(f, x).truncate() == \
(x**Rational(-3, 2) - x**Rational(-1, 2)/3 + x**Rational(1, 2)/5 -
x**Rational(3, 2)/7 + x**Rational(5, 2)/9 - x**Rational(7, 2)/11 +
x**Rational(9, 2)/13 - x**Rational(11, 2)/15 + O(x**6))
f = exp(sqrt(x))
assert fps(f, x).truncate().expand() == \
(1 + x/2 + x**2/24 + x**3/720 + x**4/40320 + x**5/3628800 + sqrt(x) +
x**Rational(3, 2)/6 + x**Rational(5, 2)/120 + x**Rational(7, 2)/5040 +
x**Rational(9, 2)/362880 + x**Rational(11, 2)/39916800 + O(x**6))
f = exp(sqrt(x))*x
assert fps(f, x).truncate().expand() == \
(x + x**2/2 + x**3/24 + x**4/720 + x**5/40320 + x**Rational(3, 2) +
x**Rational(5, 2)/6 + x**Rational(7, 2)/120 + x**Rational(9, 2)/5040 +
x**Rational(11, 2)/362880 + O(x**6))
def test_fps__logarithmic_singularity():
f = log(1 + 1/x)
assert fps(f, x) != \
-log(x) + x - x**2/2 + x**3/3 - x**4/4 + x**5/5 + O(x**6)
assert fps(f, x, rational=False) != \
-log(x) + x - x**2/2 + x**3/3 - x**4/4 + x**5/5 + O(x**6)
@XFAIL
def test_fps__logarithmic_singularity_fail():
f = asech(x) # Algorithms for computing limits probably needs improvemnts
assert fps(f, x) == log(2) - log(x) - x**2/4 - 3*x**4/64 + O(x**6)
@XFAIL
def test_fps__symbolic():
f = x**n*sin(x**2)
assert fps(f, x).truncate(8) == x**2*x**n - x**6*x**n/6 + O(x**(n + 8), x)
f = x**(n - 2)*cos(x)
assert fps(f, x).truncate() == \
(x**n*(-S(1)/2 + x**(-2)) + x**2*x**n/24 - x**4*x**n/720 +
O(x**(n + 6), x))
f = x**n*log(1 + x)
fp = fps(f, x)
k = fp.ak.variables[0]
assert fp.infinite == \
Sum((-(-1)**(-k)*x**k*x**n)/k, (k, 1, oo))
f = x**(n - 2)*sin(x) + x**n*exp(x)
assert fps(f, x).truncate() == \
(x**n*(1 + 1/x) + 5*x*x**n/6 + x**2*x**n/2 + 7*x**3*x**n/40 +
x**4*x**n/24 + 41*x**5*x**n/5040 + O(x**(n + 6), x))
f = (x - 2)**n*log(1 + x)
assert fps(f, x, 2).truncate() == \
((x - 2)**n*log(3) - (x - 2)**2*(x - 2)**n/18 +
(x - 2)**3*(x - 2)**n/81 - (x - 2)**4*(x - 2)**n/324 +
(x - 2)**5*(x - 2)**n/1215 + (x/3 - S(2)/3)*(x - 2)**n +
O((x - 2)**(n + 6), (x, 2)))
f = x**n*atan(x)
assert fps(f, x, oo).truncate() == \
(-x**n/(5*x**5) + x**n/(3*x**3) + x**n*(pi/2 - 1/x) +
O(x**(n - 6), (x, oo)))
@slow
def test_fps__slow():
f = x*exp(x)*sin(2*x) # TODO: rsolve needs improvement
assert fps(f, x).truncate() == 2*x**2 + 2*x**3 - x**4/3 - x**5 + O(x**6)
def test_fps__operations():
f1, f2 = fps(sin(x)), fps(cos(x))
fsum = f1 + f2
assert fsum.function == sin(x) + cos(x)
assert fsum.truncate() == \
1 + x - x**2/2 - x**3/6 + x**4/24 + x**5/120 + O(x**6)
fsum = f1 + 1
assert fsum.function == sin(x) + 1
assert fsum.truncate() == 1 + x - x**3/6 + x**5/120 + O(x**6)
fsum = 1 + f2
assert fsum.function == cos(x) + 1
assert fsum.truncate() == 2 - x**2/2 + x**4/24 + O(x**6)
assert (f1 + x) == Add(f1, x)
assert -f2.truncate() == -1 + x**2/2 - x**4/24 + O(x**6)
assert (f1 - f1) == S.Zero
fsub = f1 - f2
assert fsub.function == sin(x) - cos(x)
assert fsub.truncate() == \
-1 + x + x**2/2 - x**3/6 - x**4/24 + x**5/120 + O(x**6)
fsub = f1 - 1
assert fsub.function == sin(x) - 1
assert fsub.truncate() == -1 + x - x**3/6 + x**5/120 + O(x**6)
fsub = 1 - f2
assert fsub.function == -cos(x) + 1
assert fsub.truncate() == x**2/2 - x**4/24 + O(x**6)
raises(ValueError, lambda: f1 + fps(exp(x), dir=-1))
raises(ValueError, lambda: f1 + fps(exp(x), x0=1))
fm = f1 * 3
assert fm.function == 3*sin(x)
assert fm.truncate() == 3*x - x**3/2 + x**5/40 + O(x**6)
fm = 3 * f2
assert fm.function == 3*cos(x)
assert fm.truncate() == 3 - 3*x**2/2 + x**4/8 + O(x**6)
assert (f1 * f2) == Mul(f1, f2)
assert (f1 * x) == Mul(f1, x)
fd = f1.diff()
assert fd.function == cos(x)
assert fd.truncate() == 1 - x**2/2 + x**4/24 + O(x**6)
fd = f2.diff()
assert fd.function == -sin(x)
assert fd.truncate() == -x + x**3/6 - x**5/120 + O(x**6)
fd = f2.diff().diff()
assert fd.function == -cos(x)
assert fd.truncate() == -1 + x**2/2 - x**4/24 + O(x**6)
f3 = fps(exp(sqrt(x)))
fd = f3.diff()
assert fd.truncate().expand() == \
(1/(2*sqrt(x)) + S(1)/2 + x/12 + x**2/240 + x**3/10080 + x**4/725760 +
x**5/79833600 + sqrt(x)/4 + x**(S(3)/2)/48 + x**(S(5)/2)/1440 +
x**(S(7)/2)/80640 + x**(S(9)/2)/7257600 + x**(S(11)/2)/958003200 +
O(x**6))
assert f1.integrate((x, 0, 1)) == -cos(1) + 1
fi = f1.integrate(x)
assert fi.function == -cos(x)
assert fi.truncate() == -1 + x**2/2 - x**4/24 + O(x**6)
fi = f2.integrate()
assert fi.function == sin(x)
assert fi.truncate() == x - x**3/6 + x**5/120 + O(x**6)
| 17,232 | 33.743952 | 80 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/series/tests/test_residues.py
|
from sympy import residue, Symbol, Function, sin, S, I, exp, log, pi, factorial
from sympy.utilities.pytest import XFAIL, raises
from sympy.abc import x, z, a, s
def test_basic1():
assert residue(1/x, x, 0) == 1
assert residue(-2/x, x, 0) == -2
assert residue(81/x, x, 0) == 81
assert residue(1/x**2, x, 0) == 0
assert residue(0, x, 0) == 0
assert residue(5, x, 0) == 0
assert residue(x, x, 0) == 0
assert residue(x**2, x, 0) == 0
def test_basic2():
assert residue(1/x, x, 1) == 0
assert residue(-2/x, x, 1) == 0
assert residue(81/x, x, -1) == 0
assert residue(1/x**2, x, 1) == 0
assert residue(0, x, 1) == 0
assert residue(5, x, 1) == 0
assert residue(x, x, 1) == 0
assert residue(x**2, x, 5) == 0
def test_f():
f = Function("f")
assert residue(f(x)/x**5, x, 0) == f(x).diff(x, 4).subs(x, 0)/24
def test_functions():
assert residue(1/sin(x), x, 0) == 1
assert residue(2/sin(x), x, 0) == 2
assert residue(1/sin(x)**2, x, 0) == 0
assert residue(1/sin(x)**5, x, 0) == S(3)/8
def test_expressions():
assert residue(1/(x + 1), x, 0) == 0
assert residue(1/(x + 1), x, -1) == 1
assert residue(1/(x**2 + 1), x, -1) == 0
assert residue(1/(x**2 + 1), x, I) == -I/2
assert residue(1/(x**2 + 1), x, -I) == I/2
assert residue(1/(x**4 + 1), x, 0) == 0
@XFAIL
def test_expressions_failing():
assert residue(1/(x**4 + 1), x, exp(I*pi/4)) == -(S(1)/4 + I/4)/sqrt(2)
n = Symbol('n', integer=True, positive=True)
assert residue(exp(z)/(z - pi*I/4*a)**n, z, I*pi*a) == \
exp(I*pi*a/4)/factorial(n - 1)
assert residue(1/(x**2 + a**2)**2, x, a*I) == -I/4/a**3
def test_NotImplemented():
raises(NotImplementedError, lambda: residue(exp(1/z), z, 0))
def test_bug():
assert residue(2**(z)*(s + z)*(1 - s - z)/z**2, z, 0) == \
1 + s*log(2) - s**2*log(2) - 2*s
def test_issue_5654():
assert residue(1/(x**2 + a**2)**2, x, a*I) == -I/(4*a**3)
def test_issue_6499():
assert residue(1/(exp(z) - 1), z, 0) == 1
| 2,062 | 26.878378 | 79 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/series/tests/test_gruntz.py
|
from sympy import Symbol, exp, log, oo, Rational, I, sin, gamma, loggamma, S, \
atan, acot, pi, cancel, E, erf, sqrt, zeta, cos, digamma, Integer, Ei, EulerGamma
from sympy.functions.elementary.hyperbolic import cosh, coth, sinh, tanh
from sympy.series.gruntz import compare, mrv, rewrite, mrv_leadterm, gruntz, \
sign
from sympy.utilities.pytest import XFAIL, skip, slow
"""
This test suite is testing the limit algorithm using the bottom up approach.
See the documentation in limits2.py. The algorithm itself is highly recursive
by nature, so "compare" is logically the lowest part of the algorithm, yet in
some sense it's the most complex part, because it needs to calculate a limit
to return the result.
Nevertheless, the rest of the algorithm depends on compare working correctly.
"""
x = Symbol('x', real=True)
m = Symbol('m', real=True)
runslow = False
def _sskip():
if not runslow:
skip("slow")
@slow
def test_gruntz_evaluation():
# Gruntz' thesis pp. 122 to 123
# 8.1
assert gruntz(exp(x)*(exp(1/x - exp(-x)) - exp(1/x)), x, oo) == -1
# 8.2
assert gruntz(exp(x)*(exp(1/x + exp(-x) + exp(-x**2))
- exp(1/x - exp(-exp(x)))), x, oo) == 1
# 8.3
assert gruntz(exp(exp(x - exp(-x))/(1 - 1/x)) - exp(exp(x)), x, oo) == oo
# 8.5
assert gruntz(exp(exp(exp(x + exp(-x)))) / exp(exp(exp(x))), x, oo) == oo
# 8.6
assert gruntz(exp(exp(exp(x))) / exp(exp(exp(x - exp(-exp(x))))),
x, oo) == oo
# 8.7
assert gruntz(exp(exp(exp(x))) / exp(exp(exp(x - exp(-exp(exp(x)))))),
x, oo) == 1
# 8.8
assert gruntz(exp(exp(x)) / exp(exp(x - exp(-exp(exp(x))))), x, oo) == 1
# 8.9
assert gruntz(log(x)**2 * exp(sqrt(log(x))*(log(log(x)))**2
* exp(sqrt(log(log(x))) * (log(log(log(x))))**3)) / sqrt(x),
x, oo) == 0
# 8.10
assert gruntz((x*log(x)*(log(x*exp(x) - x**2))**2)
/ (log(log(x**2 + 2*exp(exp(3*x**3*log(x)))))), x, oo) == S(1)/3
# 8.11
assert gruntz((exp(x*exp(-x)/(exp(-x) + exp(-2*x**2/(x + 1)))) - exp(x))/x,
x, oo) == -exp(2)
# 8.12
assert gruntz((3**x + 5**x)**(1/x), x, oo) == 5
# 8.13
assert gruntz(x/log(x**(log(x**(log(2)/log(x))))), x, oo) == oo
# 8.14
assert gruntz(exp(exp(2*log(x**5 + x)*log(log(x))))
/ exp(exp(10*log(x)*log(log(x)))), x, oo) == oo
# 8.15
assert gruntz(exp(exp(S(5)/2*x**(-S(5)/7) + S(21)/8*x**(S(6)/11)
+ 2*x**(-8) + S(54)/17*x**(S(49)/45) ))**8
/ log(log(-log(S(4)/3*x**(-S(5)/14))))**(S(7)/6), x, oo) == oo
# 8.16
assert gruntz((exp(4*x*exp(-x)/(1/exp(x) + 1/exp(2*x**2/(x + 1)))) - exp(x))
/ exp(x)**4, x, oo) == 1
# 8.17
assert gruntz(exp(x*exp(-x)/(exp(-x) + exp(-2*x**2/(x + 1))))/exp(x), x, oo) \
== 1
# 8.19
assert gruntz(log(x)*(log(log(x) + log(log(x))) - log(log(x)))
/ (log(log(x) + log(log(log(x))))), x, oo) == 1
# 8.20
assert gruntz(exp((log(log(x + exp(log(x)*log(log(x))))))
/ (log(log(log(exp(x) + x + log(x)))))), x, oo) == E
# Another
assert gruntz(exp(exp(exp(x + exp(-x)))) / exp(exp(x)), x, oo) == oo
def test_gruntz_evaluation_slow():
_sskip()
# 8.4
assert gruntz(exp(exp(exp(x)/(1 - 1/x)))
- exp(exp(exp(x)/(1 - 1/x - log(x)**(-log(x))))), x, oo) == -oo
# 8.18
assert gruntz((exp(exp(-x/(1 + exp(-x))))*exp(-x/(1 + exp(-x/(1 + exp(-x)))))
*exp(exp(-x + exp(-x/(1 + exp(-x))))))
/ (exp(-x/(1 + exp(-x))))**2 - exp(x) + x, x, oo) == 2
@slow
def test_gruntz_eval_special():
# Gruntz, p. 126
assert gruntz(exp(x)*(sin(1/x + exp(-x)) - sin(1/x + exp(-x**2))), x, oo) == 1
assert gruntz((erf(x - exp(-exp(x))) - erf(x)) * exp(exp(x)) * exp(x**2),
x, oo) == -2/sqrt(pi)
assert gruntz(exp(exp(x)) * (exp(sin(1/x + exp(-exp(x)))) - exp(sin(1/x))),
x, oo) == 1
assert gruntz(exp(x)*(gamma(x + exp(-x)) - gamma(x)), x, oo) == oo
assert gruntz(exp(exp(digamma(digamma(x))))/x, x, oo) == exp(-S(1)/2)
assert gruntz(exp(exp(digamma(log(x))))/x, x, oo) == exp(-S(1)/2)
assert gruntz(digamma(digamma(digamma(x))), x, oo) == oo
assert gruntz(loggamma(loggamma(x)), x, oo) == oo
assert gruntz(((gamma(x + 1/gamma(x)) - gamma(x))/log(x) - cos(1/x))
* x*log(x), x, oo) == -S(1)/2
assert gruntz(x * (gamma(x - 1/gamma(x)) - gamma(x) + log(x)), x, oo) \
== S(1)/2
assert gruntz((gamma(x + 1/gamma(x)) - gamma(x)) / log(x), x, oo) == 1
def test_gruntz_eval_special_slow():
_sskip()
assert gruntz(gamma(x + 1)/sqrt(2*pi)
- exp(-x)*(x**(x + S(1)/2) + x**(x - S(1)/2)/12), x, oo) == oo
assert gruntz(exp(exp(exp(digamma(digamma(digamma(x))))))/x, x, oo) == 0
@XFAIL
def test_grunts_eval_special_slow_sometimes_fail():
_sskip()
# XXX This sometimes fails!!!
assert gruntz(exp(gamma(x - exp(-x))*exp(1/x)) - exp(gamma(x)), x, oo) == oo
@XFAIL
def test_gruntz_eval_special_fail():
# TODO exponential integral Ei
assert gruntz(
(Ei(x - exp(-exp(x))) - Ei(x)) *exp(-x)*exp(exp(x))*x, x, oo) == -1
# TODO zeta function series
assert gruntz(
exp((log(2) + 1)*x) * (zeta(x + exp(-x)) - zeta(x)), x, oo) == -log(2)
# TODO 8.35 - 8.37 (bessel, max-min)
def test_gruntz_hyperbolic():
assert gruntz(cosh(x), x, oo) == oo
assert gruntz(cosh(x), x, -oo) == oo
assert gruntz(sinh(x), x, oo) == oo
assert gruntz(sinh(x), x, -oo) == -oo
assert gruntz(2*cosh(x)*exp(x), x, oo) == oo
assert gruntz(2*cosh(x)*exp(x), x, -oo) == 1
assert gruntz(2*sinh(x)*exp(x), x, oo) == oo
assert gruntz(2*sinh(x)*exp(x), x, -oo) == -1
assert gruntz(tanh(x), x, oo) == 1
assert gruntz(tanh(x), x, -oo) == -1
assert gruntz(coth(x), x, oo) == 1
assert gruntz(coth(x), x, -oo) == -1
def test_compare1():
assert compare(2, x, x) == "<"
assert compare(x, exp(x), x) == "<"
assert compare(exp(x), exp(x**2), x) == "<"
assert compare(exp(x**2), exp(exp(x)), x) == "<"
assert compare(1, exp(exp(x)), x) == "<"
assert compare(x, 2, x) == ">"
assert compare(exp(x), x, x) == ">"
assert compare(exp(x**2), exp(x), x) == ">"
assert compare(exp(exp(x)), exp(x**2), x) == ">"
assert compare(exp(exp(x)), 1, x) == ">"
assert compare(2, 3, x) == "="
assert compare(3, -5, x) == "="
assert compare(2, -5, x) == "="
assert compare(x, x**2, x) == "="
assert compare(x**2, x**3, x) == "="
assert compare(x**3, 1/x, x) == "="
assert compare(1/x, x**m, x) == "="
assert compare(x**m, -x, x) == "="
assert compare(exp(x), exp(-x), x) == "="
assert compare(exp(-x), exp(2*x), x) == "="
assert compare(exp(2*x), exp(x)**2, x) == "="
assert compare(exp(x)**2, exp(x + exp(-x)), x) == "="
assert compare(exp(x), exp(x + exp(-x)), x) == "="
assert compare(exp(x**2), 1/exp(x**2), x) == "="
def test_compare2():
assert compare(exp(x), x**5, x) == ">"
assert compare(exp(x**2), exp(x)**2, x) == ">"
assert compare(exp(x), exp(x + exp(-x)), x) == "="
assert compare(exp(x + exp(-x)), exp(x), x) == "="
assert compare(exp(x + exp(-x)), exp(-x), x) == "="
assert compare(exp(-x), x, x) == ">"
assert compare(x, exp(-x), x) == "<"
assert compare(exp(x + 1/x), x, x) == ">"
assert compare(exp(-exp(x)), exp(x), x) == ">"
assert compare(exp(exp(-exp(x)) + x), exp(-exp(x)), x) == "<"
def test_compare3():
assert compare(exp(exp(x)), exp(x + exp(-exp(x))), x) == ">"
def test_sign1():
assert sign(Rational(0), x) == 0
assert sign(Rational(3), x) == 1
assert sign(Rational(-5), x) == -1
assert sign(log(x), x) == 1
assert sign(exp(-x), x) == 1
assert sign(exp(x), x) == 1
assert sign(-exp(x), x) == -1
assert sign(3 - 1/x, x) == 1
assert sign(-3 - 1/x, x) == -1
assert sign(sin(1/x), x) == 1
assert sign((x**Integer(2)), x) == 1
def test_sign2():
assert sign(x, x) == 1
assert sign(-x, x) == -1
y = Symbol("y", positive=True)
assert sign(y, x) == 1
assert sign(-y, x) == -1
assert sign(y*x, x) == 1
assert sign(-y*x, x) == -1
def mmrv(a, b):
return set(mrv(a, b)[0].keys())
def test_mrv1():
assert mmrv(x, x) == {x}
assert mmrv(x + 1/x, x) == {x}
assert mmrv(x**2, x) == {x}
assert mmrv(log(x), x) == {x}
assert mmrv(exp(x), x) == {exp(x)}
assert mmrv(exp(-x), x) == {exp(-x)}
assert mmrv(exp(x**2), x) == {exp(x**2)}
assert mmrv(-exp(1/x), x) == {x}
assert mmrv(exp(x + 1/x), x) == {exp(x + 1/x)}
def test_mrv2a():
assert mmrv(exp(x + exp(-exp(x))), x) == {exp(-exp(x))}
assert mmrv(exp(x + exp(-x)), x) == {exp(x + exp(-x)), exp(-x)}
assert mmrv(exp(1/x + exp(-x)), x) == {exp(-x)}
#sometimes infinite recursion due to log(exp(x**2)) not simplifying
def test_mrv2b():
assert mmrv(exp(x + exp(-x**2)), x) == {exp(-x**2)}
#sometimes infinite recursion due to log(exp(x**2)) not simplifying
def test_mrv2c():
assert mmrv(
exp(-x + 1/x**2) - exp(x + 1/x), x) == {exp(x + 1/x), exp(1/x**2 - x)}
#sometimes infinite recursion due to log(exp(x**2)) not simplifying
def test_mrv3():
assert mmrv(exp(x**2) + x*exp(x) + log(x)**x/x, x) == {exp(x**2)}
assert mmrv(
exp(x)*(exp(1/x + exp(-x)) - exp(1/x)), x) == {exp(x), exp(-x)}
assert mmrv(log(
x**2 + 2*exp(exp(3*x**3*log(x)))), x) == {exp(exp(3*x**3*log(x)))}
assert mmrv(log(x - log(x))/log(x), x) == {x}
assert mmrv(
(exp(1/x - exp(-x)) - exp(1/x))*exp(x), x) == {exp(x), exp(-x)}
assert mmrv(
1/exp(-x + exp(-x)) - exp(x), x) == {exp(x), exp(-x), exp(x - exp(-x))}
assert mmrv(log(log(x*exp(x*exp(x)) + 1)), x) == {exp(x*exp(x))}
assert mmrv(exp(exp(log(log(x) + 1/x))), x) == {x}
def test_mrv4():
ln = log
assert mmrv((ln(ln(x) + ln(ln(x))) - ln(ln(x)))/ln(ln(x) + ln(ln(ln(x))))*ln(x),
x) == {x}
assert mmrv(log(log(x*exp(x*exp(x)) + 1)) - exp(exp(log(log(x) + 1/x))), x) == \
{exp(x*exp(x))}
def mrewrite(a, b, c):
return rewrite(a[1], a[0], b, c)
def test_rewrite1():
e = exp(x)
assert mrewrite(mrv(e, x), x, m) == (1/m, -x)
e = exp(x**2)
assert mrewrite(mrv(e, x), x, m) == (1/m, -x**2)
e = exp(x + 1/x)
assert mrewrite(mrv(e, x), x, m) == (1/m, -x - 1/x)
e = 1/exp(-x + exp(-x)) - exp(x)
assert mrewrite(mrv(e, x), x, m) == (1/(m*exp(m)) - 1/m, -x)
def test_rewrite2():
e = exp(x)*log(log(exp(x)))
assert mmrv(e, x) == {exp(x)}
assert mrewrite(mrv(e, x), x, m) == (1/m*log(x), -x)
#sometimes infinite recursion due to log(exp(x**2)) not simplifying
def test_rewrite3():
e = exp(-x + 1/x**2) - exp(x + 1/x)
#both of these are correct and should be equivalent:
assert mrewrite(mrv(e, x), x, m) in [(-1/m + m*exp(
1/x + 1/x**2), -x - 1/x), (m - 1/m*exp(1/x + x**(-2)), x**(-2) - x)]
def test_mrv_leadterm1():
assert mrv_leadterm(-exp(1/x), x) == (-1, 0)
assert mrv_leadterm(1/exp(-x + exp(-x)) - exp(x), x) == (-1, 0)
assert mrv_leadterm(
(exp(1/x - exp(-x)) - exp(1/x))*exp(x), x) == (-exp(1/x), 0)
def test_mrv_leadterm2():
#Gruntz: p51, 3.25
assert mrv_leadterm((log(exp(x) + x) - x)/log(exp(x) + log(x))*exp(x), x) == \
(1, 0)
def test_mrv_leadterm3():
#Gruntz: p56, 3.27
assert mmrv(exp(-x + exp(-x)*exp(-x*log(x))), x) == {exp(-x - x*log(x))}
assert mrv_leadterm(exp(-x + exp(-x)*exp(-x*log(x))), x) == (exp(-x), 0)
def test_limit1():
assert gruntz(x, x, oo) == oo
assert gruntz(x, x, -oo) == -oo
assert gruntz(-x, x, oo) == -oo
assert gruntz(x**2, x, -oo) == oo
assert gruntz(-x**2, x, oo) == -oo
assert gruntz(x*log(x), x, 0, dir="+") == 0
assert gruntz(1/x, x, oo) == 0
assert gruntz(exp(x), x, oo) == oo
assert gruntz(-exp(x), x, oo) == -oo
assert gruntz(exp(x)/x, x, oo) == oo
assert gruntz(1/x - exp(-x), x, oo) == 0
assert gruntz(x + 1/x, x, oo) == oo
def test_limit2():
assert gruntz(x**x, x, 0, dir="+") == 1
assert gruntz((exp(x) - 1)/x, x, 0) == 1
assert gruntz(1 + 1/x, x, oo) == 1
assert gruntz(-exp(1/x), x, oo) == -1
assert gruntz(x + exp(-x), x, oo) == oo
assert gruntz(x + exp(-x**2), x, oo) == oo
assert gruntz(x + exp(-exp(x)), x, oo) == oo
assert gruntz(13 + 1/x - exp(-x), x, oo) == 13
def test_limit3():
a = Symbol('a')
assert gruntz(x - log(1 + exp(x)), x, oo) == 0
assert gruntz(x - log(a + exp(x)), x, oo) == 0
assert gruntz(exp(x)/(1 + exp(x)), x, oo) == 1
assert gruntz(exp(x)/(a + exp(x)), x, oo) == 1
def test_limit4():
#issue 3463
assert gruntz((3**x + 5**x)**(1/x), x, oo) == 5
#issue 3463
assert gruntz((3**(1/x) + 5**(1/x))**x, x, 0) == 5
@XFAIL
def test_MrvTestCase_page47_ex3_21():
h = exp(-x/(1 + exp(-x)))
expr = exp(h)*exp(-x/(1 + h))*exp(exp(-x + h))/h**2 - exp(x) + x
expected = {1/h, exp(x), exp(x - h), exp(x/(1 + h))}
# XXX Incorrect result
assert mrv(expr, x).difference(expected) == set()
def test_I():
from sympy.functions import sign as sgn
y = Symbol("y")
assert gruntz(I*x, x, oo) == I*oo
assert gruntz(y*I*x, x, oo) == y*I*oo
assert gruntz(y*3*I*x, x, oo) == y*I*oo
assert gruntz(y*3*sin(I)*x, x, oo).simplify() == sgn(y)*I*oo
def test_issue_4814():
assert gruntz((x + 1)**(1/log(x + 1)), x, oo) == E
def test_intractable():
assert gruntz(1/gamma(x), x, oo) == 0
assert gruntz(1/loggamma(x), x, oo) == 0
assert gruntz(gamma(x)/loggamma(x), x, oo) == oo
assert gruntz(exp(gamma(x))/gamma(x), x, oo) == oo
assert gruntz(gamma(x), x, 3) == 2
assert gruntz(gamma(S(1)/7 + 1/x), x, oo) == gamma(S(1)/7)
assert gruntz(log(x**x)/log(gamma(x)), x, oo) == 1
assert gruntz(log(gamma(gamma(x)))/exp(x), x, oo) == oo
def test_aseries_trig():
assert cancel(gruntz(1/log(atan(x)), x, oo)
- 1/(log(pi) + log(S(1)/2))) == 0
assert gruntz(1/acot(x), x, -oo) == -oo
def test_exp_log_series():
assert gruntz(x/log(log(x*exp(x))), x, oo) == oo
def test_issue_3644():
assert gruntz(((x**7 + x + 1)/(2**x + x**2))**(-1/x), x, oo) == 2
def test_issue_6843():
n = Symbol('n', integer=True, positive=True)
r = (n + 1)*x**(n + 1)/(x**(n + 1) - 1) - x/(x - 1)
assert gruntz(r, x, 1).simplify() == n/2
def test_issue_4190():
assert gruntz(x - gamma(1/x), x, oo) == S.EulerGamma
@XFAIL
def test_issue_5172():
n = Symbol('n')
r = Symbol('r', positive=True)
c = Symbol('c')
p = Symbol('p', positive=True)
m = Symbol('m', negative=True)
expr = ((2*n*(n - r + 1)/(n + r*(n - r + 1)))**c + \
(r - 1)*(n*(n - r + 2)/(n + r*(n - r + 1)))**c - n)/(n**c - n)
expr = expr.subs(c, c + 1)
assert gruntz(expr.subs(c, m), n, oo) == 1
# fail:
assert gruntz(expr.subs(c, p), n, oo).simplify() == \
(2**(p + 1) + r - 1)/(r + 1)**(p + 1)
def test_issue_4109():
assert gruntz(1/gamma(x), x, 0) == 0
assert gruntz(x*gamma(x), x, 0) == 1
def test_issue_6682():
assert gruntz(exp(2*Ei(-x))/x**2, x, 0) == exp(2*EulerGamma)
def test_issue_7096():
from sympy.functions import sign
assert gruntz(x**-pi, x, 0, dir='-') == oo*sign((-1)**(-pi))
| 15,491 | 32.102564 | 85 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/series/tests/test_demidovich.py
|
from sympy import limit, Symbol, oo, sqrt, Rational, log, exp, cos, sin, tan, \
pi, asin, together, root
# Numbers listed with the tests refer to problem numbers in the book
# "Anti-demidovich, problemas resueltos, Ed. URSS"
x = Symbol("x")
def test_leadterm():
assert (3 + 2*x**(log(3)/log(2) - 1)).leadterm(x) == (3, 0)
def root3(x):
return root(x, 3)
def root4(x):
return root(x, 4)
def test_Limits_simple_0():
assert limit((2**(x + 1) + 3**(x + 1))/(2**x + 3**x), x, oo) == 3 # 175
def test_Limits_simple_1():
assert limit((x + 1)*(x + 2)*(x + 3)/x**3, x, oo) == 1 # 172
assert limit(sqrt(x + 1) - sqrt(x), x, oo) == 0 # 179
assert limit((2*x - 3)*(3*x + 5)*(4*x - 6)/(3*x**3 + x - 1), x, oo) == 8 # Primjer 1
assert limit(x/root3(x**3 + 10), x, oo) == 1 # Primjer 2
assert limit((x + 1)**2/(x**2 + 1), x, oo) == 1 # 181
def test_Limits_simple_2():
assert limit(1000*x/(x**2 - 1), x, oo) == 0 # 182
assert limit((x**2 - 5*x + 1)/(3*x + 7), x, oo) == oo # 183
assert limit((2*x**2 - x + 3)/(x**3 - 8*x + 5), x, oo) == 0 # 184
assert limit((2*x**2 - 3*x - 4)/sqrt(x**4 + 1), x, oo) == 2 # 186
assert limit((2*x + 3)/(x + root3(x)), x, oo) == 2 # 187
assert limit(x**2/(10 + x*sqrt(x)), x, oo) == oo # 188
assert limit(root3(x**2 + 1)/(x + 1), x, oo) == 0 # 189
assert limit(sqrt(x)/sqrt(x + sqrt(x + sqrt(x))), x, oo) == 1 # 190
def test_Limits_simple_3a():
a = Symbol('a')
#issue 3513
assert together(limit((x**2 - (a + 1)*x + a)/(x**3 - a**3), x, a)) == \
(a - 1)/(3*a**2) # 196
def test_Limits_simple_3b():
h = Symbol("h")
assert limit(((x + h)**3 - x**3)/h, h, 0) == 3*x**2 # 197
assert limit((1/(1 - x) - 3/(1 - x**3)), x, 1) == -1 # 198
assert limit((sqrt(1 + x) - 1)/(root3(1 + x) - 1), x, 0) == Rational(3)/2 # Primer 4
assert limit((sqrt(x) - 1)/(x - 1), x, 1) == Rational(1)/2 # 199
assert limit((sqrt(x) - 8)/(root3(x) - 4), x, 64) == 3 # 200
assert limit((root3(x) - 1)/(root4(x) - 1), x, 1) == Rational(4)/3 # 201
assert limit(
(root3(x**2) - 2*root3(x) + 1)/(x - 1)**2, x, 1) == Rational(1)/9 # 202
def test_Limits_simple_4a():
a = Symbol('a')
assert limit((sqrt(x) - sqrt(a))/(x - a), x, a) == 1/(2*sqrt(a)) # Primer 5
assert limit((sqrt(x) - 1)/(root3(x) - 1), x, 1) == Rational(3)/2 # 205
assert limit((sqrt(1 + x) - sqrt(1 - x))/x, x, 0) == 1 # 207
assert limit(sqrt(x**2 - 5*x + 6) - x, x, oo) == -Rational(5)/2 # 213
def test_limits_simple_4aa():
assert limit(x*(sqrt(x**2 + 1) - x), x, oo) == Rational(1)/2 # 214
def test_Limits_simple_4b():
#issue 3511
assert limit(x - root3(x**3 - 1), x, oo) == 0 # 215
def test_Limits_simple_4c():
assert limit(log(1 + exp(x))/x, x, -oo) == 0 # 267a
assert limit(log(1 + exp(x))/x, x, oo) == 1 # 267b
def test_bounded():
assert limit(sin(x)/x, x, oo) == 0 # 216b
assert limit(x*sin(1/x), x, 0) == 0 # 227a
def test_f1a():
h = Symbol("h")
#issue 3508:
assert limit((sin(2*x)/x)**(1 + x), x, 0) == 2 # Primer 7
def test_f1a2():
#issue 3509:
assert limit(((x - 1)/(x + 1))**x, x, oo) == exp(-2) # Primer 9
def test_f1b():
m = Symbol("m")
n = Symbol("n")
h = Symbol("h")
a = Symbol("a")
assert limit(sin(x)/x, x, 2) == sin(2)/2 # 216a
assert limit(sin(3*x)/x, x, 0) == 3 # 217
assert limit(sin(5*x)/sin(2*x), x, 0) == Rational(5)/2 # 218
assert limit(sin(pi*x)/sin(3*pi*x), x, 0) == Rational(1)/3 # 219
assert limit(x*sin(pi/x), x, oo) == pi # 220
assert limit((1 - cos(x))/x**2, x, 0) == Rational(1, 2) # 221
assert limit(x*sin(1/x), x, oo) == 1 # 227b
assert limit((cos(m*x) - cos(n*x))/x**2, x, 0) == ((n**2 - m**2)/2) # 232
assert limit((tan(x) - sin(x))/x**3, x, 0) == Rational(1, 2) # 233
assert limit((x - sin(2*x))/(x + sin(3*x)), x, 0) == -Rational(1, 4) # 237
assert limit((1 - sqrt(cos(x)))/x**2, x, 0) == Rational(1, 4) # 239
assert limit((sqrt(1 + sin(x)) - sqrt(1 - sin(x)))/x, x, 0) == 1 # 240
assert limit((1 + h/x)**x, x, oo) == exp(h) # Primer 9
assert limit((sin(x) - sin(a))/(x - a), x, a) == cos(a) # 222, *176
assert limit((cos(x) - cos(a))/(x - a), x, a) == -sin(a) # 223
assert limit((sin(x + h) - sin(x))/h, h, 0) == cos(x) # 225
def test_f2a():
assert limit(((x + 1)/(2*x + 1))**(x**2), x, oo) == 0 # Primer 8
def test_f2():
assert limit((sqrt(
cos(x)) - root3(cos(x)))/(sin(x)**2), x, 0) == -Rational(1, 12) # *184
def test_f3():
a = Symbol('a')
#issue 3504
assert limit(asin(a*x)/x, x, 0) == a
| 4,679 | 32.669065 | 89 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/parsing/mathematica.py
|
from __future__ import print_function, division
from re import match
from sympy import sympify
def mathematica(s):
return sympify(parse(s))
def parse(s):
s = s.strip()
# Begin rules
rules = (
# Arithmetic operation between a constant and a function
(r"\A(\d+)([*/+-^])(\w+\[[^\]]+[^\[]*\])\Z",
lambda m: m.group(
1) + translateFunction(m.group(2)) + parse(m.group(3))),
# Arithmetic operation between two functions
(r"\A(\w+\[[^\]]+[^\[]*\])([*/+-^])(\w+\[[^\]]+[^\[]*\])\Z",
lambda m: parse(m.group(1)) + translateFunction(
m.group(2)) + parse(m.group(3))),
(r"\A(\w+)\[([^\]]+[^\[]*)\]\Z", # Function call
lambda m: translateFunction(
m.group(1)) + "(" + parse(m.group(2)) + ")"),
(r"\((.+)\)\((.+)\)", # Parenthesized implied multiplication
lambda m: "(" + parse(m.group(1)) + ")*(" + parse(m.group(2)) + ")"),
(r"\A\((.+)\)\Z", # Parenthesized expression
lambda m: "(" + parse(m.group(1)) + ")"),
(r"\A(.*[\w\.])\((.+)\)\Z", # Implied multiplication - a(b)
lambda m: parse(m.group(1)) + "*(" + parse(m.group(2)) + ")"),
(r"\A\((.+)\)([\w\.].*)\Z", # Implied multiplication - (a)b
lambda m: "(" + parse(m.group(1)) + ")*" + parse(m.group(2))),
(r"\A(-? *[\d\.]+)([a-zA-Z].*)\Z", # Implied multiplication - 2a
lambda m: parse(m.group(1)) + "*" + parse(m.group(2))),
(r"\A([^=]+)([\^\-\*/\+=]=?)(.+)\Z", # Infix operator
lambda m: parse(m.group(1)) + translateOperator(m.group(2)) + parse(m.group(3))))
# End rules
for rule, action in rules:
m = match(rule, s)
if m:
return action(m)
return s
def translateFunction(s):
if s.startswith("Arc"):
return "a" + s[3:]
return s.lower()
def translateOperator(s):
dictionary = {'^': '**'}
if s in dictionary:
return dictionary[s]
return s
| 1,996 | 28.367647 | 89 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/parsing/sympy_parser.py
|
"""Transform a string with Python-like source code into SymPy expression. """
from __future__ import print_function, division
from .sympy_tokenize import \
generate_tokens, untokenize, TokenError, \
NUMBER, STRING, NAME, OP, ENDMARKER
from keyword import iskeyword
import ast
import re
import unicodedata
import sympy
from sympy.core.compatibility import exec_, StringIO
from sympy.core.basic import Basic
_re_repeated = re.compile(r"^(\d*)\.(\d*)\[(\d+)\]$")
def _token_splittable(token):
"""
Predicate for whether a token name can be split into multiple tokens.
A token is splittable if it does not contain an underscore character and
it is not the name of a Greek letter. This is used to implicitly convert
expressions like 'xyz' into 'x*y*z'.
"""
if '_' in token:
return False
else:
try:
return not unicodedata.lookup('GREEK SMALL LETTER ' + token)
except KeyError:
pass
if len(token) > 1:
return True
return False
def _token_callable(token, local_dict, global_dict, nextToken=None):
"""
Predicate for whether a token name represents a callable function.
Essentially wraps ``callable``, but looks up the token name in the
locals and globals.
"""
func = local_dict.get(token[1])
if not func:
func = global_dict.get(token[1])
return callable(func) and not isinstance(func, sympy.Symbol)
def _add_factorial_tokens(name, result):
if result == [] or result[-1][1] == '(':
raise TokenError()
beginning = [(NAME, name), (OP, '(')]
end = [(OP, ')')]
diff = 0
length = len(result)
for index, token in enumerate(result[::-1]):
toknum, tokval = token
i = length - index - 1
if tokval == ')':
diff += 1
elif tokval == '(':
diff -= 1
if diff == 0:
if i - 1 >= 0 and result[i - 1][0] == NAME:
return result[:i - 1] + beginning + result[i - 1:] + end
else:
return result[:i] + beginning + result[i:] + end
return result
class AppliedFunction(object):
"""
A group of tokens representing a function and its arguments.
`exponent` is for handling the shorthand sin^2, ln^2, etc.
"""
def __init__(self, function, args, exponent=None):
if exponent is None:
exponent = []
self.function = function
self.args = args
self.exponent = exponent
self.items = ['function', 'args', 'exponent']
def expand(self):
"""Return a list of tokens representing the function"""
result = []
result.append(self.function)
result.extend(self.args)
return result
def __getitem__(self, index):
return getattr(self, self.items[index])
def __repr__(self):
return "AppliedFunction(%s, %s, %s)" % (self.function, self.args,
self.exponent)
class ParenthesisGroup(list):
"""List of tokens representing an expression in parentheses."""
pass
def _flatten(result):
result2 = []
for tok in result:
if isinstance(tok, AppliedFunction):
result2.extend(tok.expand())
else:
result2.append(tok)
return result2
def _group_parentheses(recursor):
def _inner(tokens, local_dict, global_dict):
"""Group tokens between parentheses with ParenthesisGroup.
Also processes those tokens recursively.
"""
result = []
stacks = []
stacklevel = 0
for token in tokens:
if token[0] == OP:
if token[1] == '(':
stacks.append(ParenthesisGroup([]))
stacklevel += 1
elif token[1] == ')':
stacks[-1].append(token)
stack = stacks.pop()
if len(stacks) > 0:
# We don't recurse here since the upper-level stack
# would reprocess these tokens
stacks[-1].extend(stack)
else:
# Recurse here to handle nested parentheses
# Strip off the outer parentheses to avoid an infinite loop
inner = stack[1:-1]
inner = recursor(inner,
local_dict,
global_dict)
parenGroup = [stack[0]] + inner + [stack[-1]]
result.append(ParenthesisGroup(parenGroup))
stacklevel -= 1
continue
if stacklevel:
stacks[-1].append(token)
else:
result.append(token)
if stacklevel:
raise TokenError("Mismatched parentheses")
return result
return _inner
def _apply_functions(tokens, local_dict, global_dict):
"""Convert a NAME token + ParenthesisGroup into an AppliedFunction.
Note that ParenthesisGroups, if not applied to any function, are
converted back into lists of tokens.
"""
result = []
symbol = None
for tok in tokens:
if tok[0] == NAME:
symbol = tok
result.append(tok)
elif isinstance(tok, ParenthesisGroup):
if symbol and _token_callable(symbol, local_dict, global_dict):
result[-1] = AppliedFunction(symbol, tok)
symbol = None
else:
result.extend(tok)
else:
symbol = None
result.append(tok)
return result
def _implicit_multiplication(tokens, local_dict, global_dict):
"""Implicitly adds '*' tokens.
Cases:
- Two AppliedFunctions next to each other ("sin(x)cos(x)")
- AppliedFunction next to an open parenthesis ("sin x (cos x + 1)")
- A close parenthesis next to an AppliedFunction ("(x+2)sin x")\
- A close parenthesis next to an open parenthesis ("(x+2)(x+3)")
- AppliedFunction next to an implicitly applied function ("sin(x)cos x")
"""
result = []
for tok, nextTok in zip(tokens, tokens[1:]):
result.append(tok)
if (isinstance(tok, AppliedFunction) and
isinstance(nextTok, AppliedFunction)):
result.append((OP, '*'))
elif (isinstance(tok, AppliedFunction) and
nextTok[0] == OP and nextTok[1] == '('):
# Applied function followed by an open parenthesis
result.append((OP, '*'))
elif (tok[0] == OP and tok[1] == ')' and
isinstance(nextTok, AppliedFunction)):
# Close parenthesis followed by an applied function
result.append((OP, '*'))
elif (tok[0] == OP and tok[1] == ')' and
nextTok[0] == NAME):
# Close parenthesis followed by an implicitly applied function
result.append((OP, '*'))
elif (tok[0] == nextTok[0] == OP
and tok[1] == ')' and nextTok[1] == '('):
# Close parenthesis followed by an open parenthesis
result.append((OP, '*'))
elif (isinstance(tok, AppliedFunction) and nextTok[0] == NAME):
# Applied function followed by implicitly applied function
result.append((OP, '*'))
elif (tok[0] == NAME and
not _token_callable(tok, local_dict, global_dict) and
nextTok[0] == OP and nextTok[1] == '('):
# Constant followed by parenthesis
result.append((OP, '*'))
elif (tok[0] == NAME and
not _token_callable(tok, local_dict, global_dict) and
nextTok[0] == NAME and
not _token_callable(nextTok, local_dict, global_dict)):
# Constant followed by constant
result.append((OP, '*'))
elif (tok[0] == NAME and
not _token_callable(tok, local_dict, global_dict) and
(isinstance(nextTok, AppliedFunction) or nextTok[0] == NAME)):
# Constant followed by (implicitly applied) function
result.append((OP, '*'))
if tokens:
result.append(tokens[-1])
return result
def _implicit_application(tokens, local_dict, global_dict):
"""Adds parentheses as needed after functions."""
result = []
appendParen = 0 # number of closing parentheses to add
skip = 0 # number of tokens to delay before adding a ')' (to
# capture **, ^, etc.)
exponentSkip = False # skipping tokens before inserting parentheses to
# work with function exponentiation
for tok, nextTok in zip(tokens, tokens[1:]):
result.append(tok)
if (tok[0] == NAME and
nextTok[0] != OP and
nextTok[0] != ENDMARKER):
if _token_callable(tok, local_dict, global_dict, nextTok):
result.append((OP, '('))
appendParen += 1
# name followed by exponent - function exponentiation
elif (tok[0] == NAME and nextTok[0] == OP and nextTok[1] == '**'):
if _token_callable(tok, local_dict, global_dict):
exponentSkip = True
elif exponentSkip:
# if the last token added was an applied function (i.e. the
# power of the function exponent) OR a multiplication (as
# implicit multiplication would have added an extraneous
# multiplication)
if (isinstance(tok, AppliedFunction)
or (tok[0] == OP and tok[1] == '*')):
# don't add anything if the next token is a multiplication
# or if there's already a parenthesis (if parenthesis, still
# stop skipping tokens)
if not (nextTok[0] == OP and nextTok[1] == '*'):
if not(nextTok[0] == OP and nextTok[1] == '('):
result.append((OP, '('))
appendParen += 1
exponentSkip = False
elif appendParen:
if nextTok[0] == OP and nextTok[1] in ('^', '**', '*'):
skip = 1
continue
if skip:
skip -= 1
continue
result.append((OP, ')'))
appendParen -= 1
if tokens:
result.append(tokens[-1])
if appendParen:
result.extend([(OP, ')')] * appendParen)
return result
def function_exponentiation(tokens, local_dict, global_dict):
"""Allows functions to be exponentiated, e.g. ``cos**2(x)``.
Examples
========
>>> from sympy.parsing.sympy_parser import (parse_expr,
... standard_transformations, function_exponentiation)
>>> transformations = standard_transformations + (function_exponentiation,)
>>> parse_expr('sin**4(x)', transformations=transformations)
sin(x)**4
"""
result = []
exponent = []
consuming_exponent = False
level = 0
for tok, nextTok in zip(tokens, tokens[1:]):
if tok[0] == NAME and nextTok[0] == OP and nextTok[1] == '**':
if _token_callable(tok, local_dict, global_dict):
consuming_exponent = True
elif consuming_exponent:
exponent.append(tok)
# only want to stop after hitting )
if tok[0] == nextTok[0] == OP and tok[1] == ')' and nextTok[1] == '(':
consuming_exponent = False
# if implicit multiplication was used, we may have )*( instead
if tok[0] == nextTok[0] == OP and tok[1] == '*' and nextTok[1] == '(':
consuming_exponent = False
del exponent[-1]
continue
elif exponent and not consuming_exponent:
if tok[0] == OP:
if tok[1] == '(':
level += 1
elif tok[1] == ')':
level -= 1
if level == 0:
result.append(tok)
result.extend(exponent)
exponent = []
continue
result.append(tok)
if tokens:
result.append(tokens[-1])
if exponent:
result.extend(exponent)
return result
def split_symbols_custom(predicate):
"""Creates a transformation that splits symbol names.
``predicate`` should return True if the symbol name is to be split.
For instance, to retain the default behavior but avoid splitting certain
symbol names, a predicate like this would work:
>>> from sympy.parsing.sympy_parser import (parse_expr, _token_splittable,
... standard_transformations, implicit_multiplication,
... split_symbols_custom)
>>> def can_split(symbol):
... if symbol not in ('list', 'of', 'unsplittable', 'names'):
... return _token_splittable(symbol)
... return False
...
>>> transformation = split_symbols_custom(can_split)
>>> parse_expr('unsplittable', transformations=standard_transformations +
... (transformation, implicit_multiplication))
unsplittable
"""
def _split_symbols(tokens, local_dict, global_dict):
result = []
split = False
split_previous=False
for tok in tokens:
if split_previous:
# throw out closing parenthesis of Symbol that was split
split_previous=False
continue
split_previous=False
if tok[0] == NAME and tok[1] == 'Symbol':
split = True
elif split and tok[0] == NAME:
symbol = tok[1][1:-1]
if predicate(symbol):
for char in symbol:
if char in local_dict or char in global_dict:
# Get rid of the call to Symbol
del result[-2:]
result.extend([(NAME, "%s" % char),
(NAME, 'Symbol'), (OP, '(')])
else:
result.extend([(NAME, "'%s'" % char), (OP, ')'),
(NAME, 'Symbol'), (OP, '(')])
# Delete the last two tokens: get rid of the extraneous
# Symbol( we just added
# Also, set split_previous=True so will skip
# the closing parenthesis of the original Symbol
del result[-2:]
split = False
split_previous = True
continue
else:
split = False
result.append(tok)
return result
return _split_symbols
#: Splits symbol names for implicit multiplication.
#:
#: Intended to let expressions like ``xyz`` be parsed as ``x*y*z``. Does not
#: split Greek character names, so ``theta`` will *not* become
#: ``t*h*e*t*a``. Generally this should be used with
#: ``implicit_multiplication``.
split_symbols = split_symbols_custom(_token_splittable)
def implicit_multiplication(result, local_dict, global_dict):
"""Makes the multiplication operator optional in most cases.
Use this before :func:`implicit_application`, otherwise expressions like
``sin 2x`` will be parsed as ``x * sin(2)`` rather than ``sin(2*x)``.
Examples
========
>>> from sympy.parsing.sympy_parser import (parse_expr,
... standard_transformations, implicit_multiplication)
>>> transformations = standard_transformations + (implicit_multiplication,)
>>> parse_expr('3 x y', transformations=transformations)
3*x*y
"""
# These are interdependent steps, so we don't expose them separately
for step in (_group_parentheses(implicit_multiplication),
_apply_functions,
_implicit_multiplication):
result = step(result, local_dict, global_dict)
result = _flatten(result)
return result
def implicit_application(result, local_dict, global_dict):
"""Makes parentheses optional in some cases for function calls.
Use this after :func:`implicit_multiplication`, otherwise expressions
like ``sin 2x`` will be parsed as ``x * sin(2)`` rather than
``sin(2*x)``.
Examples
========
>>> from sympy.parsing.sympy_parser import (parse_expr,
... standard_transformations, implicit_application)
>>> transformations = standard_transformations + (implicit_application,)
>>> parse_expr('cot z + csc z', transformations=transformations)
cot(z) + csc(z)
"""
for step in (_group_parentheses(implicit_application),
_apply_functions,
_implicit_application,):
result = step(result, local_dict, global_dict)
result = _flatten(result)
return result
def implicit_multiplication_application(result, local_dict, global_dict):
"""Allows a slightly relaxed syntax.
- Parentheses for single-argument method calls are optional.
- Multiplication is implicit.
- Symbol names can be split (i.e. spaces are not needed between
symbols).
- Functions can be exponentiated.
Examples
========
>>> from sympy.parsing.sympy_parser import (parse_expr,
... standard_transformations, implicit_multiplication_application)
>>> parse_expr("10sin**2 x**2 + 3xyz + tan theta",
... transformations=(standard_transformations +
... (implicit_multiplication_application,)))
3*x*y*z + 10*sin(x**2)**2 + tan(theta)
"""
for step in (split_symbols, implicit_multiplication,
implicit_application, function_exponentiation):
result = step(result, local_dict, global_dict)
return result
def auto_symbol(tokens, local_dict, global_dict):
"""Inserts calls to ``Symbol`` for undefined variables."""
result = []
prevTok = (None, None)
tokens.append((None, None)) # so zip traverses all tokens
for tok, nextTok in zip(tokens, tokens[1:]):
tokNum, tokVal = tok
nextTokNum, nextTokVal = nextTok
if tokNum == NAME:
name = tokVal
if (name in ['True', 'False', 'None']
or iskeyword(name)
or name in local_dict
# Don't convert attribute access
or (prevTok[0] == OP and prevTok[1] == '.')
# Don't convert keyword arguments
or (prevTok[0] == OP and prevTok[1] in ('(', ',')
and nextTokNum == OP and nextTokVal == '=')):
result.append((NAME, name))
continue
elif name in global_dict:
obj = global_dict[name]
if isinstance(obj, (Basic, type)) or callable(obj):
result.append((NAME, name))
continue
result.extend([
(NAME, 'Symbol'),
(OP, '('),
(NAME, repr(str(name))),
(OP, ')'),
])
else:
result.append((tokNum, tokVal))
prevTok = (tokNum, tokVal)
return result
def lambda_notation(tokens, local_dict, global_dict):
"""Substitutes "lambda" with its Sympy equivalent Lambda().
However, the conversion doesn't take place if only "lambda"
is passed because that is a syntax error.
"""
result = []
flag = False
toknum, tokval = tokens[0]
tokLen = len(tokens)
if toknum == NAME and tokval == 'lambda':
if tokLen == 2:
result.extend(tokens)
elif tokLen > 2:
result.extend([
(NAME, 'Lambda'),
(OP, '('),
(OP, '('),
(OP, ')'),
(OP, ')'),
])
for tokNum, tokVal in tokens[1:]:
if tokNum == OP and tokVal == ':':
tokVal = ','
flag = True
if not flag and tokNum == OP and tokVal in ['*', '**']:
raise TokenError("Starred arguments in lambda not supported")
if flag:
result.insert(-1, (tokNum, tokVal))
else:
result.insert(-2, (tokNum, tokVal))
else:
result.extend(tokens)
return result
def factorial_notation(tokens, local_dict, global_dict):
"""Allows standard notation for factorial."""
result = []
prevtoken = ''
for toknum, tokval in tokens:
if toknum == OP:
op = tokval
if op == '!!':
if prevtoken == '!' or prevtoken == '!!':
raise TokenError
result = _add_factorial_tokens('factorial2', result)
elif op == '!':
if prevtoken == '!' or prevtoken == '!!':
raise TokenError
result = _add_factorial_tokens('factorial', result)
else:
result.append((OP, op))
else:
result.append((toknum, tokval))
prevtoken = tokval
return result
def convert_xor(tokens, local_dict, global_dict):
"""Treats XOR, ``^``, as exponentiation, ``**``."""
result = []
for toknum, tokval in tokens:
if toknum == OP:
if tokval == '^':
result.append((OP, '**'))
else:
result.append((toknum, tokval))
else:
result.append((toknum, tokval))
return result
def auto_number(tokens, local_dict, global_dict):
"""Converts numeric literals to use SymPy equivalents.
Complex numbers use ``I``; integer literals use ``Integer``, float
literals use ``Float``, and repeating decimals use ``Rational``.
"""
result = []
prevtoken = ''
for toknum, tokval in tokens:
if toknum == NUMBER:
number = tokval
postfix = []
if number.endswith('j') or number.endswith('J'):
number = number[:-1]
postfix = [(OP, '*'), (NAME, 'I')]
if '.' in number or (('e' in number or 'E' in number) and
not (number.startswith('0x') or number.startswith('0X'))):
match = _re_repeated.match(number)
if match is not None:
# Clear repeating decimals, e.g. 3.4[31] -> (3 + 4/10 + 31/990)
pre, post, repetend = match.groups()
zeros = '0'*len(post)
post, repetends = [w.lstrip('0') for w in [post, repetend]]
# or else interpreted as octal
a = pre or '0'
b, c = post or '0', '1' + zeros
d, e = repetends, ('9'*len(repetend)) + zeros
seq = [
(OP, '('),
(NAME,
'Integer'), (OP, '('), (NUMBER, a), (OP, ')'),
(OP, '+'),
(NAME, 'Rational'), (OP, '('), (
NUMBER, b), (OP, ','), (NUMBER, c), (OP, ')'),
(OP, '+'),
(NAME, 'Rational'), (OP, '('), (
NUMBER, d), (OP, ','), (NUMBER, e), (OP, ')'),
(OP, ')'),
]
else:
seq = [(NAME, 'Float'), (OP, '('),
(NUMBER, repr(str(number))), (OP, ')')]
else:
seq = [(NAME, 'Integer'), (OP, '('), (
NUMBER, number), (OP, ')')]
result.extend(seq + postfix)
else:
result.append((toknum, tokval))
return result
def rationalize(tokens, local_dict, global_dict):
"""Converts floats into ``Rational``. Run AFTER ``auto_number``."""
result = []
passed_float = False
for toknum, tokval in tokens:
if toknum == NAME:
if tokval == 'Float':
passed_float = True
tokval = 'Rational'
result.append((toknum, tokval))
elif passed_float == True and toknum == NUMBER:
passed_float = False
result.append((STRING, tokval))
else:
result.append((toknum, tokval))
return result
def _transform_equals_sign(tokens, local_dict, global_dict):
"""Transforms the equals sign ``=`` to instances of Eq.
This is a helper function for `convert_equals_signs`.
Works with expressions containing one equals sign and no
nesting. Expressions like `(1=2)=False` won't work with this
and should be used with `convert_equals_signs`.
Examples: 1=2 to Eq(1,2)
1*2=x to Eq(1*2, x)
This does not deal with function arguments yet.
"""
result = []
if (OP, "=") in tokens:
result.append((NAME, "Eq"))
result.append((OP, "("))
for index, token in enumerate(tokens):
if token == (OP, "="):
result.append((OP, ","))
continue
result.append(token)
result.append((OP, ")"))
else:
result = tokens
return result
def convert_equals_signs(result, local_dict, global_dict):
""" Transforms all the equals signs ``=`` to instances of Eq.
Parses the equals signs in the expression and replaces them with
appropriate Eq instances.Also works with nested equals signs.
Does not yet play well with function arguments.
For example, the expression `(x=y)` is ambiguous and can be interpreted
as x being an argument to a function and `convert_equals_signs` won't
work for this.
See also
========
convert_equality_operators
Examples:
=========
>>> from sympy.parsing.sympy_parser import (parse_expr,
... standard_transformations, convert_equals_signs)
>>> parse_expr("1*2=x", transformations=(
... standard_transformations + (convert_equals_signs,)))
Eq(2, x)
>>> parse_expr("(1*2=x)=False", transformations=(
... standard_transformations + (convert_equals_signs,)))
Eq(Eq(2, x), False)
"""
for step in (_group_parentheses(convert_equals_signs),
_apply_functions,
_transform_equals_sign):
result = step(result, local_dict, global_dict)
result = _flatten(result)
return result
#: Standard transformations for :func:`parse_expr`.
#: Inserts calls to :class:`Symbol`, :class:`Integer`, and other SymPy
#: datatypes and allows the use of standard factorial notation (e.g. ``x!``).
standard_transformations = (lambda_notation, auto_symbol, auto_number, factorial_notation)
def stringify_expr(s, local_dict, global_dict, transformations):
"""
Converts the string ``s`` to Python code, in ``local_dict``
Generally, ``parse_expr`` should be used.
"""
tokens = []
input_code = StringIO(s.strip())
for toknum, tokval, _, _, _ in generate_tokens(input_code.readline):
tokens.append((toknum, tokval))
for transform in transformations:
tokens = transform(tokens, local_dict, global_dict)
return untokenize(tokens)
def eval_expr(code, local_dict, global_dict):
"""
Evaluate Python code generated by ``stringify_expr``.
Generally, ``parse_expr`` should be used.
"""
expr = eval(
code, global_dict, local_dict) # take local objects in preference
return expr
def parse_expr(s, local_dict=None, transformations=standard_transformations,
global_dict=None, evaluate=True):
"""Converts the string ``s`` to a SymPy expression, in ``local_dict``
Parameters
==========
s : str
The string to parse.
local_dict : dict, optional
A dictionary of local variables to use when parsing.
global_dict : dict, optional
A dictionary of global variables. By default, this is initialized
with ``from sympy import *``; provide this parameter to override
this behavior (for instance, to parse ``"Q & S"``).
transformations : tuple, optional
A tuple of transformation functions used to modify the tokens of the
parsed expression before evaluation. The default transformations
convert numeric literals into their SymPy equivalents, convert
undefined variables into SymPy symbols, and allow the use of standard
mathematical factorial notation (e.g. ``x!``).
evaluate : bool, optional
When False, the order of the arguments will remain as they were in the
string and automatic simplification that would normally occur is
suppressed. (see examples)
Examples
========
>>> from sympy.parsing.sympy_parser import parse_expr
>>> parse_expr("1/2")
1/2
>>> type(_)
<class 'sympy.core.numbers.Half'>
>>> from sympy.parsing.sympy_parser import standard_transformations,\\
... implicit_multiplication_application
>>> transformations = (standard_transformations +
... (implicit_multiplication_application,))
>>> parse_expr("2x", transformations=transformations)
2*x
When evaluate=False, some automatic simplifications will not occur:
>>> parse_expr("2**3"), parse_expr("2**3", evaluate=False)
(8, 2**3)
In addition the order of the arguments will not be made canonical.
This feature allows one to tell exactly how the expression was entered:
>>> a = parse_expr('1 + x', evaluate=False)
>>> b = parse_expr('x + 1', evaluate=0)
>>> a == b
False
>>> a.args
(1, x)
>>> b.args
(x, 1)
See Also
========
stringify_expr, eval_expr, standard_transformations,
implicit_multiplication_application
"""
if local_dict is None:
local_dict = {}
if global_dict is None:
global_dict = {}
exec_('from sympy import *', global_dict)
code = stringify_expr(s, local_dict, global_dict, transformations)
if not evaluate:
code = compile(evaluateFalse(code), '<string>', 'eval')
return eval_expr(code, local_dict, global_dict)
def evaluateFalse(s):
"""
Replaces operators with the SymPy equivalent and sets evaluate=False.
"""
node = ast.parse(s)
node = EvaluateFalseTransformer().visit(node)
# node is a Module, we want an Expression
node = ast.Expression(node.body[0].value)
return ast.fix_missing_locations(node)
class EvaluateFalseTransformer(ast.NodeTransformer):
operators = {
ast.Add: 'Add',
ast.Mult: 'Mul',
ast.Pow: 'Pow',
ast.Sub: 'Add',
ast.Div: 'Mul',
ast.BitOr: 'Or',
ast.BitAnd: 'And',
ast.BitXor: 'Not',
}
def flatten(self, args, func):
result = []
for arg in args:
if isinstance(arg, ast.Call) and arg.func.id == func:
result.extend(self.flatten(arg.args, func))
else:
result.append(arg)
return result
def visit_BinOp(self, node):
if node.op.__class__ in self.operators:
sympy_class = self.operators[node.op.__class__]
right = self.visit(node.right)
left = self.visit(node.left)
if isinstance(node.left, ast.UnaryOp) and (isinstance(node.right, ast.UnaryOp) == 0) and sympy_class in ('Mul',):
left, right = right, left
if isinstance(node.op, ast.Sub):
right = ast.UnaryOp(op=ast.USub(), operand=right)
if isinstance(node.op, ast.Div):
if isinstance(node.left, ast.UnaryOp):
if isinstance(node.right,ast.UnaryOp):
left, right = right, left
left = ast.Call(
func=ast.Name(id='Pow', ctx=ast.Load()),
args=[left, ast.UnaryOp(op=ast.USub(), operand=ast.Num(1))],
keywords=[ast.keyword(arg='evaluate', value=ast.Name(id='False', ctx=ast.Load()))],
starargs=None,
kwargs=None
)
else:
right = ast.Call(
func=ast.Name(id='Pow', ctx=ast.Load()),
args=[right, ast.UnaryOp(op=ast.USub(), operand=ast.Num(1))],
keywords=[ast.keyword(arg='evaluate', value=ast.Name(id='False', ctx=ast.Load()))],
starargs=None,
kwargs=None
)
new_node = ast.Call(
func=ast.Name(id=sympy_class, ctx=ast.Load()),
args=[left, right],
keywords=[ast.keyword(arg='evaluate', value=ast.Name(id='False', ctx=ast.Load()))],
starargs=None,
kwargs=None
)
if sympy_class in ('Add', 'Mul'):
# Denest Add or Mul as appropriate
new_node.args = self.flatten(new_node.args, sympy_class)
return new_node
return node
| 32,979 | 32.89517 | 125 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/parsing/sympy_tokenize.py
|
"""Tokenization help for Python programs.
generate_tokens(readline) is a generator that breaks a stream of
text into Python tokens. It accepts a readline-like method which is called
repeatedly to get the next line of input (or "" for EOF). It generates
5-tuples with these members:
the token type (see token.py)
the token (a string)
the starting (row, column) indices of the token (a 2-tuple of ints)
the ending (row, column) indices of the token (a 2-tuple of ints)
the original line (string)
It is designed to match the working of the Python tokenizer exactly, except
that it produces COMMENT tokens for comments and gives type OP for all
operators
Older entry points
tokenize_loop(readline, tokeneater)
tokenize(readline, tokeneater=printtoken)
are the same, except instead of generating tokens, tokeneater is a callback
function to which the 5 fields described above are passed as 5 arguments,
each time a new token is found."""
from __future__ import print_function, division
__author__ = 'Ka-Ping Yee <[email protected]>'
__credits__ = \
'GvR, ESR, Tim Peters, Thomas Wouters, Fred Drake, Skip Montanaro, Raymond Hettinger'
import string
import re
from token import *
import token
__all__ = [x for x in dir(token) if x[0] != '_'] + ["COMMENT", "tokenize",
"generate_tokens", "NL", "untokenize"]
del token
COMMENT = N_TOKENS
tok_name[COMMENT] = 'COMMENT'
NL = N_TOKENS + 1
tok_name[NL] = 'NL'
N_TOKENS += 2
def group(*choices):
return '(' + '|'.join(choices) + ')'
def any(*choices):
return group(*choices) + '*'
def maybe(*choices):
return group(*choices) + '?'
Whitespace = r'[ \f\t]*'
Comment = r'#[^\r\n]*'
Ignore = Whitespace + any(r'\\\r?\n' + Whitespace) + maybe(Comment)
Name = r'[a-zA-Z_]\w*'
Hexnumber = r'0[xX][\da-fA-F]+[lL]?'
Octnumber = r'(0[oO][0-7]+)|(0[0-7]*)[lL]?'
Binnumber = r'0[bB][01]+[lL]?'
Decnumber = r'[1-9]\d*[lL]?'
Intnumber = group(Hexnumber, Binnumber, Octnumber, Decnumber)
Exponent = r'[eE][-+]?\d+'
Pointfloat = group(r'\d+\.\d*', r'\.\d+') + maybe(Exponent)
Repeatedfloat = r'\d*\.\d*\[\d+\]'
Expfloat = r'\d+' + Exponent
Floatnumber = group(Repeatedfloat, Pointfloat, Expfloat)
Imagnumber = group(r'\d+[jJ]', Floatnumber + r'[jJ]')
Number = group(Imagnumber, Floatnumber, Intnumber)
# Tail end of ' string.
Single = r"[^'\\]*(?:\\.[^'\\]*)*'"
# Tail end of " string.
Double = r'[^"\\]*(?:\\.[^"\\]*)*"'
# Tail end of ''' string.
Single3 = r"[^'\\]*(?:(?:\\.|'(?!''))[^'\\]*)*'''"
# Tail end of """ string.
Double3 = r'[^"\\]*(?:(?:\\.|"(?!""))[^"\\]*)*"""'
Triple = group("[uU]?[rR]?'''", '[uU]?[rR]?"""')
# Single-line ' or " string.
String = group(r"[uU]?[rR]?'[^\n'\\]*(?:\\.[^\n'\\]*)*'",
r'[uU]?[rR]?"[^\n"\\]*(?:\\.[^\n"\\]*)*"')
# Because of leftmost-then-longest match semantics, be sure to put the
# longest operators first (e.g., if = came before ==, == would get
# recognized as two instances of =).
Operator = group(r"\*\*=?", r">>=?", r"<<=?", r"<>", r"!=",
r"//=?",
r"[+\-*/%&|^=<>]=?",
r"~")
Bracket = '[][(){}]'
Special = group(r'\r?\n', r'[:;.,`@]', r'\!\!', r'\!')
Funny = group(Operator, Bracket, Special)
PlainToken = group(Number, Funny, String, Name)
Token = Ignore + PlainToken
# First (or only) line of ' or " string.
ContStr = group(r"[uU]?[rR]?'[^\n'\\]*(?:\\.[^\n'\\]*)*" +
group("'", r'\\\r?\n'),
r'[uU]?[rR]?"[^\n"\\]*(?:\\.[^\n"\\]*)*' +
group('"', r'\\\r?\n'))
PseudoExtras = group(r'\\\r?\n', Comment, Triple)
PseudoToken = Whitespace + group(PseudoExtras, Number, Funny, ContStr, Name)
tokenprog, pseudoprog, single3prog, double3prog = map(
re.compile, (Token, PseudoToken, Single3, Double3))
endprogs = {"'": re.compile(Single), '"': re.compile(Double),
"'''": single3prog, '"""': double3prog,
"r'''": single3prog, 'r"""': double3prog,
"u'''": single3prog, 'u"""': double3prog,
"ur'''": single3prog, 'ur"""': double3prog,
"R'''": single3prog, 'R"""': double3prog,
"U'''": single3prog, 'U"""': double3prog,
"uR'''": single3prog, 'uR"""': double3prog,
"Ur'''": single3prog, 'Ur"""': double3prog,
"UR'''": single3prog, 'UR"""': double3prog,
"b'''": single3prog, 'b"""': double3prog,
"br'''": single3prog, 'br"""': double3prog,
"B'''": single3prog, 'B"""': double3prog,
"bR'''": single3prog, 'bR"""': double3prog,
"Br'''": single3prog, 'Br"""': double3prog,
"BR'''": single3prog, 'BR"""': double3prog,
'r': None, 'R': None, 'u': None, 'U': None,
'b': None, 'B': None}
triple_quoted = {}
for t in ("'''", '"""',
"r'''", 'r"""', "R'''", 'R"""',
"u'''", 'u"""', "U'''", 'U"""',
"ur'''", 'ur"""', "Ur'''", 'Ur"""',
"uR'''", 'uR"""', "UR'''", 'UR"""',
"b'''", 'b"""', "B'''", 'B"""',
"br'''", 'br"""', "Br'''", 'Br"""',
"bR'''", 'bR"""', "BR'''", 'BR"""'):
triple_quoted[t] = t
single_quoted = {}
for t in ("'", '"',
"r'", 'r"', "R'", 'R"',
"u'", 'u"', "U'", 'U"',
"ur'", 'ur"', "Ur'", 'Ur"',
"uR'", 'uR"', "UR'", 'UR"',
"b'", 'b"', "B'", 'B"',
"br'", 'br"', "Br'", 'Br"',
"bR'", 'bR"', "BR'", 'BR"' ):
single_quoted[t] = t
tabsize = 8
class TokenError(Exception):
pass
class StopTokenizing(Exception):
pass
def printtoken(type, token, srow_scol, erow_ecol, line): # for testing
srow, scol = srow_scol
erow, ecol = erow_ecol
print("%d,%d-%d,%d:\t%s\t%s" % \
(srow, scol, erow, ecol, tok_name[type], repr(token)))
def tokenize(readline, tokeneater=printtoken):
"""
The tokenize() function accepts two parameters: one representing the
input stream, and one providing an output mechanism for tokenize().
The first parameter, readline, must be a callable object which provides
the same interface as the readline() method of built-in file objects.
Each call to the function should return one line of input as a string.
The second parameter, tokeneater, must also be a callable object. It is
called once for each token, with five arguments, corresponding to the
tuples generated by generate_tokens().
"""
try:
tokenize_loop(readline, tokeneater)
except StopTokenizing:
pass
# backwards compatible interface
def tokenize_loop(readline, tokeneater):
for token_info in generate_tokens(readline):
tokeneater(*token_info)
class Untokenizer:
def __init__(self):
self.tokens = []
self.prev_row = 1
self.prev_col = 0
def add_whitespace(self, start):
row, col = start
if row > self.prev_row:
raise ValueError("row should not be greater than prev_row")
col_offset = col - self.prev_col
if col_offset:
self.tokens.append(" " * col_offset)
def untokenize(self, iterable):
for t in iterable:
if len(t) == 2:
self.compat(t, iterable)
break
tok_type, token, start, end, line = t
self.add_whitespace(start)
self.tokens.append(token)
self.prev_row, self.prev_col = end
if tok_type in (NEWLINE, NL):
self.prev_row += 1
self.prev_col = 0
return "".join(self.tokens)
def compat(self, token, iterable):
startline = False
indents = []
toks_append = self.tokens.append
toknum, tokval = token
if toknum in (NAME, NUMBER):
tokval += ' '
if toknum in (NEWLINE, NL):
startline = True
prevstring = False
for tok in iterable:
toknum, tokval = tok[:2]
if toknum in (NAME, NUMBER):
tokval += ' '
# Insert a space between two consecutive strings
if toknum == STRING:
if prevstring:
tokval = ' ' + tokval
prevstring = True
else:
prevstring = False
if toknum == INDENT:
indents.append(tokval)
continue
elif toknum == DEDENT:
indents.pop()
continue
elif toknum in (NEWLINE, NL):
startline = True
elif startline and indents:
toks_append(indents[-1])
startline = False
toks_append(tokval)
def untokenize(iterable):
"""Transform tokens back into Python source code.
Each element returned by the iterable must be a token sequence
with at least two elements, a token number and token value. If
only two tokens are passed, the resulting output is poor.
Round-trip invariant for full input:
Untokenized source will match input source exactly
Round-trip invariant for limited intput::
# Output text will tokenize the back to the input
t1 = [tok[:2] for tok in generate_tokens(f.readline)]
newcode = untokenize(t1)
readline = iter(newcode.splitlines(1)).next
t2 = [tok[:2] for tok in generate_tokens(readline)]
if t1 != t2:
raise ValueError("t1 should be equal to t2")
"""
ut = Untokenizer()
return ut.untokenize(iterable)
def generate_tokens(readline):
"""
The generate_tokens() generator requires one argment, readline, which
must be a callable object which provides the same interface as the
readline() method of built-in file objects. Each call to the function
should return one line of input as a string. Alternately, readline
can be a callable function terminating with StopIteration::
readline = open(myfile).next # Example of alternate readline
The generator produces 5-tuples with these members: the token type; the
token string; a 2-tuple (srow, scol) of ints specifying the row and
column where the token begins in the source; a 2-tuple (erow, ecol) of
ints specifying the row and column where the token ends in the source;
and the line on which the token was found. The line passed is the
logical line; continuation lines are included.
"""
lnum = parenlev = continued = 0
namechars, numchars = string.ascii_letters + '_', '0123456789'
contstr, needcont = '', 0
contline = None
indents = [0]
while 1: # loop over lines in stream
try:
line = readline()
except StopIteration:
line = ''
lnum = lnum + 1
pos, max = 0, len(line)
if contstr: # continued string
if not line:
raise TokenError("EOF in multi-line string", strstart)
endmatch = endprog.match(line)
if endmatch:
pos = end = endmatch.end(0)
yield (STRING, contstr + line[:end],
strstart, (lnum, end), contline + line)
contstr, needcont = '', 0
contline = None
elif needcont and line[-2:] != '\\\n' and line[-3:] != '\\\r\n':
yield (ERRORTOKEN, contstr + line,
strstart, (lnum, len(line)), contline)
contstr = ''
contline = None
continue
else:
contstr = contstr + line
contline = contline + line
continue
elif parenlev == 0 and not continued: # new statement
if not line:
break
column = 0
while pos < max: # measure leading whitespace
if line[pos] == ' ':
column = column + 1
elif line[pos] == '\t':
column = (column/tabsize + 1)*tabsize
elif line[pos] == '\f':
column = 0
else:
break
pos = pos + 1
if pos == max:
break
if line[pos] in '#\r\n': # skip comments or blank lines
if line[pos] == '#':
comment_token = line[pos:].rstrip('\r\n')
nl_pos = pos + len(comment_token)
yield (COMMENT, comment_token,
(lnum, pos), (lnum, pos + len(comment_token)), line)
yield (NL, line[nl_pos:],
(lnum, nl_pos), (lnum, len(line)), line)
else:
yield ((NL, COMMENT)[line[pos] == '#'], line[pos:],
(lnum, pos), (lnum, len(line)), line)
continue
if column > indents[-1]: # count indents or dedents
indents.append(column)
yield (INDENT, line[:pos], (lnum, 0), (lnum, pos), line)
while column < indents[-1]:
if column not in indents:
raise IndentationError(
"unindent does not match any outer indentation level",
("<tokenize>", lnum, pos, line))
indents = indents[:-1]
yield (DEDENT, '', (lnum, pos), (lnum, pos), line)
else: # continued statement
if not line:
raise TokenError("EOF in multi-line statement", (lnum, 0))
continued = 0
while pos < max:
pseudomatch = pseudoprog.match(line, pos)
if pseudomatch: # scan for tokens
start, end = pseudomatch.span(1)
spos, epos, pos = (lnum, start), (lnum, end), end
token, initial = line[start:end], line[start]
if initial in numchars or \
(initial == '.' and token != '.'): # ordinary number
yield (NUMBER, token, spos, epos, line)
elif initial in '\r\n':
yield (NL if parenlev > 0 else NEWLINE, token, spos, epos, line)
elif initial == '#':
if token.endswith("\n"):
raise ValueError("Token should not end with \n")
yield (COMMENT, token, spos, epos, line)
elif token in triple_quoted:
endprog = endprogs[token]
endmatch = endprog.match(line, pos)
if endmatch: # all on one line
pos = endmatch.end(0)
token = line[start:pos]
yield (STRING, token, spos, (lnum, pos), line)
else:
strstart = (lnum, start) # multiple lines
contstr = line[start:]
contline = line
break
elif initial in single_quoted or \
token[:2] in single_quoted or \
token[:3] in single_quoted:
if token[-1] == '\n': # continued string
strstart = (lnum, start)
endprog = (endprogs[initial] or endprogs[token[1]] or
endprogs[token[2]])
contstr, needcont = line[start:], 1
contline = line
break
else: # ordinary string
yield (STRING, token, spos, epos, line)
elif initial in namechars: # ordinary name
yield (NAME, token, spos, epos, line)
elif initial == '\\': # continued stmt
continued = 1
else:
if initial in '([{':
parenlev = parenlev + 1
elif initial in ')]}':
parenlev = parenlev - 1
yield (OP, token, spos, epos, line)
else:
yield (ERRORTOKEN, line[pos],
(lnum, pos), (lnum, pos + 1), line)
pos = pos + 1
for indent in indents[1:]: # pop remaining indent levels
yield (DEDENT, '', (lnum, 0), (lnum, 0), '')
yield (ENDMARKER, '', (lnum, 0), (lnum, 0), '')
if __name__ == '__main__': # testing
import sys
if len(sys.argv) > 1:
tokenize(open(sys.argv[1]).readline)
else:
tokenize(sys.stdin.readline)
| 16,817 | 36.207965 | 89 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/parsing/maxima.py
|
from __future__ import print_function, division
import re
from sympy import sympify, Sum, product, sin, cos
class MaximaHelpers:
def maxima_expand(expr):
return expr.expand()
def maxima_float(expr):
return expr.evalf()
def maxima_trigexpand(expr):
return expr.expand(trig=True)
def maxima_sum(a1, a2, a3, a4):
return Sum(a1, (a2, a3, a4)).doit()
def maxima_product(a1, a2, a3, a4):
return product(a1, (a2, a3, a4))
def maxima_csc(expr):
return 1/sin(expr)
def maxima_sec(expr):
return 1/cos(expr)
sub_dict = {
'pi': re.compile('%pi'),
'E': re.compile('%e'),
'I': re.compile('%i'),
'**': re.compile('\^'),
'oo': re.compile(r'\binf\b'),
'-oo': re.compile(r'\bminf\b'),
"'-'": re.compile(r'\bminus\b'),
'maxima_expand': re.compile(r'\bexpand\b'),
'maxima_float': re.compile(r'\bfloat\b'),
'maxima_trigexpand': re.compile(r'\btrigexpand'),
'maxima_sum': re.compile(r'\bsum\b'),
'maxima_product': re.compile(r'\bproduct\b'),
'cancel': re.compile(r'\bratsimp\b'),
'maxima_csc': re.compile(r'\bcsc\b'),
'maxima_sec': re.compile(r'\bsec\b')
}
var_name = re.compile('^\s*(\w+)\s*:')
def parse_maxima(str, globals=None, name_dict={}):
str = str.strip()
str = str.rstrip('; ')
for k, v in sub_dict.items():
str = v.sub(k, str)
assign_var = None
var_match = var_name.search(str)
if var_match:
assign_var = var_match.group(1)
str = str[var_match.end():].strip()
dct = MaximaHelpers.__dict__.copy()
dct.update(name_dict)
obj = sympify(str, locals=dct)
if assign_var and globals:
globals[assign_var] = obj
return obj
| 1,740 | 23.521127 | 53 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/parsing/__init__.py
|
"""Used for translating a string into a SymPy expression. """
| 62 | 30.5 | 61 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/parsing/ast_parser.py
|
"""
This module implements the functionality to take any Python expression as a
string and fix all numbers and other things before evaluating it,
thus
1/2
returns
Integer(1)/Integer(2)
We use the Python ast module for that, which is in python2.6 and later. It is
well documented at docs.python.org.
Some tips to understand how this works: use dump() to get a nice
representation of any node. Then write a string of what you want to get,
e.g. "Integer(1)", parse it, dump it and you'll see that you need to do
"Call(Name('Integer', Load()), [node], [], None, None)". You don't need
to bother with lineno and col_offset, just call fix_missing_locations()
before returning the node.
"""
from __future__ import print_function, division
from sympy.core.basic import Basic
from sympy.core.compatibility import exec_
from sympy.core.sympify import SympifyError
from ast import parse, NodeTransformer, Call, Name, Load, \
fix_missing_locations, Str, Tuple
class Transform(NodeTransformer):
def __init__(self, local_dict, global_dict):
NodeTransformer.__init__(self)
self.local_dict = local_dict
self.global_dict = global_dict
def visit_Num(self, node):
if isinstance(node.n, int):
return fix_missing_locations(Call(Name('Integer', Load()),
[node], [], None, None))
elif isinstance(node.n, float):
return fix_missing_locations(Call(Name('Float', Load()),
[node], [], None, None))
return node
def visit_Name(self, node):
if node.id in self.local_dict:
return node
elif node.id in self.global_dict:
name_obj = self.global_dict[node.id]
if isinstance(name_obj, (Basic, type)) or callable(name_obj):
return node
elif node.id in ['True', 'False']:
return node
return fix_missing_locations(Call(Name('Symbol', Load()),
[Str(node.id)], [], None, None))
def visit_Lambda(self, node):
args = [self.visit(arg) for arg in node.args.args]
body = self.visit(node.body)
n = Call(Name('Lambda', Load()),
[Tuple(args, Load()), body], [], None, None)
return fix_missing_locations(n)
def parse_expr(s, local_dict):
"""
Converts the string "s" to a SymPy expression, in local_dict.
It converts all numbers to Integers before feeding it to Python and
automatically creates Symbols.
"""
global_dict = {}
exec_('from sympy import *', global_dict)
try:
a = parse(s.strip(), mode="eval")
except SyntaxError:
raise SympifyError("Cannot parse %s." % repr(s))
a = Transform(local_dict, global_dict).visit(a)
e = compile(a, "<string>", "eval")
return eval(e, global_dict, local_dict)
| 2,811 | 32.47619 | 77 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/parsing/tests/test_mathematica.py
|
from sympy.parsing.mathematica import mathematica
from sympy import sympify
def test_mathematica():
d = {
'- 6x': '-6*x',
'Sin[x]^2': 'sin(x)**2',
'2(x-1)': '2*(x-1)',
'3y+8': '3*y+8',
'Arcsin[2x+9(4-x)^2]/x': 'asin(2*x+9*(4-x)**2)/x',
'x+y': 'x+y',
'355/113': '355/113',
'2.718281828': '2.718281828',
'Sin[12]': 'sin(12)',
'Exp[Log[4]]': 'exp(log(4))',
'(x+1)(x+3)': '(x+1)*(x+3)',
'Cos[Arccos[3.6]]': 'cos(acos(3.6))',
'Cos[x]==Sin[y]': 'cos(x)==sin(y)',
'2*Sin[x+y]': '2*sin(x+y)',
'Sin[x]+Cos[y]': 'sin(x)+cos(y)',
'Sin[Cos[x]]': 'sin(cos(x))',
'2*Sqrt[x+y]': '2*sqrt(x+y)'} # Test case from the issue 4259
for e in d:
assert mathematica(e) == sympify(d[e])
| 818 | 30.5 | 71 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/parsing/tests/test_implicit_multiplication_application.py
|
import sympy
from sympy.parsing.sympy_parser import (
parse_expr,
standard_transformations,
convert_xor,
implicit_multiplication_application,
implicit_multiplication,
implicit_application,
function_exponentiation,
split_symbols,
split_symbols_custom,
_token_splittable
)
from sympy.utilities.pytest import raises
def test_implicit_multiplication():
cases = {
'5x': '5*x',
'abc': 'a*b*c',
'3sin(x)': '3*sin(x)',
'(x+1)(x+2)': '(x+1)*(x+2)',
'(5 x**2)sin(x)': '(5*x**2)*sin(x)',
'2 sin(x) cos(x)': '2*sin(x)*cos(x)',
'pi x': 'pi*x',
'x pi': 'x*pi',
'E x': 'E*x',
'EulerGamma y': 'EulerGamma*y',
'E pi': 'E*pi',
'pi (x + 2)': 'pi*(x+2)',
'(x + 2) pi': '(x+2)*pi',
'pi sin(x)': 'pi*sin(x)',
}
transformations = standard_transformations + (convert_xor,)
transformations2 = transformations + (split_symbols,
implicit_multiplication)
for case in cases:
implicit = parse_expr(case, transformations=transformations2)
normal = parse_expr(cases[case], transformations=transformations)
assert(implicit == normal)
application = ['sin x', 'cos 2*x', 'sin cos x']
for case in application:
raises(SyntaxError,
lambda: parse_expr(case, transformations=transformations2))
raises(TypeError,
lambda: parse_expr('sin**2(x)', transformations=transformations2))
def test_implicit_application():
cases = {
'factorial': 'factorial',
'sin x': 'sin(x)',
'tan y**3': 'tan(y**3)',
'cos 2*x': 'cos(2*x)',
'(cot)': 'cot',
'sin cos tan x': 'sin(cos(tan(x)))'
}
transformations = standard_transformations + (convert_xor,)
transformations2 = transformations + (implicit_application,)
for case in cases:
implicit = parse_expr(case, transformations=transformations2)
normal = parse_expr(cases[case], transformations=transformations)
assert(implicit == normal)
multiplication = ['x y', 'x sin x', '2x']
for case in multiplication:
raises(SyntaxError,
lambda: parse_expr(case, transformations=transformations2))
raises(TypeError,
lambda: parse_expr('sin**2(x)', transformations=transformations2))
def test_function_exponentiation():
cases = {
'sin**2(x)': 'sin(x)**2',
'exp^y(z)': 'exp(z)^y',
'sin**2(E^(x))': 'sin(E^(x))**2'
}
transformations = standard_transformations + (convert_xor,)
transformations2 = transformations + (function_exponentiation,)
for case in cases:
implicit = parse_expr(case, transformations=transformations2)
normal = parse_expr(cases[case], transformations=transformations)
assert(implicit == normal)
other_implicit = ['x y', 'x sin x', '2x', 'sin x',
'cos 2*x', 'sin cos x']
for case in other_implicit:
raises(SyntaxError,
lambda: parse_expr(case, transformations=transformations2))
assert parse_expr('x**2', local_dict={ 'x': sympy.Symbol('x') },
transformations=transformations2) == parse_expr('x**2')
def test_symbol_splitting():
# By default Greek letter names should not be split (lambda is a keyword
# so skip it)
transformations = standard_transformations + (split_symbols,)
greek_letters = ('alpha', 'beta', 'gamma', 'delta', 'epsilon', 'zeta',
'eta', 'theta', 'iota', 'kappa', 'mu', 'nu', 'xi',
'omicron', 'pi', 'rho', 'sigma', 'tau', 'upsilon',
'phi', 'chi', 'psi', 'omega')
for letter in greek_letters:
assert(parse_expr(letter, transformations=transformations) ==
parse_expr(letter))
# Make sure symbol splitting resolves names
transformations += (implicit_multiplication,)
local_dict = { 'e': sympy.E }
cases = {
'xe': 'E*x',
'Iy': 'I*y',
'ee': 'E*E',
}
for case, expected in cases.items():
assert(parse_expr(case, local_dict=local_dict,
transformations=transformations) ==
parse_expr(expected))
# Make sure custom splitting works
def can_split(symbol):
if symbol not in ('unsplittable', 'names'):
return _token_splittable(symbol)
return False
transformations = standard_transformations
transformations += (split_symbols_custom(can_split),
implicit_multiplication)
assert(parse_expr('unsplittable', transformations=transformations) ==
parse_expr('unsplittable'))
assert(parse_expr('names', transformations=transformations) ==
parse_expr('names'))
assert(parse_expr('xy', transformations=transformations) ==
parse_expr('x*y'))
for letter in greek_letters:
assert(parse_expr(letter, transformations=transformations) ==
parse_expr(letter))
def test_all_implicit_steps():
cases = {
'2x': '2*x', # implicit multiplication
'x y': 'x*y',
'xy': 'x*y',
'sin x': 'sin(x)', # add parentheses
'2sin x': '2*sin(x)',
'x y z': 'x*y*z',
'sin(2 * 3x)': 'sin(2 * 3 * x)',
'sin(x) (1 + cos(x))': 'sin(x) * (1 + cos(x))',
'(x + 2) sin(x)': '(x + 2) * sin(x)',
'(x + 2) sin x': '(x + 2) * sin(x)',
'sin(sin x)': 'sin(sin(x))',
'sin x!': 'sin(factorial(x))',
'sin x!!': 'sin(factorial2(x))',
'factorial': 'factorial', # don't apply a bare function
'x sin x': 'x * sin(x)', # both application and multiplication
'xy sin x': 'x * y * sin(x)',
'(x+2)(x+3)': '(x + 2) * (x+3)',
'x**2 + 2xy + y**2': 'x**2 + 2 * x * y + y**2', # split the xy
'pi': 'pi', # don't mess with constants
'None': 'None',
'ln sin x': 'ln(sin(x))', # multiple implicit function applications
'factorial': 'factorial', # don't add parentheses
'sin x**2': 'sin(x**2)', # implicit application to an exponential
'alpha': 'Symbol("alpha")', # don't split Greek letters/subscripts
'x_2': 'Symbol("x_2")',
'sin^2 x**2': 'sin(x**2)**2', # function raised to a power
'sin**3(x)': 'sin(x)**3',
'(factorial)': 'factorial',
'tan 3x': 'tan(3*x)',
'sin^2(3*E^(x))': 'sin(3*E**(x))**2',
'sin**2(E^(3x))': 'sin(E**(3*x))**2',
'sin^2 (3x*E^(x))': 'sin(3*x*E^x)**2',
'pi sin x': 'pi*sin(x)',
}
transformations = standard_transformations + (convert_xor,)
transformations2 = transformations + (implicit_multiplication_application,)
for case in cases:
implicit = parse_expr(case, transformations=transformations2)
normal = parse_expr(cases[case], transformations=transformations)
assert(implicit == normal)
| 6,984 | 36.553763 | 79 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/parsing/tests/test_sympy_parser.py
|
from sympy.core import Symbol, Function, Float, Rational, Integer, I, Mul, Pow, Eq
from sympy.functions import exp, factorial, sin
from sympy.logic import And
from sympy.series import Limit
from sympy.utilities.pytest import raises
from sympy.parsing.sympy_parser import (
parse_expr, standard_transformations, rationalize, TokenError,
split_symbols, implicit_multiplication, convert_equals_signs,
)
def test_sympy_parser():
x = Symbol('x')
inputs = {
'2*x': 2 * x,
'3.00': Float(3),
'22/7': Rational(22, 7),
'2+3j': 2 + 3*I,
'exp(x)': exp(x),
'x!': factorial(x),
'3.[3]': Rational(10, 3),
'10!': 3628800,
'-(2)': -Integer(2),
'[-1, -2, 3]': [Integer(-1), Integer(-2), Integer(3)],
'Symbol("x").free_symbols': x.free_symbols,
"S('S(3).n(n=3)')": 3.00,
'factorint(12, visual=True)': Mul(
Pow(2, 2, evaluate=False),
Pow(3, 1, evaluate=False),
evaluate=False),
'Limit(sin(x), x, 0, dir="-")': Limit(sin(x), x, 0, dir='-'),
}
for text, result in inputs.items():
assert parse_expr(text) == result
def test_rationalize():
inputs = {
'0.123': Rational(123, 1000)
}
transformations = standard_transformations + (rationalize,)
for text, result in inputs.items():
assert parse_expr(text, transformations=transformations) == result
def test_factorial_fail():
inputs = ['x!!!', 'x!!!!', '(!)']
for text in inputs:
try:
parse_expr(text)
assert False
except TokenError:
assert True
def test_local_dict():
local_dict = {
'my_function': lambda x: x + 2
}
inputs = {
'my_function(2)': Integer(4)
}
for text, result in inputs.items():
assert parse_expr(text, local_dict=local_dict) == result
def test_global_dict():
global_dict = {
'Symbol': Symbol
}
inputs = {
'Q & S': And(Symbol('Q'), Symbol('S'))
}
for text, result in inputs.items():
assert parse_expr(text, global_dict=global_dict) == result
def test_issue_2515():
raises(TokenError, lambda: parse_expr('(()'))
raises(TokenError, lambda: parse_expr('"""'))
def test_issue_7663():
x = Symbol('x')
e = '2*(x+1)'
assert parse_expr(e, evaluate=0) == parse_expr(e, evaluate=False)
def test_issue_10560():
inputs = {
'4*-3' : '(-3)*4',
'-4*3' : '(-4)*3',
}
for text, result in inputs.items():
assert parse_expr(text, evaluate=False) == parse_expr(result, evaluate=False)
def test_issue_10773():
inputs = {
'-10/5': '(-10)/5',
'-10/-5' : '(-10)/(-5)',
}
for text, result in inputs.items():
assert parse_expr(text, evaluate=False) == parse_expr(result, evaluate=False)
def test_split_symbols():
transformations = standard_transformations + \
(split_symbols, implicit_multiplication,)
x = Symbol('x')
y = Symbol('y')
xy = Symbol('xy')
assert parse_expr("xy") == xy
assert parse_expr("xy", transformations=transformations) == x*y
def test_split_symbols_function():
transformations = standard_transformations + \
(split_symbols, implicit_multiplication,)
x = Symbol('x')
y = Symbol('y')
a = Symbol('a')
f = Function('f')
assert parse_expr("ay(x+1)", transformations=transformations) == a*y*(x+1)
assert parse_expr("af(x+1)", transformations=transformations,
local_dict={'f':f}) == a*f(x+1)
def test_match_parentheses_implicit_multiplication():
transformations = standard_transformations + \
(implicit_multiplication,)
raises(TokenError, lambda: parse_expr('(1,2),(3,4]',transformations=transformations))
def test_convert_equals_signs():
transformations = standard_transformations + \
(convert_equals_signs, )
x = Symbol('x')
y = Symbol('y')
assert parse_expr("1*2=x", transformations=transformations) == Eq(2, x)
assert parse_expr("y = x", transformations=transformations) == Eq(y, x)
assert parse_expr("(2*y = x) = False",
transformations=transformations) == Eq(Eq(2*y, x), False)
| 4,284 | 28.551724 | 89 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/parsing/tests/__init__.py
| 0 | 0 | 0 |
py
|
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/parsing/tests/test_maxima.py
|
from sympy.parsing.maxima import parse_maxima
from sympy import Rational, Abs, Symbol, sin, cos, E, oo, log, factorial
from sympy.abc import x
n = Symbol('n', integer=True)
def test_parser():
assert Abs(parse_maxima('float(1/3)') - 0.333333333) < 10**(-5)
assert parse_maxima('13^26') == 91733330193268616658399616009
assert parse_maxima('sin(%pi/2) + cos(%pi/3)') == Rational(3, 2)
assert parse_maxima('log(%e)') == 1
def test_injection():
parse_maxima('c: x+1', globals=globals())
assert c == x + 1
parse_maxima('g: sqrt(81)', globals=globals())
assert g == 9
def test_maxima_functions():
assert parse_maxima('expand( (x+1)^2)') == x**2 + 2*x + 1
assert parse_maxima('factor( x**2 + 2*x + 1)') == (x + 1)**2
assert parse_maxima('2*cos(x)^2 + sin(x)^2') == 2*cos(x)**2 + sin(x)**2
assert parse_maxima('trigexpand(sin(2*x)+cos(2*x))') == \
-1 + 2*cos(x)**2 + 2*cos(x)*sin(x)
assert parse_maxima('solve(x^2-4,x)') == [-2, 2]
assert parse_maxima('limit((1+1/x)^x,x,inf)') == E
assert parse_maxima('limit(sqrt(-x)/x,x,0,minus)') == -oo
assert parse_maxima('diff(x^x, x)') == x**x*(1 + log(x))
assert parse_maxima('sum(k, k, 1, n)', name_dict=dict(
n=Symbol('n', integer=True),
k=Symbol('k', integer=True)
)) == (n**2 + n)/2
assert parse_maxima('product(k, k, 1, n)', name_dict=dict(
n=Symbol('n', integer=True),
k=Symbol('k', integer=True)
)) == factorial(n)
assert parse_maxima('ratsimp((x^2-1)/(x+1))') == x - 1
assert Abs( parse_maxima(
'float(sec(%pi/3) + csc(%pi/3))') - 3.154700538379252) < 10**(-5)
| 1,647 | 36.454545 | 75 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/experimental_lambdify.py
|
""" rewrite of lambdify - This stuff is not stable at all.
It is for internal use in the new plotting module.
It may (will! see the Q'n'A in the source) be rewritten.
It's completely self contained. Especially it does not use lambdarepr.
It does not aim to replace the current lambdify. Most importantly it will never
ever support anything else than sympy expressions (no Matrices, dictionaries
and so on).
"""
from __future__ import print_function, division
import re
from sympy import Symbol, NumberSymbol, I, zoo, oo
from sympy.core.compatibility import exec_
from sympy.utilities.iterables import numbered_symbols
# We parse the expression string into a tree that identifies functions. Then
# we translate the names of the functions and we translate also some strings
# that are not names of functions (all this according to translation
# dictionaries).
# If the translation goes to another module (like numpy) the
# module is imported and 'func' is translated to 'module.func'.
# If a function can not be translated, the inner nodes of that part of the
# tree are not translated. So if we have Integral(sqrt(x)), sqrt is not
# translated to np.sqrt and the Integral does not crash.
# A namespace for all this is generated by crawling the (func, args) tree of
# the expression. The creation of this namespace involves many ugly
# workarounds.
# The namespace consists of all the names needed for the sympy expression and
# all the name of modules used for translation. Those modules are imported only
# as a name (import numpy as np) in order to keep the namespace small and
# manageable.
# Please, if there is a bug, do not try to fix it here! Rewrite this by using
# the method proposed in the last Q'n'A below. That way the new function will
# work just as well, be just as simple, but it wont need any new workarounds.
# If you insist on fixing it here, look at the workarounds in the function
# sympy_expression_namespace and in lambdify.
# Q: Why are you not using python abstract syntax tree?
# A: Because it is more complicated and not much more powerful in this case.
# Q: What if I have Symbol('sin') or g=Function('f')?
# A: You will break the algorithm. We should use srepr to defend against this?
# The problem with Symbol('sin') is that it will be printed as 'sin'. The
# parser will distinguish it from the function 'sin' because functions are
# detected thanks to the opening parenthesis, but the lambda expression won't
# understand the difference if we have also the sin function.
# The solution (complicated) is to use srepr and maybe ast.
# The problem with the g=Function('f') is that it will be printed as 'f' but in
# the global namespace we have only 'g'. But as the same printer is used in the
# constructor of the namespace there will be no problem.
# Q: What if some of the printers are not printing as expected?
# A: The algorithm wont work. You must use srepr for those cases. But even
# srepr may not print well. All problems with printers should be considered
# bugs.
# Q: What about _imp_ functions?
# A: Those are taken care for by evalf. A special case treatment will work
# faster but it's not worth the code complexity.
# Q: Will ast fix all possible problems?
# A: No. You will always have to use some printer. Even srepr may not work in
# some cases. But if the printer does not work, that should be considered a
# bug.
# Q: Is there same way to fix all possible problems?
# A: Probably by constructing our strings ourself by traversing the (func,
# args) tree and creating the namespace at the same time. That actually sounds
# good.
from sympy.external import import_module
import warnings
#TODO debuging output
class vectorized_lambdify(object):
""" Return a sufficiently smart, vectorized and lambdified function.
Returns only reals.
This function uses experimental_lambdify to created a lambdified
expression ready to be used with numpy. Many of the functions in sympy
are not implemented in numpy so in some cases we resort to python cmath or
even to evalf.
The following translations are tried:
only numpy complex
- on errors raised by sympy trying to work with ndarray:
only python cmath and then vectorize complex128
When using python cmath there is no need for evalf or float/complex
because python cmath calls those.
This function never tries to mix numpy directly with evalf because numpy
does not understand sympy Float. If this is needed one can use the
float_wrap_evalf/complex_wrap_evalf options of experimental_lambdify or
better one can be explicit about the dtypes that numpy works with.
Check numpy bug http://projects.scipy.org/numpy/ticket/1013 to know what
types of errors to expect.
"""
def __init__(self, args, expr):
self.args = args
self.expr = expr
self.lambda_func = experimental_lambdify(args, expr, use_np=True)
self.vector_func = self.lambda_func
self.failure = False
def __call__(self, *args):
np = import_module('numpy')
np_old_err = np.seterr(invalid='raise')
try:
temp_args = (np.array(a, dtype=np.complex) for a in args)
results = self.vector_func(*temp_args)
results = np.ma.masked_where(
np.abs(results.imag) > 1e-7 * np.abs(results),
results.real, copy=False)
except Exception as e:
#DEBUG: print 'Error', type(e), e
if ((isinstance(e, TypeError)
and 'unhashable type: \'numpy.ndarray\'' in str(e))
or
(isinstance(e, ValueError)
and ('Invalid limits given:' in str(e)
or 'negative dimensions are not allowed' in str(e) # XXX
or 'sequence too large; must be smaller than 32' in str(e)))): # XXX
# Almost all functions were translated to numpy, but some were
# left as sympy functions. They recieved an ndarray as an
# argument and failed.
# sin(ndarray(...)) raises "unhashable type"
# Integral(x, (x, 0, ndarray(...))) raises "Invalid limits"
# other ugly exceptions that are not well understood (marked with XXX)
# TODO: Cleanup the ugly special cases marked with xxx above.
# Solution: use cmath and vectorize the final lambda.
self.lambda_func = experimental_lambdify(
self.args, self.expr, use_python_cmath=True)
self.vector_func = np.vectorize(
self.lambda_func, otypes=[np.complex])
results = self.vector_func(*args)
results = np.ma.masked_where(
np.abs(results.imag) > 1e-7 * np.abs(results),
results.real, copy=False)
else:
# Complete failure. One last try with no translations, only
# wrapping in complex((...).evalf()) and returning the real
# part.
if self.failure:
raise e
else:
self.failure = True
self.lambda_func = experimental_lambdify(
self.args, self.expr, use_evalf=True,
complex_wrap_evalf=True)
self.vector_func = np.vectorize(
self.lambda_func, otypes=[np.complex])
results = self.vector_func(*args)
results = np.ma.masked_where(
np.abs(results.imag) > 1e-7 * np.abs(results),
results.real, copy=False)
warnings.warn('The evaluation of the expression is'
' problematic. We are trying a failback method'
' that may still work. Please report this as a bug.')
finally:
np.seterr(**np_old_err)
return results
class lambdify(object):
"""Returns the lambdified function.
This function uses experimental_lambdify to create a lambdified
expression. It uses cmath to lambdify the expression. If the function
is not implemented in python cmath, python cmath calls evalf on those
functions.
"""
def __init__(self, args, expr):
self.args = args
self.expr = expr
self.lambda_func = experimental_lambdify(args, expr, use_evalf=True,
use_python_cmath=True)
self.failure = False
def __call__(self, args):
args = complex(args)
try:
#The result can be sympy.Float. Hence wrap it with complex type.
result = complex(self.lambda_func(args))
if abs(result.imag) > 1e-7 * abs(result):
return None
else:
return result.real
except Exception as e:
# The exceptions raised by sympy, cmath are not consistent and
# hence it is not possible to specify all the exceptions that
# are to be caught. Presently there are no cases for which the code
# reaches this block other than ZeroDivisionError and complex
# comparision. Also the exception is caught only once. If the
# exception repeats itself,
# then it is not caught and the corresponding error is raised.
# XXX: Remove catching all exceptions once the plotting module
# is heavily tested.
if isinstance(e, ZeroDivisionError):
return None
elif isinstance(e, TypeError) and ('no ordering relation is'
' defined for complex numbers'
in str(e) or 'unorderable '
'types' in str(e) or "'>' not "
"supported between instances of"
in str(e)):
self.lambda_func = experimental_lambdify(self.args, self.expr,
use_evalf=True,
use_python_math=True)
result = self.lambda_func(args.real)
return result
else:
if self.failure:
raise e
#Failure
#Try wrapping it with complex(..).evalf()
self.failure = True
self.lambda_func = experimental_lambdify(self.args, self.expr,
use_evalf=True,
complex_wrap_evalf=True)
result = self.lambda_func(args)
warnings.warn('The evaluation of the expression is'
' problematic. We are trying a failback method'
' that may still work. Please report this as a bug.')
if abs(result.imag) > 1e-7 * abs(result):
return None
else:
return result.real
def experimental_lambdify(*args, **kwargs):
l = Lambdifier(*args, **kwargs)
return l
class Lambdifier(object):
def __init__(self, args, expr, print_lambda=False, use_evalf=False,
float_wrap_evalf=False, complex_wrap_evalf=False,
use_np=False, use_python_math=False, use_python_cmath=False,
use_interval=False):
self.print_lambda = print_lambda
self.use_evalf = use_evalf
self.float_wrap_evalf = float_wrap_evalf
self.complex_wrap_evalf = complex_wrap_evalf
self.use_np = use_np
self.use_python_math = use_python_math
self.use_python_cmath = use_python_cmath
self.use_interval = use_interval
# Constructing the argument string
# - check
if not all([isinstance(a, Symbol) for a in args]):
raise ValueError('The arguments must be Symbols.')
# - use numbered symbols
syms = numbered_symbols(exclude=expr.free_symbols)
newargs = [next(syms) for i in args]
expr = expr.xreplace(dict(zip(args, newargs)))
argstr = ', '.join([str(a) for a in newargs])
del syms, newargs, args
# Constructing the translation dictionaries and making the translation
self.dict_str = self.get_dict_str()
self.dict_fun = self.get_dict_fun()
exprstr = str(expr)
# the & and | operators don't work on tuples, see discussion #12108
exprstr = exprstr.replace(" & "," and ").replace(" | "," or ")
newexpr = self.tree2str_translate(self.str2tree(exprstr))
# Constructing the namespaces
namespace = {}
namespace.update(self.sympy_atoms_namespace(expr))
namespace.update(self.sympy_expression_namespace(expr))
# XXX Workaround
# Ugly workaround because Pow(a,Half) prints as sqrt(a)
# and sympy_expression_namespace can not catch it.
from sympy import sqrt
namespace.update({'sqrt': sqrt})
namespace.update({'Eq': lambda x, y: x == y})
# End workaround.
if use_python_math:
namespace.update({'math': __import__('math')})
if use_python_cmath:
namespace.update({'cmath': __import__('cmath')})
if use_np:
try:
namespace.update({'np': __import__('numpy')})
except ImportError:
raise ImportError(
'experimental_lambdify failed to import numpy.')
if use_interval:
namespace.update({'imath': __import__(
'sympy.plotting.intervalmath', fromlist=['intervalmath'])})
namespace.update({'math': __import__('math')})
# Construct the lambda
if self.print_lambda:
print(newexpr)
eval_str = 'lambda %s : ( %s )' % (argstr, newexpr)
self.eval_str = eval_str
exec_("from __future__ import division; MYNEWLAMBDA = %s" % eval_str, namespace)
self.lambda_func = namespace['MYNEWLAMBDA']
def __call__(self, *args, **kwargs):
return self.lambda_func(*args, **kwargs)
##############################################################################
# Dicts for translating from sympy to other modules
##############################################################################
###
# builtins
###
# Functions with different names in builtins
builtin_functions_different = {
'Min': 'min',
'Max': 'max',
'Abs': 'abs',
}
# Strings that should be translated
builtin_not_functions = {
'I': '1j',
# 'oo': '1e400',
}
###
# numpy
###
# Functions that are the same in numpy
numpy_functions_same = [
'sin', 'cos', 'tan', 'sinh', 'cosh', 'tanh', 'exp', 'log',
'sqrt', 'floor', 'conjugate',
]
# Functions with different names in numpy
numpy_functions_different = {
"acos": "arccos",
"acosh": "arccosh",
"arg": "angle",
"asin": "arcsin",
"asinh": "arcsinh",
"atan": "arctan",
"atan2": "arctan2",
"atanh": "arctanh",
"ceiling": "ceil",
"im": "imag",
"ln": "log",
"Max": "amax",
"Min": "amin",
"re": "real",
"Abs": "abs",
}
# Strings that should be translated
numpy_not_functions = {
'pi': 'np.pi',
'oo': 'np.inf',
'E': 'np.e',
}
###
# python math
###
# Functions that are the same in math
math_functions_same = [
'sin', 'cos', 'tan', 'asin', 'acos', 'atan', 'atan2',
'sinh', 'cosh', 'tanh', 'asinh', 'acosh', 'atanh',
'exp', 'log', 'erf', 'sqrt', 'floor', 'factorial', 'gamma',
]
# Functions with different names in math
math_functions_different = {
'ceiling': 'ceil',
'ln': 'log',
'loggamma': 'lgamma'
}
# Strings that should be translated
math_not_functions = {
'pi': 'math.pi',
'E': 'math.e',
}
###
# python cmath
###
# Functions that are the same in cmath
cmath_functions_same = [
'sin', 'cos', 'tan', 'asin', 'acos', 'atan',
'sinh', 'cosh', 'tanh', 'asinh', 'acosh', 'atanh',
'exp', 'log', 'sqrt',
]
# Functions with different names in cmath
cmath_functions_different = {
'ln': 'log',
'arg': 'phase',
}
# Strings that should be translated
cmath_not_functions = {
'pi': 'cmath.pi',
'E': 'cmath.e',
}
###
# intervalmath
###
interval_not_functions = {
'pi': 'math.pi',
'E': 'math.e'
}
interval_functions_same = [
'sin', 'cos', 'exp', 'tan', 'atan', 'log',
'sqrt', 'cosh', 'sinh', 'tanh', 'floor',
'acos', 'asin', 'acosh', 'asinh', 'atanh',
'Abs', 'And', 'Or'
]
interval_functions_different = {
'Min': 'imin',
'Max': 'imax',
'ceiling': 'ceil',
}
###
# mpmath, etc
###
#TODO
###
# Create the final ordered tuples of dictionaries
###
# For strings
def get_dict_str(self):
dict_str = dict(self.builtin_not_functions)
if self.use_np:
dict_str.update(self.numpy_not_functions)
if self.use_python_math:
dict_str.update(self.math_not_functions)
if self.use_python_cmath:
dict_str.update(self.cmath_not_functions)
if self.use_interval:
dict_str.update(self.interval_not_functions)
return dict_str
# For functions
def get_dict_fun(self):
dict_fun = dict(self.builtin_functions_different)
if self.use_np:
for s in self.numpy_functions_same:
dict_fun[s] = 'np.' + s
for k, v in self.numpy_functions_different.items():
dict_fun[k] = 'np.' + v
if self.use_python_math:
for s in self.math_functions_same:
dict_fun[s] = 'math.' + s
for k, v in self.math_functions_different.items():
dict_fun[k] = 'math.' + v
if self.use_python_cmath:
for s in self.cmath_functions_same:
dict_fun[s] = 'cmath.' + s
for k, v in self.cmath_functions_different.items():
dict_fun[k] = 'cmath.' + v
if self.use_interval:
for s in self.interval_functions_same:
dict_fun[s] = 'imath.' + s
for k, v in self.interval_functions_different.items():
dict_fun[k] = 'imath.' + v
return dict_fun
##############################################################################
# The translator functions, tree parsers, etc.
##############################################################################
def str2tree(self, exprstr):
"""Converts an expression string to a tree.
Functions are represented by ('func_name(', tree_of_arguments).
Other expressions are (head_string, mid_tree, tail_str).
Expressions that do not contain functions are directly returned.
Examples
========
>>> from sympy.abc import x, y, z
>>> from sympy import Integral, sin
>>> from sympy.plotting.experimental_lambdify import Lambdifier
>>> str2tree = Lambdifier([x], x).str2tree
>>> str2tree(str(Integral(x, (x, 1, y))))
('', ('Integral(', 'x, (x, 1, y)'), ')')
>>> str2tree(str(x+y))
'x + y'
>>> str2tree(str(x+y*sin(z)+1))
('x + y*', ('sin(', 'z'), ') + 1')
>>> str2tree('sin(y*(y + 1.1) + (sin(y)))')
('', ('sin(', ('y*(y + 1.1) + (', ('sin(', 'y'), '))')), ')')
"""
#matches the first 'function_name('
first_par = re.search(r'(\w+\()', exprstr)
if first_par is None:
return exprstr
else:
start = first_par.start()
end = first_par.end()
head = exprstr[:start]
func = exprstr[start:end]
tail = exprstr[end:]
count = 0
for i, c in enumerate(tail):
if c == '(':
count += 1
elif c == ')':
count -= 1
if count == -1:
break
func_tail = self.str2tree(tail[:i])
tail = self.str2tree(tail[i:])
return (head, (func, func_tail), tail)
@classmethod
def tree2str(cls, tree):
"""Converts a tree to string without translations.
Examples
========
>>> from sympy.abc import x, y, z
>>> from sympy import Integral, sin
>>> from sympy.plotting.experimental_lambdify import Lambdifier
>>> str2tree = Lambdifier([x], x).str2tree
>>> tree2str = Lambdifier([x], x).tree2str
>>> tree2str(str2tree(str(x+y*sin(z)+1)))
'x + y*sin(z) + 1'
"""
if isinstance(tree, str):
return tree
else:
return ''.join(map(cls.tree2str, tree))
def tree2str_translate(self, tree):
"""Converts a tree to string with translations.
Function names are translated by translate_func.
Other strings are translated by translate_str.
"""
if isinstance(tree, str):
return self.translate_str(tree)
elif isinstance(tree, tuple) and len(tree) == 2:
return self.translate_func(tree[0][:-1], tree[1])
else:
return ''.join([self.tree2str_translate(t) for t in tree])
def translate_str(self, estr):
"""Translate substrings of estr using in order the dictionaries in
dict_tuple_str."""
for pattern, repl in self.dict_str.items():
estr = re.sub(pattern, repl, estr)
return estr
def translate_func(self, func_name, argtree):
"""Translate function names and the tree of arguments.
If the function name is not in the dictionaries of dict_tuple_fun then the
function is surrounded by a float((...).evalf()).
The use of float is necessary as np.<function>(sympy.Float(..)) raises an
error."""
if func_name in self.dict_fun:
new_name = self.dict_fun[func_name]
argstr = self.tree2str_translate(argtree)
return new_name + '(' + argstr
else:
template = '(%s(%s)).evalf(' if self.use_evalf else '%s(%s'
if self.float_wrap_evalf:
template = 'float(%s)' % template
elif self.complex_wrap_evalf:
template = 'complex(%s)' % template
# Wrapping should only happen on the outermost expression, which
# is the only thing we know will be a number.
float_wrap_evalf = self.float_wrap_evalf
complex_wrap_evalf = self.complex_wrap_evalf
self.float_wrap_evalf = False
self.complex_wrap_evalf = False
ret = template % (func_name, self.tree2str_translate(argtree))
self.float_wrap_evalf = float_wrap_evalf
self.complex_wrap_evalf = complex_wrap_evalf
return ret
##############################################################################
# The namespace constructors
##############################################################################
@classmethod
def sympy_expression_namespace(cls, expr):
"""Traverses the (func, args) tree of an expression and creates a sympy
namespace. All other modules are imported only as a module name. That way
the namespace is not poluted and rests quite small. It probably causes much
more variable lookups and so it takes more time, but there are no tests on
that for the moment."""
if expr is None:
return {}
else:
funcname = str(expr.func)
# XXX Workaround
# Here we add an ugly workaround because str(func(x))
# is not always the same as str(func). Eg
# >>> str(Integral(x))
# "Integral(x)"
# >>> str(Integral)
# "<class 'sympy.integrals.integrals.Integral'>"
# >>> str(sqrt(x))
# "sqrt(x)"
# >>> str(sqrt)
# "<function sqrt at 0x3d92de8>"
# >>> str(sin(x))
# "sin(x)"
# >>> str(sin)
# "sin"
# Either one of those can be used but not all at the same time.
# The code considers the sin example as the right one.
regexlist = [
r'<class \'sympy[\w.]*?.([\w]*)\'>$',
# the example Integral
r'<function ([\w]*) at 0x[\w]*>$', # the example sqrt
]
for r in regexlist:
m = re.match(r, funcname)
if m is not None:
funcname = m.groups()[0]
# End of the workaround
# XXX debug: print funcname
args_dict = {}
for a in expr.args:
if (isinstance(a, Symbol) or
isinstance(a, NumberSymbol) or
a in [I, zoo, oo]):
continue
else:
args_dict.update(cls.sympy_expression_namespace(a))
args_dict.update({funcname: expr.func})
return args_dict
@staticmethod
def sympy_atoms_namespace(expr):
"""For no real reason this function is separated from
sympy_expression_namespace. It can be moved to it."""
atoms = expr.atoms(Symbol, NumberSymbol, I, zoo, oo)
d = {}
for a in atoms:
# XXX debug: print 'atom:' + str(a)
d[str(a)] = a
return d
| 26,136 | 37.664201 | 91 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/plot_implicit.py
|
"""Implicit plotting module for SymPy
The module implements a data series called ImplicitSeries which is used by
``Plot`` class to plot implicit plots for different backends. The module,
by default, implements plotting using interval arithmetic. It switches to a
fall back algorithm if the expression cannot be plotted using interval arithmetic.
It is also possible to specify to use the fall back algorithm for all plots.
Boolean combinations of expressions cannot be plotted by the fall back
algorithm.
See Also
========
sympy.plotting.plot
References
==========
- Jeffrey Allen Tupper. Reliable Two-Dimensional Graphing Methods for
Mathematical Formulae with Two Free Variables.
- Jeffrey Allen Tupper. Graphing Equations with Generalized Interval
Arithmetic. Master's thesis. University of Toronto, 1996
"""
from __future__ import print_function, division
from .plot import BaseSeries, Plot
from .experimental_lambdify import experimental_lambdify, vectorized_lambdify
from .intervalmath import interval
from sympy.core.relational import (Equality, GreaterThan, LessThan,
Relational, StrictLessThan, StrictGreaterThan)
from sympy import Eq, Tuple, sympify, Symbol, Dummy
from sympy.external import import_module
from sympy.logic.boolalg import BooleanFunction
from sympy.polys.polyutils import _sort_gens
from sympy.utilities.decorator import doctest_depends_on
from sympy.utilities.iterables import flatten
import warnings
class ImplicitSeries(BaseSeries):
""" Representation for Implicit plot """
is_implicit = True
def __init__(self, expr, var_start_end_x, var_start_end_y,
has_equality, use_interval_math, depth, nb_of_points,
line_color):
super(ImplicitSeries, self).__init__()
self.expr = sympify(expr)
self.var_x = sympify(var_start_end_x[0])
self.start_x = float(var_start_end_x[1])
self.end_x = float(var_start_end_x[2])
self.var_y = sympify(var_start_end_y[0])
self.start_y = float(var_start_end_y[1])
self.end_y = float(var_start_end_y[2])
self.get_points = self.get_raster
self.has_equality = has_equality # If the expression has equality, i.e.
#Eq, Greaterthan, LessThan.
self.nb_of_points = nb_of_points
self.use_interval_math = use_interval_math
self.depth = 4 + depth
self.line_color = line_color
def __str__(self):
return ('Implicit equation: %s for '
'%s over %s and %s over %s') % (
str(self.expr),
str(self.var_x),
str((self.start_x, self.end_x)),
str(self.var_y),
str((self.start_y, self.end_y)))
def get_raster(self):
func = experimental_lambdify((self.var_x, self.var_y), self.expr,
use_interval=True)
xinterval = interval(self.start_x, self.end_x)
yinterval = interval(self.start_y, self.end_y)
try:
temp = func(xinterval, yinterval)
except AttributeError:
if self.use_interval_math:
warnings.warn("Adaptive meshing could not be applied to the"
" expression. Using uniform meshing.")
self.use_interval_math = False
if self.use_interval_math:
return self._get_raster_interval(func)
else:
return self._get_meshes_grid()
def _get_raster_interval(self, func):
""" Uses interval math to adaptively mesh and obtain the plot"""
k = self.depth
interval_list = []
#Create initial 32 divisions
np = import_module('numpy')
xsample = np.linspace(self.start_x, self.end_x, 33)
ysample = np.linspace(self.start_y, self.end_y, 33)
#Add a small jitter so that there are no false positives for equality.
# Ex: y==x becomes True for x interval(1, 2) and y interval(1, 2)
#which will draw a rectangle.
jitterx = (np.random.rand(
len(xsample)) * 2 - 1) * (self.end_x - self.start_x) / 2**20
jittery = (np.random.rand(
len(ysample)) * 2 - 1) * (self.end_y - self.start_y) / 2**20
xsample += jitterx
ysample += jittery
xinter = [interval(x1, x2) for x1, x2 in zip(xsample[:-1],
xsample[1:])]
yinter = [interval(y1, y2) for y1, y2 in zip(ysample[:-1],
ysample[1:])]
interval_list = [[x, y] for x in xinter for y in yinter]
plot_list = []
#recursive call refinepixels which subdivides the intervals which are
#neither True nor False according to the expression.
def refine_pixels(interval_list):
""" Evaluates the intervals and subdivides the interval if the
expression is partially satisfied."""
temp_interval_list = []
plot_list = []
for intervals in interval_list:
#Convert the array indices to x and y values
intervalx = intervals[0]
intervaly = intervals[1]
func_eval = func(intervalx, intervaly)
#The expression is valid in the interval. Change the contour
#array values to 1.
if func_eval[1] is False or func_eval[0] is False:
pass
elif func_eval == (True, True):
plot_list.append([intervalx, intervaly])
elif func_eval[1] is None or func_eval[0] is None:
#Subdivide
avgx = intervalx.mid
avgy = intervaly.mid
a = interval(intervalx.start, avgx)
b = interval(avgx, intervalx.end)
c = interval(intervaly.start, avgy)
d = interval(avgy, intervaly.end)
temp_interval_list.append([a, c])
temp_interval_list.append([a, d])
temp_interval_list.append([b, c])
temp_interval_list.append([b, d])
return temp_interval_list, plot_list
while k >= 0 and len(interval_list):
interval_list, plot_list_temp = refine_pixels(interval_list)
plot_list.extend(plot_list_temp)
k = k - 1
#Check whether the expression represents an equality
#If it represents an equality, then none of the intervals
#would have satisfied the expression due to floating point
#differences. Add all the undecided values to the plot.
if self.has_equality:
for intervals in interval_list:
intervalx = intervals[0]
intervaly = intervals[1]
func_eval = func(intervalx, intervaly)
if func_eval[1] and func_eval[0] is not False:
plot_list.append([intervalx, intervaly])
return plot_list, 'fill'
def _get_meshes_grid(self):
"""Generates the mesh for generating a contour.
In the case of equality, ``contour`` function of matplotlib can
be used. In other cases, matplotlib's ``contourf`` is used.
"""
equal = False
if isinstance(self.expr, Equality):
expr = self.expr.lhs - self.expr.rhs
equal = True
elif isinstance(self.expr, (GreaterThan, StrictGreaterThan)):
expr = self.expr.lhs - self.expr.rhs
elif isinstance(self.expr, (LessThan, StrictLessThan)):
expr = self.expr.rhs - self.expr.lhs
else:
raise NotImplementedError("The expression is not supported for "
"plotting in uniform meshed plot.")
np = import_module('numpy')
xarray = np.linspace(self.start_x, self.end_x, self.nb_of_points)
yarray = np.linspace(self.start_y, self.end_y, self.nb_of_points)
x_grid, y_grid = np.meshgrid(xarray, yarray)
func = vectorized_lambdify((self.var_x, self.var_y), expr)
z_grid = func(x_grid, y_grid)
z_grid[np.ma.where(z_grid < 0)] = -1
z_grid[np.ma.where(z_grid > 0)] = 1
if equal:
return xarray, yarray, z_grid, 'contour'
else:
return xarray, yarray, z_grid, 'contourf'
@doctest_depends_on(modules=('matplotlib',))
def plot_implicit(expr, x_var=None, y_var=None, **kwargs):
"""A plot function to plot implicit equations / inequalities.
Arguments
=========
- ``expr`` : The equation / inequality that is to be plotted.
- ``x_var`` (optional) : symbol to plot on x-axis or tuple giving symbol
and range as ``(symbol, xmin, xmax)``
- ``y_var`` (optional) : symbol to plot on y-axis or tuple giving symbol
and range as ``(symbol, ymin, ymax)``
If neither ``x_var`` nor ``y_var`` are given then the free symbols in the
expression will be assigned in the order they are sorted.
The following keyword arguments can also be used:
- ``adaptive``. Boolean. The default value is set to True. It has to be
set to False if you want to use a mesh grid.
- ``depth`` integer. The depth of recursion for adaptive mesh grid.
Default value is 0. Takes value in the range (0, 4).
- ``points`` integer. The number of points if adaptive mesh grid is not
used. Default value is 200.
- ``title`` string .The title for the plot.
- ``xlabel`` string. The label for the x-axis
- ``ylabel`` string. The label for the y-axis
Aesthetics options:
- ``line_color``: float or string. Specifies the color for the plot.
See ``Plot`` to see how to set color for the plots.
plot_implicit, by default, uses interval arithmetic to plot functions. If
the expression cannot be plotted using interval arithmetic, it defaults to
a generating a contour using a mesh grid of fixed number of points. By
setting adaptive to False, you can force plot_implicit to use the mesh
grid. The mesh grid method can be effective when adaptive plotting using
interval arithmetic, fails to plot with small line width.
Examples
========
Plot expressions:
>>> from sympy import plot_implicit, cos, sin, symbols, Eq, And
>>> x, y = symbols('x y')
Without any ranges for the symbols in the expression
>>> p1 = plot_implicit(Eq(x**2 + y**2, 5))
With the range for the symbols
>>> p2 = plot_implicit(Eq(x**2 + y**2, 3),
... (x, -3, 3), (y, -3, 3))
With depth of recursion as argument.
>>> p3 = plot_implicit(Eq(x**2 + y**2, 5),
... (x, -4, 4), (y, -4, 4), depth = 2)
Using mesh grid and not using adaptive meshing.
>>> p4 = plot_implicit(Eq(x**2 + y**2, 5),
... (x, -5, 5), (y, -2, 2), adaptive=False)
Using mesh grid with number of points as input.
>>> p5 = plot_implicit(Eq(x**2 + y**2, 5),
... (x, -5, 5), (y, -2, 2),
... adaptive=False, points=400)
Plotting regions.
>>> p6 = plot_implicit(y > x**2)
Plotting Using boolean conjunctions.
>>> p7 = plot_implicit(And(y > x, y > -x))
When plotting an expression with a single variable (y - 1, for example),
specify the x or the y variable explicitly:
>>> p8 = plot_implicit(y - 1, y_var=y)
>>> p9 = plot_implicit(x - 1, x_var=x)
"""
has_equality = False # Represents whether the expression contains an Equality,
#GreaterThan or LessThan
def arg_expand(bool_expr):
"""
Recursively expands the arguments of an Boolean Function
"""
for arg in bool_expr.args:
if isinstance(arg, BooleanFunction):
arg_expand(arg)
elif isinstance(arg, Relational):
arg_list.append(arg)
arg_list = []
if isinstance(expr, BooleanFunction):
arg_expand(expr)
#Check whether there is an equality in the expression provided.
if any(isinstance(e, (Equality, GreaterThan, LessThan))
for e in arg_list):
has_equality = True
elif not isinstance(expr, Relational):
expr = Eq(expr, 0)
has_equality = True
elif isinstance(expr, (Equality, GreaterThan, LessThan)):
has_equality = True
xyvar = [i for i in (x_var, y_var) if i is not None]
free_symbols = expr.free_symbols
range_symbols = Tuple(*flatten(xyvar)).free_symbols
undeclared = free_symbols - range_symbols
if len(free_symbols & range_symbols) > 2:
raise NotImplementedError("Implicit plotting is not implemented for "
"more than 2 variables")
#Create default ranges if the range is not provided.
default_range = Tuple(-5, 5)
def _range_tuple(s):
if isinstance(s, Symbol):
return Tuple(s) + default_range
if len(s) == 3:
return Tuple(*s)
raise ValueError('symbol or `(symbol, min, max)` expected but got %s' % s)
if len(xyvar) == 0:
xyvar = list(_sort_gens(free_symbols))
var_start_end_x = _range_tuple(xyvar[0])
x = var_start_end_x[0]
if len(xyvar) != 2:
if x in undeclared or not undeclared:
xyvar.append(Dummy('f(%s)' % x.name))
else:
xyvar.append(undeclared.pop())
var_start_end_y = _range_tuple(xyvar[1])
use_interval = kwargs.pop('adaptive', True)
nb_of_points = kwargs.pop('points', 300)
depth = kwargs.pop('depth', 0)
line_color = kwargs.pop('line_color', "blue")
#Check whether the depth is greater than 4 or less than 0.
if depth > 4:
depth = 4
elif depth < 0:
depth = 0
series_argument = ImplicitSeries(expr, var_start_end_x, var_start_end_y,
has_equality, use_interval, depth,
nb_of_points, line_color)
show = kwargs.pop('show', True)
#set the x and y limits
kwargs['xlim'] = tuple(float(x) for x in var_start_end_x[1:])
kwargs['ylim'] = tuple(float(y) for y in var_start_end_y[1:])
# set the x and y labels
kwargs.setdefault('xlabel', var_start_end_x[0].name)
kwargs.setdefault('ylabel', var_start_end_y[0].name)
p = Plot(series_argument, **kwargs)
if show:
p.show()
return p
| 14,400 | 37.300532 | 83 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/textplot.py
|
from __future__ import print_function, division
from sympy.core.symbol import Dummy
from sympy.core.compatibility import range
from sympy.utilities.lambdify import lambdify
def textplot(expr, a, b, W=55, H=18):
"""
Print a crude ASCII art plot of the SymPy expression 'expr' (which
should contain a single symbol, e.g. x or something else) over the
interval [a, b].
Examples
========
textplot(sin(t)*t, 0, 15)
"""
free = expr.free_symbols
if len(free) > 1:
raise ValueError("length can not be greater than 1")
x = free.pop() if free else Dummy()
f = lambdify([x], expr)
a = float(a)
b = float(b)
# Calculate function values
y = [0] * W
for x in range(W):
try:
y[x] = f(a + (b - a)/float(W)*x)
except (TypeError, ValueError):
y[x] = 0
# Normalize height to screen space
ma = max(y)
mi = min(y)
if ma == mi:
if ma:
mi, ma = sorted([0, 2*ma])
else:
mi, ma = -1, 1
for x in range(W):
y[x] = int(float(H)*(y[x] - mi)/(ma - mi))
margin = 7
print
for h in range(H - 1, -1, -1):
s = [' '] * W
for x in range(W):
if y[x] == h:
if (x == 0 or y[x - 1] == h - 1) and (x == W - 1 or y[x + 1] == h + 1):
s[x] = '/'
elif (x == 0 or y[x - 1] == h + 1) and (x == W - 1 or y[x + 1] == h - 1):
s[x] = '\\'
else:
s[x] = '.'
# Print y values
if h == H - 1:
prefix = ("%g" % ma).rjust(margin)[:margin]
elif h == H//2:
prefix = ("%g" % ((mi + ma)/2)).rjust(margin)[:margin]
elif h == 0:
prefix = ("%g" % mi).rjust(margin)[:margin]
else:
prefix = " "*margin
s = "".join(s)
if h == H//2:
s = s.replace(" ", "-")
print(prefix + " | " + s)
# Print x values
bottom = " " * (margin + 3)
bottom += ("%g" % a).ljust(W//2 - 4)
bottom += ("%g" % ((a + b)/2)).ljust(W//2)
bottom += "%g" % b
print(bottom)
| 2,162 | 26.0375 | 89 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/plot.py
|
"""Plotting module for Sympy.
A plot is represented by the ``Plot`` class that contains a reference to the
backend and a list of the data series to be plotted. The data series are
instances of classes meant to simplify getting points and meshes from sympy
expressions. ``plot_backends`` is a dictionary with all the backends.
This module gives only the essential. For all the fancy stuff use directly
the backend. You can get the backend wrapper for every plot from the
``_backend`` attribute. Moreover the data series classes have various useful
methods like ``get_points``, ``get_segments``, ``get_meshes``, etc, that may
be useful if you wish to use another plotting library.
Especially if you need publication ready graphs and this module is not enough
for you - just get the ``_backend`` attribute and add whatever you want
directly to it. In the case of matplotlib (the common way to graph data in
python) just copy ``_backend.fig`` which is the figure and ``_backend.ax``
which is the axis and work on them as you would on any other matplotlib object.
Simplicity of code takes much greater importance than performance. Don't use it
if you care at all about performance. A new backend instance is initialized
every time you call ``show()`` and the old one is left to the garbage collector.
"""
from __future__ import print_function, division
import inspect
from collections import Callable
import warnings
import sys
from sympy import sympify, Expr, Tuple, Dummy, Symbol
from sympy.external import import_module
from sympy.core.compatibility import range
from sympy.utilities.decorator import doctest_depends_on
from sympy.utilities.iterables import is_sequence
from .experimental_lambdify import (vectorized_lambdify, lambdify)
# N.B.
# When changing the minimum module version for matplotlib, please change
# the same in the `SymPyDocTestFinder`` in `sympy/utilities/runtests.py`
# Backend specific imports - textplot
from sympy.plotting.textplot import textplot
# Global variable
# Set to False when running tests / doctests so that the plots don't show.
_show = True
def unset_show():
global _show
_show = False
##############################################################################
# The public interface
##############################################################################
def _arity(f):
"""
Python 2 and 3 compatible version that do not raise a Deprecation warning.
"""
if sys.version_info < (3,):
return len(inspect.getargspec(f)[0])
else:
param = inspect.signature(f).parameters.values()
return len([p for p in param if p.kind == p.POSITIONAL_OR_KEYWORD])
class Plot(object):
"""The central class of the plotting module.
For interactive work the function ``plot`` is better suited.
This class permits the plotting of sympy expressions using numerous
backends (matplotlib, textplot, the old pyglet module for sympy, Google
charts api, etc).
The figure can contain an arbitrary number of plots of sympy expressions,
lists of coordinates of points, etc. Plot has a private attribute _series that
contains all data series to be plotted (expressions for lines or surfaces,
lists of points, etc (all subclasses of BaseSeries)). Those data series are
instances of classes not imported by ``from sympy import *``.
The customization of the figure is on two levels. Global options that
concern the figure as a whole (eg title, xlabel, scale, etc) and
per-data series options (eg name) and aesthetics (eg. color, point shape,
line type, etc.).
The difference between options and aesthetics is that an aesthetic can be
a function of the coordinates (or parameters in a parametric plot). The
supported values for an aesthetic are:
- None (the backend uses default values)
- a constant
- a function of one variable (the first coordinate or parameter)
- a function of two variables (the first and second coordinate or
parameters)
- a function of three variables (only in nonparametric 3D plots)
Their implementation depends on the backend so they may not work in some
backends.
If the plot is parametric and the arity of the aesthetic function permits
it the aesthetic is calculated over parameters and not over coordinates.
If the arity does not permit calculation over parameters the calculation is
done over coordinates.
Only cartesian coordinates are supported for the moment, but you can use
the parametric plots to plot in polar, spherical and cylindrical
coordinates.
The arguments for the constructor Plot must be subclasses of BaseSeries.
Any global option can be specified as a keyword argument.
The global options for a figure are:
- title : str
- xlabel : str
- ylabel : str
- legend : bool
- xscale : {'linear', 'log'}
- yscale : {'linear', 'log'}
- axis : bool
- axis_center : tuple of two floats or {'center', 'auto'}
- xlim : tuple of two floats
- ylim : tuple of two floats
- aspect_ratio : tuple of two floats or {'auto'}
- autoscale : bool
- margin : float in [0, 1]
The per data series options and aesthetics are:
There are none in the base series. See below for options for subclasses.
Some data series support additional aesthetics or options:
ListSeries, LineOver1DRangeSeries, Parametric2DLineSeries,
Parametric3DLineSeries support the following:
Aesthetics:
- line_color : function which returns a float.
options:
- label : str
- steps : bool
- integers_only : bool
SurfaceOver2DRangeSeries, ParametricSurfaceSeries support the following:
aesthetics:
- surface_color : function which returns a float.
"""
def __init__(self, *args, **kwargs):
super(Plot, self).__init__()
# Options for the graph as a whole.
# The possible values for each option are described in the docstring of
# Plot. They are based purely on convention, no checking is done.
self.title = None
self.xlabel = None
self.ylabel = None
self.aspect_ratio = 'auto'
self.xlim = None
self.ylim = None
self.axis_center = 'auto'
self.axis = True
self.xscale = 'linear'
self.yscale = 'linear'
self.legend = False
self.autoscale = True
self.margin = 0
# Contains the data objects to be plotted. The backend should be smart
# enough to iterate over this list.
self._series = []
self._series.extend(args)
# The backend type. On every show() a new backend instance is created
# in self._backend which is tightly coupled to the Plot instance
# (thanks to the parent attribute of the backend).
self.backend = DefaultBackend
# The keyword arguments should only contain options for the plot.
for key, val in kwargs.items():
if hasattr(self, key):
setattr(self, key, val)
def show(self):
# TODO move this to the backend (also for save)
if hasattr(self, '_backend'):
self._backend.close()
self._backend = self.backend(self)
self._backend.show()
def save(self, path):
if hasattr(self, '_backend'):
self._backend.close()
self._backend = self.backend(self)
self._backend.save(path)
def __str__(self):
series_strs = [('[%d]: ' % i) + str(s)
for i, s in enumerate(self._series)]
return 'Plot object containing:\n' + '\n'.join(series_strs)
def __getitem__(self, index):
return self._series[index]
def __setitem__(self, index, *args):
if len(args) == 1 and isinstance(args[0], BaseSeries):
self._series[index] = args
def __delitem__(self, index):
del self._series[index]
@doctest_depends_on(modules=('numpy', 'matplotlib',))
def append(self, arg):
"""Adds an element from a plot's series to an existing plot.
Examples
========
Consider two ``Plot`` objects, ``p1`` and ``p2``. To add the
second plot's first series object to the first, use the
``append`` method, like so:
>>> from sympy import symbols
>>> from sympy.plotting import plot
>>> x = symbols('x')
>>> p1 = plot(x*x)
>>> p2 = plot(x)
>>> p1.append(p2[0])
>>> p1
Plot object containing:
[0]: cartesian line: x**2 for x over (-10.0, 10.0)
[1]: cartesian line: x for x over (-10.0, 10.0)
See Also
========
extend
"""
if isinstance(arg, BaseSeries):
self._series.append(arg)
else:
raise TypeError('Must specify element of plot to append.')
@doctest_depends_on(modules=('numpy', 'matplotlib',))
def extend(self, arg):
"""Adds all series from another plot.
Examples
========
Consider two ``Plot`` objects, ``p1`` and ``p2``. To add the
second plot to the first, use the ``extend`` method, like so:
>>> from sympy import symbols
>>> from sympy.plotting import plot
>>> x = symbols('x')
>>> p1 = plot(x*x)
>>> p2 = plot(x)
>>> p1.extend(p2)
>>> p1
Plot object containing:
[0]: cartesian line: x**2 for x over (-10.0, 10.0)
[1]: cartesian line: x for x over (-10.0, 10.0)
"""
if isinstance(arg, Plot):
self._series.extend(arg._series)
elif is_sequence(arg):
self._series.extend(arg)
else:
raise TypeError('Expecting Plot or sequence of BaseSeries')
##############################################################################
# Data Series
##############################################################################
#TODO more general way to calculate aesthetics (see get_color_array)
### The base class for all series
class BaseSeries(object):
"""Base class for the data objects containing stuff to be plotted.
The backend should check if it supports the data series that it's given.
(eg TextBackend supports only LineOver1DRange).
It's the backend responsibility to know how to use the class of
data series that it's given.
Some data series classes are grouped (using a class attribute like is_2Dline)
according to the api they present (based only on convention). The backend is
not obliged to use that api (eg. The LineOver1DRange belongs to the
is_2Dline group and presents the get_points method, but the
TextBackend does not use the get_points method).
"""
# Some flags follow. The rationale for using flags instead of checking base
# classes is that setting multiple flags is simpler than multiple
# inheritance.
is_2Dline = False
# Some of the backends expect:
# - get_points returning 1D np.arrays list_x, list_y
# - get_segments returning np.array (done in Line2DBaseSeries)
# - get_color_array returning 1D np.array (done in Line2DBaseSeries)
# with the colors calculated at the points from get_points
is_3Dline = False
# Some of the backends expect:
# - get_points returning 1D np.arrays list_x, list_y, list_y
# - get_segments returning np.array (done in Line2DBaseSeries)
# - get_color_array returning 1D np.array (done in Line2DBaseSeries)
# with the colors calculated at the points from get_points
is_3Dsurface = False
# Some of the backends expect:
# - get_meshes returning mesh_x, mesh_y, mesh_z (2D np.arrays)
# - get_points an alias for get_meshes
is_contour = False
# Some of the backends expect:
# - get_meshes returning mesh_x, mesh_y, mesh_z (2D np.arrays)
# - get_points an alias for get_meshes
is_implicit = False
# Some of the backends expect:
# - get_meshes returning mesh_x (1D array), mesh_y(1D array,
# mesh_z (2D np.arrays)
# - get_points an alias for get_meshes
#Different from is_contour as the colormap in backend will be
#different
is_parametric = False
# The calculation of aesthetics expects:
# - get_parameter_points returning one or two np.arrays (1D or 2D)
# used for calculation aesthetics
def __init__(self):
super(BaseSeries, self).__init__()
@property
def is_3D(self):
flags3D = [
self.is_3Dline,
self.is_3Dsurface
]
return any(flags3D)
@property
def is_line(self):
flagslines = [
self.is_2Dline,
self.is_3Dline
]
return any(flagslines)
### 2D lines
class Line2DBaseSeries(BaseSeries):
"""A base class for 2D lines.
- adding the label, steps and only_integers options
- making is_2Dline true
- defining get_segments and get_color_array
"""
is_2Dline = True
_dim = 2
def __init__(self):
super(Line2DBaseSeries, self).__init__()
self.label = None
self.steps = False
self.only_integers = False
self.line_color = None
def get_segments(self):
np = import_module('numpy')
points = self.get_points()
if self.steps is True:
x = np.array((points[0], points[0])).T.flatten()[1:]
y = np.array((points[1], points[1])).T.flatten()[:-1]
points = (x, y)
points = np.ma.array(points).T.reshape(-1, 1, self._dim)
return np.ma.concatenate([points[:-1], points[1:]], axis=1)
def get_color_array(self):
np = import_module('numpy')
c = self.line_color
if hasattr(c, '__call__'):
f = np.vectorize(c)
arity = _arity(c)
if arity == 1 and self.is_parametric:
x = self.get_parameter_points()
return f(centers_of_segments(x))
else:
variables = list(map(centers_of_segments, self.get_points()))
if arity == 1:
return f(variables[0])
elif arity == 2:
return f(*variables[:2])
else: # only if the line is 3D (otherwise raises an error)
return f(*variables)
else:
return c*np.ones(self.nb_of_points)
class List2DSeries(Line2DBaseSeries):
"""Representation for a line consisting of list of points."""
def __init__(self, list_x, list_y):
np = import_module('numpy')
super(List2DSeries, self).__init__()
self.list_x = np.array(list_x)
self.list_y = np.array(list_y)
self.label = 'list'
def __str__(self):
return 'list plot'
def get_points(self):
return (self.list_x, self.list_y)
class LineOver1DRangeSeries(Line2DBaseSeries):
"""Representation for a line consisting of a SymPy expression over a range."""
def __init__(self, expr, var_start_end, **kwargs):
super(LineOver1DRangeSeries, self).__init__()
self.expr = sympify(expr)
self.label = str(self.expr)
self.var = sympify(var_start_end[0])
self.start = float(var_start_end[1])
self.end = float(var_start_end[2])
self.nb_of_points = kwargs.get('nb_of_points', 300)
self.adaptive = kwargs.get('adaptive', True)
self.depth = kwargs.get('depth', 12)
self.line_color = kwargs.get('line_color', None)
def __str__(self):
return 'cartesian line: %s for %s over %s' % (
str(self.expr), str(self.var), str((self.start, self.end)))
def get_segments(self):
"""
Adaptively gets segments for plotting.
The adaptive sampling is done by recursively checking if three
points are almost collinear. If they are not collinear, then more
points are added between those points.
References
==========
[1] Adaptive polygonal approximation of parametric curves,
Luiz Henrique de Figueiredo.
"""
if self.only_integers or not self.adaptive:
return super(LineOver1DRangeSeries, self).get_segments()
else:
f = lambdify([self.var], self.expr)
list_segments = []
def sample(p, q, depth):
""" Samples recursively if three points are almost collinear.
For depth < 6, points are added irrespective of whether they
satisfy the collinearity condition or not. The maximum depth
allowed is 12.
"""
np = import_module('numpy')
#Randomly sample to avoid aliasing.
random = 0.45 + np.random.rand() * 0.1
xnew = p[0] + random * (q[0] - p[0])
ynew = f(xnew)
new_point = np.array([xnew, ynew])
#Maximum depth
if depth > self.depth:
list_segments.append([p, q])
#Sample irrespective of whether the line is flat till the
#depth of 6. We are not using linspace to avoid aliasing.
elif depth < 6:
sample(p, new_point, depth + 1)
sample(new_point, q, depth + 1)
#Sample ten points if complex values are encountered
#at both ends. If there is a real value in between, then
#sample those points further.
elif p[1] is None and q[1] is None:
xarray = np.linspace(p[0], q[0], 10)
yarray = list(map(f, xarray))
if any(y is not None for y in yarray):
for i in range(len(yarray) - 1):
if yarray[i] is not None or yarray[i + 1] is not None:
sample([xarray[i], yarray[i]],
[xarray[i + 1], yarray[i + 1]], depth + 1)
#Sample further if one of the end points in None( i.e. a complex
#value) or the three points are not almost collinear.
elif (p[1] is None or q[1] is None or new_point[1] is None
or not flat(p, new_point, q)):
sample(p, new_point, depth + 1)
sample(new_point, q, depth + 1)
else:
list_segments.append([p, q])
f_start = f(self.start)
f_end = f(self.end)
sample([self.start, f_start], [self.end, f_end], 0)
return list_segments
def get_points(self):
np = import_module('numpy')
if self.only_integers is True:
list_x = np.linspace(int(self.start), int(self.end),
num=int(self.end) - int(self.start) + 1)
else:
list_x = np.linspace(self.start, self.end, num=self.nb_of_points)
f = vectorized_lambdify([self.var], self.expr)
list_y = f(list_x)
return (list_x, list_y)
class Parametric2DLineSeries(Line2DBaseSeries):
"""Representation for a line consisting of two parametric sympy expressions
over a range."""
is_parametric = True
def __init__(self, expr_x, expr_y, var_start_end, **kwargs):
super(Parametric2DLineSeries, self).__init__()
self.expr_x = sympify(expr_x)
self.expr_y = sympify(expr_y)
self.label = "(%s, %s)" % (str(self.expr_x), str(self.expr_y))
self.var = sympify(var_start_end[0])
self.start = float(var_start_end[1])
self.end = float(var_start_end[2])
self.nb_of_points = kwargs.get('nb_of_points', 300)
self.adaptive = kwargs.get('adaptive', True)
self.depth = kwargs.get('depth', 12)
self.line_color = kwargs.get('line_color', None)
def __str__(self):
return 'parametric cartesian line: (%s, %s) for %s over %s' % (
str(self.expr_x), str(self.expr_y), str(self.var),
str((self.start, self.end)))
def get_parameter_points(self):
np = import_module('numpy')
return np.linspace(self.start, self.end, num=self.nb_of_points)
def get_points(self):
param = self.get_parameter_points()
fx = vectorized_lambdify([self.var], self.expr_x)
fy = vectorized_lambdify([self.var], self.expr_y)
list_x = fx(param)
list_y = fy(param)
return (list_x, list_y)
def get_segments(self):
"""
Adaptively gets segments for plotting.
The adaptive sampling is done by recursively checking if three
points are almost collinear. If they are not collinear, then more
points are added between those points.
References
==========
[1] Adaptive polygonal approximation of parametric curves,
Luiz Henrique de Figueiredo.
"""
if not self.adaptive:
return super(Parametric2DLineSeries, self).get_segments()
f_x = lambdify([self.var], self.expr_x)
f_y = lambdify([self.var], self.expr_y)
list_segments = []
def sample(param_p, param_q, p, q, depth):
""" Samples recursively if three points are almost collinear.
For depth < 6, points are added irrespective of whether they
satisfy the collinearity condition or not. The maximum depth
allowed is 12.
"""
#Randomly sample to avoid aliasing.
np = import_module('numpy')
random = 0.45 + np.random.rand() * 0.1
param_new = param_p + random * (param_q - param_p)
xnew = f_x(param_new)
ynew = f_y(param_new)
new_point = np.array([xnew, ynew])
#Maximum depth
if depth > self.depth:
list_segments.append([p, q])
#Sample irrespective of whether the line is flat till the
#depth of 6. We are not using linspace to avoid aliasing.
elif depth < 6:
sample(param_p, param_new, p, new_point, depth + 1)
sample(param_new, param_q, new_point, q, depth + 1)
#Sample ten points if complex values are encountered
#at both ends. If there is a real value in between, then
#sample those points further.
elif ((p[0] is None and q[1] is None) or
(p[1] is None and q[1] is None)):
param_array = np.linspace(param_p, param_q, 10)
x_array = list(map(f_x, param_array))
y_array = list(map(f_y, param_array))
if any(x is not None and y is not None
for x, y in zip(x_array, y_array)):
for i in range(len(y_array) - 1):
if ((x_array[i] is not None and y_array[i] is not None) or
(x_array[i + 1] is not None and y_array[i + 1] is not None)):
point_a = [x_array[i], y_array[i]]
point_b = [x_array[i + 1], y_array[i + 1]]
sample(param_array[i], param_array[i], point_a,
point_b, depth + 1)
#Sample further if one of the end points in None( ie a complex
#value) or the three points are not almost collinear.
elif (p[0] is None or p[1] is None
or q[1] is None or q[0] is None
or not flat(p, new_point, q)):
sample(param_p, param_new, p, new_point, depth + 1)
sample(param_new, param_q, new_point, q, depth + 1)
else:
list_segments.append([p, q])
f_start_x = f_x(self.start)
f_start_y = f_y(self.start)
start = [f_start_x, f_start_y]
f_end_x = f_x(self.end)
f_end_y = f_y(self.end)
end = [f_end_x, f_end_y]
sample(self.start, self.end, start, end, 0)
return list_segments
### 3D lines
class Line3DBaseSeries(Line2DBaseSeries):
"""A base class for 3D lines.
Most of the stuff is derived from Line2DBaseSeries."""
is_2Dline = False
is_3Dline = True
_dim = 3
def __init__(self):
super(Line3DBaseSeries, self).__init__()
class Parametric3DLineSeries(Line3DBaseSeries):
"""Representation for a 3D line consisting of two parametric sympy
expressions and a range."""
def __init__(self, expr_x, expr_y, expr_z, var_start_end, **kwargs):
super(Parametric3DLineSeries, self).__init__()
self.expr_x = sympify(expr_x)
self.expr_y = sympify(expr_y)
self.expr_z = sympify(expr_z)
self.label = "(%s, %s)" % (str(self.expr_x), str(self.expr_y))
self.var = sympify(var_start_end[0])
self.start = float(var_start_end[1])
self.end = float(var_start_end[2])
self.nb_of_points = kwargs.get('nb_of_points', 300)
self.line_color = kwargs.get('line_color', None)
def __str__(self):
return '3D parametric cartesian line: (%s, %s, %s) for %s over %s' % (
str(self.expr_x), str(self.expr_y), str(self.expr_z),
str(self.var), str((self.start, self.end)))
def get_parameter_points(self):
np = import_module('numpy')
return np.linspace(self.start, self.end, num=self.nb_of_points)
def get_points(self):
param = self.get_parameter_points()
fx = vectorized_lambdify([self.var], self.expr_x)
fy = vectorized_lambdify([self.var], self.expr_y)
fz = vectorized_lambdify([self.var], self.expr_z)
list_x = fx(param)
list_y = fy(param)
list_z = fz(param)
return (list_x, list_y, list_z)
### Surfaces
class SurfaceBaseSeries(BaseSeries):
"""A base class for 3D surfaces."""
is_3Dsurface = True
def __init__(self):
super(SurfaceBaseSeries, self).__init__()
self.surface_color = None
def get_color_array(self):
np = import_module('numpy')
c = self.surface_color
if isinstance(c, Callable):
f = np.vectorize(c)
arity = _arity(c)
if self.is_parametric:
variables = list(map(centers_of_faces, self.get_parameter_meshes()))
if arity == 1:
return f(variables[0])
elif arity == 2:
return f(*variables)
variables = list(map(centers_of_faces, self.get_meshes()))
if arity == 1:
return f(variables[0])
elif arity == 2:
return f(*variables[:2])
else:
return f(*variables)
else:
return c*np.ones(self.nb_of_points)
class SurfaceOver2DRangeSeries(SurfaceBaseSeries):
"""Representation for a 3D surface consisting of a sympy expression and 2D
range."""
def __init__(self, expr, var_start_end_x, var_start_end_y, **kwargs):
super(SurfaceOver2DRangeSeries, self).__init__()
self.expr = sympify(expr)
self.var_x = sympify(var_start_end_x[0])
self.start_x = float(var_start_end_x[1])
self.end_x = float(var_start_end_x[2])
self.var_y = sympify(var_start_end_y[0])
self.start_y = float(var_start_end_y[1])
self.end_y = float(var_start_end_y[2])
self.nb_of_points_x = kwargs.get('nb_of_points_x', 50)
self.nb_of_points_y = kwargs.get('nb_of_points_y', 50)
self.surface_color = kwargs.get('surface_color', None)
def __str__(self):
return ('cartesian surface: %s for'
' %s over %s and %s over %s') % (
str(self.expr),
str(self.var_x),
str((self.start_x, self.end_x)),
str(self.var_y),
str((self.start_y, self.end_y)))
def get_meshes(self):
np = import_module('numpy')
mesh_x, mesh_y = np.meshgrid(np.linspace(self.start_x, self.end_x,
num=self.nb_of_points_x),
np.linspace(self.start_y, self.end_y,
num=self.nb_of_points_y))
f = vectorized_lambdify((self.var_x, self.var_y), self.expr)
return (mesh_x, mesh_y, f(mesh_x, mesh_y))
class ParametricSurfaceSeries(SurfaceBaseSeries):
"""Representation for a 3D surface consisting of three parametric sympy
expressions and a range."""
is_parametric = True
def __init__(
self, expr_x, expr_y, expr_z, var_start_end_u, var_start_end_v,
**kwargs):
super(ParametricSurfaceSeries, self).__init__()
self.expr_x = sympify(expr_x)
self.expr_y = sympify(expr_y)
self.expr_z = sympify(expr_z)
self.var_u = sympify(var_start_end_u[0])
self.start_u = float(var_start_end_u[1])
self.end_u = float(var_start_end_u[2])
self.var_v = sympify(var_start_end_v[0])
self.start_v = float(var_start_end_v[1])
self.end_v = float(var_start_end_v[2])
self.nb_of_points_u = kwargs.get('nb_of_points_u', 50)
self.nb_of_points_v = kwargs.get('nb_of_points_v', 50)
self.surface_color = kwargs.get('surface_color', None)
def __str__(self):
return ('parametric cartesian surface: (%s, %s, %s) for'
' %s over %s and %s over %s') % (
str(self.expr_x),
str(self.expr_y),
str(self.expr_z),
str(self.var_u),
str((self.start_u, self.end_u)),
str(self.var_v),
str((self.start_v, self.end_v)))
def get_parameter_meshes(self):
np = import_module('numpy')
return np.meshgrid(np.linspace(self.start_u, self.end_u,
num=self.nb_of_points_u),
np.linspace(self.start_v, self.end_v,
num=self.nb_of_points_v))
def get_meshes(self):
mesh_u, mesh_v = self.get_parameter_meshes()
fx = vectorized_lambdify((self.var_u, self.var_v), self.expr_x)
fy = vectorized_lambdify((self.var_u, self.var_v), self.expr_y)
fz = vectorized_lambdify((self.var_u, self.var_v), self.expr_z)
return (fx(mesh_u, mesh_v), fy(mesh_u, mesh_v), fz(mesh_u, mesh_v))
### Contours
class ContourSeries(BaseSeries):
"""Representation for a contour plot."""
#The code is mostly repetition of SurfaceOver2DRange.
#XXX: Presently not used in any of those functions.
#XXX: Add contour plot and use this seties.
is_contour = True
def __init__(self, expr, var_start_end_x, var_start_end_y):
super(ContourSeries, self).__init__()
self.nb_of_points_x = 50
self.nb_of_points_y = 50
self.expr = sympify(expr)
self.var_x = sympify(var_start_end_x[0])
self.start_x = float(var_start_end_x[1])
self.end_x = float(var_start_end_x[2])
self.var_y = sympify(var_start_end_y[0])
self.start_y = float(var_start_end_y[1])
self.end_y = float(var_start_end_y[2])
self.get_points = self.get_meshes
def __str__(self):
return ('contour: %s for '
'%s over %s and %s over %s') % (
str(self.expr),
str(self.var_x),
str((self.start_x, self.end_x)),
str(self.var_y),
str((self.start_y, self.end_y)))
def get_meshes(self):
np = import_module('numpy')
mesh_x, mesh_y = np.meshgrid(np.linspace(self.start_x, self.end_x,
num=self.nb_of_points_x),
np.linspace(self.start_y, self.end_y,
num=self.nb_of_points_y))
f = vectorized_lambdify((self.var_x, self.var_y), self.expr)
return (mesh_x, mesh_y, f(mesh_x, mesh_y))
##############################################################################
# Backends
##############################################################################
class BaseBackend(object):
def __init__(self, parent):
super(BaseBackend, self).__init__()
self.parent = parent
## don't have to check for the success of importing matplotlib in each case;
## we will only be using this backend if we can successfully import matploblib
class MatplotlibBackend(BaseBackend):
def __init__(self, parent):
super(MatplotlibBackend, self).__init__(parent)
are_3D = [s.is_3D for s in self.parent._series]
self.matplotlib = import_module('matplotlib',
__import__kwargs={'fromlist': ['pyplot', 'cm', 'collections']},
min_module_version='1.1.0', catch=(RuntimeError,))
self.plt = self.matplotlib.pyplot
self.cm = self.matplotlib.cm
self.LineCollection = self.matplotlib.collections.LineCollection
if any(are_3D) and not all(are_3D):
raise ValueError('The matplotlib backend can not mix 2D and 3D.')
elif not any(are_3D):
self.fig = self.plt.figure()
self.ax = self.fig.add_subplot(111)
self.ax.spines['left'].set_position('zero')
self.ax.spines['right'].set_color('none')
self.ax.spines['bottom'].set_position('zero')
self.ax.spines['top'].set_color('none')
self.ax.spines['left'].set_smart_bounds(True)
self.ax.spines['bottom'].set_smart_bounds(False)
self.ax.xaxis.set_ticks_position('bottom')
self.ax.yaxis.set_ticks_position('left')
elif all(are_3D):
## mpl_toolkits.mplot3d is necessary for
## projection='3d'
mpl_toolkits = import_module('mpl_toolkits',
__import__kwargs={'fromlist': ['mplot3d']})
self.fig = self.plt.figure()
self.ax = self.fig.add_subplot(111, projection='3d')
def process_series(self):
parent = self.parent
for s in self.parent._series:
# Create the collections
if s.is_2Dline:
collection = self.LineCollection(s.get_segments())
self.ax.add_collection(collection)
elif s.is_contour:
self.ax.contour(*s.get_meshes())
elif s.is_3Dline:
# TODO too complicated, I blame matplotlib
mpl_toolkits = import_module('mpl_toolkits',
__import__kwargs={'fromlist': ['mplot3d']})
art3d = mpl_toolkits.mplot3d.art3d
collection = art3d.Line3DCollection(s.get_segments())
self.ax.add_collection(collection)
x, y, z = s.get_points()
self.ax.set_xlim((min(x), max(x)))
self.ax.set_ylim((min(y), max(y)))
self.ax.set_zlim((min(z), max(z)))
elif s.is_3Dsurface:
x, y, z = s.get_meshes()
collection = self.ax.plot_surface(x, y, z,
cmap=getattr(self.cm, 'viridis', self.cm.jet),
rstride=1, cstride=1, linewidth=0.1)
elif s.is_implicit:
#Smart bounds have to be set to False for implicit plots.
self.ax.spines['left'].set_smart_bounds(False)
self.ax.spines['bottom'].set_smart_bounds(False)
points = s.get_raster()
if len(points) == 2:
#interval math plotting
x, y = _matplotlib_list(points[0])
self.ax.fill(x, y, facecolor=s.line_color, edgecolor='None')
else:
# use contourf or contour depending on whether it is
# an inequality or equality.
#XXX: ``contour`` plots multiple lines. Should be fixed.
ListedColormap = self.matplotlib.colors.ListedColormap
colormap = ListedColormap(["white", s.line_color])
xarray, yarray, zarray, plot_type = points
if plot_type == 'contour':
self.ax.contour(xarray, yarray, zarray,
contours=(0, 0), fill=False, cmap=colormap)
else:
self.ax.contourf(xarray, yarray, zarray, cmap=colormap)
else:
raise ValueError('The matplotlib backend supports only '
'is_2Dline, is_3Dline, is_3Dsurface and '
'is_contour objects.')
# Customise the collections with the corresponding per-series
# options.
if hasattr(s, 'label'):
collection.set_label(s.label)
if s.is_line and s.line_color:
if isinstance(s.line_color, (float, int)) or isinstance(s.line_color, Callable):
color_array = s.get_color_array()
collection.set_array(color_array)
else:
collection.set_color(s.line_color)
if s.is_3Dsurface and s.surface_color:
if self.matplotlib.__version__ < "1.2.0": # TODO in the distant future remove this check
warnings.warn('The version of matplotlib is too old to use surface coloring.')
elif isinstance(s.surface_color, (float, int)) or isinstance(s.surface_color, Callable):
color_array = s.get_color_array()
color_array = color_array.reshape(color_array.size)
collection.set_array(color_array)
else:
collection.set_color(s.surface_color)
# Set global options.
# TODO The 3D stuff
# XXX The order of those is important.
mpl_toolkits = import_module('mpl_toolkits',
__import__kwargs={'fromlist': ['mplot3d']})
Axes3D = mpl_toolkits.mplot3d.Axes3D
if parent.xscale and not isinstance(self.ax, Axes3D):
self.ax.set_xscale(parent.xscale)
if parent.yscale and not isinstance(self.ax, Axes3D):
self.ax.set_yscale(parent.yscale)
if parent.xlim:
self.ax.set_xlim(parent.xlim)
else:
if all(isinstance(s, LineOver1DRangeSeries) for s in parent._series):
starts = [s.start for s in parent._series]
ends = [s.end for s in parent._series]
self.ax.set_xlim(min(starts), max(ends))
if parent.ylim:
self.ax.set_ylim(parent.ylim)
if not isinstance(self.ax, Axes3D) or self.matplotlib.__version__ >= '1.2.0': # XXX in the distant future remove this check
self.ax.set_autoscale_on(parent.autoscale)
if parent.axis_center:
val = parent.axis_center
if isinstance(self.ax, Axes3D):
pass
elif val == 'center':
self.ax.spines['left'].set_position('center')
self.ax.spines['bottom'].set_position('center')
elif val == 'auto':
xl, xh = self.ax.get_xlim()
yl, yh = self.ax.get_ylim()
pos_left = ('data', 0) if xl*xh <= 0 else 'center'
pos_bottom = ('data', 0) if yl*yh <= 0 else 'center'
self.ax.spines['left'].set_position(pos_left)
self.ax.spines['bottom'].set_position(pos_bottom)
else:
self.ax.spines['left'].set_position(('data', val[0]))
self.ax.spines['bottom'].set_position(('data', val[1]))
if not parent.axis:
self.ax.set_axis_off()
if parent.legend:
if self.ax.legend():
self.ax.legend_.set_visible(parent.legend)
if parent.margin:
self.ax.set_xmargin(parent.margin)
self.ax.set_ymargin(parent.margin)
if parent.title:
self.ax.set_title(parent.title)
if parent.xlabel:
self.ax.set_xlabel(parent.xlabel, position=(1, 0))
if parent.ylabel:
self.ax.set_ylabel(parent.ylabel, position=(0, 1))
def show(self):
self.process_series()
#TODO after fixing https://github.com/ipython/ipython/issues/1255
# you can uncomment the next line and remove the pyplot.show() call
#self.fig.show()
if _show:
self.plt.show()
def save(self, path):
self.process_series()
self.fig.savefig(path)
def close(self):
self.plt.close(self.fig)
class TextBackend(BaseBackend):
def __init__(self, parent):
super(TextBackend, self).__init__(parent)
def show(self):
if len(self.parent._series) != 1:
raise ValueError(
'The TextBackend supports only one graph per Plot.')
elif not isinstance(self.parent._series[0], LineOver1DRangeSeries):
raise ValueError(
'The TextBackend supports only expressions over a 1D range')
else:
ser = self.parent._series[0]
textplot(ser.expr, ser.start, ser.end)
def close(self):
pass
class DefaultBackend(BaseBackend):
def __new__(cls, parent):
matplotlib = import_module('matplotlib', min_module_version='1.1.0', catch=(RuntimeError,))
if matplotlib:
return MatplotlibBackend(parent)
else:
return TextBackend(parent)
plot_backends = {
'matplotlib': MatplotlibBackend,
'text': TextBackend,
'default': DefaultBackend
}
##############################################################################
# Finding the centers of line segments or mesh faces
##############################################################################
def centers_of_segments(array):
np = import_module('numpy')
return np.mean(np.vstack((array[:-1], array[1:])), 0)
def centers_of_faces(array):
np = import_module('numpy')
return np.mean(np.dstack((array[:-1, :-1],
array[1:, :-1],
array[:-1, 1: ],
array[:-1, :-1],
)), 2)
def flat(x, y, z, eps=1e-3):
"""Checks whether three points are almost collinear"""
np = import_module('numpy')
# Workaround plotting piecewise (#8577):
# workaround for `lambdify` in `.experimental_lambdify` fails
# to return numerical values in some cases. Lower-level fix
# in `lambdify` is possible.
vector_a = (x - y).astype(np.float)
vector_b = (z - y).astype(np.float)
dot_product = np.dot(vector_a, vector_b)
vector_a_norm = np.linalg.norm(vector_a)
vector_b_norm = np.linalg.norm(vector_b)
cos_theta = dot_product / (vector_a_norm * vector_b_norm)
return abs(cos_theta + 1) < eps
def _matplotlib_list(interval_list):
"""
Returns lists for matplotlib ``fill`` command from a list of bounding
rectangular intervals
"""
xlist = []
ylist = []
if len(interval_list):
for intervals in interval_list:
intervalx = intervals[0]
intervaly = intervals[1]
xlist.extend([intervalx.start, intervalx.start,
intervalx.end, intervalx.end, None])
ylist.extend([intervaly.start, intervaly.end,
intervaly.end, intervaly.start, None])
else:
#XXX Ugly hack. Matplotlib does not accept empty lists for ``fill``
xlist.extend([None, None, None, None])
ylist.extend([None, None, None, None])
return xlist, ylist
####New API for plotting module ####
# TODO: Add color arrays for plots.
# TODO: Add more plotting options for 3d plots.
# TODO: Adaptive sampling for 3D plots.
@doctest_depends_on(modules=('numpy', 'matplotlib',))
def plot(*args, **kwargs):
"""
Plots a function of a single variable and returns an instance of
the ``Plot`` class (also, see the description of the
``show`` keyword argument below).
The plotting uses an adaptive algorithm which samples recursively to
accurately plot the plot. The adaptive algorithm uses a random point near
the midpoint of two points that has to be further sampled. Hence the same
plots can appear slightly different.
Usage
=====
Single Plot
``plot(expr, range, **kwargs)``
If the range is not specified, then a default range of (-10, 10) is used.
Multiple plots with same range.
``plot(expr1, expr2, ..., range, **kwargs)``
If the range is not specified, then a default range of (-10, 10) is used.
Multiple plots with different ranges.
``plot((expr1, range), (expr2, range), ..., **kwargs)``
Range has to be specified for every expression.
Default range may change in the future if a more advanced default range
detection algorithm is implemented.
Arguments
=========
``expr`` : Expression representing the function of single variable
``range``: (x, 0, 5), A 3-tuple denoting the range of the free variable.
Keyword Arguments
=================
Arguments for ``plot`` function:
``show``: Boolean. The default value is set to ``True``. Set show to
``False`` and the function will not display the plot. The returned
instance of the ``Plot`` class can then be used to save or display
the plot by calling the ``save()`` and ``show()`` methods
respectively.
Arguments for ``LineOver1DRangeSeries`` class:
``adaptive``: Boolean. The default value is set to True. Set adaptive to False and
specify ``nb_of_points`` if uniform sampling is required.
``depth``: int Recursion depth of the adaptive algorithm. A depth of value ``n``
samples a maximum of `2^{n}` points.
``nb_of_points``: int. Used when the ``adaptive`` is set to False. The function
is uniformly sampled at ``nb_of_points`` number of points.
Aesthetics options:
``line_color``: float. Specifies the color for the plot.
See ``Plot`` to see how to set color for the plots.
If there are multiple plots, then the same series series are applied to
all the plots. If you want to set these options separately, you can index
the ``Plot`` object returned and set it.
Arguments for ``Plot`` class:
``title`` : str. Title of the plot. It is set to the latex representation of
the expression, if the plot has only one expression.
``xlabel`` : str. Label for the x-axis.
``ylabel`` : str. Label for the y-axis.
``xscale``: {'linear', 'log'} Sets the scaling of the x-axis.
``yscale``: {'linear', 'log'} Sets the scaling if the y-axis.
``axis_center``: tuple of two floats denoting the coordinates of the center or
{'center', 'auto'}
``xlim`` : tuple of two floats, denoting the x-axis limits.
``ylim`` : tuple of two floats, denoting the y-axis limits.
Examples
========
>>> from sympy import symbols
>>> from sympy.plotting import plot
>>> x = symbols('x')
Single Plot
>>> plot(x**2, (x, -5, 5))
Plot object containing:
[0]: cartesian line: x**2 for x over (-5.0, 5.0)
Multiple plots with single range.
>>> plot(x, x**2, x**3, (x, -5, 5))
Plot object containing:
[0]: cartesian line: x for x over (-5.0, 5.0)
[1]: cartesian line: x**2 for x over (-5.0, 5.0)
[2]: cartesian line: x**3 for x over (-5.0, 5.0)
Multiple plots with different ranges.
>>> plot((x**2, (x, -6, 6)), (x, (x, -5, 5)))
Plot object containing:
[0]: cartesian line: x**2 for x over (-6.0, 6.0)
[1]: cartesian line: x for x over (-5.0, 5.0)
No adaptive sampling.
>>> plot(x**2, adaptive=False, nb_of_points=400)
Plot object containing:
[0]: cartesian line: x**2 for x over (-10.0, 10.0)
See Also
========
Plot, LineOver1DRangeSeries.
"""
args = list(map(sympify, args))
free = set()
for a in args:
if isinstance(a, Expr):
free |= a.free_symbols
if len(free) > 1:
raise ValueError(
'The same variable should be used in all '
'univariate expressions being plotted.')
x = free.pop() if free else Symbol('x')
kwargs.setdefault('xlabel', x.name)
kwargs.setdefault('ylabel', 'f(%s)' % x.name)
show = kwargs.pop('show', True)
series = []
plot_expr = check_arguments(args, 1, 1)
series = [LineOver1DRangeSeries(*arg, **kwargs) for arg in plot_expr]
plots = Plot(*series, **kwargs)
if show:
plots.show()
return plots
@doctest_depends_on(modules=('numpy', 'matplotlib',))
def plot_parametric(*args, **kwargs):
"""
Plots a 2D parametric plot.
The plotting uses an adaptive algorithm which samples recursively to
accurately plot the plot. The adaptive algorithm uses a random point near
the midpoint of two points that has to be further sampled. Hence the same
plots can appear slightly different.
Usage
=====
Single plot.
``plot_parametric(expr_x, expr_y, range, **kwargs)``
If the range is not specified, then a default range of (-10, 10) is used.
Multiple plots with same range.
``plot_parametric((expr1_x, expr1_y), (expr2_x, expr2_y), range, **kwargs)``
If the range is not specified, then a default range of (-10, 10) is used.
Multiple plots with different ranges.
``plot_parametric((expr_x, expr_y, range), ..., **kwargs)``
Range has to be specified for every expression.
Default range may change in the future if a more advanced default range
detection algorithm is implemented.
Arguments
=========
``expr_x`` : Expression representing the function along x.
``expr_y`` : Expression representing the function along y.
``range``: (u, 0, 5), A 3-tuple denoting the range of the parameter
variable.
Keyword Arguments
=================
Arguments for ``Parametric2DLineSeries`` class:
``adaptive``: Boolean. The default value is set to True. Set adaptive to
False and specify ``nb_of_points`` if uniform sampling is required.
``depth``: int Recursion depth of the adaptive algorithm. A depth of
value ``n`` samples a maximum of `2^{n}` points.
``nb_of_points``: int. Used when the ``adaptive`` is set to False. The
function is uniformly sampled at ``nb_of_points`` number of points.
Aesthetics
----------
``line_color``: function which returns a float. Specifies the color for the
plot. See ``sympy.plotting.Plot`` for more details.
If there are multiple plots, then the same Series arguments are applied to
all the plots. If you want to set these options separately, you can index
the returned ``Plot`` object and set it.
Arguments for ``Plot`` class:
``xlabel`` : str. Label for the x-axis.
``ylabel`` : str. Label for the y-axis.
``xscale``: {'linear', 'log'} Sets the scaling of the x-axis.
``yscale``: {'linear', 'log'} Sets the scaling if the y-axis.
``axis_center``: tuple of two floats denoting the coordinates of the center
or {'center', 'auto'}
``xlim`` : tuple of two floats, denoting the x-axis limits.
``ylim`` : tuple of two floats, denoting the y-axis limits.
Examples
========
>>> from sympy import symbols, cos, sin
>>> from sympy.plotting import plot_parametric
>>> u = symbols('u')
Single Parametric plot
>>> plot_parametric(cos(u), sin(u), (u, -5, 5))
Plot object containing:
[0]: parametric cartesian line: (cos(u), sin(u)) for u over (-5.0, 5.0)
Multiple parametric plot with single range.
>>> plot_parametric((cos(u), sin(u)), (u, cos(u)))
Plot object containing:
[0]: parametric cartesian line: (cos(u), sin(u)) for u over (-10.0, 10.0)
[1]: parametric cartesian line: (u, cos(u)) for u over (-10.0, 10.0)
Multiple parametric plots.
>>> plot_parametric((cos(u), sin(u), (u, -5, 5)),
... (cos(u), u, (u, -5, 5)))
Plot object containing:
[0]: parametric cartesian line: (cos(u), sin(u)) for u over (-5.0, 5.0)
[1]: parametric cartesian line: (cos(u), u) for u over (-5.0, 5.0)
See Also
========
Plot, Parametric2DLineSeries
"""
args = list(map(sympify, args))
show = kwargs.pop('show', True)
series = []
plot_expr = check_arguments(args, 2, 1)
series = [Parametric2DLineSeries(*arg, **kwargs) for arg in plot_expr]
plots = Plot(*series, **kwargs)
if show:
plots.show()
return plots
@doctest_depends_on(modules=('numpy', 'matplotlib',))
def plot3d_parametric_line(*args, **kwargs):
"""
Plots a 3D parametric line plot.
Usage
=====
Single plot:
``plot3d_parametric_line(expr_x, expr_y, expr_z, range, **kwargs)``
If the range is not specified, then a default range of (-10, 10) is used.
Multiple plots.
``plot3d_parametric_line((expr_x, expr_y, expr_z, range), ..., **kwargs)``
Ranges have to be specified for every expression.
Default range may change in the future if a more advanced default range
detection algorithm is implemented.
Arguments
=========
``expr_x`` : Expression representing the function along x.
``expr_y`` : Expression representing the function along y.
``expr_z`` : Expression representing the function along z.
``range``: ``(u, 0, 5)``, A 3-tuple denoting the range of the parameter
variable.
Keyword Arguments
=================
Arguments for ``Parametric3DLineSeries`` class.
``nb_of_points``: The range is uniformly sampled at ``nb_of_points``
number of points.
Aesthetics:
``line_color``: function which returns a float. Specifies the color for the
plot. See ``sympy.plotting.Plot`` for more details.
If there are multiple plots, then the same series arguments are applied to
all the plots. If you want to set these options separately, you can index
the returned ``Plot`` object and set it.
Arguments for ``Plot`` class.
``title`` : str. Title of the plot.
Examples
========
>>> from sympy import symbols, cos, sin
>>> from sympy.plotting import plot3d_parametric_line
>>> u = symbols('u')
Single plot.
>>> plot3d_parametric_line(cos(u), sin(u), u, (u, -5, 5))
Plot object containing:
[0]: 3D parametric cartesian line: (cos(u), sin(u), u) for u over (-5.0, 5.0)
Multiple plots.
>>> plot3d_parametric_line((cos(u), sin(u), u, (u, -5, 5)),
... (sin(u), u**2, u, (u, -5, 5)))
Plot object containing:
[0]: 3D parametric cartesian line: (cos(u), sin(u), u) for u over (-5.0, 5.0)
[1]: 3D parametric cartesian line: (sin(u), u**2, u) for u over (-5.0, 5.0)
See Also
========
Plot, Parametric3DLineSeries
"""
args = list(map(sympify, args))
show = kwargs.pop('show', True)
series = []
plot_expr = check_arguments(args, 3, 1)
series = [Parametric3DLineSeries(*arg, **kwargs) for arg in plot_expr]
plots = Plot(*series, **kwargs)
if show:
plots.show()
return plots
@doctest_depends_on(modules=('numpy', 'matplotlib',))
def plot3d(*args, **kwargs):
"""
Plots a 3D surface plot.
Usage
=====
Single plot
``plot3d(expr, range_x, range_y, **kwargs)``
If the ranges are not specified, then a default range of (-10, 10) is used.
Multiple plot with the same range.
``plot3d(expr1, expr2, range_x, range_y, **kwargs)``
If the ranges are not specified, then a default range of (-10, 10) is used.
Multiple plots with different ranges.
``plot3d((expr1, range_x, range_y), (expr2, range_x, range_y), ..., **kwargs)``
Ranges have to be specified for every expression.
Default range may change in the future if a more advanced default range
detection algorithm is implemented.
Arguments
=========
``expr`` : Expression representing the function along x.
``range_x``: (x, 0, 5), A 3-tuple denoting the range of the x
variable.
``range_y``: (y, 0, 5), A 3-tuple denoting the range of the y
variable.
Keyword Arguments
=================
Arguments for ``SurfaceOver2DRangeSeries`` class:
``nb_of_points_x``: int. The x range is sampled uniformly at
``nb_of_points_x`` of points.
``nb_of_points_y``: int. The y range is sampled uniformly at
``nb_of_points_y`` of points.
Aesthetics:
``surface_color``: Function which returns a float. Specifies the color for
the surface of the plot. See ``sympy.plotting.Plot`` for more details.
If there are multiple plots, then the same series arguments are applied to
all the plots. If you want to set these options separately, you can index
the returned ``Plot`` object and set it.
Arguments for ``Plot`` class:
``title`` : str. Title of the plot.
Examples
========
>>> from sympy import symbols
>>> from sympy.plotting import plot3d
>>> x, y = symbols('x y')
Single plot
>>> plot3d(x*y, (x, -5, 5), (y, -5, 5))
Plot object containing:
[0]: cartesian surface: x*y for x over (-5.0, 5.0) and y over (-5.0, 5.0)
Multiple plots with same range
>>> plot3d(x*y, -x*y, (x, -5, 5), (y, -5, 5))
Plot object containing:
[0]: cartesian surface: x*y for x over (-5.0, 5.0) and y over (-5.0, 5.0)
[1]: cartesian surface: -x*y for x over (-5.0, 5.0) and y over (-5.0, 5.0)
Multiple plots with different ranges.
>>> plot3d((x**2 + y**2, (x, -5, 5), (y, -5, 5)),
... (x*y, (x, -3, 3), (y, -3, 3)))
Plot object containing:
[0]: cartesian surface: x**2 + y**2 for x over (-5.0, 5.0) and y over (-5.0, 5.0)
[1]: cartesian surface: x*y for x over (-3.0, 3.0) and y over (-3.0, 3.0)
See Also
========
Plot, SurfaceOver2DRangeSeries
"""
args = list(map(sympify, args))
show = kwargs.pop('show', True)
series = []
plot_expr = check_arguments(args, 1, 2)
series = [SurfaceOver2DRangeSeries(*arg, **kwargs) for arg in plot_expr]
plots = Plot(*series, **kwargs)
if show:
plots.show()
return plots
@doctest_depends_on(modules=('numpy', 'matplotlib',))
def plot3d_parametric_surface(*args, **kwargs):
"""
Plots a 3D parametric surface plot.
Usage
=====
Single plot.
``plot3d_parametric_surface(expr_x, expr_y, expr_z, range_u, range_v, **kwargs)``
If the ranges is not specified, then a default range of (-10, 10) is used.
Multiple plots.
``plot3d_parametric_surface((expr_x, expr_y, expr_z, range_u, range_v), ..., **kwargs)``
Ranges have to be specified for every expression.
Default range may change in the future if a more advanced default range
detection algorithm is implemented.
Arguments
=========
``expr_x``: Expression representing the function along ``x``.
``expr_y``: Expression representing the function along ``y``.
``expr_z``: Expression representing the function along ``z``.
``range_u``: ``(u, 0, 5)``, A 3-tuple denoting the range of the ``u``
variable.
``range_v``: ``(v, 0, 5)``, A 3-tuple denoting the range of the v
variable.
Keyword Arguments
=================
Arguments for ``ParametricSurfaceSeries`` class:
``nb_of_points_u``: int. The ``u`` range is sampled uniformly at
``nb_of_points_v`` of points
``nb_of_points_y``: int. The ``v`` range is sampled uniformly at
``nb_of_points_y`` of points
Aesthetics:
``surface_color``: Function which returns a float. Specifies the color for
the surface of the plot. See ``sympy.plotting.Plot`` for more details.
If there are multiple plots, then the same series arguments are applied for
all the plots. If you want to set these options separately, you can index
the returned ``Plot`` object and set it.
Arguments for ``Plot`` class:
``title`` : str. Title of the plot.
Examples
========
>>> from sympy import symbols, cos, sin
>>> from sympy.plotting import plot3d_parametric_surface
>>> u, v = symbols('u v')
Single plot.
>>> plot3d_parametric_surface(cos(u + v), sin(u - v), u - v,
... (u, -5, 5), (v, -5, 5))
Plot object containing:
[0]: parametric cartesian surface: (cos(u + v), sin(u - v), u - v) for u over (-5.0, 5.0) and v over (-5.0, 5.0)
See Also
========
Plot, ParametricSurfaceSeries
"""
args = list(map(sympify, args))
show = kwargs.pop('show', True)
series = []
plot_expr = check_arguments(args, 3, 2)
series = [ParametricSurfaceSeries(*arg, **kwargs) for arg in plot_expr]
plots = Plot(*series, **kwargs)
if show:
plots.show()
return plots
def check_arguments(args, expr_len, nb_of_free_symbols):
"""
Checks the arguments and converts into tuples of the
form (exprs, ranges)
Examples
========
>>> from sympy import plot, cos, sin, symbols
>>> from sympy.plotting.plot import check_arguments
>>> x = symbols('x')
>>> check_arguments([cos(x), sin(x)], 2, 1)
[(cos(x), sin(x), (x, -10, 10))]
>>> check_arguments([x, x**2], 1, 1)
[(x, (x, -10, 10)), (x**2, (x, -10, 10))]
"""
if expr_len > 1 and isinstance(args[0], Expr):
# Multiple expressions same range.
# The arguments are tuples when the expression length is
# greater than 1.
if len(args) < expr_len:
raise ValueError("len(args) should not be less than expr_len")
for i in range(len(args)):
if isinstance(args[i], Tuple):
break
else:
i = len(args) + 1
exprs = Tuple(*args[:i])
free_symbols = list(set().union(*[e.free_symbols for e in exprs]))
if len(args) == expr_len + nb_of_free_symbols:
#Ranges given
plots = [exprs + Tuple(*args[expr_len:])]
else:
default_range = Tuple(-10, 10)
ranges = []
for symbol in free_symbols:
ranges.append(Tuple(symbol) + default_range)
for i in range(len(free_symbols) - nb_of_free_symbols):
ranges.append(Tuple(Dummy()) + default_range)
plots = [exprs + Tuple(*ranges)]
return plots
if isinstance(args[0], Expr) or (isinstance(args[0], Tuple) and
len(args[0]) == expr_len and
expr_len != 3):
# Cannot handle expressions with number of expression = 3. It is
# not possible to differentiate between expressions and ranges.
#Series of plots with same range
for i in range(len(args)):
if isinstance(args[i], Tuple) and len(args[i]) != expr_len:
break
if not isinstance(args[i], Tuple):
args[i] = Tuple(args[i])
else:
i = len(args) + 1
exprs = args[:i]
assert all(isinstance(e, Expr) for expr in exprs for e in expr)
free_symbols = list(set().union(*[e.free_symbols for expr in exprs
for e in expr]))
if len(free_symbols) > nb_of_free_symbols:
raise ValueError("The number of free_symbols in the expression "
"is greater than %d" % nb_of_free_symbols)
if len(args) == i + nb_of_free_symbols and isinstance(args[i], Tuple):
ranges = Tuple(*[range_expr for range_expr in args[
i:i + nb_of_free_symbols]])
plots = [expr + ranges for expr in exprs]
return plots
else:
#Use default ranges.
default_range = Tuple(-10, 10)
ranges = []
for symbol in free_symbols:
ranges.append(Tuple(symbol) + default_range)
for i in range(len(free_symbols) - nb_of_free_symbols):
ranges.append(Tuple(Dummy()) + default_range)
ranges = Tuple(*ranges)
plots = [expr + ranges for expr in exprs]
return plots
elif isinstance(args[0], Tuple) and len(args[0]) == expr_len + nb_of_free_symbols:
#Multiple plots with different ranges.
for arg in args:
for i in range(expr_len):
if not isinstance(arg[i], Expr):
raise ValueError("Expected an expression, given %s" %
str(arg[i]))
for i in range(nb_of_free_symbols):
if not len(arg[i + expr_len]) == 3:
raise ValueError("The ranges should be a tuple of "
"length 3, got %s" % str(arg[i + expr_len]))
return args
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py
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cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/__init__.py
|
from .plot import plot_backends
from .plot_implicit import plot_implicit
from .textplot import textplot
from .pygletplot import PygletPlot
from .plot import (plot, plot_parametric, plot3d, plot3d_parametric_surface,
plot3d_parametric_line)
| 258 | 36 | 76 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/pygletplot/plot_modes.py
|
from __future__ import print_function, division
from plot_curve import PlotCurve
from plot_surface import PlotSurface
from sympy import pi, lambdify
from sympy.functions import sin, cos
from math import sin as p_sin
from math import cos as p_cos
def float_vec3(f):
def inner(*args):
v = f(*args)
return float(v[0]), float(v[1]), float(v[2])
return inner
class Cartesian2D(PlotCurve):
i_vars, d_vars = 'x', 'y'
intervals = [[-5, 5, 100]]
aliases = ['cartesian']
is_default = True
def _get_sympy_evaluator(self):
fy = self.d_vars[0]
x = self.t_interval.v
@float_vec3
def e(_x):
return (_x, fy.subs(x, _x), 0.0)
return e
def _get_lambda_evaluator(self):
fy = self.d_vars[0]
x = self.t_interval.v
return lambdify([x], [x, fy, 0.0])
class Cartesian3D(PlotSurface):
i_vars, d_vars = 'xy', 'z'
intervals = [[-1, 1, 40], [-1, 1, 40]]
aliases = ['cartesian', 'monge']
is_default = True
def _get_sympy_evaluator(self):
fz = self.d_vars[0]
x = self.u_interval.v
y = self.v_interval.v
@float_vec3
def e(_x, _y):
return (_x, _y, fz.subs(x, _x).subs(y, _y))
return e
def _get_lambda_evaluator(self):
fz = self.d_vars[0]
x = self.u_interval.v
y = self.v_interval.v
return lambdify([x, y], [x, y, fz])
class ParametricCurve2D(PlotCurve):
i_vars, d_vars = 't', 'xy'
intervals = [[0, 2*pi, 100]]
aliases = ['parametric']
is_default = True
def _get_sympy_evaluator(self):
fx, fy = self.d_vars
t = self.t_interval.v
@float_vec3
def e(_t):
return (fx.subs(t, _t), fy.subs(t, _t), 0.0)
return e
def _get_lambda_evaluator(self):
fx, fy = self.d_vars
t = self.t_interval.v
return lambdify([t], [fx, fy, 0.0])
class ParametricCurve3D(PlotCurve):
i_vars, d_vars = 't', 'xyz'
intervals = [[0, 2*pi, 100]]
aliases = ['parametric']
is_default = True
def _get_sympy_evaluator(self):
fx, fy, fz = self.d_vars
t = self.t_interval.v
@float_vec3
def e(_t):
return (fx.subs(t, _t), fy.subs(t, _t), fz.subs(t, _t))
return e
def _get_lambda_evaluator(self):
fx, fy, fz = self.d_vars
t = self.t_interval.v
return lambdify([t], [fx, fy, fz])
class ParametricSurface(PlotSurface):
i_vars, d_vars = 'uv', 'xyz'
intervals = [[-1, 1, 40], [-1, 1, 40]]
aliases = ['parametric']
is_default = True
def _get_sympy_evaluator(self):
fx, fy, fz = self.d_vars
u = self.u_interval.v
v = self.v_interval.v
@float_vec3
def e(_u, _v):
return (fx.subs(u, _u).subs(v, _v),
fy.subs(u, _u).subs(v, _v),
fz.subs(u, _u).subs(v, _v))
return e
def _get_lambda_evaluator(self):
fx, fy, fz = self.d_vars
u = self.u_interval.v
v = self.v_interval.v
return lambdify([u, v], [fx, fy, fz])
class Polar(PlotCurve):
i_vars, d_vars = 't', 'r'
intervals = [[0, 2*pi, 100]]
aliases = ['polar']
is_default = False
def _get_sympy_evaluator(self):
fr = self.d_vars[0]
t = self.t_interval.v
def e(_t):
_r = float(fr.subs(t, _t))
return (_r*p_cos(_t), _r*p_sin(_t), 0.0)
return e
def _get_lambda_evaluator(self):
fr = self.d_vars[0]
t = self.t_interval.v
fx, fy = fr*cos(t), fr*sin(t)
return lambdify([t], [fx, fy, 0.0])
class Cylindrical(PlotSurface):
i_vars, d_vars = 'th', 'r'
intervals = [[0, 2*pi, 40], [-1, 1, 20]]
aliases = ['cylindrical', 'polar']
is_default = False
def _get_sympy_evaluator(self):
fr = self.d_vars[0]
t = self.u_interval.v
h = self.v_interval.v
def e(_t, _h):
_r = float(fr.subs(t, _t).subs(h, _h))
return (_r*p_cos(_t), _r*p_sin(_t), _h)
return e
def _get_lambda_evaluator(self):
fr = self.d_vars[0]
t = self.u_interval.v
h = self.v_interval.v
fx, fy = fr*cos(t), fr*sin(t)
return lambdify([t, h], [fx, fy, h])
class Spherical(PlotSurface):
i_vars, d_vars = 'tp', 'r'
intervals = [[0, 2*pi, 40], [0, pi, 20]]
aliases = ['spherical']
is_default = False
def _get_sympy_evaluator(self):
fr = self.d_vars[0]
t = self.u_interval.v
p = self.v_interval.v
def e(_t, _p):
_r = float(fr.subs(t, _t).subs(p, _p))
return (_r*p_cos(_t)*p_sin(_p),
_r*p_sin(_t)*p_sin(_p),
_r*p_cos(_p))
return e
def _get_lambda_evaluator(self):
fr = self.d_vars[0]
t = self.u_interval.v
p = self.v_interval.v
fx = fr * cos(t) * sin(p)
fy = fr * sin(t) * sin(p)
fz = fr * cos(p)
return lambdify([t, p], [fx, fy, fz])
Cartesian2D._register()
Cartesian3D._register()
ParametricCurve2D._register()
ParametricCurve3D._register()
ParametricSurface._register()
Polar._register()
Cylindrical._register()
Spherical._register()
| 5,300 | 24.123223 | 67 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/pygletplot/plot_rotation.py
|
from __future__ import print_function, division
try:
from pyglet.gl.gl import c_float
except ImportError:
pass
from pyglet.gl import *
from math import sqrt as _sqrt, acos as _acos
def cross(a, b):
return (a[1] * b[2] - a[2] * b[1],
a[2] * b[0] - a[0] * b[2],
a[0] * b[1] - a[1] * b[0])
def dot(a, b):
return a[0] * b[0] + a[1] * b[1] + a[2] * b[2]
def mag(a):
return _sqrt(a[0]**2 + a[1]**2 + a[2]**2)
def norm(a):
m = mag(a)
return (a[0] / m, a[1] / m, a[2] / m)
def get_sphere_mapping(x, y, width, height):
x = min([max([x, 0]), width])
y = min([max([y, 0]), height])
sr = _sqrt((width/2)**2 + (height/2)**2)
sx = ((x - width / 2) / sr)
sy = ((y - height / 2) / sr)
sz = 1.0 - sx**2 - sy**2
if sz > 0.0:
sz = _sqrt(sz)
return (sx, sy, sz)
else:
sz = 0
return norm((sx, sy, sz))
rad2deg = 180.0 / 3.141592
def get_spherical_rotatation(p1, p2, width, height, theta_multiplier):
v1 = get_sphere_mapping(p1[0], p1[1], width, height)
v2 = get_sphere_mapping(p2[0], p2[1], width, height)
d = min(max([dot(v1, v2), -1]), 1)
if abs(d - 1.0) < 0.000001:
return None
raxis = norm( cross(v1, v2) )
rtheta = theta_multiplier * rad2deg * _acos(d)
glPushMatrix()
glLoadIdentity()
glRotatef(rtheta, *raxis)
mat = (c_float*16)()
glGetFloatv(GL_MODELVIEW_MATRIX, mat)
glPopMatrix()
return mat
| 1,478 | 19.830986 | 70 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/pygletplot/plot_camera.py
|
from __future__ import print_function, division
from pyglet.gl import *
from plot_rotation import get_spherical_rotatation
from util import get_model_matrix
from util import screen_to_model, model_to_screen
from util import vec_subs
class PlotCamera(object):
min_dist = 0.05
max_dist = 500.0
min_ortho_dist = 100.0
max_ortho_dist = 10000.0
_default_dist = 6.0
_default_ortho_dist = 600.0
rot_presets = {
'xy': (0, 0, 0),
'xz': (-90, 0, 0),
'yz': (0, 90, 0),
'perspective': (-45, 0, -45)
}
def __init__(self, window, ortho=False):
self.window = window
self.axes = self.window.plot.axes
self.ortho = ortho
self.reset()
def init_rot_matrix(self):
glPushMatrix()
glLoadIdentity()
self._rot = get_model_matrix()
glPopMatrix()
def set_rot_preset(self, preset_name):
self.init_rot_matrix()
try:
r = self.rot_presets[preset_name]
except AttributeError:
raise ValueError(
"%s is not a valid rotation preset." % preset_name)
try:
self.euler_rotate(r[0], 1, 0, 0)
self.euler_rotate(r[1], 0, 1, 0)
self.euler_rotate(r[2], 0, 0, 1)
except AttributeError:
pass
def reset(self):
self._dist = 0.0
self._x, self._y = 0.0, 0.0
self._rot = None
if self.ortho:
self._dist = self._default_ortho_dist
else:
self._dist = self._default_dist
self.init_rot_matrix()
def mult_rot_matrix(self, rot):
glPushMatrix()
glLoadMatrixf(rot)
glMultMatrixf(self._rot)
self._rot = get_model_matrix()
glPopMatrix()
def setup_projection(self):
glMatrixMode(GL_PROJECTION)
glLoadIdentity()
if self.ortho:
# yep, this is pseudo ortho (don't tell anyone)
gluPerspective(
0.3, float(self.window.width)/float(self.window.height),
self.min_ortho_dist - 0.01, self.max_ortho_dist + 0.01)
else:
gluPerspective(
30.0, float(self.window.width)/float(self.window.height),
self.min_dist - 0.01, self.max_dist + 0.01)
glMatrixMode(GL_MODELVIEW)
def _get_scale(self):
return 1.0, 1.0, 1.0
def apply_transformation(self):
glLoadIdentity()
glTranslatef(self._x, self._y, -self._dist)
if self._rot is not None:
glMultMatrixf(self._rot)
glScalef(*self._get_scale())
def spherical_rotate(self, p1, p2, sensitivity=1.0):
mat = get_spherical_rotatation(p1, p2, self.window.width,
self.window.height, sensitivity)
if mat is not None:
self.mult_rot_matrix(mat)
def euler_rotate(self, angle, x, y, z):
glPushMatrix()
glLoadMatrixf(self._rot)
glRotatef(angle, x, y, z)
self._rot = get_model_matrix()
glPopMatrix()
def zoom_relative(self, clicks, sensitivity):
if self.ortho:
dist_d = clicks * sensitivity * 50.0
min_dist = self.min_ortho_dist
max_dist = self.max_ortho_dist
else:
dist_d = clicks * sensitivity
min_dist = self.min_dist
max_dist = self.max_dist
new_dist = (self._dist - dist_d)
if (clicks < 0 and new_dist < max_dist) or new_dist > min_dist:
self._dist = new_dist
def mouse_translate(self, x, y, dx, dy):
glPushMatrix()
glLoadIdentity()
glTranslatef(0, 0, -self._dist)
z = model_to_screen(0, 0, 0)[2]
d = vec_subs(screen_to_model(x, y, z), screen_to_model(x - dx, y - dy, z))
glPopMatrix()
self._x += d[0]
self._y += d[1]
| 3,888 | 28.462121 | 82 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/pygletplot/color_scheme.py
|
from __future__ import print_function, division
from sympy import Basic, Symbol, symbols, lambdify
from util import interpolate, rinterpolate, create_bounds, update_bounds
from sympy.core.compatibility import range
class ColorGradient(object):
colors = [0.4, 0.4, 0.4], [0.9, 0.9, 0.9]
intervals = 0.0, 1.0
def __init__(self, *args):
if len(args) == 2:
self.colors = list(args)
self.intervals = [0.0, 1.0]
elif len(args) > 0:
if len(args) % 2 != 0:
raise ValueError("len(args) should be even")
self.colors = [args[i] for i in range(1, len(args), 2)]
self.intervals = [args[i] for i in range(0, len(args), 2)]
assert len(self.colors) == len(self.intervals)
def copy(self):
c = ColorGradient()
c.colors = [e[::] for e in self.colors]
c.intervals = self.intervals[::]
return c
def _find_interval(self, v):
m = len(self.intervals)
i = 0
while i < m - 1 and self.intervals[i] <= v:
i += 1
return i
def _interpolate_axis(self, axis, v):
i = self._find_interval(v)
v = rinterpolate(self.intervals[i - 1], self.intervals[i], v)
return interpolate(self.colors[i - 1][axis], self.colors[i][axis], v)
def __call__(self, r, g, b):
c = self._interpolate_axis
return c(0, r), c(1, g), c(2, b)
default_color_schemes = {} # defined at the bottom of this file
class ColorScheme(object):
def __init__(self, *args, **kwargs):
self.args = args
self.f, self.gradient = None, ColorGradient()
if len(args) == 1 and not isinstance(args[0], Basic) and callable(args[0]):
self.f = args[0]
elif len(args) == 1 and isinstance(args[0], str):
if args[0] in default_color_schemes:
cs = default_color_schemes[args[0]]
self.f, self.gradient = cs.f, cs.gradient.copy()
else:
self.f = lambdify('x,y,z,u,v', args[0])
else:
self.f, self.gradient = self._interpret_args(args, kwargs)
self._test_color_function()
if not isinstance(self.gradient, ColorGradient):
raise ValueError("Color gradient not properly initialized. "
"(Not a ColorGradient instance.)")
def _interpret_args(self, args, kwargs):
f, gradient = None, self.gradient
atoms, lists = self._sort_args(args)
s = self._pop_symbol_list(lists)
s = self._fill_in_vars(s)
# prepare the error message for lambdification failure
f_str = ', '.join(str(fa) for fa in atoms)
s_str = (str(sa) for sa in s)
s_str = ', '.join(sa for sa in s_str if sa.find('unbound') < 0)
f_error = ValueError("Could not interpret arguments "
"%s as functions of %s." % (f_str, s_str))
# try to lambdify args
if len(atoms) == 1:
fv = atoms[0]
try:
f = lambdify(s, [fv, fv, fv])
except TypeError:
raise f_error
elif len(atoms) == 3:
fr, fg, fb = atoms
try:
f = lambdify(s, [fr, fg, fb])
except TypeError:
raise f_error
else:
raise ValueError("A ColorScheme must provide 1 or 3 "
"functions in x, y, z, u, and/or v.")
# try to intrepret any given color information
if len(lists) == 0:
gargs = []
elif len(lists) == 1:
gargs = lists[0]
elif len(lists) == 2:
try:
(r1, g1, b1), (r2, g2, b2) = lists
except TypeError:
raise ValueError("If two color arguments are given, "
"they must be given in the format "
"(r1, g1, b1), (r2, g2, b2).")
gargs = lists
elif len(lists) == 3:
try:
(r1, r2), (g1, g2), (b1, b2) = lists
except Exception:
raise ValueError("If three color arguments are given, "
"they must be given in the format "
"(r1, r2), (g1, g2), (b1, b2). To create "
"a multi-step gradient, use the syntax "
"[0, colorStart, step1, color1, ..., 1, "
"colorEnd].")
gargs = [[r1, g1, b1], [r2, g2, b2]]
else:
raise ValueError("Don't know what to do with collection "
"arguments %s." % (', '.join(str(l) for l in lists)))
if gargs:
try:
gradient = ColorGradient(*gargs)
except Exception as ex:
raise ValueError(("Could not initialize a gradient "
"with arguments %s. Inner "
"exception: %s") % (gargs, str(ex)))
return f, gradient
def _pop_symbol_list(self, lists):
symbol_lists = []
for l in lists:
mark = True
for s in l:
if s is not None and not isinstance(s, Symbol):
mark = False
break
if mark:
lists.remove(l)
symbol_lists.append(l)
if len(symbol_lists) == 1:
return symbol_lists[0]
elif len(symbol_lists) == 0:
return []
else:
raise ValueError("Only one list of Symbols "
"can be given for a color scheme.")
def _fill_in_vars(self, args):
defaults = symbols('x,y,z,u,v')
if len(args) == 0:
return defaults
if not isinstance(args, (tuple, list)):
raise v_error
if len(args) == 0:
return defaults
for s in args:
if s is not None and not isinstance(s, Symbol):
raise v_error
# when vars are given explicitly, any vars
# not given are marked 'unbound' as to not
# be accidentally used in an expression
vars = [Symbol('unbound%i' % (i)) for i in range(1, 6)]
# interpret as t
if len(args) == 1:
vars[3] = args[0]
# interpret as u,v
elif len(args) == 2:
if args[0] is not None:
vars[3] = args[0]
if args[1] is not None:
vars[4] = args[1]
# interpret as x,y,z
elif len(args) >= 3:
# allow some of x,y,z to be
# left unbound if not given
if args[0] is not None:
vars[0] = args[0]
if args[1] is not None:
vars[1] = args[1]
if args[2] is not None:
vars[2] = args[2]
# interpret the rest as t
if len(args) >= 4:
vars[3] = args[3]
# ...or u,v
if len(args) >= 5:
vars[4] = args[4]
return vars
def _sort_args(self, args):
atoms, lists = [], []
for a in args:
if isinstance(a, (tuple, list)):
lists.append(a)
else:
atoms.append(a)
return atoms, lists
def _test_color_function(self):
if not callable(self.f):
raise ValueError("Color function is not callable.")
try:
result = self.f(0, 0, 0, 0, 0)
if len(result) != 3:
raise ValueError("length should be equal to 3")
except TypeError as te:
raise ValueError("Color function needs to accept x,y,z,u,v, "
"as arguments even if it doesn't use all of them.")
except AssertionError as ae:
raise ValueError("Color function needs to return 3-tuple r,g,b.")
except Exception as ie:
pass # color function probably not valid at 0,0,0,0,0
def __call__(self, x, y, z, u, v):
try:
return self.f(x, y, z, u, v)
except Exception as e:
return None
def apply_to_curve(self, verts, u_set, set_len=None, inc_pos=None):
"""
Apply this color scheme to a
set of vertices over a single
independent variable u.
"""
bounds = create_bounds()
cverts = list()
if callable(set_len):
set_len(len(u_set)*2)
# calculate f() = r,g,b for each vert
# and find the min and max for r,g,b
for _u in range(len(u_set)):
if verts[_u] is None:
cverts.append(None)
else:
x, y, z = verts[_u]
u, v = u_set[_u], None
c = self(x, y, z, u, v)
if c is not None:
c = list(c)
update_bounds(bounds, c)
cverts.append(c)
if callable(inc_pos):
inc_pos()
# scale and apply gradient
for _u in range(len(u_set)):
if cverts[_u] is not None:
for _c in range(3):
# scale from [f_min, f_max] to [0,1]
cverts[_u][_c] = rinterpolate(bounds[_c][0], bounds[_c][1],
cverts[_u][_c])
# apply gradient
cverts[_u] = self.gradient(*cverts[_u])
if callable(inc_pos):
inc_pos()
return cverts
def apply_to_surface(self, verts, u_set, v_set, set_len=None, inc_pos=None):
"""
Apply this color scheme to a
set of vertices over two
independent variables u and v.
"""
bounds = create_bounds()
cverts = list()
if callable(set_len):
set_len(len(u_set)*len(v_set)*2)
# calculate f() = r,g,b for each vert
# and find the min and max for r,g,b
for _u in range(len(u_set)):
column = list()
for _v in range(len(v_set)):
if verts[_u][_v] is None:
column.append(None)
else:
x, y, z = verts[_u][_v]
u, v = u_set[_u], v_set[_v]
c = self(x, y, z, u, v)
if c is not None:
c = list(c)
update_bounds(bounds, c)
column.append(c)
if callable(inc_pos):
inc_pos()
cverts.append(column)
# scale and apply gradient
for _u in range(len(u_set)):
for _v in range(len(v_set)):
if cverts[_u][_v] is not None:
# scale from [f_min, f_max] to [0,1]
for _c in range(3):
cverts[_u][_v][_c] = rinterpolate(bounds[_c][0],
bounds[_c][1], cverts[_u][_v][_c])
# apply gradient
cverts[_u][_v] = self.gradient(*cverts[_u][_v])
if callable(inc_pos):
inc_pos()
return cverts
def str_base(self):
return ", ".join(str(a) for a in self.args)
def __repr__(self):
return "%s" % (self.str_base())
x, y, z, t, u, v = symbols('x,y,z,t,u,v')
default_color_schemes['rainbow'] = ColorScheme(z, y, x)
default_color_schemes['zfade'] = ColorScheme(z, (0.4, 0.4, 0.97),
(0.97, 0.4, 0.4), (None, None, z))
default_color_schemes['zfade3'] = ColorScheme(z, (None, None, z),
[0.00, (0.2, 0.2, 1.0),
0.35, (0.2, 0.8, 0.4),
0.50, (0.3, 0.9, 0.3),
0.65, (0.4, 0.8, 0.2),
1.00, (1.0, 0.2, 0.2)])
default_color_schemes['zfade4'] = ColorScheme(z, (None, None, z),
[0.0, (0.3, 0.3, 1.0),
0.30, (0.3, 1.0, 0.3),
0.55, (0.95, 1.0, 0.2),
0.65, (1.0, 0.95, 0.2),
0.85, (1.0, 0.7, 0.2),
1.0, (1.0, 0.3, 0.2)])
| 12,579 | 36 | 83 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/pygletplot/plot_mode_base.py
|
from __future__ import print_function, division
from pyglet.gl import *
from plot_mode import PlotMode
from threading import Thread, Event, RLock
from color_scheme import ColorScheme
from sympy.core import S
from sympy.core.compatibility import is_sequence
from time import sleep
import warnings
class PlotModeBase(PlotMode):
"""
Intended parent class for plotting
modes. Provides base functionality
in conjunction with its parent,
PlotMode.
"""
##
## Class-Level Attributes
##
"""
The following attributes are meant
to be set at the class level, and serve
as parameters to the plot mode registry
(in PlotMode). See plot_modes.py for
concrete examples.
"""
"""
i_vars
'x' for Cartesian2D
'xy' for Cartesian3D
etc.
d_vars
'y' for Cartesian2D
'r' for Polar
etc.
"""
i_vars, d_vars = '', ''
"""
intervals
Default intervals for each i_var, and in the
same order. Specified [min, max, steps].
No variable can be given (it is bound later).
"""
intervals = []
"""
aliases
A list of strings which can be used to
access this mode.
'cartesian' for Cartesian2D and Cartesian3D
'polar' for Polar
'cylindrical', 'polar' for Cylindrical
Note that _init_mode chooses the first alias
in the list as the mode's primary_alias, which
will be displayed to the end user in certain
contexts.
"""
aliases = []
"""
is_default
Whether to set this mode as the default
for arguments passed to PlotMode() containing
the same number of d_vars as this mode and
at most the same number of i_vars.
"""
is_default = False
"""
All of the above attributes are defined in PlotMode.
The following ones are specific to PlotModeBase.
"""
"""
A list of the render styles. Do not modify.
"""
styles = {'wireframe': 1, 'solid': 2, 'both': 3}
"""
style_override
Always use this style if not blank.
"""
style_override = ''
"""
default_wireframe_color
default_solid_color
Can be used when color is None or being calculated.
Used by PlotCurve and PlotSurface, but not anywhere
in PlotModeBase.
"""
default_wireframe_color = (0.85, 0.85, 0.85)
default_solid_color = (0.6, 0.6, 0.9)
default_rot_preset = 'xy'
##
## Instance-Level Attributes
##
## 'Abstract' member functions
def _get_evaluator(self):
if self.use_lambda_eval:
try:
e = self._get_lambda_evaluator()
return e
except Exception:
warnings.warn("\nWarning: creating lambda evaluator failed. "
"Falling back on sympy subs evaluator.")
return self._get_sympy_evaluator()
def _get_sympy_evaluator(self):
raise NotImplementedError()
def _get_lambda_evaluator(self):
raise NotImplementedError()
def _on_calculate_verts(self):
raise NotImplementedError()
def _on_calculate_cverts(self):
raise NotImplementedError()
## Base member functions
def __init__(self, *args, **kwargs):
self.verts = []
self.cverts = []
self.bounds = [[S.Infinity, -S.Infinity, 0],
[S.Infinity, -S.Infinity, 0],
[S.Infinity, -S.Infinity, 0]]
self.cbounds = [[S.Infinity, -S.Infinity, 0],
[S.Infinity, -S.Infinity, 0],
[S.Infinity, -S.Infinity, 0]]
self._draw_lock = RLock()
self._calculating_verts = Event()
self._calculating_cverts = Event()
self._calculating_verts_pos = 0.0
self._calculating_verts_len = 0.0
self._calculating_cverts_pos = 0.0
self._calculating_cverts_len = 0.0
self._max_render_stack_size = 3
self._draw_wireframe = [-1]
self._draw_solid = [-1]
self._style = None
self._color = None
self.predraw = []
self.postdraw = []
self.use_lambda_eval = self.options.pop('use_sympy_eval', None) is None
self.style = self.options.pop('style', '')
self.color = self.options.pop('color', 'rainbow')
self.bounds_callback = kwargs.pop('bounds_callback', None)
self._on_calculate()
def synchronized(f):
def w(self, *args, **kwargs):
self._draw_lock.acquire()
try:
r = f(self, *args, **kwargs)
return r
finally:
self._draw_lock.release()
return w
@synchronized
def push_wireframe(self, function):
"""
Push a function which performs gl commands
used to build a display list. (The list is
built outside of the function)
"""
assert callable(function)
self._draw_wireframe.append(function)
if len(self._draw_wireframe) > self._max_render_stack_size:
del self._draw_wireframe[1] # leave marker element
@synchronized
def push_solid(self, function):
"""
Push a function which performs gl commands
used to build a display list. (The list is
built outside of the function)
"""
assert callable(function)
self._draw_solid.append(function)
if len(self._draw_solid) > self._max_render_stack_size:
del self._draw_solid[1] # leave marker element
def _create_display_list(self, function):
dl = glGenLists(1)
glNewList(dl, GL_COMPILE)
function()
glEndList()
return dl
def _render_stack_top(self, render_stack):
top = render_stack[-1]
if top == -1:
return -1 # nothing to display
elif callable(top):
dl = self._create_display_list(top)
render_stack[-1] = (dl, top)
return dl # display newly added list
elif len(top) == 2:
if GL_TRUE == glIsList(top[0]):
return top[0] # display stored list
dl = self._create_display_list(top[1])
render_stack[-1] = (dl, top[1])
return dl # display regenerated list
def _draw_solid_display_list(self, dl):
glPushAttrib(GL_ENABLE_BIT | GL_POLYGON_BIT)
glPolygonMode(GL_FRONT_AND_BACK, GL_FILL)
glCallList(dl)
glPopAttrib()
def _draw_wireframe_display_list(self, dl):
glPushAttrib(GL_ENABLE_BIT | GL_POLYGON_BIT)
glPolygonMode(GL_FRONT_AND_BACK, GL_LINE)
glEnable(GL_POLYGON_OFFSET_LINE)
glPolygonOffset(-0.005, -50.0)
glCallList(dl)
glPopAttrib()
@synchronized
def draw(self):
for f in self.predraw:
if callable(f):
f()
if self.style_override:
style = self.styles[self.style_override]
else:
style = self.styles[self._style]
# Draw solid component if style includes solid
if style & 2:
dl = self._render_stack_top(self._draw_solid)
if dl > 0 and GL_TRUE == glIsList(dl):
self._draw_solid_display_list(dl)
# Draw wireframe component if style includes wireframe
if style & 1:
dl = self._render_stack_top(self._draw_wireframe)
if dl > 0 and GL_TRUE == glIsList(dl):
self._draw_wireframe_display_list(dl)
for f in self.postdraw:
if callable(f):
f()
def _on_change_color(self, color):
Thread(target=self._calculate_cverts).start()
def _on_calculate(self):
Thread(target=self._calculate_all).start()
def _calculate_all(self):
self._calculate_verts()
self._calculate_cverts()
def _calculate_verts(self):
if self._calculating_verts.isSet():
return
self._calculating_verts.set()
try:
self._on_calculate_verts()
finally:
self._calculating_verts.clear()
if callable(self.bounds_callback):
self.bounds_callback()
def _calculate_cverts(self):
if self._calculating_verts.isSet():
return
while self._calculating_cverts.isSet():
sleep(0) # wait for previous calculation
self._calculating_cverts.set()
try:
self._on_calculate_cverts()
finally:
self._calculating_cverts.clear()
def _get_calculating_verts(self):
return self._calculating_verts.isSet()
def _get_calculating_verts_pos(self):
return self._calculating_verts_pos
def _get_calculating_verts_len(self):
return self._calculating_verts_len
def _get_calculating_cverts(self):
return self._calculating_cverts.isSet()
def _get_calculating_cverts_pos(self):
return self._calculating_cverts_pos
def _get_calculating_cverts_len(self):
return self._calculating_cverts_len
## Property handlers
def _get_style(self):
return self._style
@synchronized
def _set_style(self, v):
if v is None:
return
if v == '':
step_max = 0
for i in self.intervals:
if i.v_steps is None:
continue
step_max = max([step_max, int(i.v_steps)])
v = ['both', 'solid'][step_max > 40]
if v not in self.styles:
raise ValueError("v should be there in self.styles")
if v == self._style:
return
self._style = v
def _get_color(self):
return self._color
@synchronized
def _set_color(self, v):
try:
if v is not None:
if is_sequence(v):
v = ColorScheme(*v)
else:
v = ColorScheme(v)
if repr(v) == repr(self._color):
return
self._on_change_color(v)
self._color = v
except Exception as e:
raise RuntimeError(("Color change failed. "
"Reason: %s" % (str(e))))
style = property(_get_style, _set_style)
color = property(_get_color, _set_color)
calculating_verts = property(_get_calculating_verts)
calculating_verts_pos = property(_get_calculating_verts_pos)
calculating_verts_len = property(_get_calculating_verts_len)
calculating_cverts = property(_get_calculating_cverts)
calculating_cverts_pos = property(_get_calculating_cverts_pos)
calculating_cverts_len = property(_get_calculating_cverts_len)
## String representations
def __str__(self):
f = ", ".join(str(d) for d in self.d_vars)
o = "'mode=%s'" % (self.primary_alias)
return ", ".join([f, o])
def __repr__(self):
f = ", ".join(str(d) for d in self.d_vars)
i = ", ".join(str(i) for i in self.intervals)
d = [('mode', self.primary_alias),
('color', str(self.color)),
('style', str(self.style))]
o = "'%s'" % (("; ".join("%s=%s" % (k, v)
for k, v in d if v != 'None')))
return ", ".join([f, i, o])
| 11,337 | 28.75853 | 79 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/pygletplot/plot_axes.py
|
from __future__ import print_function, division
from pyglet.gl import *
from pyglet import font
from plot_object import PlotObject
from util import strided_range, billboard_matrix
from util import get_direction_vectors
from util import dot_product, vec_sub, vec_mag
from sympy.core import S
from sympy.core.compatibility import is_sequence, range
class PlotAxes(PlotObject):
def __init__(self, *args, **kwargs):
# initialize style parameter
style = kwargs.pop('style', '').lower()
# allow alias kwargs to override style kwarg
if kwargs.pop('none', None) is not None:
style = 'none'
if kwargs.pop('frame', None) is not None:
style = 'frame'
if kwargs.pop('box', None) is not None:
style = 'box'
if kwargs.pop('ordinate', None) is not None:
style = 'ordinate'
if style in ['', 'ordinate']:
self._render_object = PlotAxesOrdinate(self)
elif style in ['frame', 'box']:
self._render_object = PlotAxesFrame(self)
elif style in ['none']:
self._render_object = None
else:
raise ValueError(("Unrecognized axes style %s.") % (style))
# initialize stride parameter
stride = kwargs.pop('stride', 0.25)
try:
stride = eval(stride)
except TypeError:
pass
if is_sequence(stride):
if len(stride) != 3:
raise ValueError("length should be equal to 3")
self._stride = stride
else:
self._stride = [stride, stride, stride]
self._tick_length = float(kwargs.pop('tick_length', 0.1))
# setup bounding box and ticks
self._origin = [0, 0, 0]
self.reset_bounding_box()
def flexible_boolean(input, default):
if input in [True, False]:
return input
if input in ['f', 'F', 'false', 'False']:
return False
if input in ['t', 'T', 'true', 'True']:
return True
return default
# initialize remaining parameters
self.visible = flexible_boolean(kwargs.pop('visible', ''), True)
self._overlay = flexible_boolean(kwargs.pop('overlay', ''), True)
self._colored = flexible_boolean(kwargs.pop('colored', ''), False)
self._label_axes = flexible_boolean(
kwargs.pop('label_axes', ''), False)
self._label_ticks = flexible_boolean(
kwargs.pop('label_ticks', ''), True)
# setup label font
self.font_face = kwargs.pop('font_face', 'Arial')
self.font_size = kwargs.pop('font_size', 28)
# this is also used to reinit the
# font on window close/reopen
self.reset_resources()
def reset_resources(self):
self.label_font = None
def reset_bounding_box(self):
self._bounding_box = [[None, None], [None, None], [None, None]]
self._axis_ticks = [[], [], []]
def draw(self):
if self._render_object:
glPushAttrib(GL_ENABLE_BIT | GL_POLYGON_BIT | GL_DEPTH_BUFFER_BIT)
if self._overlay:
glDisable(GL_DEPTH_TEST)
self._render_object.draw()
glPopAttrib()
def adjust_bounds(self, child_bounds):
b = self._bounding_box
c = child_bounds
for i in [0, 1, 2]:
if abs(c[i][0]) is S.Infinity or abs(c[i][1]) is S.Infinity:
continue
b[i][0] = [min([b[i][0], c[i][0]]), c[i][0]][b[i][0] is None]
b[i][1] = [max([b[i][1], c[i][1]]), c[i][1]][b[i][1] is None]
self._recalculate_axis_ticks(i)
def _recalculate_axis_ticks(self, axis):
b = self._bounding_box
if b[axis][0] is None or b[axis][1] is None:
self._axis_ticks[axis] = []
else:
self._axis_ticks[axis] = strided_range(b[axis][0], b[axis][1],
self._stride[axis])
def toggle_visible(self):
self.visible = not self.visible
def toggle_colors(self):
self._colored = not self._colored
class PlotAxesBase(PlotObject):
def __init__(self, parent_axes):
self._p = parent_axes
def draw(self):
color = [([0.2, 0.1, 0.3], [0.2, 0.1, 0.3], [0.2, 0.1, 0.3]),
([0.9, 0.3, 0.5], [0.5, 1.0, 0.5], [0.3, 0.3, 0.9])][self._p._colored]
self.draw_background(color)
self.draw_axis(2, color[2])
self.draw_axis(1, color[1])
self.draw_axis(0, color[0])
def draw_background(self, color):
pass # optional
def draw_axis(self, axis, color):
raise NotImplementedError()
def draw_text(self, text, position, color, scale=1.0):
if len(color) == 3:
color = (color[0], color[1], color[2], 1.0)
if self._p.label_font is None:
self._p.label_font = font.load(self._p.font_face,
self._p.font_size,
bold=True, italic=False)
label = font.Text(self._p.label_font, text,
color=color,
valign=font.Text.BASELINE,
halign=font.Text.CENTER)
glPushMatrix()
glTranslatef(*position)
billboard_matrix()
scale_factor = 0.005 * scale
glScalef(scale_factor, scale_factor, scale_factor)
glColor4f(0, 0, 0, 0)
label.draw()
glPopMatrix()
def draw_line(self, v, color):
o = self._p._origin
glBegin(GL_LINES)
glColor3f(*color)
glVertex3f(v[0][0] + o[0], v[0][1] + o[1], v[0][2] + o[2])
glVertex3f(v[1][0] + o[0], v[1][1] + o[1], v[1][2] + o[2])
glEnd()
class PlotAxesOrdinate(PlotAxesBase):
def __init__(self, parent_axes):
super(PlotAxesOrdinate, self).__init__(parent_axes)
def draw_axis(self, axis, color):
ticks = self._p._axis_ticks[axis]
radius = self._p._tick_length / 2.0
if len(ticks) < 2:
return
# calculate the vector for this axis
axis_lines = [[0, 0, 0], [0, 0, 0]]
axis_lines[0][axis], axis_lines[1][axis] = ticks[0], ticks[-1]
axis_vector = vec_sub(axis_lines[1], axis_lines[0])
# calculate angle to the z direction vector
pos_z = get_direction_vectors()[2]
d = abs(dot_product(axis_vector, pos_z))
d = d / vec_mag(axis_vector)
# don't draw labels if we're looking down the axis
labels_visible = abs(d - 1.0) > 0.02
# draw the ticks and labels
for tick in ticks:
self.draw_tick_line(axis, color, radius, tick, labels_visible)
# draw the axis line and labels
self.draw_axis_line(axis, color, ticks[0], ticks[-1], labels_visible)
def draw_axis_line(self, axis, color, a_min, a_max, labels_visible):
axis_line = [[0, 0, 0], [0, 0, 0]]
axis_line[0][axis], axis_line[1][axis] = a_min, a_max
self.draw_line(axis_line, color)
if labels_visible:
self.draw_axis_line_labels(axis, color, axis_line)
def draw_axis_line_labels(self, axis, color, axis_line):
if not self._p._label_axes:
return
axis_labels = [axis_line[0][::], axis_line[1][::]]
axis_labels[0][axis] -= 0.3
axis_labels[1][axis] += 0.3
a_str = ['X', 'Y', 'Z'][axis]
self.draw_text("-" + a_str, axis_labels[0], color)
self.draw_text("+" + a_str, axis_labels[1], color)
def draw_tick_line(self, axis, color, radius, tick, labels_visible):
tick_axis = {0: 1, 1: 0, 2: 1}[axis]
tick_line = [[0, 0, 0], [0, 0, 0]]
tick_line[0][axis] = tick_line[1][axis] = tick
tick_line[0][tick_axis], tick_line[1][tick_axis] = -radius, radius
self.draw_line(tick_line, color)
if labels_visible:
self.draw_tick_line_label(axis, color, radius, tick)
def draw_tick_line_label(self, axis, color, radius, tick):
if not self._p._label_axes:
return
tick_label_vector = [0, 0, 0]
tick_label_vector[axis] = tick
tick_label_vector[{0: 1, 1: 0, 2: 1}[axis]] = [-1, 1, 1][
axis] * radius * 3.5
self.draw_text(str(tick), tick_label_vector, color, scale=0.5)
class PlotAxesFrame(PlotAxesBase):
def __init__(self, parent_axes):
super(PlotAxesFrame, self).__init__(parent_axes)
def draw_background(self, color):
pass
def draw_axis(self, axis, color):
raise NotImplementedError()
| 8,666 | 33.52988 | 87 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/pygletplot/plot_mode.py
|
from __future__ import print_function, division
from sympy import Symbol, sympify
from plot_interval import PlotInterval
from plot_object import PlotObject
from util import parse_option_string
from sympy.geometry.entity import GeometryEntity
from sympy.core.compatibility import is_sequence, range
class PlotMode(PlotObject):
"""
Grandparent class for plotting
modes. Serves as interface for
registration, lookup, and init
of modes.
To create a new plot mode,
inherit from PlotModeBase
or one of its children, such
as PlotSurface or PlotCurve.
"""
## Class-level attributes
## used to register and lookup
## plot modes. See PlotModeBase
## for descriptions and usage.
i_vars, d_vars = '', ''
intervals = []
aliases = []
is_default = False
## Draw is the only method here which
## is meant to be overridden in child
## classes, and PlotModeBase provides
## a base implementation.
def draw(self):
raise NotImplementedError()
## Everything else in this file has to
## do with registration and retrieval
## of plot modes. This is where I've
## hidden much of the ugliness of automatic
## plot mode divination...
## Plot mode registry data structures
_mode_alias_list = []
_mode_map = {
1: {1: {}, 2: {}},
2: {1: {}, 2: {}},
3: {1: {}, 2: {}},
} # [d][i][alias_str]: class
_mode_default_map = {
1: {},
2: {},
3: {},
} # [d][i]: class
_i_var_max, _d_var_max = 2, 3
def __new__(cls, *args, **kwargs):
"""
This is the function which interprets
arguments given to Plot.__init__ and
Plot.__setattr__. Returns an initialized
instance of the appropriate child class.
"""
newargs, newkwargs = PlotMode._extract_options(args, kwargs)
mode_arg = newkwargs.get('mode', '')
# Interpret the arguments
d_vars, intervals = PlotMode._interpret_args(newargs)
i_vars = PlotMode._find_i_vars(d_vars, intervals)
i, d = max([len(i_vars), len(intervals)]), len(d_vars)
# Find the appropriate mode
subcls = PlotMode._get_mode(mode_arg, i, d)
# Create the object
o = object.__new__(subcls)
# Do some setup for the mode instance
o.d_vars = d_vars
o._fill_i_vars(i_vars)
o._fill_intervals(intervals)
o.options = newkwargs
return o
@staticmethod
def _get_mode(mode_arg, i_var_count, d_var_count):
"""
Tries to return an appropriate mode class.
Intended to be called only by __new__.
mode_arg
Can be a string or a class. If it is a
PlotMode subclass, it is simply returned.
If it is a string, it can an alias for
a mode or an empty string. In the latter
case, we try to find a default mode for
the i_var_count and d_var_count.
i_var_count
The number of independent variables
needed to evaluate the d_vars.
d_var_count
The number of dependent variables;
usually the number of functions to
be evaluated in plotting.
For example, a Cartesian function y = f(x) has
one i_var (x) and one d_var (y). A parametric
form x,y,z = f(u,v), f(u,v), f(u,v) has two
two i_vars (u,v) and three d_vars (x,y,z).
"""
# if the mode_arg is simply a PlotMode class,
# check that the mode supports the numbers
# of independent and dependent vars, then
# return it
try:
m = None
if issubclass(mode_arg, PlotMode):
m = mode_arg
except TypeError:
pass
if m:
if not m._was_initialized:
raise ValueError(("To use unregistered plot mode %s "
"you must first call %s._init_mode().")
% (m.__name__, m.__name__))
if d_var_count != m.d_var_count:
raise ValueError(("%s can only plot functions "
"with %i dependent variables.")
% (m.__name__,
m.d_var_count))
if i_var_count > m.i_var_count:
raise ValueError(("%s cannot plot functions "
"with more than %i independent "
"variables.")
% (m.__name__,
m.i_var_count))
return m
# If it is a string, there are two possibilities.
if isinstance(mode_arg, str):
i, d = i_var_count, d_var_count
if i > PlotMode._i_var_max:
raise ValueError(var_count_error(True, True))
if d > PlotMode._d_var_max:
raise ValueError(var_count_error(False, True))
# If the string is '', try to find a suitable
# default mode
if not mode_arg:
return PlotMode._get_default_mode(i, d)
# Otherwise, interpret the string as a mode
# alias (e.g. 'cartesian', 'parametric', etc)
else:
return PlotMode._get_aliased_mode(mode_arg, i, d)
else:
raise ValueError("PlotMode argument must be "
"a class or a string")
@staticmethod
def _get_default_mode(i, d, i_vars=-1):
if i_vars == -1:
i_vars = i
try:
return PlotMode._mode_default_map[d][i]
except TypeError:
# Keep looking for modes in higher i var counts
# which support the given d var count until we
# reach the max i_var count.
if i < PlotMode._i_var_max:
return PlotMode._get_default_mode(i + 1, d, i_vars)
else:
raise ValueError(("Couldn't find a default mode "
"for %i independent and %i "
"dependent variables.") % (i_vars, d))
@staticmethod
def _get_aliased_mode(alias, i, d, i_vars=-1):
if i_vars == -1:
i_vars = i
if alias not in PlotMode._mode_alias_list:
raise ValueError(("Couldn't find a mode called"
" %s. Known modes: %s.")
% (alias, ", ".join(PlotMode._mode_alias_list)))
try:
return PlotMode._mode_map[d][i][alias]
except TypeError:
# Keep looking for modes in higher i var counts
# which support the given d var count and alias
# until we reach the max i_var count.
if i < PlotMode._i_var_max:
return PlotMode._get_aliased_mode(alias, i + 1, d, i_vars)
else:
raise ValueError(("Couldn't find a %s mode "
"for %i independent and %i "
"dependent variables.")
% (alias, i_vars, d))
@classmethod
def _register(cls):
"""
Called once for each user-usable plot mode.
For Cartesian2D, it is invoked after the
class definition: Cartesian2D._register()
"""
name = cls.__name__
cls._init_mode()
try:
i, d = cls.i_var_count, cls.d_var_count
# Add the mode to _mode_map under all
# given aliases
for a in cls.aliases:
if a not in PlotMode._mode_alias_list:
# Also track valid aliases, so
# we can quickly know when given
# an invalid one in _get_mode.
PlotMode._mode_alias_list.append(a)
PlotMode._mode_map[d][i][a] = cls
if cls.is_default:
# If this mode was marked as the
# default for this d,i combination,
# also set that.
PlotMode._mode_default_map[d][i] = cls
except Exception as e:
raise RuntimeError(("Failed to register "
"plot mode %s. Reason: %s")
% (name, (str(e))))
@classmethod
def _init_mode(cls):
"""
Initializes the plot mode based on
the 'mode-specific parameters' above.
Only intended to be called by
PlotMode._register(). To use a mode without
registering it, you can directly call
ModeSubclass._init_mode().
"""
def symbols_list(symbol_str):
return [Symbol(s) for s in symbol_str]
# Convert the vars strs into
# lists of symbols.
cls.i_vars = symbols_list(cls.i_vars)
cls.d_vars = symbols_list(cls.d_vars)
# Var count is used often, calculate
# it once here
cls.i_var_count = len(cls.i_vars)
cls.d_var_count = len(cls.d_vars)
if cls.i_var_count > PlotMode._i_var_max:
raise ValueError(var_count_error(True, False))
if cls.d_var_count > PlotMode._d_var_max:
raise ValueError(var_count_error(False, False))
# Try to use first alias as primary_alias
if len(cls.aliases) > 0:
cls.primary_alias = cls.aliases[0]
else:
cls.primary_alias = cls.__name__
di = cls.intervals
if len(di) != cls.i_var_count:
raise ValueError("Plot mode must provide a "
"default interval for each i_var.")
for i in range(cls.i_var_count):
# default intervals must be given [min,max,steps]
# (no var, but they must be in the same order as i_vars)
if len(di[i]) != 3:
raise ValueError("length should be equal to 3")
# Initialize an incomplete interval,
# to later be filled with a var when
# the mode is instantiated.
di[i] = PlotInterval(None, *di[i])
# To prevent people from using modes
# without these required fields set up.
cls._was_initialized = True
_was_initialized = False
## Initializer Helper Methods
@staticmethod
def _find_i_vars(functions, intervals):
i_vars = []
# First, collect i_vars in the
# order they are given in any
# intervals.
for i in intervals:
if i.v is None:
continue
elif i.v in i_vars:
raise ValueError(("Multiple intervals given "
"for %s.") % (str(i.v)))
i_vars.append(i.v)
# Then, find any remaining
# i_vars in given functions
# (aka d_vars)
for f in functions:
for a in f.free_symbols:
if a not in i_vars:
i_vars.append(a)
return i_vars
def _fill_i_vars(self, i_vars):
# copy default i_vars
self.i_vars = [Symbol(str(i)) for i in self.i_vars]
# replace with given i_vars
for i in range(len(i_vars)):
self.i_vars[i] = i_vars[i]
def _fill_intervals(self, intervals):
# copy default intervals
self.intervals = [PlotInterval(i) for i in self.intervals]
# track i_vars used so far
v_used = []
# fill copy of default
# intervals with given info
for i in range(len(intervals)):
self.intervals[i].fill_from(intervals[i])
if self.intervals[i].v is not None:
v_used.append(self.intervals[i].v)
# Find any orphan intervals and
# assign them i_vars
for i in range(len(self.intervals)):
if self.intervals[i].v is None:
u = [v for v in self.i_vars if v not in v_used]
if len(u) == 0:
raise ValueError("length should not be equal to 0")
self.intervals[i].v = u[0]
v_used.append(u[0])
@staticmethod
def _interpret_args(args):
interval_wrong_order = "PlotInterval %s was given before any function(s)."
interpret_error = "Could not interpret %s as a function or interval."
functions, intervals = [], []
if isinstance(args[0], GeometryEntity):
for coords in list(args[0].arbitrary_point()):
functions.append(coords)
intervals.append(PlotInterval.try_parse(args[0].plot_interval()))
else:
for a in args:
i = PlotInterval.try_parse(a)
if i is not None:
if len(functions) == 0:
raise ValueError(interval_wrong_order % (str(i)))
else:
intervals.append(i)
else:
if is_sequence(a, include=str):
raise ValueError(interpret_error % (str(a)))
try:
f = sympify(a)
functions.append(f)
except TypeError:
raise ValueError(interpret_error % str(a))
return functions, intervals
@staticmethod
def _extract_options(args, kwargs):
newkwargs, newargs = {}, []
for a in args:
if isinstance(a, str):
newkwargs = dict(newkwargs, **parse_option_string(a))
else:
newargs.append(a)
newkwargs = dict(newkwargs, **kwargs)
return newargs, newkwargs
def var_count_error(is_independent, is_plotting):
"""
Used to format an error message which differs
slightly in 4 places.
"""
if is_plotting:
v = "Plotting"
else:
v = "Registering plot modes"
if is_independent:
n, s = PlotMode._i_var_max, "independent"
else:
n, s = PlotMode._d_var_max, "dependent"
return ("%s with more than %i %s variables "
"is not supported.") % (v, n, s)
| 14,167 | 34.243781 | 82 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/pygletplot/plot_curve.py
|
from __future__ import print_function, division
from pyglet.gl import *
from plot_mode_base import PlotModeBase
from sympy.core import S
from sympy.core.compatibility import range
class PlotCurve(PlotModeBase):
style_override = 'wireframe'
def _on_calculate_verts(self):
self.t_interval = self.intervals[0]
self.t_set = list(self.t_interval.frange())
self.bounds = [[S.Infinity, -S.Infinity, 0],
[S.Infinity, -S.Infinity, 0],
[S.Infinity, -S.Infinity, 0]]
evaluate = self._get_evaluator()
self._calculating_verts_pos = 0.0
self._calculating_verts_len = float(self.t_interval.v_len)
self.verts = list()
b = self.bounds
for t in self.t_set:
try:
_e = evaluate(t) # calculate vertex
except (NameError, ZeroDivisionError):
_e = None
if _e is not None: # update bounding box
for axis in range(3):
b[axis][0] = min([b[axis][0], _e[axis]])
b[axis][1] = max([b[axis][1], _e[axis]])
self.verts.append(_e)
self._calculating_verts_pos += 1.0
for axis in range(3):
b[axis][2] = b[axis][1] - b[axis][0]
if b[axis][2] == 0.0:
b[axis][2] = 1.0
self.push_wireframe(self.draw_verts(False))
def _on_calculate_cverts(self):
if not self.verts or not self.color:
return
def set_work_len(n):
self._calculating_cverts_len = float(n)
def inc_work_pos():
self._calculating_cverts_pos += 1.0
set_work_len(1)
self._calculating_cverts_pos = 0
self.cverts = self.color.apply_to_curve(self.verts,
self.t_set,
set_len=set_work_len,
inc_pos=inc_work_pos)
self.push_wireframe(self.draw_verts(True))
def calculate_one_cvert(self, t):
vert = self.verts[t]
return self.color(vert[0], vert[1], vert[2],
self.t_set[t], None)
def draw_verts(self, use_cverts):
def f():
glBegin(GL_LINE_STRIP)
for t in range(len(self.t_set)):
p = self.verts[t]
if p is None:
glEnd()
glBegin(GL_LINE_STRIP)
continue
if use_cverts:
c = self.cverts[t]
if c is None:
c = (0, 0, 0)
glColor3f(*c)
else:
glColor3f(*self.default_wireframe_color)
glVertex3f(*p)
glEnd()
return f
| 2,851 | 32.162791 | 69 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/pygletplot/managed_window.py
|
from __future__ import print_function, division
from pyglet.gl import *
from pyglet.window import Window
from pyglet.clock import Clock
from threading import Thread, Lock
gl_lock = Lock()
class ManagedWindow(Window):
"""
A pyglet window with an event loop which executes automatically
in a separate thread. Behavior is added by creating a subclass
which overrides setup, update, and/or draw.
"""
fps_limit = 30
default_win_args = dict(width=600,
height=500,
vsync=False,
resizable=True)
def __init__(self, **win_args):
"""
It is best not to override this function in the child
class, unless you need to take additional arguments.
Do any OpenGL initialization calls in setup().
"""
# check if this is run from the doctester
if win_args.get('runfromdoctester', False):
return
self.win_args = dict(self.default_win_args, **win_args)
self.Thread = Thread(target=self.__event_loop__)
self.Thread.start()
def __event_loop__(self, **win_args):
"""
The event loop thread function. Do not override or call
directly (it is called by __init__).
"""
gl_lock.acquire()
try:
try:
super(ManagedWindow, self).__init__(**self.win_args)
self.switch_to()
self.setup()
except Exception as e:
print("Window initialization failed: %s" % (str(e)))
self.has_exit = True
finally:
gl_lock.release()
clock = Clock()
clock.set_fps_limit(self.fps_limit)
while not self.has_exit:
dt = clock.tick()
gl_lock.acquire()
try:
try:
self.switch_to()
self.dispatch_events()
self.clear()
self.update(dt)
self.draw()
self.flip()
except Exception as e:
print("Uncaught exception in event loop: %s" % str(e))
self.has_exit = True
finally:
gl_lock.release()
super(ManagedWindow, self).close()
def close(self):
"""
Closes the window.
"""
self.has_exit = True
def setup(self):
"""
Called once before the event loop begins.
Override this method in a child class. This
is the best place to put things like OpenGL
initialization calls.
"""
pass
def update(self, dt):
"""
Called before draw during each iteration of
the event loop. dt is the elapsed time in
seconds since the last update. OpenGL rendering
calls are best put in draw() rather than here.
"""
pass
def draw(self):
"""
Called after update during each iteration of
the event loop. Put OpenGL rendering calls
here.
"""
pass
if __name__ == '__main__':
ManagedWindow()
| 3,178 | 27.9 | 74 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/pygletplot/util.py
|
from __future__ import print_function, division
try:
from pyglet.gl.gl import c_float
except ImportError:
pass
from pyglet.gl import *
from sympy.core import S
from sympy.core.compatibility import range
def get_model_matrix(array_type=c_float, glGetMethod=glGetFloatv):
"""
Returns the current modelview matrix.
"""
m = (array_type*16)()
glGetMethod(GL_MODELVIEW_MATRIX, m)
return m
def get_projection_matrix(array_type=c_float, glGetMethod=glGetFloatv):
"""
Returns the current modelview matrix.
"""
m = (array_type*16)()
glGetMethod(GL_PROJECTION_MATRIX, m)
return m
def get_viewport():
"""
Returns the current viewport.
"""
m = (c_int*4)()
glGetIntegerv(GL_VIEWPORT, m)
return m
def get_direction_vectors():
m = get_model_matrix()
return ((m[0], m[4], m[8]),
(m[1], m[5], m[9]),
(m[2], m[6], m[10]))
def get_view_direction_vectors():
m = get_model_matrix()
return ((m[0], m[1], m[2]),
(m[4], m[5], m[6]),
(m[8], m[9], m[10]))
def get_basis_vectors():
return ((1, 0, 0), (0, 1, 0), (0, 0, 1))
def screen_to_model(x, y, z):
m = get_model_matrix(c_double, glGetDoublev)
p = get_projection_matrix(c_double, glGetDoublev)
w = get_viewport()
mx, my, mz = c_double(), c_double(), c_double()
gluUnProject(x, y, z, m, p, w, mx, my, mz)
return float(mx.value), float(my.value), float(mz.value)
def model_to_screen(x, y, z):
m = get_model_matrix(c_double, glGetDoublev)
p = get_projection_matrix(c_double, glGetDoublev)
w = get_viewport()
mx, my, mz = c_double(), c_double(), c_double()
gluProject(x, y, z, m, p, w, mx, my, mz)
return float(mx.value), float(my.value), float(mz.value)
def vec_subs(a, b):
return tuple(a[i] - b[i] for i in range(len(a)))
def billboard_matrix():
"""
Removes rotational components of
current matrix so that primitives
are always drawn facing the viewer.
|1|0|0|x|
|0|1|0|x|
|0|0|1|x| (x means left unchanged)
|x|x|x|x|
"""
m = get_model_matrix()
# XXX: for i in range(11): m[i] = i ?
m[0] = 1
m[1] = 0
m[2] = 0
m[4] = 0
m[5] = 1
m[6] = 0
m[8] = 0
m[9] = 0
m[10] = 1
glLoadMatrixf(m)
def create_bounds():
return [[S.Infinity, -S.Infinity, 0],
[S.Infinity, -S.Infinity, 0],
[S.Infinity, -S.Infinity, 0]]
def update_bounds(b, v):
if v is None:
return
for axis in range(3):
b[axis][0] = min([b[axis][0], v[axis]])
b[axis][1] = max([b[axis][1], v[axis]])
def interpolate(a_min, a_max, a_ratio):
return a_min + a_ratio * (a_max - a_min)
def rinterpolate(a_min, a_max, a_value):
a_range = a_max - a_min
if a_range == 0:
a_range = 1.0
return (a_value - a_min) / float(a_range)
def interpolate_color(color1, color2, ratio):
return tuple(interpolate(color1[i], color2[i], ratio) for i in range(3))
def scale_value(v, v_min, v_len):
return (v - v_min) / v_len
def scale_value_list(flist):
v_min, v_max = min(flist), max(flist)
v_len = v_max - v_min
return list(scale_value(f, v_min, v_len) for f in flist)
def strided_range(r_min, r_max, stride, max_steps=50):
o_min, o_max = r_min, r_max
if abs(r_min - r_max) < 0.001:
return []
try:
range(int(r_min - r_max))
except TypeError:
return []
if r_min > r_max:
raise ValueError("r_min can not be greater than r_max")
r_min_s = (r_min % stride)
r_max_s = stride - (r_max % stride)
if abs(r_max_s - stride) < 0.001:
r_max_s = 0.0
r_min -= r_min_s
r_max += r_max_s
r_steps = int((r_max - r_min)/stride)
if max_steps and r_steps > max_steps:
return strided_range(o_min, o_max, stride*2)
return [r_min] + list(r_min + e*stride for e in range(1, r_steps + 1)) + [r_max]
def parse_option_string(s):
if not isinstance(s, str):
return None
options = {}
for token in s.split(';'):
pieces = token.split('=')
if len(pieces) == 1:
option, value = pieces[0], ""
elif len(pieces) == 2:
option, value = pieces
else:
raise ValueError("Plot option string '%s' is malformed." % (s))
options[option.strip()] = value.strip()
return options
def dot_product(v1, v2):
return sum(v1[i]*v2[i] for i in range(3))
def vec_sub(v1, v2):
return tuple(v1[i] - v2[i] for i in range(3))
def vec_mag(v):
return sum(v[i]**2 for i in range(3))**(0.5)
| 4,619 | 23.0625 | 84 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/pygletplot/plot_controller.py
|
from __future__ import print_function, division
from pyglet.window import key
from pyglet.window.mouse import LEFT, RIGHT, MIDDLE
from util import get_direction_vectors, get_basis_vectors
class PlotController(object):
normal_mouse_sensitivity = 4.0
modified_mouse_sensitivity = 1.0
normal_key_sensitivity = 160.0
modified_key_sensitivity = 40.0
keymap = {
key.LEFT: 'left',
key.A: 'left',
key.NUM_4: 'left',
key.RIGHT: 'right',
key.D: 'right',
key.NUM_6: 'right',
key.UP: 'up',
key.W: 'up',
key.NUM_8: 'up',
key.DOWN: 'down',
key.S: 'down',
key.NUM_2: 'down',
key.Z: 'rotate_z_neg',
key.NUM_1: 'rotate_z_neg',
key.C: 'rotate_z_pos',
key.NUM_3: 'rotate_z_pos',
key.Q: 'spin_left',
key.NUM_7: 'spin_left',
key.E: 'spin_right',
key.NUM_9: 'spin_right',
key.X: 'reset_camera',
key.NUM_5: 'reset_camera',
key.NUM_ADD: 'zoom_in',
key.PAGEUP: 'zoom_in',
key.R: 'zoom_in',
key.NUM_SUBTRACT: 'zoom_out',
key.PAGEDOWN: 'zoom_out',
key.F: 'zoom_out',
key.RSHIFT: 'modify_sensitivity',
key.LSHIFT: 'modify_sensitivity',
key.F1: 'rot_preset_xy',
key.F2: 'rot_preset_xz',
key.F3: 'rot_preset_yz',
key.F4: 'rot_preset_perspective',
key.F5: 'toggle_axes',
key.F6: 'toggle_axe_colors',
key.F8: 'save_image'
}
def __init__(self, window, **kwargs):
self.invert_mouse_zoom = kwargs.pop('invert_mouse_zoom', False)
self.window = window
self.camera = window.camera
self.action = {
# Rotation around the view Y (up) vector
'left': False,
'right': False,
# Rotation around the view X vector
'up': False,
'down': False,
# Rotation around the view Z vector
'spin_left': False,
'spin_right': False,
# Rotation around the model Z vector
'rotate_z_neg': False,
'rotate_z_pos': False,
# Reset to the default rotation
'reset_camera': False,
# Performs camera z-translation
'zoom_in': False,
'zoom_out': False,
# Use alternative sensitivity (speed)
'modify_sensitivity': False,
# Rotation presets
'rot_preset_xy': False,
'rot_preset_xz': False,
'rot_preset_yz': False,
'rot_preset_perspective': False,
# axes
'toggle_axes': False,
'toggle_axe_colors': False,
# screenshot
'save_image': False
}
def update(self, dt):
z = 0
if self.action['zoom_out']:
z -= 1
if self.action['zoom_in']:
z += 1
if z != 0:
self.camera.zoom_relative(z/10.0, self.get_key_sensitivity()/10.0)
dx, dy, dz = 0, 0, 0
if self.action['left']:
dx -= 1
if self.action['right']:
dx += 1
if self.action['up']:
dy -= 1
if self.action['down']:
dy += 1
if self.action['spin_left']:
dz += 1
if self.action['spin_right']:
dz -= 1
if not self.is_2D():
if dx != 0:
self.camera.euler_rotate(dx*dt*self.get_key_sensitivity(),
*(get_direction_vectors()[1]))
if dy != 0:
self.camera.euler_rotate(dy*dt*self.get_key_sensitivity(),
*(get_direction_vectors()[0]))
if dz != 0:
self.camera.euler_rotate(dz*dt*self.get_key_sensitivity(),
*(get_direction_vectors()[2]))
else:
self.camera.mouse_translate(0, 0, dx*dt*self.get_key_sensitivity(),
-dy*dt*self.get_key_sensitivity())
rz = 0
if self.action['rotate_z_neg'] and not self.is_2D():
rz -= 1
if self.action['rotate_z_pos'] and not self.is_2D():
rz += 1
if rz != 0:
self.camera.euler_rotate(rz*dt*self.get_key_sensitivity(),
*(get_basis_vectors()[2]))
if self.action['reset_camera']:
self.camera.reset()
if self.action['rot_preset_xy']:
self.camera.set_rot_preset('xy')
if self.action['rot_preset_xz']:
self.camera.set_rot_preset('xz')
if self.action['rot_preset_yz']:
self.camera.set_rot_preset('yz')
if self.action['rot_preset_perspective']:
self.camera.set_rot_preset('perspective')
if self.action['toggle_axes']:
self.action['toggle_axes'] = False
self.camera.axes.toggle_visible()
if self.action['toggle_axe_colors']:
self.action['toggle_axe_colors'] = False
self.camera.axes.toggle_colors()
if self.action['save_image']:
self.action['save_image'] = False
self.window.plot.saveimage()
return True
def get_mouse_sensitivity(self):
if self.action['modify_sensitivity']:
return self.modified_mouse_sensitivity
else:
return self.normal_mouse_sensitivity
def get_key_sensitivity(self):
if self.action['modify_sensitivity']:
return self.modified_key_sensitivity
else:
return self.normal_key_sensitivity
def on_key_press(self, symbol, modifiers):
if symbol in self.keymap:
self.action[self.keymap[symbol]] = True
def on_key_release(self, symbol, modifiers):
if symbol in self.keymap:
self.action[self.keymap[symbol]] = False
def on_mouse_drag(self, x, y, dx, dy, buttons, modifiers):
if buttons & LEFT:
if self.is_2D():
self.camera.mouse_translate(x, y, dx, dy)
else:
self.camera.spherical_rotate((x - dx, y - dy), (x, y),
self.get_mouse_sensitivity())
if buttons & MIDDLE:
self.camera.zoom_relative([1, -1][self.invert_mouse_zoom]*dy,
self.get_mouse_sensitivity()/20.0)
if buttons & RIGHT:
self.camera.mouse_translate(x, y, dx, dy)
def on_mouse_scroll(self, x, y, dx, dy):
self.camera.zoom_relative([1, -1][self.invert_mouse_zoom]*dy,
self.get_mouse_sensitivity())
def is_2D(self):
functions = self.window.plot._functions
for i in functions:
if len(functions[i].i_vars) > 1 or len(functions[i].d_vars) > 2:
return False
return True
| 6,965 | 30.520362 | 79 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/pygletplot/plot_surface.py
|
from __future__ import print_function, division
from pyglet.gl import *
from plot_mode_base import PlotModeBase
from sympy.core import S
from sympy.core.compatibility import range
class PlotSurface(PlotModeBase):
default_rot_preset = 'perspective'
def _on_calculate_verts(self):
self.u_interval = self.intervals[0]
self.u_set = list(self.u_interval.frange())
self.v_interval = self.intervals[1]
self.v_set = list(self.v_interval.frange())
self.bounds = [[S.Infinity, -S.Infinity, 0],
[S.Infinity, -S.Infinity, 0],
[S.Infinity, -S.Infinity, 0]]
evaluate = self._get_evaluator()
self._calculating_verts_pos = 0.0
self._calculating_verts_len = float(
self.u_interval.v_len*self.v_interval.v_len)
verts = list()
b = self.bounds
for u in self.u_set:
column = list()
for v in self.v_set:
try:
_e = evaluate(u, v) # calculate vertex
except ZeroDivisionError:
_e = None
if _e is not None: # update bounding box
for axis in range(3):
b[axis][0] = min([b[axis][0], _e[axis]])
b[axis][1] = max([b[axis][1], _e[axis]])
column.append(_e)
self._calculating_verts_pos += 1.0
verts.append(column)
for axis in range(3):
b[axis][2] = b[axis][1] - b[axis][0]
if b[axis][2] == 0.0:
b[axis][2] = 1.0
self.verts = verts
self.push_wireframe(self.draw_verts(False, False))
self.push_solid(self.draw_verts(False, True))
def _on_calculate_cverts(self):
if not self.verts or not self.color:
return
def set_work_len(n):
self._calculating_cverts_len = float(n)
def inc_work_pos():
self._calculating_cverts_pos += 1.0
set_work_len(1)
self._calculating_cverts_pos = 0
self.cverts = self.color.apply_to_surface(self.verts,
self.u_set,
self.v_set,
set_len=set_work_len,
inc_pos=inc_work_pos)
self.push_solid(self.draw_verts(True, True))
def calculate_one_cvert(self, u, v):
vert = self.verts[u][v]
return self.color(vert[0], vert[1], vert[2],
self.u_set[u], self.v_set[v])
def draw_verts(self, use_cverts, use_solid_color):
def f():
for u in range(1, len(self.u_set)):
glBegin(GL_QUAD_STRIP)
for v in range(len(self.v_set)):
pa = self.verts[u - 1][v]
pb = self.verts[u][v]
if pa is None or pb is None:
glEnd()
glBegin(GL_QUAD_STRIP)
continue
if use_cverts:
ca = self.cverts[u - 1][v]
cb = self.cverts[u][v]
if ca is None:
ca = (0, 0, 0)
if cb is None:
cb = (0, 0, 0)
else:
if use_solid_color:
ca = cb = self.default_solid_color
else:
ca = cb = self.default_wireframe_color
glColor3f(*ca)
glVertex3f(*pa)
glColor3f(*cb)
glVertex3f(*pb)
glEnd()
return f
| 3,815 | 35.342857 | 71 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/pygletplot/plot_object.py
|
from __future__ import print_function, division
class PlotObject(object):
"""
Base class for objects which can be displayed in
a Plot.
"""
visible = True
def _draw(self):
if self.visible:
self.draw()
def draw(self):
"""
OpenGL rendering code for the plot object.
Override in base class.
"""
pass
| 387 | 18.4 | 52 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/pygletplot/plot_window.py
|
from __future__ import print_function, division
from pyglet.gl import *
from managed_window import ManagedWindow
from plot_camera import PlotCamera
from plot_controller import PlotController
from time import clock
class PlotWindow(ManagedWindow):
def __init__(self, plot, **kwargs):
"""
Named Arguments
===============
antialiasing = True
True OR False
ortho = False
True OR False
invert_mouse_zoom = False
True OR False
"""
self.plot = plot
self.camera = None
self._calculating = False
self.antialiasing = kwargs.pop('antialiasing', True)
self.ortho = kwargs.pop('ortho', False)
self.invert_mouse_zoom = kwargs.pop('invert_mouse_zoom', False)
self.linewidth = kwargs.pop('linewidth', 1.5)
self.title = kwargs.setdefault('caption', "SymPy Plot")
self.last_caption_update = 0
self.caption_update_interval = 0.2
self.drawing_first_object = True
super(PlotWindow, self).__init__(**kwargs)
def setup(self):
self.camera = PlotCamera(self, ortho=self.ortho)
self.controller = PlotController(self,
invert_mouse_zoom=self.invert_mouse_zoom)
self.push_handlers(self.controller)
glClearColor(1.0, 1.0, 1.0, 0.0)
glClearDepth(1.0)
glDepthFunc(GL_LESS)
glEnable(GL_DEPTH_TEST)
glEnable(GL_LINE_SMOOTH)
glShadeModel(GL_SMOOTH)
glLineWidth(self.linewidth)
glEnable(GL_BLEND)
glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA)
if self.antialiasing:
glHint(GL_LINE_SMOOTH_HINT, GL_NICEST)
glHint(GL_POLYGON_SMOOTH_HINT, GL_NICEST)
self.camera.setup_projection()
def on_resize(self, w, h):
super(PlotWindow, self).on_resize(w, h)
if self.camera is not None:
self.camera.setup_projection()
def update(self, dt):
self.controller.update(dt)
def draw(self):
self.plot._render_lock.acquire()
self.camera.apply_transformation()
calc_verts_pos, calc_verts_len = 0, 0
calc_cverts_pos, calc_cverts_len = 0, 0
should_update_caption = (clock() - self.last_caption_update >
self.caption_update_interval)
if len(self.plot._functions.values()) == 0:
self.drawing_first_object = True
for r in self.plot._functions.itervalues():
if self.drawing_first_object:
self.camera.set_rot_preset(r.default_rot_preset)
self.drawing_first_object = False
glPushMatrix()
r._draw()
glPopMatrix()
# might as well do this while we are
# iterating and have the lock rather
# than locking and iterating twice
# per frame:
if should_update_caption:
try:
if r.calculating_verts:
calc_verts_pos += r.calculating_verts_pos
calc_verts_len += r.calculating_verts_len
if r.calculating_cverts:
calc_cverts_pos += r.calculating_cverts_pos
calc_cverts_len += r.calculating_cverts_len
except ValueError:
pass
for r in self.plot._pobjects:
glPushMatrix()
r._draw()
glPopMatrix()
if should_update_caption:
self.update_caption(calc_verts_pos, calc_verts_len,
calc_cverts_pos, calc_cverts_len)
self.last_caption_update = clock()
if self.plot._screenshot:
self.plot._screenshot._execute_saving()
self.plot._render_lock.release()
def update_caption(self, calc_verts_pos, calc_verts_len,
calc_cverts_pos, calc_cverts_len):
caption = self.title
if calc_verts_len or calc_cverts_len:
caption += " (calculating"
if calc_verts_len > 0:
p = (calc_verts_pos / calc_verts_len) * 100
caption += " vertices %i%%" % (p)
if calc_cverts_len > 0:
p = (calc_cverts_pos / calc_cverts_len) * 100
caption += " colors %i%%" % (p)
caption += ")"
if self.caption != caption:
self.set_caption(caption)
| 4,467 | 30.464789 | 71 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/pygletplot/plot.py
|
from __future__ import print_function, division
from sympy import Integer
from sympy.core.compatibility import is_sequence
from threading import RLock
# it is sufficient to import "pyglet" here once
try:
from pyglet.gl import *
except ImportError:
raise ImportError("pyglet is required for plotting.\n "
"visit http://www.pyglet.org/")
from plot_object import PlotObject
from plot_axes import PlotAxes
from plot_window import PlotWindow
from plot_mode import PlotMode
from time import sleep
from os import getcwd, listdir
from util import parse_option_string
from sympy.geometry.entity import GeometryEntity
from sympy.utilities.decorator import doctest_depends_on
@doctest_depends_on(modules=('pyglet',))
class PygletPlot(object):
"""
Plot Examples
=============
See examples/advaned/pyglet_plotting.py for many more examples.
>>> from sympy.plotting.pygletplot import PygletPlot as Plot
>>> from sympy.abc import x, y, z
>>> Plot(x*y**3-y*x**3)
[0]: -x**3*y + x*y**3, 'mode=cartesian'
>>> p = Plot()
>>> p[1] = x*y
>>> p[1].color = z, (0.4,0.4,0.9), (0.9,0.4,0.4)
>>> p = Plot()
>>> p[1] = x**2+y**2
>>> p[2] = -x**2-y**2
Variable Intervals
==================
The basic format is [var, min, max, steps], but the
syntax is flexible and arguments left out are taken
from the defaults for the current coordinate mode:
>>> Plot(x**2) # implies [x,-5,5,100]
[0]: x**2, 'mode=cartesian'
>>> Plot(x**2, [], []) # [x,-1,1,40], [y,-1,1,40]
[0]: x**2, 'mode=cartesian'
>>> Plot(x**2-y**2, [100], [100]) # [x,-1,1,100], [y,-1,1,100]
[0]: x**2 - y**2, 'mode=cartesian'
>>> Plot(x**2, [x,-13,13,100])
[0]: x**2, 'mode=cartesian'
>>> Plot(x**2, [-13,13]) # [x,-13,13,100]
[0]: x**2, 'mode=cartesian'
>>> Plot(x**2, [x,-13,13]) # [x,-13,13,10]
[0]: x**2, 'mode=cartesian'
>>> Plot(1*x, [], [x], mode='cylindrical')
... # [unbound_theta,0,2*Pi,40], [x,-1,1,20]
[0]: x, 'mode=cartesian'
Coordinate Modes
================
Plot supports several curvilinear coordinate modes, and
they independent for each plotted function. You can specify
a coordinate mode explicitly with the 'mode' named argument,
but it can be automatically determined for Cartesian or
parametric plots, and therefore must only be specified for
polar, cylindrical, and spherical modes.
Specifically, Plot(function arguments) and Plot[n] =
(function arguments) will interpret your arguments as a
Cartesian plot if you provide one function and a parametric
plot if you provide two or three functions. Similarly, the
arguments will be interpreted as a curve if one variable is
used, and a surface if two are used.
Supported mode names by number of variables:
1: parametric, cartesian, polar
2: parametric, cartesian, cylindrical = polar, spherical
>>> Plot(1, mode='spherical') # doctest: +SKIP
Calculator-like Interface
=========================
>>> p = Plot(visible=False)
>>> f = x**2
>>> p[1] = f
>>> p[2] = f.diff(x)
>>> p[3] = f.diff(x).diff(x) # doctest: +SKIP
>>> p # doctest: +SKIP
[1]: x**2, 'mode=cartesian'
[2]: 2*x, 'mode=cartesian'
[3]: 2, 'mode=cartesian'
>>> p.show()
>>> p.clear()
>>> p
<blank plot>
>>> p[1] = x**2+y**2
>>> p[1].style = 'solid'
>>> p[2] = -x**2-y**2
>>> p[2].style = 'wireframe'
>>> p[1].color = z, (0.4,0.4,0.9), (0.9,0.4,0.4)
>>> p[1].style = 'both'
>>> p[2].style = 'both'
>>> p.close()
Plot Window Keyboard Controls
=============================
Screen Rotation:
X,Y axis Arrow Keys, A,S,D,W, Numpad 4,6,8,2
Z axis Q,E, Numpad 7,9
Model Rotation:
Z axis Z,C, Numpad 1,3
Zoom: R,F, PgUp,PgDn, Numpad +,-
Reset Camera: X, Numpad 5
Camera Presets:
XY F1
XZ F2
YZ F3
Perspective F4
Sensitivity Modifier: SHIFT
Axes Toggle:
Visible F5
Colors F6
Close Window: ESCAPE
=============================
"""
@doctest_depends_on(modules=('pyglet',))
def __init__(self, *fargs, **win_args):
"""
Positional Arguments
====================
Any given positional arguments are used to
initialize a plot function at index 1. In
other words...
>>> from sympy.plotting.pygletplot import PygletPlot as Plot
>>> from sympy.core import Symbol
>>> from sympy.abc import x
>>> p = Plot(x**2, visible=False)
...is equivalent to...
>>> p = Plot(visible=False)
>>> p[1] = x**2
Note that in earlier versions of the plotting
module, you were able to specify multiple
functions in the initializer. This functionality
has been dropped in favor of better automatic
plot plot_mode detection.
Named Arguments
===============
axes
An option string of the form
"key1=value1; key2 = value2" which
can use the following options:
style = ordinate
none OR frame OR box OR ordinate
stride = 0.25
val OR (val_x, val_y, val_z)
overlay = True (draw on top of plot)
True OR False
colored = False (False uses Black,
True uses colors
R,G,B = X,Y,Z)
True OR False
label_axes = False (display axis names
at endpoints)
True OR False
visible = True (show immediately
True OR False
The following named arguments are passed as
arguments to window initialization:
antialiasing = True
True OR False
ortho = False
True OR False
invert_mouse_zoom = False
True OR False
"""
self._win_args = win_args
self._window = None
self._render_lock = RLock()
self._functions = {}
self._pobjects = []
self._screenshot = ScreenShot(self)
axe_options = parse_option_string(win_args.pop('axes', ''))
self.axes = PlotAxes(**axe_options)
self._pobjects.append(self.axes)
self[0] = fargs
if win_args.get('visible', True):
self.show()
## Window Interfaces
def show(self):
"""
Creates and displays a plot window, or activates it
(gives it focus) if it has already been created.
"""
if self._window and not self._window.has_exit:
self._window.activate()
else:
self._win_args['visible'] = True
self.axes.reset_resources()
if hasattr(self, '_doctest_depends_on'):
self._win_args['runfromdoctester'] = True
self._window = PlotWindow(self, **self._win_args)
def close(self):
"""
Closes the plot window.
"""
if self._window:
self._window.close()
def saveimage(self, outfile=None, format='', size=(600, 500)):
"""
Saves a screen capture of the plot window to an
image file.
If outfile is given, it can either be a path
or a file object. Otherwise a png image will
be saved to the current working directory.
If the format is omitted, it is determined from
the filename extension.
"""
self._screenshot.save(outfile, format, size)
## Function List Interfaces
def clear(self):
"""
Clears the function list of this plot.
"""
self._render_lock.acquire()
self._functions = {}
self.adjust_all_bounds()
self._render_lock.release()
def __getitem__(self, i):
"""
Returns the function at position i in the
function list.
"""
return self._functions[i]
def __setitem__(self, i, args):
"""
Parses and adds a PlotMode to the function
list.
"""
if not (isinstance(i, (int, Integer)) and i >= 0):
raise ValueError("Function index must "
"be an integer >= 0.")
if isinstance(args, PlotObject):
f = args
else:
if (not is_sequence(args)) or isinstance(args, GeometryEntity):
args = [args]
if len(args) == 0:
return # no arguments given
kwargs = dict(bounds_callback=self.adjust_all_bounds)
f = PlotMode(*args, **kwargs)
if f:
self._render_lock.acquire()
self._functions[i] = f
self._render_lock.release()
else:
raise ValueError("Failed to parse '%s'."
% ', '.join(str(a) for a in args))
def __delitem__(self, i):
"""
Removes the function in the function list at
position i.
"""
self._render_lock.acquire()
del self._functions[i]
self.adjust_all_bounds()
self._render_lock.release()
def firstavailableindex(self):
"""
Returns the first unused index in the function list.
"""
i = 0
self._render_lock.acquire()
while i in self._functions:
i += 1
self._render_lock.release()
return i
def append(self, *args):
"""
Parses and adds a PlotMode to the function
list at the first available index.
"""
self.__setitem__(self.firstavailableindex(), args)
def __len__(self):
"""
Returns the number of functions in the function list.
"""
return len(self._functions)
def __iter__(self):
"""
Allows iteration of the function list.
"""
return self._functions.itervalues()
def __repr__(self):
return str(self)
def __str__(self):
"""
Returns a string containing a new-line separated
list of the functions in the function list.
"""
s = ""
if len(self._functions) == 0:
s += "<blank plot>"
else:
self._render_lock.acquire()
s += "\n".join(["%s[%i]: %s" % ("", i, str(self._functions[i]))
for i in self._functions])
self._render_lock.release()
return s
def adjust_all_bounds(self):
self._render_lock.acquire()
self.axes.reset_bounding_box()
for f in self._functions:
self.axes.adjust_bounds(self._functions[f].bounds)
self._render_lock.release()
def wait_for_calculations(self):
sleep(0)
self._render_lock.acquire()
for f in self._functions:
a = self._functions[f]._get_calculating_verts
b = self._functions[f]._get_calculating_cverts
while a() or b():
sleep(0)
self._render_lock.release()
class ScreenShot:
def __init__(self, plot):
self._plot = plot
self.screenshot_requested = False
self.outfile = None
self.format = ''
self.invisibleMode = False
self.flag = 0
def __nonzero__(self):
if self.screenshot_requested:
return 1
return 0
__bool__ = __nonzero__
def _execute_saving(self):
if self.flag < 3:
self.flag += 1
return
size_x, size_y = self._plot._window.get_size()
size = size_x*size_y*4*sizeof(c_ubyte)
image = create_string_buffer(size)
glReadPixels(0, 0, size_x, size_y, GL_RGBA, GL_UNSIGNED_BYTE, image)
from PIL import Image
im = Image.frombuffer('RGBA', (size_x, size_y),
image.raw, 'raw', 'RGBA', 0, 1)
im.transpose(Image.FLIP_TOP_BOTTOM).save(self.outfile, self.format)
self.flag = 0
self.screenshot_requested = False
if self.invisibleMode:
self._plot._window.close()
def save(self, outfile=None, format='', size=(600, 500)):
self.outfile = outfile
self.format = format
self.size = size
self.screenshot_requested = True
if not self._plot._window or self._plot._window.has_exit:
self._plot._win_args['visible'] = False
self._plot._win_args['width'] = size[0]
self._plot._win_args['height'] = size[1]
self._plot.axes.reset_resources()
self._plot._window = PlotWindow(self._plot, **self._plot._win_args)
self.invisibleMode = True
if self.outfile is None:
self.outfile = self._create_unique_path()
print(self.outfile)
def _create_unique_path(self):
cwd = getcwd()
l = listdir(cwd)
path = ''
i = 0
while True:
if not 'plot_%s.png' % i in l:
path = cwd + '/plot_%s.png' % i
break
i += 1
return path
| 13,256 | 27.206383 | 79 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/pygletplot/plot_interval.py
|
from __future__ import print_function, division
from sympy import Symbol, Integer, sympify
from sympy.core.compatibility import range
class PlotInterval(object):
"""
"""
_v, _v_min, _v_max, _v_steps = None, None, None, None
def require_all_args(f):
def check(self, *args, **kwargs):
for g in [self._v, self._v_min, self._v_max, self._v_steps]:
if g is None:
raise ValueError("PlotInterval is incomplete.")
return f(self, *args, **kwargs)
return check
def __init__(self, *args):
if len(args) == 1:
if isinstance(args[0], PlotInterval):
self.fill_from(args[0])
return
elif isinstance(args[0], str):
try:
args = eval(args[0])
except TypeError:
s_eval_error = "Could not interpret string %s."
raise ValueError(s_eval_error % (args[0]))
elif isinstance(args[0], (tuple, list)):
args = args[0]
else:
raise ValueError("Not an interval.")
if not isinstance(args, (tuple, list)) or len(args) > 4:
f_error = "PlotInterval must be a tuple or list of length 4 or less."
raise ValueError(f_error)
args = list(args)
if len(args) > 0 and (args[0] is None or isinstance(args[0], Symbol)):
self.v = args.pop(0)
if len(args) in [2, 3]:
self.v_min = args.pop(0)
self.v_max = args.pop(0)
if len(args) == 1:
self.v_steps = args.pop(0)
elif len(args) == 1:
self.v_steps = args.pop(0)
def get_v(self):
return self._v
def set_v(self, v):
if v is None:
self._v = None
return
if not isinstance(v, Symbol):
raise ValueError("v must be a sympy Symbol.")
self._v = v
def get_v_min(self):
return self._v_min
def set_v_min(self, v_min):
if v_min is None:
self._v_min = None
return
try:
self._v_min = sympify(v_min)
float(self._v_min.evalf())
except TypeError:
raise ValueError("v_min could not be interpreted as a number.")
def get_v_max(self):
return self._v_max
def set_v_max(self, v_max):
if v_max is None:
self._v_max = None
return
try:
self._v_max = sympify(v_max)
float(self._v_max.evalf())
except TypeError:
raise ValueError("v_max could not be interpreted as a number.")
def get_v_steps(self):
return self._v_steps
def set_v_steps(self, v_steps):
if v_steps is None:
self._v_steps = None
return
if isinstance(v_steps, int):
v_steps = Integer(v_steps)
elif not isinstance(v_steps, Integer):
raise ValueError("v_steps must be an int or sympy Integer.")
if v_steps <= Integer(0):
raise ValueError("v_steps must be positive.")
self._v_steps = v_steps
@require_all_args
def get_v_len(self):
return self.v_steps + 1
v = property(get_v, set_v)
v_min = property(get_v_min, set_v_min)
v_max = property(get_v_max, set_v_max)
v_steps = property(get_v_steps, set_v_steps)
v_len = property(get_v_len)
def fill_from(self, b):
if b.v is not None:
self.v = b.v
if b.v_min is not None:
self.v_min = b.v_min
if b.v_max is not None:
self.v_max = b.v_max
if b.v_steps is not None:
self.v_steps = b.v_steps
@staticmethod
def try_parse(*args):
"""
Returns a PlotInterval if args can be interpreted
as such, otherwise None.
"""
if len(args) == 1 and isinstance(args[0], PlotInterval):
return args[0]
try:
return PlotInterval(*args)
except ValueError:
return None
def _str_base(self):
return ",".join([str(self.v), str(self.v_min),
str(self.v_max), str(self.v_steps)])
def __repr__(self):
"""
A string representing the interval in class constructor form.
"""
return "PlotInterval(%s)" % (self._str_base())
def __str__(self):
"""
A string representing the interval in list form.
"""
return "[%s]" % (self._str_base())
@require_all_args
def assert_complete(self):
pass
@require_all_args
def vrange(self):
"""
Yields v_steps+1 sympy numbers ranging from
v_min to v_max.
"""
d = (self.v_max - self.v_min) / self.v_steps
for i in range(self.v_steps + 1):
a = self.v_min + (d * Integer(i))
yield a
@require_all_args
def vrange2(self):
"""
Yields v_steps pairs of sympy numbers ranging from
(v_min, v_min + step) to (v_max - step, v_max).
"""
d = (self.v_max - self.v_min) / self.v_steps
a = self.v_min + (d * Integer(0))
for i in range(self.v_steps):
b = self.v_min + (d * Integer(i + 1))
yield a, b
a = b
def frange(self):
for i in self.vrange():
yield float(i.evalf())
| 5,432 | 28.851648 | 81 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/pygletplot/__init__.py
|
"""Plotting module that can plot 2D and 3D functions
"""
from sympy.utilities.decorator import doctest_depends_on
try:
@doctest_depends_on(modules=('pyglet',))
def PygletPlot(*args, **kwargs):
"""
Plot Examples
=============
See examples/advanced/pyglet_plotting.py for many more examples.
>>> from sympy.plotting.pygletplot import PygletPlot as Plot
>>> from sympy import symbols
>>> from sympy.abc import x, y, z
>>> Plot(x*y**3-y*x**3)
[0]: -x**3*y + x*y**3, 'mode=cartesian'
>>> p = Plot()
>>> p[1] = x*y
>>> p[1].color = z, (0.4,0.4,0.9), (0.9,0.4,0.4)
>>> p = Plot()
>>> p[1] = x**2+y**2
>>> p[2] = -x**2-y**2
Variable Intervals
==================
The basic format is [var, min, max, steps], but the
syntax is flexible and arguments left out are taken
from the defaults for the current coordinate mode:
>>> Plot(x**2) # implies [x,-5,5,100]
[0]: x**2, 'mode=cartesian'
>>> Plot(x**2, [], []) # [x,-1,1,40], [y,-1,1,40]
[0]: x**2, 'mode=cartesian'
>>> Plot(x**2-y**2, [100], [100]) # [x,-1,1,100], [y,-1,1,100]
[0]: x**2 - y**2, 'mode=cartesian'
>>> Plot(x**2, [x,-13,13,100])
[0]: x**2, 'mode=cartesian'
>>> Plot(x**2, [-13,13]) # [x,-13,13,100]
[0]: x**2, 'mode=cartesian'
>>> Plot(x**2, [x,-13,13]) # [x,-13,13,100]
[0]: x**2, 'mode=cartesian'
>>> Plot(1*x, [], [x], mode='cylindrical')
... # [unbound_theta,0,2*Pi,40], [x,-1,1,20]
[0]: x, 'mode=cartesian'
Coordinate Modes
================
Plot supports several curvilinear coordinate modes, and
they independent for each plotted function. You can specify
a coordinate mode explicitly with the 'mode' named argument,
but it can be automatically determined for Cartesian or
parametric plots, and therefore must only be specified for
polar, cylindrical, and spherical modes.
Specifically, Plot(function arguments) and Plot[n] =
(function arguments) will interpret your arguments as a
Cartesian plot if you provide one function and a parametric
plot if you provide two or three functions. Similarly, the
arguments will be interpreted as a curve if one variable is
used, and a surface if two are used.
Supported mode names by number of variables:
1: parametric, cartesian, polar
2: parametric, cartesian, cylindrical = polar, spherical
>>> Plot(1, mode='spherical') # doctest: +SKIP
Calculator-like Interface
=========================
>>> p = Plot(visible=False)
>>> f = x**2
>>> p[1] = f
>>> p[2] = f.diff(x)
>>> p[3] = f.diff(x).diff(x) # doctest: +SKIP
>>> p # doctest: +SKIP
[1]: x**2, 'mode=cartesian'
[2]: 2*x, 'mode=cartesian'
[3]: 2, 'mode=cartesian'
>>> p.show()
>>> p.clear()
>>> p
<blank plot>
>>> p[1] = x**2+y**2
>>> p[1].style = 'solid'
>>> p[2] = -x**2-y**2
>>> p[2].style = 'wireframe'
>>> p[1].color = z, (0.4,0.4,0.9), (0.9,0.4,0.4)
>>> p[1].style = 'both'
>>> p[2].style = 'both'
>>> p.close()
Plot Window Keyboard Controls
=============================
Screen Rotation:
X,Y axis Arrow Keys, A,S,D,W, Numpad 4,6,8,2
Z axis Q,E, Numpad 7,9
Model Rotation:
Z axis Z,C, Numpad 1,3
Zoom: R,F, PgUp,PgDn, Numpad +,-
Reset Camera: X, Numpad 5
Camera Presets:
XY F1
XZ F2
YZ F3
Perspective F4
Sensitivity Modifier: SHIFT
Axes Toggle:
Visible F5
Colors F6
Close Window: ESCAPE
=============================
"""
import plot
return plot.PygletPlot(*args, **kwargs)
except Exception as e:
def PygletPlot(*args, **kwargs):
raise e
| 4,266 | 28.427586 | 72 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/pygletplot/tests/test_plotting.py
|
from sympy.external.importtools import import_module
disabled = False
# if pyglet.gl fails to import, e.g. opengl is missing, we disable the tests
pyglet_gl = import_module("pyglet.gl", catch=(OSError,))
pyglet_window = import_module("pyglet.window", catch=(OSError,))
if not pyglet_gl or not pyglet_window:
disabled = True
from sympy import symbols, sin, cos
x, y, z = symbols('x, y, z')
def test_import():
from sympy.plotting.pygletplot import PygletPlot
def test_plot_2d():
from sympy.plotting.pygletplot import PygletPlot
p = PygletPlot(x, [x, -5, 5, 4], visible=False)
p.wait_for_calculations()
def test_plot_2d_discontinuous():
from sympy.plotting.pygletplot import PygletPlot
p = PygletPlot(1/x, [x, -1, 1, 2], visible=False)
p.wait_for_calculations()
def test_plot_3d():
from sympy.plotting.pygletplot import PygletPlot
p = PygletPlot(x*y, [x, -5, 5, 5], [y, -5, 5, 5], visible=False)
p.wait_for_calculations()
def test_plot_3d_discontinuous():
from sympy.plotting.pygletplot import PygletPlot
p = PygletPlot(1/x, [x, -3, 3, 6], [y, -1, 1, 1], visible=False)
p.wait_for_calculations()
def test_plot_2d_polar():
from sympy.plotting.pygletplot import PygletPlot
p = PygletPlot(1/x, [x, -1, 1, 4], 'mode=polar', visible=False)
p.wait_for_calculations()
def test_plot_3d_cylinder():
from sympy.plotting.pygletplot import PygletPlot
p = PygletPlot(
1/y, [x, 0, 6.282, 4], [y, -1, 1, 4], 'mode=polar;style=solid',
visible=False)
p.wait_for_calculations()
def test_plot_3d_spherical():
from sympy.plotting.pygletplot import PygletPlot
p = PygletPlot(
1, [x, 0, 6.282, 4], [y, 0, 3.141,
4], 'mode=spherical;style=wireframe',
visible=False)
p.wait_for_calculations()
def test_plot_2d_parametric():
from sympy.plotting.pygletplot import PygletPlot
p = PygletPlot(sin(x), cos(x), [x, 0, 6.282, 4], visible=False)
p.wait_for_calculations()
def test_plot_3d_parametric():
from sympy.plotting.pygletplot import PygletPlot
p = PygletPlot(sin(x), cos(x), x/5.0, [x, 0, 6.282, 4], visible=False)
p.wait_for_calculations()
def _test_plot_log():
from sympy.plotting.pygletplot import PygletPlot
p = PygletPlot(log(x), [x, 0, 6.282, 4], 'mode=polar', visible=False)
p.wait_for_calculations()
def test_plot_integral():
# Make sure it doesn't treat x as an independent variable
from sympy.plotting.pygletplot import PygletPlot
from sympy import Integral
p = PygletPlot(Integral(z*x, (x, 1, z), (z, 1, y)), visible=False)
p.wait_for_calculations()
| 2,653 | 28.164835 | 76 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/pygletplot/tests/__init__.py
| 0 | 0 | 0 |
py
|
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/intervalmath/interval_arithmetic.py
|
"""
Interval Arithmetic for plotting.
This module does not implement interval arithmetic accurately and
hence cannot be used for purposes other than plotting. If you want
to use interval arithmetic, use mpmath's interval arithmetic.
The module implements interval arithmetic using numpy and
python floating points. The rounding up and down is not handled
and hence this is not an accurate implementation of interval
arithmetic.
The module uses numpy for speed which cannot be achieved with mpmath.
"""
# Q: Why use numpy? Why not simply use mpmath's interval arithmetic?
# A: mpmath's interval arithmetic simulates a floating point unit
# and hence is slow, while numpy evaluations are orders of magnitude
# faster.
# Q: Why create a separate class for intervals? Why not use sympy's
# Interval Sets?
# A: The functionalities that will be required for plotting is quite
# different from what Interval Sets implement.
# Q: Why is rounding up and down according to IEEE754 not handled?
# A: It is not possible to do it in both numpy and python. An external
# library has to used, which defeats the whole purpose i.e., speed. Also
# rounding is handled for very few functions in those libraries.
# Q Will my plots be affected?
# A It will not affect most of the plots. The interval arithmetic
# module based suffers the same problems as that of floating point
# arithmetic.
from __future__ import print_function, division
from sympy.simplify.simplify import nsimplify
class interval(object):
""" Represents an interval containing floating points as start and
end of the interval
The is_valid variable tracks whether the interval obtained as the
result of the function is in the domain and is continuous.
- True: Represents the interval result of a function is continuous and
in the domain of the function.
- False: The interval argument of the function was not in the domain of
the function, hence the is_valid of the result interval is False
- None: The function was not continuous over the interval or
the function's argument interval is partly in the domain of the
function
The comparison of two intervals returns a tuple of two 3-valued logic
values.
The first value determines the comparison as follows:
- True: If the comparison is True throughout the intervals.
- False: If the comparison is False throughout the intervals.
- None: If the comparison is True for some part of the intervals.
The second value is determined as follows:
- True: If both the intervals in comparison are valid.
- False: If at least one of the intervals is False, else
- None
"""
def __init__(self, *args, **kwargs):
self.is_valid = kwargs.pop('is_valid', True)
if len(args) == 1:
if isinstance(args[0], interval):
self.start, self.end = args[0].start, args[0].end
else:
self.start = float(args[0])
self.end = float(args[0])
elif len(args) == 2:
if args[0] < args[1]:
self.start = float(args[0])
self.end = float(args[1])
else:
self.start = float(args[1])
self.end = float(args[0])
else:
raise ValueError("interval takes a maximum of two float values "
"as arguments")
@property
def mid(self):
return (self.start + self.end) / 2.0
@property
def width(self):
return self.end - self.start
def __repr__(self):
return "interval(%f, %f)" % (self.start, self.end)
def __str__(self):
return "[%f, %f]" % (self.start, self.end)
def __lt__(self, other):
if isinstance(other, (int, float)):
if self.end < other:
return (True, self.is_valid)
elif self.start > other:
return (False, self.is_valid)
else:
return (None, self.is_valid)
elif isinstance(other, interval):
if self.is_valid is False or other.is_valid is False:
valid = False
elif self.is_valid is None or other.is_valid is None:
valid = None
else:
valid = True
if self.end < other. start:
return (True, valid)
if self.start > other.end:
return (False, valid)
return (None, valid)
else:
return NotImplemented
def __gt__(self, other):
if isinstance(other, (int, float)):
if self.start > other:
return (True, self.is_valid)
elif self.end < other:
return (False, self.is_valid)
else:
return (None, self.is_valid)
elif isinstance(other, interval):
return other.__lt__(self)
else:
return NotImplemented
def __eq__(self, other):
if isinstance(other, (int, float)):
if self.start == other and self.end == other:
return (True, self.is_valid)
if other in self:
return (None, self.is_valid)
else:
return (False, self.is_valid)
if isinstance(other, interval):
if self.is_valid is False or other.is_valid is False:
valid = False
elif self.is_valid is None or other.is_valid is None:
valid = None
else:
valid = True
if self.start == other.start and self.end == other.end:
return (True, valid)
elif self.__lt__(other)[0] is not None:
return (False, valid)
else:
return (None, valid)
else:
return NotImplemented
def __ne__(self, other):
if isinstance(other, (int, float)):
if self.start == other and self.end == other:
return (False, self.is_valid)
if other in self:
return (None, self.is_valid)
else:
return (True, self.is_valid)
if isinstance(other, interval):
if self.is_valid is False or other.is_valid is False:
valid = False
elif self.is_valid is None or other.is_valid is None:
valid = None
else:
valid = True
if self.start == other.start and self.end == other.end:
return (False, valid)
if not self.__lt__(other)[0] is None:
return (True, valid)
return (None, valid)
else:
return NotImplemented
def __le__(self, other):
if isinstance(other, (int, float)):
if self.end <= other:
return (True, self.is_valid)
if self.start > other:
return (False, self.is_valid)
else:
return (None, self.is_valid)
if isinstance(other, interval):
if self.is_valid is False or other.is_valid is False:
valid = False
elif self.is_valid is None or other.is_valid is None:
valid = None
else:
valid = True
if self.end <= other.start:
return (True, valid)
if self.start > other.end:
return (False, valid)
return (None, valid)
else:
return NotImplemented
def __ge__(self, other):
if isinstance(other, (int, float)):
if self.start >= other:
return (True, self.is_valid)
elif self.end < other:
return (False, self.is_valid)
else:
return (None, self.is_valid)
elif isinstance(other, interval):
return other.__le__(self)
def __add__(self, other):
if isinstance(other, (int, float)):
if self.is_valid:
return interval(self.start + other, self.end + other)
else:
start = self.start + other
end = self.end + other
return interval(start, end, is_valid=self.is_valid)
elif isinstance(other, interval):
start = self.start + other.start
end = self.end + other.end
if self.is_valid and other.is_valid:
return interval(start, end)
elif self.is_valid is False or other.is_valid is False:
return interval(start, end, is_valid=False)
else:
return interval(start, end, is_valid=None)
else:
return NotImplemented
__radd__ = __add__
def __sub__(self, other):
if isinstance(other, (int, float)):
start = self.start - other
end = self.end - other
return interval(start, end, is_valid=self.is_valid)
elif isinstance(other, interval):
start = self.start - other.end
end = self.end - other.start
if self.is_valid and other.is_valid:
return interval(self.start - other.end, self.end - other.start)
elif self.is_valid is False or other.is_valid is False:
return interval(start, end, is_valid=False)
else:
return interval(start, end, is_valid=None)
else:
return NotImplemented
def __rsub__(self, other):
if isinstance(other, (int, float)):
start = other - self.end
end = other - self.start
return interval(start, end, is_valid=self.is_valid)
elif isinstance(other, interval):
return other.__sub__(self)
else:
return NotImplemented
def __neg__(self):
if self.is_valid:
return interval(-self.end, -self.start)
else:
return interval(-self.end, -self.start, is_valid=self.is_valid)
def __mul__(self, other):
if isinstance(other, interval):
if self.is_valid is False or other.is_valid is False:
return interval(-float('inf'), float('inf'), is_valid=False)
elif self.is_valid is None or other.is_valid is None:
return interval(-float('inf'), float('inf'), is_valid=None)
else:
inters = []
inters.append(self.start * other.start)
inters.append(self.end * other.start)
inters.append(self.start * other.end)
inters.append(self.end * other.end)
start = min(inters)
end = max(inters)
return interval(start, end)
elif isinstance(other, (int, float)):
return interval(self.start*other, self.end*other, is_valid=self.is_valid)
else:
return NotImplemented
__rmul__ = __mul__
def __contains__(self, other):
if isinstance(other, (int, float)):
return self.start <= other and self.end >= other
else:
return self.start <= other.start and other.end <= self.end
def __rdiv__(self, other):
if isinstance(other, (int, float)):
other = interval(other)
return other.__div__(self)
elif isinstance(other, interval):
return other.__div__(self)
else:
return NotImplemented
def __div__(self, other):
# Both None and False are handled
if not self.is_valid:
# Don't divide as the value is not valid
return interval(-float('inf'), float('inf'), is_valid=self.is_valid)
if isinstance(other, (int, float)):
if other == 0:
# Divide by zero encountered. valid nowhere
return interval(-float('inf'), float('inf'), is_valid=False)
else:
return interval(self.start / other, self.end / other)
elif isinstance(other, interval):
if other.is_valid is False or self.is_valid is False:
return interval(-float('inf'), float('inf'), is_valid=False)
elif other.is_valid is None or self.is_valid is None:
return interval(-float('inf'), float('inf'), is_valid=None)
else:
# denominator contains both signs, i.e. being divided by zero
# return the whole real line with is_valid = None
if 0 in other:
return interval(-float('inf'), float('inf'), is_valid=None)
# denominator negative
this = self
if other.end < 0:
this = -this
other = -other
# denominator positive
inters = []
inters.append(this.start / other.start)
inters.append(this.end / other.start)
inters.append(this.start / other.end)
inters.append(this.end / other.end)
start = max(inters)
end = min(inters)
return interval(start, end)
else:
return NotImplemented
__truediv__ = __div__
__rtruediv__ = __rdiv__
def __pow__(self, other):
# Implements only power to an integer.
from .lib_interval import exp, log
if not self.is_valid:
return self
if isinstance(other, interval):
return exp(other * log(self))
elif isinstance(other, (float, int)):
if other < 0:
return 1 / self.__pow__(abs(other))
else:
if int(other) == other:
return _pow_int(self, other)
else:
return _pow_float(self, other)
else:
return NotImplemented
def __rpow__(self, other):
if isinstance(other, (float, int)):
if not self.is_valid:
#Don't do anything
return self
elif other < 0:
if self.width > 0:
return interval(-float('inf'), float('inf'), is_valid=False)
else:
power_rational = nsimplify(self.start)
num, denom = power_rational.as_numer_denom()
if denom % 2 == 0:
return interval(-float('inf'), float('inf'),
is_valid=False)
else:
start = -abs(other)**self.start
end = start
return interval(start, end)
else:
return interval(other**self.start, other**self.end)
elif isinstance(other, interval):
return other.__pow__(self)
else:
return NotImplemented
def __hash__(self):
return hash((self.is_valid, self.start, self.end))
def _pow_float(inter, power):
"""Evaluates an interval raised to a floating point."""
power_rational = nsimplify(power)
num, denom = power_rational.as_numer_denom()
if num % 2 == 0:
start = abs(inter.start)**power
end = abs(inter.end)**power
if start < 0:
ret = interval(0, max(start, end))
else:
ret = interval(start, end)
return ret
elif denom % 2 == 0:
if inter.end < 0:
return interval(-float('inf'), float('inf'), is_valid=False)
elif inter.start < 0:
return interval(0, inter.end**power, is_valid=None)
else:
return interval(inter.start**power, inter.end**power)
else:
if inter.start < 0:
start = -abs(inter.start)**power
else:
start = inter.start**power
if inter.end < 0:
end = -abs(inter.end)**power
else:
end = inter.end**power
return interval(start, end, is_valid=inter.is_valid)
def _pow_int(inter, power):
"""Evaluates an interval raised to an integer power"""
power = int(power)
if power & 1:
return interval(inter.start**power, inter.end**power)
else:
if inter.start < 0 and inter.end > 0:
start = 0
end = max(inter.start**power, inter.end**power)
return interval(start, end)
else:
return interval(inter.start**power, inter.end**power)
| 16,450 | 35.476718 | 85 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/intervalmath/lib_interval.py
|
from __future__ import print_function, division
from sympy.plotting.intervalmath import interval
from sympy.external import import_module
from sympy.core.compatibility import reduce
""" The module contains implemented functions for interval arithmetic."""
def Abs(x):
if isinstance(x, (int, float)):
return interval(abs(x))
elif isinstance(x, interval):
if x.start < 0 and x.end > 0:
return interval(0, max(abs(x.start), abs(x.end)), is_valid=x.is_valid)
else:
return interval(abs(x.start), abs(x.end))
else:
raise NotImplementedError
#Monotonic
def exp(x):
"""evaluates the exponential of an interval"""
np = import_module('numpy')
if isinstance(x, (int, float)):
return interval(np.exp(x), np.exp(x))
elif isinstance(x, interval):
return interval(np.exp(x.start), np.exp(x.end), is_valid=x.is_valid)
else:
raise NotImplementedError
#Monotonic
def log(x):
"""evaluates the natural logarithm of an interval"""
np = import_module('numpy')
if isinstance(x, (int, float)):
if x <= 0:
return interval(-np.inf, np.inf, is_valid=False)
else:
return interval(np.log(x))
elif isinstance(x, interval):
if not x.is_valid:
return interval(-np.inf, np.inf, is_valid=x.is_valid)
elif x.end <= 0:
return interval(-np.inf, np.inf, is_valid=False)
elif x.start <= 0:
return interval(-np.inf, np.inf, is_valid=None)
return interval(np.log(x.start), np.log(x.end))
else:
raise NotImplementedError
#Monotonic
def log10(x):
"""evaluates the logarithm to the base 10 of an interval"""
np = import_module('numpy')
if isinstance(x, (int, float)):
if x <= 0:
return interval(-np.inf, np.inf, is_valid=False)
else:
return interval(np.log10(x))
elif isinstance(x, interval):
if not x.is_valid:
return interval(-np.inf, np.inf, is_valid=x.is_valid)
elif x.end <= 0:
return interval(-np.inf, np.inf, is_valid=False)
elif x.start <= 0:
return interval(-np.inf, np.inf, is_valid=None)
return interval(np.log10(x.start), np.log10(x.end))
else:
raise NotImplementedError
#Monotonic
def atan(x):
"""evaluates the tan inverse of an interval"""
np = import_module('numpy')
if isinstance(x, (int, float)):
return interval(np.arctan(x))
elif isinstance(x, interval):
start = np.arctan(x.start)
end = np.arctan(x.end)
return interval(start, end, is_valid=x.is_valid)
else:
raise NotImplementedError
#periodic
def sin(x):
"""evaluates the sine of an interval"""
np = import_module('numpy')
if isinstance(x, (int, float)):
return interval(np.sin(x))
elif isinstance(x, interval):
if not x.is_valid:
return interval(-1, 1, is_valid=x.is_valid)
na, __ = divmod(x.start, np.pi / 2.0)
nb, __ = divmod(x.end, np.pi / 2.0)
start = min(np.sin(x.start), np.sin(x.end))
end = max(np.sin(x.start), np.sin(x.end))
if nb - na > 4:
return interval(-1, 1, is_valid=x.is_valid)
elif na == nb:
return interval(start, end, is_valid=x.is_valid)
else:
if (na - 1) // 4 != (nb - 1) // 4:
#sin has max
end = 1
if (na - 3) // 4 != (nb - 3) // 4:
#sin has min
start = -1
return interval(start, end)
else:
raise NotImplementedError
#periodic
def cos(x):
"""Evaluates the cos of an interval"""
np = import_module('numpy')
if isinstance(x, (int, float)):
return interval(np.sin(x))
elif isinstance(x, interval):
if not (np.isfinite(x.start) and np.isfinite(x.end)):
return interval(-1, 1, is_valid=x.is_valid)
na, __ = divmod(x.start, np.pi / 2.0)
nb, __ = divmod(x.end, np.pi / 2.0)
start = min(np.cos(x.start), np.cos(x.end))
end = max(np.cos(x.start), np.cos(x.end))
if nb - na > 4:
#differ more than 2*pi
return interval(-1, 1, is_valid=x.is_valid)
elif na == nb:
#in the same quadarant
return interval(start, end, is_valid=x.is_valid)
else:
if (na) // 4 != (nb) // 4:
#cos has max
end = 1
if (na - 2) // 4 != (nb - 2) // 4:
#cos has min
start = -1
return interval(start, end, is_valid=x.is_valid)
else:
raise NotImplementedError
def tan(x):
"""Evaluates the tan of an interval"""
return sin(x) / cos(x)
#Monotonic
def sqrt(x):
"""Evaluates the square root of an interval"""
np = import_module('numpy')
if isinstance(x, (int, float)):
if x > 0:
return interval(np.sqrt(x))
else:
return interval(-np.inf, np.inf, is_valid=False)
elif isinstance(x, interval):
#Outside the domain
if x.end < 0:
return interval(-np.inf, np.inf, is_valid=False)
#Partially outside the domain
elif x.start < 0:
return interval(-np.inf, np.inf, is_valid=None)
else:
return interval(np.sqrt(x.start), np.sqrt(x.end),
is_valid=x.is_valid)
else:
raise NotImplementedError
def imin(*args):
"""Evaluates the minimum of a list of intervals"""
np = import_module('numpy')
if not all(isinstance(arg, (int, float, interval)) for arg in args):
return NotImplementedError
else:
new_args = [a for a in args if isinstance(a, (int, float))
or a.is_valid]
if len(new_args) == 0:
if all(a.is_valid is False for a in args):
return interval(-np.inf, np.inf, is_valid=False)
else:
return interval(-np.inf, np.inf, is_valid=None)
start_array = [a if isinstance(a, (int, float)) else a.start
for a in new_args]
end_array = [a if isinstance(a, (int, float)) else a.end
for a in new_args]
return interval(min(start_array), min(end_array))
def imax(*args):
"""Evaluates the maximum of a list of intervals"""
np = import_module('numpy')
if not all(isinstance(arg, (int, float, interval)) for arg in args):
return NotImplementedError
else:
new_args = [a for a in args if isinstance(a, (int, float))
or a.is_valid]
if len(new_args) == 0:
if all(a.is_valid is False for a in args):
return interval(-np.inf, np.inf, is_valid=False)
else:
return interval(-np.inf, np.inf, is_valid=None)
start_array = [a if isinstance(a, (int, float)) else a.start
for a in new_args]
end_array = [a if isinstance(a, (int, float)) else a.end
for a in new_args]
return interval(max(start_array), max(end_array))
#Monotonic
def sinh(x):
"""Evaluates the hyperbolic sine of an interval"""
np = import_module('numpy')
if isinstance(x, (int, float)):
return interval(np.sinh(x), np.sinh(x))
elif isinstance(x, interval):
return interval(np.sinh(x.start), np.sinh(x.end), is_valid=x.is_valid)
else:
raise NotImplementedError
def cosh(x):
"""Evaluates the hyperbolic cos of an interval"""
np = import_module('numpy')
if isinstance(x, (int, float)):
return interval(np.cosh(x), np.cosh(x))
elif isinstance(x, interval):
#both signs
if x.start < 0 and x.end > 0:
end = max(np.cosh(x.start), np.cosh(x.end))
return interval(1, end, is_valid=x.is_valid)
else:
#Monotonic
start = np.cosh(x.start)
end = np.cosh(x.end)
return interval(start, end, is_valid=x.is_valid)
else:
raise NotImplementedError
#Monotonic
def tanh(x):
"""Evaluates the hyperbolic tan of an interval"""
np = import_module('numpy')
if isinstance(x, (int, float)):
return interval(np.tanh(x), np.tanh(x))
elif isinstance(x, interval):
return interval(np.tanh(x.start), np.tanh(x.end), is_valid=x.is_valid)
else:
raise NotImplementedError
def asin(x):
"""Evaluates the inverse sine of an interval"""
np = import_module('numpy')
if isinstance(x, (int, float)):
#Outside the domain
if abs(x) > 1:
return interval(-np.inf, np.inf, is_valid=False)
else:
return interval(np.arcsin(x), np.arcsin(x))
elif isinstance(x, interval):
#Outside the domain
if x.is_valid is False or x.start > 1 or x.end < -1:
return interval(-np.inf, np.inf, is_valid=False)
#Partially outside the domain
elif x.start < -1 or x.end > 1:
return interval(-np.inf, np.inf, is_valid=None)
else:
start = np.arcsin(x.start)
end = np.arcsin(x.end)
return interval(start, end, is_valid=x.is_valid)
def acos(x):
"""Evaluates the inverse cos of an interval"""
np = import_module('numpy')
if isinstance(x, (int, float)):
if abs(x) > 1:
#Outside the domain
return interval(-np.inf, np.inf, is_valid=False)
else:
return interval(np.arccos(x), np.arccos(x))
elif isinstance(x, interval):
#Outside the domain
if x.is_valid is False or x.start > 1 or x.end < -1:
return interval(-np.inf, np.inf, is_valid=False)
#Partially outside the domain
elif x.start < -1 or x.end > 1:
return interval(-np.inf, np.inf, is_valid=None)
else:
start = np.arccos(x.start)
end = np.arccos(x.end)
return interval(start, end, is_valid=x.is_valid)
def ceil(x):
"""Evaluates the ceiling of an interval"""
np = import_module('numpy')
if isinstance(x, (int, float)):
return interval(np.ceil(x))
elif isinstance(x, interval):
if x.is_valid is False:
return interval(-np.inf, np.inf, is_valid=False)
else:
start = np.ceil(x.start)
end = np.ceil(x.end)
#Continuous over the interval
if start == end:
return interval(start, end, is_valid=x.is_valid)
else:
#Not continuous over the interval
return interval(start, end, is_valid=None)
else:
return NotImplementedError
def floor(x):
"""Evaluates the floor of an interval"""
np = import_module('numpy')
if isinstance(x, (int, float)):
return interval(np.floor(x))
elif isinstance(x, interval):
if x.is_valid is False:
return interval(-np.inf, np.inf, is_valid=False)
else:
start = np.floor(x.start)
end = np.floor(x.end)
#continuous over the argument
if start == end:
return interval(start, end, is_valid=x.is_valid)
else:
#not continuous over the interval
return interval(start, end, is_valid=None)
else:
return NotImplementedError
def acosh(x):
"""Evaluates the inverse hyperbolic cosine of an interval"""
np = import_module('numpy')
if isinstance(x, (int, float)):
#Outside the domain
if x < 1:
return interval(-np.inf, np.inf, is_valid=False)
else:
return interval(np.arccosh(x))
elif isinstance(x, interval):
#Outside the domain
if x.end < 1:
return interval(-np.inf, np.inf, is_valid=False)
#Partly outside the domain
elif x.start < 1:
return interval(-np.inf, np.inf, is_valid=None)
else:
start = np.arccosh(x.start)
end = np.arccosh(x.end)
return interval(start, end, is_valid=x.is_valid)
else:
return NotImplementedError
#Monotonic
def asinh(x):
"""Evaluates the inverse hyperbolic sine of an interval"""
np = import_module('numpy')
if isinstance(x, (int, float)):
return interval(np.arcsinh(x))
elif isinstance(x, interval):
start = np.arcsinh(x.start)
end = np.arcsinh(x.end)
return interval(start, end, is_valid=x.is_valid)
else:
return NotImplementedError
def atanh(x):
"""Evaluates the inverse hyperbolic tangent of an interval"""
np = import_module('numpy')
if isinstance(x, (int, float)):
#Outside the domain
if abs(x) >= 1:
return interval(-np.inf, np.inf, is_valid=False)
else:
return interval(np.arctanh(x))
elif isinstance(x, interval):
#outside the domain
if x.is_valid is False or x.start >= 1 or x.end <= -1:
return interval(-np.inf, np.inf, is_valid=False)
#partly outside the domain
elif x.start <= -1 or x.end >= 1:
return interval(-np.inf, np.inf, is_valid=None)
else:
start = np.arctanh(x.start)
end = np.arctanh(x.end)
return interval(start, end, is_valid=x.is_valid)
else:
return NotImplementedError
#Three valued logic for interval plotting.
def And(*args):
"""Defines the three valued ``And`` behaviour for a 2-tuple of
three valued logic values"""
def reduce_and(cmp_intervala, cmp_intervalb):
if cmp_intervala[0] is False or cmp_intervalb[0] is False:
first = False
elif cmp_intervala[0] is None or cmp_intervalb[0] is None:
first = None
else:
first = True
if cmp_intervala[1] is False or cmp_intervalb[1] is False:
second = False
elif cmp_intervala[1] is None or cmp_intervalb[1] is None:
second = None
else:
second = True
return (first, second)
return reduce(reduce_and, args)
def Or(*args):
"""Defines the three valued ``Or`` behaviour for a 2-tuple of
three valued logic values"""
def reduce_or(cmp_intervala, cmp_intervalb):
if cmp_intervala[0] is True or cmp_intervalb[0] is True:
first = True
elif cmp_intervala[0] is None or cmp_intervalb[0] is None:
first = None
else:
first = False
if cmp_intervala[1] is True or cmp_intervalb[1] is True:
second = True
elif cmp_intervala[1] is None or cmp_intervalb[1] is None:
second = None
else:
second = False
return (first, second)
return reduce(reduce_or, args)
| 14,873 | 31.69011 | 82 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/intervalmath/__init__.py
|
from .interval_arithmetic import interval
from .lib_interval import (Abs, exp, log, log10, atan, sin, cos, tan, sqrt,
imin, imax, sinh, cosh, tanh, acosh, asinh, atanh,
asin, acos, atan, ceil, floor, And, Or)
| 261 | 51.4 | 76 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/intervalmath/tests/test_interval_functions.py
|
from __future__ import division
from sympy.external import import_module
from sympy.plotting.intervalmath import (
Abs, acos, acosh, And, asin, asinh, atan, atanh, ceil, cos, cosh,
exp, floor, imax, imin, interval, log, log10, Or, sin, sinh, sqrt,
tan, tanh,
)
np = import_module('numpy')
if not np:
disabled = True
#requires Numpy. Hence included in interval_functions
def test_interval_pow():
a = 2**interval(1, 2) == interval(2, 4)
assert a == (True, True)
a = interval(1, 2)**interval(1, 2) == interval(1, 4)
assert a == (True, True)
a = interval(-1, 1)**interval(0.5, 2)
assert a.is_valid is None
a = interval(-2, -1) ** interval(1, 2)
assert a.is_valid is False
a = interval(-2, -1) ** (1 / 2)
assert a.is_valid is False
a = interval(-1, 1)**(1 / 2)
assert a.is_valid is None
a = interval(-1, 1)**(1 / 3) == interval(-1, 1)
assert a == (True, True)
a = interval(-1, 1)**2 == interval(0, 1)
assert a == (True, True)
a = interval(-1, 1) ** (1 / 29) == interval(-1, 1)
assert a == (True, True)
a = -2**interval(1, 1) == interval(-2, -2)
assert a == (True, True)
a = interval(1, 2, is_valid=False)**2
assert a.is_valid is False
a = (-3)**interval(1, 2)
assert a.is_valid is False
a = (-4)**interval(0.5, 0.5)
assert a.is_valid is False
assert ((-3)**interval(1, 1) == interval(-3, -3)) == (True, True)
a = interval(8, 64)**(2 / 3)
assert abs(a.start - 4) < 1e-10 # eps
assert abs(a.end - 16) < 1e-10
a = interval(-8, 64)**(2 / 3)
assert abs(a.start - 4) < 1e-10 # eps
assert abs(a.end - 16) < 1e-10
def test_exp():
a = exp(interval(-np.inf, 0))
assert a.start == np.exp(-np.inf)
assert a.end == np.exp(0)
a = exp(interval(1, 2))
assert a.start == np.exp(1)
assert a.end == np.exp(2)
a = exp(1)
assert a.start == np.exp(1)
assert a.end == np.exp(1)
def test_log():
a = log(interval(1, 2))
assert a.start == 0
assert a.end == np.log(2)
a = log(interval(-1, 1))
assert a.is_valid is None
a = log(interval(-3, -1))
assert a.is_valid is False
a = log(-3)
assert a.is_valid is False
a = log(2)
assert a.start == np.log(2)
assert a.end == np.log(2)
def test_log10():
a = log10(interval(1, 2))
assert a.start == 0
assert a.end == np.log10(2)
a = log10(interval(-1, 1))
assert a.is_valid is None
a = log10(interval(-3, -1))
assert a.is_valid is False
a = log10(-3)
assert a.is_valid is False
a = log10(2)
assert a.start == np.log10(2)
assert a.end == np.log10(2)
def test_atan():
a = atan(interval(0, 1))
assert a.start == np.arctan(0)
assert a.end == np.arctan(1)
a = atan(1)
assert a.start == np.arctan(1)
assert a.end == np.arctan(1)
def test_sin():
a = sin(interval(0, np.pi / 4))
assert a.start == np.sin(0)
assert a.end == np.sin(np.pi / 4)
a = sin(interval(-np.pi / 4, np.pi / 4))
assert a.start == np.sin(-np.pi / 4)
assert a.end == np.sin(np.pi / 4)
a = sin(interval(np.pi / 4, 3 * np.pi / 4))
assert a.start == np.sin(np.pi / 4)
assert a.end == 1
a = sin(interval(7 * np.pi / 6, 7 * np.pi / 4))
assert a.start == -1
assert a.end == np.sin(7 * np.pi / 6)
a = sin(interval(0, 3 * np.pi))
assert a.start == -1
assert a.end == 1
a = sin(interval(np.pi / 3, 7 * np.pi / 4))
assert a.start == -1
assert a.end == 1
a = sin(np.pi / 4)
assert a.start == np.sin(np.pi / 4)
assert a.end == np.sin(np.pi / 4)
a = sin(interval(1, 2, is_valid=False))
assert a.is_valid is False
def test_cos():
a = cos(interval(0, np.pi / 4))
assert a.start == np.cos(np.pi / 4)
assert a.end == 1
a = cos(interval(-np.pi / 4, np.pi / 4))
assert a.start == np.cos(-np.pi / 4)
assert a.end == 1
a = cos(interval(np.pi / 4, 3 * np.pi / 4))
assert a.start == np.cos(3 * np.pi / 4)
assert a.end == np.cos(np.pi / 4)
a = cos(interval(3 * np.pi / 4, 5 * np.pi / 4))
assert a.start == -1
assert a.end == np.cos(3 * np.pi / 4)
a = cos(interval(0, 3 * np.pi))
assert a.start == -1
assert a.end == 1
a = cos(interval(- np.pi / 3, 5 * np.pi / 4))
assert a.start == -1
assert a.end == 1
a = cos(interval(1, 2, is_valid=False))
assert a.is_valid is False
def test_tan():
a = tan(interval(0, np.pi / 4))
assert a.start == 0
# must match lib_interval definition of tan:
assert a.end == np.sin(np.pi / 4)/np.cos(np.pi / 4)
a = tan(interval(np.pi / 4, 3 * np.pi / 4))
#discontinuity
assert a.is_valid is None
def test_sqrt():
a = sqrt(interval(1, 4))
assert a.start == 1
assert a.end == 2
a = sqrt(interval(0.01, 1))
assert a.start == np.sqrt(0.01)
assert a.end == 1
a = sqrt(interval(-1, 1))
assert a.is_valid is None
a = sqrt(interval(-3, -1))
assert a.is_valid is False
a = sqrt(4)
assert (a == interval(2, 2)) == (True, True)
a = sqrt(-3)
assert a.is_valid is False
def test_imin():
a = imin(interval(1, 3), interval(2, 5), interval(-1, 3))
assert a.start == -1
assert a.end == 3
a = imin(-2, interval(1, 4))
assert a.start == -2
assert a.end == -2
a = imin(5, interval(3, 4), interval(-2, 2, is_valid=False))
assert a.start == 3
assert a.end == 4
def test_imax():
a = imax(interval(-2, 2), interval(2, 7), interval(-3, 9))
assert a.start == 2
assert a.end == 9
a = imax(8, interval(1, 4))
assert a.start == 8
assert a.end == 8
a = imax(interval(1, 2), interval(3, 4), interval(-2, 2, is_valid=False))
assert a.start == 3
assert a.end == 4
def test_sinh():
a = sinh(interval(-1, 1))
assert a.start == np.sinh(-1)
assert a.end == np.sinh(1)
a = sinh(1)
assert a.start == np.sinh(1)
assert a.end == np.sinh(1)
def test_cosh():
a = cosh(interval(1, 2))
assert a.start == np.cosh(1)
assert a.end == np.cosh(2)
a = cosh(interval(-2, -1))
assert a.start == np.cosh(-1)
assert a.end == np.cosh(-2)
a = cosh(interval(-2, 1))
assert a.start == 1
assert a.end == np.cosh(-2)
a = cosh(1)
assert a.start == np.cosh(1)
assert a.end == np.cosh(1)
def test_tanh():
a = tanh(interval(-3, 3))
assert a.start == np.tanh(-3)
assert a.end == np.tanh(3)
a = tanh(3)
assert a.start == np.tanh(3)
assert a.end == np.tanh(3)
def test_asin():
a = asin(interval(-0.5, 0.5))
assert a.start == np.arcsin(-0.5)
assert a.end == np.arcsin(0.5)
a = asin(interval(-1.5, 1.5))
assert a.is_valid is None
a = asin(interval(-2, -1.5))
assert a.is_valid is False
a = asin(interval(0, 2))
assert a.is_valid is None
a = asin(interval(2, 5))
assert a.is_valid is False
a = asin(0.5)
assert a.start == np.arcsin(0.5)
assert a.end == np.arcsin(0.5)
a = asin(1.5)
assert a.is_valid is False
def test_acos():
a = acos(interval(-0.5, 0.5))
assert a.start == np.arccos(0.5)
assert a.end == np.arccos(-0.5)
a = acos(interval(-1.5, 1.5))
assert a.is_valid is None
a = acos(interval(-2, -1.5))
assert a.is_valid is False
a = acos(interval(0, 2))
assert a.is_valid is None
a = acos(interval(2, 5))
assert a.is_valid is False
a = acos(0.5)
assert a.start == np.arccos(0.5)
assert a.end == np.arccos(0.5)
a = acos(1.5)
assert a.is_valid is False
def test_ceil():
a = ceil(interval(0.2, 0.5))
assert a.start == 1
assert a.end == 1
a = ceil(interval(0.5, 1.5))
assert a.start == 1
assert a.end == 2
assert a.is_valid is None
a = ceil(interval(-5, 5))
assert a.is_valid is None
a = ceil(5.4)
assert a.start == 6
assert a.end == 6
def test_floor():
a = floor(interval(0.2, 0.5))
assert a.start == 0
assert a.end == 0
a = floor(interval(0.5, 1.5))
assert a.start == 0
assert a.end == 1
assert a.is_valid is None
a = floor(interval(-5, 5))
assert a.is_valid is None
a = floor(5.4)
assert a.start == 5
assert a.end == 5
def test_asinh():
a = asinh(interval(1, 2))
assert a.start == np.arcsinh(1)
assert a.end == np.arcsinh(2)
a = asinh(0.5)
assert a.start == np.arcsinh(0.5)
assert a.end == np.arcsinh(0.5)
def test_acosh():
a = acosh(interval(3, 5))
assert a.start == np.arccosh(3)
assert a.end == np.arccosh(5)
a = acosh(interval(0, 3))
assert a.is_valid is None
a = acosh(interval(-3, 0.5))
assert a.is_valid is False
a = acosh(0.5)
assert a.is_valid is False
a = acosh(2)
assert a.start == np.arccosh(2)
assert a.end == np.arccosh(2)
def test_atanh():
a = atanh(interval(-0.5, 0.5))
assert a.start == np.arctanh(-0.5)
assert a.end == np.arctanh(0.5)
a = atanh(interval(0, 3))
assert a.is_valid is None
a = atanh(interval(-3, -2))
assert a.is_valid is False
a = atanh(0.5)
assert a.start == np.arctanh(0.5)
assert a.end == np.arctanh(0.5)
a = atanh(1.5)
assert a.is_valid is False
def test_Abs():
assert (Abs(interval(-0.5, 0.5)) == interval(0, 0.5)) == (True, True)
assert (Abs(interval(-3, -2)) == interval(2, 3)) == (True, True)
assert (Abs(-3) == interval(3, 3)) == (True, True)
def test_And():
args = [(True, True), (True, False), (True, None)]
assert And(*args) == (True, False)
args = [(False, True), (None, None), (True, True)]
assert And(*args) == (False, None)
def test_Or():
args = [(True, True), (True, False), (False, None)]
assert Or(*args) == (True, True)
args = [(None, None), (False, None), (False, False)]
assert Or(*args) == (None, None)
| 9,883 | 22.645933 | 77 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/intervalmath/tests/test_intervalmath.py
|
from __future__ import division
from sympy.plotting.intervalmath import interval
from sympy.utilities.pytest import raises
def test_interval():
assert (interval(1, 1) == interval(1, 1, is_valid=True)) == (True, True)
assert (interval(1, 1) == interval(1, 1, is_valid=False)) == (True, False)
assert (interval(1, 1) == interval(1, 1, is_valid=None)) == (True, None)
assert (interval(1, 1.5) == interval(1, 2)) == (None, True)
assert (interval(0, 1) == interval(2, 3)) == (False, True)
assert (interval(0, 1) == interval(1, 2)) == (None, True)
assert (interval(1, 2) != interval(1, 2)) == (False, True)
assert (interval(1, 3) != interval(2, 3)) == (None, True)
assert (interval(1, 3) != interval(-5, -3)) == (True, True)
assert (
interval(1, 3, is_valid=False) != interval(-5, -3)) == (True, False)
assert (interval(1, 3, is_valid=None) != interval(-5, 3)) == (None, None)
assert (interval(4, 4) != 4) == (False, True)
assert (interval(1, 1) == 1) == (True, True)
assert (interval(1, 3, is_valid=False) == interval(1, 3)) == (True, False)
assert (interval(1, 3, is_valid=None) == interval(1, 3)) == (True, None)
inter = interval(-5, 5)
assert (interval(inter) == interval(-5, 5)) == (True, True)
assert inter.width == 10
assert 0 in inter
assert -5 in inter
assert 5 in inter
assert interval(0, 3) in inter
assert interval(-6, 2) not in inter
assert -5.05 not in inter
assert 5.3 not in inter
interb = interval(-float('inf'), float('inf'))
assert 0 in inter
assert inter in interb
assert interval(0, float('inf')) in interb
assert interval(-float('inf'), 5) in interb
assert interval(-1e50, 1e50) in interb
assert (
-interval(-1, -2, is_valid=False) == interval(1, 2)) == (True, False)
raises(ValueError, lambda: interval(1, 2, 3))
def test_interval_add():
assert (interval(1, 2) + interval(2, 3) == interval(3, 5)) == (True, True)
assert (1 + interval(1, 2) == interval(2, 3)) == (True, True)
assert (interval(1, 2) + 1 == interval(2, 3)) == (True, True)
compare = (1 + interval(0, float('inf')) == interval(1, float('inf')))
assert compare == (True, True)
a = 1 + interval(2, 5, is_valid=False)
assert a.is_valid is False
a = 1 + interval(2, 5, is_valid=None)
assert a.is_valid is None
a = interval(2, 5, is_valid=False) + interval(3, 5, is_valid=None)
assert a.is_valid is False
a = interval(3, 5) + interval(-1, 1, is_valid=None)
assert a.is_valid is None
a = interval(2, 5, is_valid=False) + 1
assert a.is_valid is False
def test_interval_sub():
assert (interval(1, 2) - interval(1, 5) == interval(-4, 1)) == (True, True)
assert (interval(1, 2) - 1 == interval(0, 1)) == (True, True)
assert (1 - interval(1, 2) == interval(-1, 0)) == (True, True)
a = 1 - interval(1, 2, is_valid=False)
assert a.is_valid is False
a = interval(1, 4, is_valid=None) - 1
assert a.is_valid is None
a = interval(1, 3, is_valid=False) - interval(1, 3)
assert a.is_valid is False
a = interval(1, 3, is_valid=None) - interval(1, 3)
assert a.is_valid is None
def test_interval_inequality():
assert (interval(1, 2) < interval(3, 4)) == (True, True)
assert (interval(1, 2) < interval(2, 4)) == (None, True)
assert (interval(1, 2) < interval(-2, 0)) == (False, True)
assert (interval(1, 2) <= interval(2, 4)) == (True, True)
assert (interval(1, 2) <= interval(1.5, 6)) == (None, True)
assert (interval(2, 3) <= interval(1, 2)) == (None, True)
assert (interval(2, 3) <= interval(1, 1.5)) == (False, True)
assert (
interval(1, 2, is_valid=False) <= interval(-2, 0)) == (False, False)
assert (interval(1, 2, is_valid=None) <= interval(-2, 0)) == (False, None)
assert (interval(1, 2) <= 1.5) == (None, True)
assert (interval(1, 2) <= 3) == (True, True)
assert (interval(1, 2) <= 0) == (False, True)
assert (interval(5, 8) > interval(2, 3)) == (True, True)
assert (interval(2, 5) > interval(1, 3)) == (None, True)
assert (interval(2, 3) > interval(3.1, 5)) == (False, True)
assert (interval(3, 5) > 2) == (True, True)
assert (interval(3, 5) < 2) == (False, True)
assert (interval(1, 5) < 2) == (None, True)
assert (interval(1, 5) > 2) == (None, True)
assert (interval(0, 1) > 2) == (False, True)
assert (interval(1, 2) >= interval(0, 1)) == (True, True)
assert (interval(1, 2) >= interval(0, 1.5)) == (None, True)
assert (interval(1, 2) >= interval(3, 4)) == (False, True)
assert (interval(1, 2) >= 0) == (True, True)
assert (interval(1, 2) >= 1.2) == (None, True)
assert (interval(1, 2) >= 3) == (False, True)
assert (2 > interval(0, 1)) == (True, True)
a = interval(-1, 1, is_valid=False) < interval(2, 5, is_valid=None)
assert a == (True, False)
a = interval(-1, 1, is_valid=None) < interval(2, 5, is_valid=False)
assert a == (True, False)
a = interval(-1, 1, is_valid=None) < interval(2, 5, is_valid=None)
assert a == (True, None)
a = interval(-1, 1, is_valid=False) > interval(-5, -2, is_valid=None)
assert a == (True, False)
a = interval(-1, 1, is_valid=None) > interval(-5, -2, is_valid=False)
assert a == (True, False)
a = interval(-1, 1, is_valid=None) > interval(-5, -2, is_valid=None)
assert a == (True, None)
def test_interval_mul():
assert (
interval(1, 5) * interval(2, 10) == interval(2, 50)) == (True, True)
a = interval(-1, 1) * interval(2, 10) == interval(-10, 10)
assert a == (True, True)
a = interval(-1, 1) * interval(-5, 3) == interval(-5, 5)
assert a == (True, True)
assert (interval(1, 3) * 2 == interval(2, 6)) == (True, True)
assert (3 * interval(-1, 2) == interval(-3, 6)) == (True, True)
a = 3 * interval(1, 2, is_valid=False)
assert a.is_valid is False
a = 3 * interval(1, 2, is_valid=None)
assert a.is_valid is None
a = interval(1, 5, is_valid=False) * interval(1, 2, is_valid=None)
assert a.is_valid is False
def test_interval_div():
div = interval(1, 2, is_valid=False) / 3
assert div == interval(-float('inf'), float('inf'), is_valid=False)
div = interval(1, 2, is_valid=None) / 3
assert div == interval(-float('inf'), float('inf'), is_valid=None)
div = 3 / interval(1, 2, is_valid=None)
assert div == interval(-float('inf'), float('inf'), is_valid=None)
a = interval(1, 2) / 0
assert a.is_valid is False
a = interval(0.5, 1) / interval(-1, 0)
assert a.is_valid is None
a = interval(0, 1) / interval(0, 1)
assert a.is_valid is None
a = interval(-1, 1) / interval(-1, 1)
assert a.is_valid is None
a = interval(-1, 2) / interval(0.5, 1) == interval(-2.0, 4.0)
assert a == (True, True)
a = interval(0, 1) / interval(0.5, 1) == interval(0.0, 2.0)
assert a == (True, True)
a = interval(-1, 0) / interval(0.5, 1) == interval(-2.0, 0.0)
assert a == (True, True)
a = interval(-0.5, -0.25) / interval(0.5, 1) == interval(-1.0, -0.25)
assert a == (True, True)
a = interval(0.5, 1) / interval(0.5, 1) == interval(0.5, 2.0)
assert a == (True, True)
a = interval(0.5, 4) / interval(0.5, 1) == interval(0.5, 8.0)
assert a == (True, True)
a = interval(-1, -0.5) / interval(0.5, 1) == interval(-2.0, -0.5)
assert a == (True, True)
a = interval(-4, -0.5) / interval(0.5, 1) == interval(-8.0, -0.5)
assert a == (True, True)
a = interval(-1, 2) / interval(-2, -0.5) == interval(-4.0, 2.0)
assert a == (True, True)
a = interval(0, 1) / interval(-2, -0.5) == interval(-2.0, 0.0)
assert a == (True, True)
a = interval(-1, 0) / interval(-2, -0.5) == interval(0.0, 2.0)
assert a == (True, True)
a = interval(-0.5, -0.25) / interval(-2, -0.5) == interval(0.125, 1.0)
assert a == (True, True)
a = interval(0.5, 1) / interval(-2, -0.5) == interval(-2.0, -0.25)
assert a == (True, True)
a = interval(0.5, 4) / interval(-2, -0.5) == interval(-8.0, -0.25)
assert a == (True, True)
a = interval(-1, -0.5) / interval(-2, -0.5) == interval(0.25, 2.0)
assert a == (True, True)
a = interval(-4, -0.5) / interval(-2, -0.5) == interval(0.25, 8.0)
assert a == (True, True)
a = interval(-5, 5, is_valid=False) / 2
assert a.is_valid is False
def test_hashable():
'''
test that interval objects are hashable.
this is required in order to be able to put them into the cache, which
appears to be necessary for plotting in py3k. For details, see:
https://github.com/sympy/sympy/pull/2101
https://github.com/sympy/sympy/issues/6533
'''
hash(interval(1, 1))
hash(interval(1, 1, is_valid=True))
hash(interval(-4, -0.5))
hash(interval(-2, -0.5))
hash(interval(0.25, 8.0))
| 8,865 | 41.421053 | 79 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/intervalmath/tests/__init__.py
| 0 | 0 | 0 |
py
|
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/tests/test_plot.py
|
from sympy import (pi, sin, cos, Symbol, Integral, Sum, sqrt, log,
oo, LambertW, I, meijerg, exp_polar, Max, Piecewise)
from sympy.plotting import (plot, plot_parametric, plot3d_parametric_line,
plot3d, plot3d_parametric_surface)
from sympy.plotting.plot import unset_show
from sympy.utilities import lambdify as lambdify_
from sympy.utilities.pytest import skip, raises
from sympy.plotting.experimental_lambdify import lambdify
from sympy.external import import_module
from tempfile import NamedTemporaryFile
import os
import warnings
unset_show()
# XXX: We could implement this as a context manager instead
# That would need rewriting the plot_and_save() function
# entirely
class TmpFileManager:
tmp_files = []
@classmethod
def tmp_file(cls, name=''):
cls.tmp_files.append(NamedTemporaryFile(prefix=name, suffix='.png').name)
return cls.tmp_files[-1]
@classmethod
def cleanup(cls):
map(os.remove, cls.tmp_files)
def plot_and_save(name):
tmp_file = TmpFileManager.tmp_file
x = Symbol('x')
y = Symbol('y')
z = Symbol('z')
###
# Examples from the 'introduction' notebook
###
p = plot(x)
p = plot(x*sin(x), x*cos(x))
p.extend(p)
p[0].line_color = lambda a: a
p[1].line_color = 'b'
p.title = 'Big title'
p.xlabel = 'the x axis'
p[1].label = 'straight line'
p.legend = True
p.aspect_ratio = (1, 1)
p.xlim = (-15, 20)
p.save(tmp_file('%s_basic_options_and_colors' % name))
p._backend.close()
p.extend(plot(x + 1))
p.append(plot(x + 3, x**2)[1])
p.save(tmp_file('%s_plot_extend_append' % name))
p[2] = plot(x**2, (x, -2, 3))
p.save(tmp_file('%s_plot_setitem' % name))
p._backend.close()
p = plot(sin(x), (x, -2*pi, 4*pi))
p.save(tmp_file('%s_line_explicit' % name))
p._backend.close()
p = plot(sin(x))
p.save(tmp_file('%s_line_default_range' % name))
p._backend.close()
p = plot((x**2, (x, -5, 5)), (x**3, (x, -3, 3)))
p.save(tmp_file('%s_line_multiple_range' % name))
p._backend.close()
raises(ValueError, lambda: plot(x, y))
p = plot(Piecewise((1, x > 0), (0, True)),(x,-1,1))
p.save(tmp_file('%s_plot_piecewise' % name))
p._backend.close()
#parametric 2d plots.
#Single plot with default range.
plot_parametric(sin(x), cos(x)).save(tmp_file())
#Single plot with range.
p = plot_parametric(sin(x), cos(x), (x, -5, 5))
p.save(tmp_file('%s_parametric_range' % name))
p._backend.close()
#Multiple plots with same range.
p = plot_parametric((sin(x), cos(x)), (x, sin(x)))
p.save(tmp_file('%s_parametric_multiple' % name))
p._backend.close()
#Multiple plots with different ranges.
p = plot_parametric((sin(x), cos(x), (x, -3, 3)), (x, sin(x), (x, -5, 5)))
p.save(tmp_file('%s_parametric_multiple_ranges' % name))
p._backend.close()
#depth of recursion specified.
p = plot_parametric(x, sin(x), depth=13)
p.save(tmp_file('%s_recursion_depth' % name))
p._backend.close()
#No adaptive sampling.
p = plot_parametric(cos(x), sin(x), adaptive=False, nb_of_points=500)
p.save(tmp_file('%s_adaptive' % name))
p._backend.close()
#3d parametric plots
p = plot3d_parametric_line(sin(x), cos(x), x)
p.save(tmp_file('%s_3d_line' % name))
p._backend.close()
p = plot3d_parametric_line(
(sin(x), cos(x), x, (x, -5, 5)), (cos(x), sin(x), x, (x, -3, 3)))
p.save(tmp_file('%s_3d_line_multiple' % name))
p._backend.close()
p = plot3d_parametric_line(sin(x), cos(x), x, nb_of_points=30)
p.save(tmp_file('%s_3d_line_points' % name))
p._backend.close()
# 3d surface single plot.
p = plot3d(x * y)
p.save(tmp_file('%s_surface' % name))
p._backend.close()
# Multiple 3D plots with same range.
p = plot3d(-x * y, x * y, (x, -5, 5))
p.save(tmp_file('%s_surface_multiple' % name))
p._backend.close()
# Multiple 3D plots with different ranges.
p = plot3d(
(x * y, (x, -3, 3), (y, -3, 3)), (-x * y, (x, -3, 3), (y, -3, 3)))
p.save(tmp_file('%s_surface_multiple_ranges' % name))
p._backend.close()
# Single Parametric 3D plot
p = plot3d_parametric_surface(sin(x + y), cos(x - y), x - y)
p.save(tmp_file('%s_parametric_surface' % name))
p._backend.close()
# Multiple Parametric 3D plots.
p = plot3d_parametric_surface(
(x*sin(z), x*cos(z), z, (x, -5, 5), (z, -5, 5)),
(sin(x + y), cos(x - y), x - y, (x, -5, 5), (y, -5, 5)))
p.save(tmp_file('%s_parametric_surface' % name))
p._backend.close()
###
# Examples from the 'colors' notebook
###
p = plot(sin(x))
p[0].line_color = lambda a: a
p.save(tmp_file('%s_colors_line_arity1' % name))
p[0].line_color = lambda a, b: b
p.save(tmp_file('%s_colors_line_arity2' % name))
p._backend.close()
p = plot(x*sin(x), x*cos(x), (x, 0, 10))
p[0].line_color = lambda a: a
p.save(tmp_file('%s_colors_param_line_arity1' % name))
p[0].line_color = lambda a, b: a
p.save(tmp_file('%s_colors_param_line_arity2a' % name))
p[0].line_color = lambda a, b: b
p.save(tmp_file('%s_colors_param_line_arity2b' % name))
p._backend.close()
p = plot3d_parametric_line(sin(x) + 0.1*sin(x)*cos(7*x),
cos(x) + 0.1*cos(x)*cos(7*x),
0.1*sin(7*x),
(x, 0, 2*pi))
p[0].line_color = lambdify_(x, sin(4*x))
p.save(tmp_file('%s_colors_3d_line_arity1' % name))
p[0].line_color = lambda a, b: b
p.save(tmp_file('%s_colors_3d_line_arity2' % name))
p[0].line_color = lambda a, b, c: c
p.save(tmp_file('%s_colors_3d_line_arity3' % name))
p._backend.close()
p = plot3d(sin(x)*y, (x, 0, 6*pi), (y, -5, 5))
p[0].surface_color = lambda a: a
p.save(tmp_file('%s_colors_surface_arity1' % name))
p[0].surface_color = lambda a, b: b
p.save(tmp_file('%s_colors_surface_arity2' % name))
p[0].surface_color = lambda a, b, c: c
p.save(tmp_file('%s_colors_surface_arity3a' % name))
p[0].surface_color = lambdify_((x, y, z), sqrt((x - 3*pi)**2 + y**2))
p.save(tmp_file('%s_colors_surface_arity3b' % name))
p._backend.close()
p = plot3d_parametric_surface(x * cos(4 * y), x * sin(4 * y), y,
(x, -1, 1), (y, -1, 1))
p[0].surface_color = lambda a: a
p.save(tmp_file('%s_colors_param_surf_arity1' % name))
p[0].surface_color = lambda a, b: a*b
p.save(tmp_file('%s_colors_param_surf_arity2' % name))
p[0].surface_color = lambdify_((x, y, z), sqrt(x**2 + y**2 + z**2))
p.save(tmp_file('%s_colors_param_surf_arity3' % name))
p._backend.close()
###
# Examples from the 'advanced' notebook
###
# XXX: This raises the warning "The evaluation of the expression is
# problematic. We are trying a failback method that may still work. Please
# report this as a bug." It has to use the fallback because using evalf()
# is the only way to evaluate the integral. We should perhaps just remove
# that warning.
with warnings.catch_warnings(record=True) as w:
i = Integral(log((sin(x)**2 + 1)*sqrt(x**2 + 1)), (x, 0, y))
p = plot(i, (y, 1, 5))
p.save(tmp_file('%s_advanced_integral' % name))
p._backend.close()
# Make sure no other warnings were raised
for i in w:
assert issubclass(i.category, UserWarning)
assert "The evaluation of the expression is problematic" in str(i.message)
s = Sum(1/x**y, (x, 1, oo))
p = plot(s, (y, 2, 10))
p.save(tmp_file('%s_advanced_inf_sum' % name))
p._backend.close()
p = plot(Sum(1/x, (x, 1, y)), (y, 2, 10), show=False)
p[0].only_integers = True
p[0].steps = True
p.save(tmp_file('%s_advanced_fin_sum' % name))
p._backend.close()
###
# Test expressions that can not be translated to np and generate complex
# results.
###
plot(sin(x) + I*cos(x)).save(tmp_file())
plot(sqrt(sqrt(-x))).save(tmp_file())
plot(LambertW(x)).save(tmp_file())
plot(sqrt(LambertW(x))).save(tmp_file())
#Characteristic function of a StudentT distribution with nu=10
plot((meijerg(((1 / 2,), ()), ((5, 0, 1 / 2), ()), 5 * x**2 * exp_polar(-I*pi)/2)
+ meijerg(((1/2,), ()), ((5, 0, 1/2), ()),
5*x**2 * exp_polar(I*pi)/2)) / (48 * pi), (x, 1e-6, 1e-2)).save(tmp_file())
def test_matplotlib():
matplotlib = import_module('matplotlib', min_module_version='1.1.0', catch=(RuntimeError,))
if matplotlib:
try:
plot_and_save('test')
finally:
# clean up
TmpFileManager.cleanup()
else:
skip("Matplotlib not the default backend")
# Tests for exception handling in experimental_lambdify
def test_experimental_lambify():
x = Symbol('x')
f = lambdify([x], Max(x, 5))
# XXX should f be tested? If f(2) is attempted, an
# error is raised because a complex produced during wrapping of the arg
# is being compared with an int.
assert Max(2, 5) == 5
assert Max(5, 7) == 7
x = Symbol('x-3')
f = lambdify([x], x + 1)
assert f(1) == 2
def test_append_issue_7140():
matplotlib = import_module('matplotlib', min_module_version='1.1.0', catch=(RuntimeError,))
if not matplotlib:
skip("Matplotlib not the default backend")
x = Symbol('x')
p1 = plot(x)
p2 = plot(x**2)
p3 = plot(x + 2)
# append a series
p2.append(p1[0])
assert len(p2._series) == 2
with raises(TypeError):
p1.append(p2)
with raises(TypeError):
p1.append(p2._series)
| 9,698 | 31.009901 | 95 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/tests/__init__.py
| 0 | 0 | 0 |
py
|
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/plotting/tests/test_plot_implicit.py
|
import warnings
from sympy import (plot_implicit, cos, Symbol, symbols, Eq, sin, re, And, Or, exp, I,
tan, pi)
from sympy.plotting.plot import unset_show
from tempfile import NamedTemporaryFile
from sympy.utilities.pytest import skip
from sympy.external import import_module
#Set plots not to show
unset_show()
def tmp_file(name=''):
return NamedTemporaryFile(suffix='.png').name
def plot_and_save(expr, *args, **kwargs):
name = kwargs.pop('name', '')
p = plot_implicit(expr, *args, **kwargs)
p.save(tmp_file(name))
# Close the plot to avoid a warning from matplotlib
p._backend.close()
def plot_implicit_tests(name):
x = Symbol('x')
y = Symbol('y')
z = Symbol('z')
#implicit plot tests
plot_and_save(Eq(y, cos(x)), (x, -5, 5), (y, -2, 2), name=name)
plot_and_save(Eq(y**2, x**3 - x), (x, -5, 5),
(y, -4, 4), name=name)
plot_and_save(y > 1 / x, (x, -5, 5),
(y, -2, 2), name=name)
plot_and_save(y < 1 / tan(x), (x, -5, 5),
(y, -2, 2), name=name)
plot_and_save(y >= 2 * sin(x) * cos(x), (x, -5, 5),
(y, -2, 2), name=name)
plot_and_save(y <= x**2, (x, -3, 3),
(y, -1, 5), name=name)
#Test all input args for plot_implicit
plot_and_save(Eq(y**2, x**3 - x))
plot_and_save(Eq(y**2, x**3 - x), adaptive=False)
plot_and_save(Eq(y**2, x**3 - x), adaptive=False, points=500)
plot_and_save(y > x, (x, -5, 5))
plot_and_save(And(y > exp(x), y > x + 2))
plot_and_save(Or(y > x, y > -x))
plot_and_save(x**2 - 1, (x, -5, 5))
plot_and_save(x**2 - 1)
plot_and_save(y > x, depth=-5)
plot_and_save(y > x, depth=5)
plot_and_save(y > cos(x), adaptive=False)
plot_and_save(y < cos(x), adaptive=False)
plot_and_save(And(y > cos(x), Or(y > x, Eq(y, x))))
plot_and_save(y - cos(pi / x))
#Test plots which cannot be rendered using the adaptive algorithm
with warnings.catch_warnings(record=True) as w:
plot_and_save(Eq(y, re(cos(x) + I*sin(x))), name=name)
for i in w: # Same warning may be issued multiple times
assert issubclass(i.category, UserWarning)
assert "Adaptive meshing could not be applied" in str(i.message)
with warnings.catch_warnings(record=True) as w:
plot_and_save(x**2 - 1, legend='An implicit plot')
for i in w:
assert issubclass(i.category, UserWarning)
assert 'No labelled objects found' in str(i.message)
def test_line_color():
x, y = symbols('x, y')
p = plot_implicit(x**2 + y**2 - 1, line_color="green", show=False)
assert p._series[0].line_color == "green"
p = plot_implicit(x**2 + y**2 - 1, line_color='r', show=False)
assert p._series[0].line_color == "r"
def test_matplotlib():
matplotlib = import_module('matplotlib', min_module_version='1.1.0', catch=(RuntimeError,))
if matplotlib:
plot_implicit_tests('test')
test_line_color()
else:
skip("Matplotlib not the default backend")
| 3,042 | 36.109756 | 95 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/decorator.py
|
"""Useful utility decorators. """
from __future__ import print_function, division
import sys
import types
import inspect
from functools import update_wrapper
from sympy.core.decorators import wraps
from sympy.core.compatibility import class_types, get_function_globals, get_function_name, iterable
def threaded_factory(func, use_add):
"""A factory for ``threaded`` decorators. """
from sympy.core import sympify
from sympy.matrices import MatrixBase
@wraps(func)
def threaded_func(expr, *args, **kwargs):
if isinstance(expr, MatrixBase):
return expr.applyfunc(lambda f: func(f, *args, **kwargs))
elif iterable(expr):
try:
return expr.__class__([func(f, *args, **kwargs) for f in expr])
except TypeError:
return expr
else:
expr = sympify(expr)
if use_add and expr.is_Add:
return expr.__class__(*[ func(f, *args, **kwargs) for f in expr.args ])
elif expr.is_Relational:
return expr.__class__(func(expr.lhs, *args, **kwargs),
func(expr.rhs, *args, **kwargs))
else:
return func(expr, *args, **kwargs)
return threaded_func
def threaded(func):
"""Apply ``func`` to sub--elements of an object, including :class:`Add`.
This decorator is intended to make it uniformly possible to apply a
function to all elements of composite objects, e.g. matrices, lists, tuples
and other iterable containers, or just expressions.
This version of :func:`threaded` decorator allows threading over
elements of :class:`Add` class. If this behavior is not desirable
use :func:`xthreaded` decorator.
Functions using this decorator must have the following signature::
@threaded
def function(expr, *args, **kwargs):
"""
return threaded_factory(func, True)
def xthreaded(func):
"""Apply ``func`` to sub--elements of an object, excluding :class:`Add`.
This decorator is intended to make it uniformly possible to apply a
function to all elements of composite objects, e.g. matrices, lists, tuples
and other iterable containers, or just expressions.
This version of :func:`threaded` decorator disallows threading over
elements of :class:`Add` class. If this behavior is not desirable
use :func:`threaded` decorator.
Functions using this decorator must have the following signature::
@xthreaded
def function(expr, *args, **kwargs):
"""
return threaded_factory(func, False)
def conserve_mpmath_dps(func):
"""After the function finishes, resets the value of mpmath.mp.dps to
the value it had before the function was run."""
import functools
import mpmath
def func_wrapper(*args, **kwargs):
dps = mpmath.mp.dps
try:
return func(*args, **kwargs)
finally:
mpmath.mp.dps = dps
func_wrapper = functools.update_wrapper(func_wrapper, func)
return func_wrapper
class no_attrs_in_subclass(object):
"""Don't 'inherit' certain attributes from a base class
>>> from sympy.utilities.decorator import no_attrs_in_subclass
>>> class A(object):
... x = 'test'
>>> A.x = no_attrs_in_subclass(A, A.x)
>>> class B(A):
... pass
>>> hasattr(A, 'x')
True
>>> hasattr(B, 'x')
False
"""
def __init__(self, cls, f):
self.cls = cls
self.f = f
def __get__(self, instance, owner=None):
if owner == self.cls:
if hasattr(self.f, '__get__'):
return self.f.__get__(instance, owner)
return self.f
raise AttributeError
def doctest_depends_on(exe=None, modules=None, disable_viewers=None):
"""Adds metadata about the depenencies which need to be met for doctesting
the docstrings of the decorated objects."""
pyglet = False
if modules is not None and 'pyglet' in modules:
pyglet = True
def depends_on_deco(fn):
fn._doctest_depends_on = dict(exe=exe, modules=modules,
disable_viewers=disable_viewers,
pyglet=pyglet)
# once we drop py2.5 support and use class decorators this evaluates
# to True
if inspect.isclass(fn):
fn._doctest_depdends_on = no_attrs_in_subclass(fn, fn._doctest_depends_on)
return fn
return depends_on_deco
def public(obj):
"""
Append ``obj``'s name to global ``__all__`` variable (call site).
By using this decorator on functions or classes you achieve the same goal
as by filling ``__all__`` variables manually, you just don't have to repeat
yourself (object's name). You also know if object is public at definition
site, not at some random location (where ``__all__`` was set).
Note that in multiple decorator setup (in almost all cases) ``@public``
decorator must be applied before any other decorators, because it relies
on the pointer to object's global namespace. If you apply other decorators
first, ``@public`` may end up modifying the wrong namespace.
Examples
========
>>> from sympy.utilities.decorator import public
>>> __all__
Traceback (most recent call last):
...
NameError: name '__all__' is not defined
>>> @public
... def some_function():
... pass
>>> __all__
['some_function']
"""
if isinstance(obj, types.FunctionType):
ns = get_function_globals(obj)
name = get_function_name(obj)
elif isinstance(obj, (type(type), class_types)):
ns = sys.modules[obj.__module__].__dict__
name = obj.__name__
else:
raise TypeError("expected a function or a class, got %s" % obj)
if "__all__" not in ns:
ns["__all__"] = [name]
else:
ns["__all__"].append(name)
return obj
def memoize_property(storage):
"""Create a property, where the lookup is stored in ``storage``"""
def decorator(method):
name = method.__name__
def wrapper(self):
if name not in storage:
storage[name] = method(self)
return storage[name]
return property(update_wrapper(wrapper, method))
return decorator
| 6,353 | 29.548077 | 99 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/benchmarking.py
|
"""benchmarking through py.test"""
from __future__ import print_function, division
import py
from py.__.test.item import Item
from py.__.test.terminal.terminal import TerminalSession
from math import ceil as _ceil, floor as _floor, log10
import timeit
from inspect import getsource
from sympy.core.compatibility import exec_, range
# from IPython.Magic.magic_timeit
units = ["s", "ms", "us", "ns"]
scaling = [1, 1e3, 1e6, 1e9]
unitn = dict((s, i) for i, s in enumerate(units))
precision = 3
# like py.test Directory but scan for 'bench_<smth>.py'
class Directory(py.test.collect.Directory):
def filefilter(self, path):
b = path.purebasename
ext = path.ext
return b.startswith('bench_') and ext == '.py'
# like py.test Module but scane for 'bench_<smth>' and 'timeit_<smth>'
class Module(py.test.collect.Module):
def funcnamefilter(self, name):
return name.startswith('bench_') or name.startswith('timeit_')
# Function level benchmarking driver
class Timer(timeit.Timer):
def __init__(self, stmt, setup='pass', timer=timeit.default_timer, globals=globals()):
# copy of timeit.Timer.__init__
# similarity index 95%
self.timer = timer
stmt = timeit.reindent(stmt, 8)
setup = timeit.reindent(setup, 4)
src = timeit.template % {'stmt': stmt, 'setup': setup}
self.src = src # Save for traceback display
code = compile(src, timeit.dummy_src_name, "exec")
ns = {}
#exec code in globals(), ns -- original timeit code
exec_(code, globals, ns) # -- we use caller-provided globals instead
self.inner = ns["inner"]
class Function(py.__.test.item.Function):
def __init__(self, *args, **kw):
super(Function, self).__init__(*args, **kw)
self.benchtime = None
self.benchtitle = None
def execute(self, target, *args):
# get func source without first 'def func(...):' line
src = getsource(target)
src = '\n'.join( src.splitlines()[1:] )
# extract benchmark title
if target.func_doc is not None:
self.benchtitle = target.func_doc
else:
self.benchtitle = src.splitlines()[0].strip()
# XXX we ignore args
timer = Timer(src, globals=target.func_globals)
if self.name.startswith('timeit_'):
# from IPython.Magic.magic_timeit
repeat = 3
number = 1
for i in range(1, 10):
t = timer.timeit(number)
if t >= 0.2:
number *= (0.2 / t)
number = int(_ceil(number))
break
if t <= 0.02:
# we are not close enough to that 0.2s
number *= 10
else:
# since we are very close to be > 0.2s we'd better adjust number
# so that timing time is not too high
number *= (0.2 / t)
number = int(_ceil(number))
break
self.benchtime = min(timer.repeat(repeat, number)) / number
# 'bench_<smth>'
else:
self.benchtime = timer.timeit(1)
class BenchSession(TerminalSession):
def header(self, colitems):
super(BenchSession, self).header(colitems)
def footer(self, colitems):
super(BenchSession, self).footer(colitems)
self.out.write('\n')
self.print_bench_results()
def print_bench_results(self):
self.out.write('==============================\n')
self.out.write(' *** BENCHMARKING RESULTS *** \n')
self.out.write('==============================\n')
self.out.write('\n')
# benchname, time, benchtitle
results = []
for item, outcome in self._memo:
if isinstance(item, Item):
best = item.benchtime
if best is None:
# skipped or failed benchmarks
tstr = '---'
else:
# from IPython.Magic.magic_timeit
if best > 0.0:
order = min(-int(_floor(log10(best)) // 3), 3)
else:
order = 3
tstr = "%.*g %s" % (
precision, best * scaling[order], units[order])
results.append( [item.name, tstr, item.benchtitle] )
# dot/unit align second column
# FIXME simpler? this is crappy -- shame on me...
wm = [0]*len(units)
we = [0]*len(units)
for s in results:
tstr = s[1]
n, u = tstr.split()
# unit n
un = unitn[u]
try:
m, e = n.split('.')
except ValueError:
m, e = n, ''
wm[un] = max(len(m), wm[un])
we[un] = max(len(e), we[un])
for s in results:
tstr = s[1]
n, u = tstr.split()
un = unitn[u]
try:
m, e = n.split('.')
except ValueError:
m, e = n, ''
m = m.rjust(wm[un])
e = e.ljust(we[un])
if e.strip():
n = '.'.join((m, e))
else:
n = ' '.join((m, e))
# let's put the number into the right place
txt = ''
for i in range(len(units)):
if i == un:
txt += n
else:
txt += ' '*(wm[i] + we[i] + 1)
s[1] = '%s %s' % (txt, u)
# align all columns besides the last one
for i in range(2):
w = max(len(s[i]) for s in results)
for s in results:
s[i] = s[i].ljust(w)
# show results
for s in results:
self.out.write('%s | %s | %s\n' % tuple(s))
def main(args=None):
# hook our Directory/Module/Function as defaults
from py.__.test import defaultconftest
defaultconftest.Directory = Directory
defaultconftest.Module = Module
defaultconftest.Function = Function
# hook BenchSession as py.test session
config = py.test.config
config._getsessionclass = lambda: BenchSession
py.test.cmdline.main(args)
| 6,352 | 27.110619 | 90 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/randtest.py
|
""" Helpers for randomized testing """
from __future__ import print_function, division
from random import uniform
import random
from sympy.core.numbers import I
from sympy.simplify.simplify import nsimplify
from sympy.core.containers import Tuple
from sympy.core.numbers import comp
from sympy.core.symbol import Symbol
from sympy.core.compatibility import is_sequence, as_int
def random_complex_number(a=2, b=-1, c=3, d=1, rational=False):
"""
Return a random complex number.
To reduce chance of hitting branch cuts or anything, we guarantee
b <= Im z <= d, a <= Re z <= c
"""
A, B = uniform(a, c), uniform(b, d)
if not rational:
return A + I*B
return nsimplify(A, rational=True) + I*nsimplify(B, rational=True)
def verify_numerically(f, g, z=None, tol=1.0e-6, a=2, b=-1, c=3, d=1):
"""
Test numerically that f and g agree when evaluated in the argument z.
If z is None, all symbols will be tested. This routine does not test
whether there are Floats present with precision higher than 15 digits
so if there are, your results may not be what you expect due to round-
off errors.
Examples
========
>>> from sympy import sin, cos
>>> from sympy.abc import x
>>> from sympy.utilities.randtest import verify_numerically as tn
>>> tn(sin(x)**2 + cos(x)**2, 1, x)
True
"""
f, g, z = Tuple(f, g, z)
z = [z] if isinstance(z, Symbol) else (f.free_symbols | g.free_symbols)
reps = list(zip(z, [random_complex_number(a, b, c, d) for zi in z]))
z1 = f.subs(reps).n()
z2 = g.subs(reps).n()
return comp(z1, z2, tol)
def test_derivative_numerically(f, z, tol=1.0e-6, a=2, b=-1, c=3, d=1):
"""
Test numerically that the symbolically computed derivative of f
with respect to z is correct.
This routine does not test whether there are Floats present with
precision higher than 15 digits so if there are, your results may
not be what you expect due to round-off errors.
Examples
========
>>> from sympy import sin
>>> from sympy.abc import x
>>> from sympy.utilities.randtest import test_derivative_numerically as td
>>> td(sin(x), x)
True
"""
from sympy.core.function import Derivative
z0 = random_complex_number(a, b, c, d)
f1 = f.diff(z).subs(z, z0)
f2 = Derivative(f, z).doit_numerically(z0)
return comp(f1.n(), f2.n(), tol)
def _randrange(seed=None):
"""Return a randrange generator. ``seed`` can be
o None - return randomly seeded generator
o int - return a generator seeded with the int
o list - the values to be returned will be taken from the list
in the order given; the provided list is not modified.
Examples
========
>>> from sympy.utilities.randtest import _randrange
>>> rr = _randrange()
>>> rr(1000) # doctest: +SKIP
999
>>> rr = _randrange(3)
>>> rr(1000) # doctest: +SKIP
238
>>> rr = _randrange([0, 5, 1, 3, 4])
>>> rr(3), rr(3)
(0, 1)
"""
if seed is None:
return random.randrange
elif isinstance(seed, int):
return random.Random(seed).randrange
elif is_sequence(seed):
seed = list(seed) # make a copy
seed.reverse()
def give(a, b=None, seq=seed):
if b is None:
a, b = 0, a
a, b = as_int(a), as_int(b)
w = b - a
if w < 1:
raise ValueError('_randrange got empty range')
try:
x = seq.pop()
except AttributeError:
raise ValueError('_randrange expects a list-like sequence')
except IndexError:
raise ValueError('_randrange sequence was too short')
if a <= x < b:
return x
else:
return give(a, b, seq)
return give
else:
raise ValueError('_randrange got an unexpected seed')
def _randint(seed=None):
"""Return a randint generator. ``seed`` can be
o None - return randomly seeded generator
o int - return a generator seeded with the int
o list - the values to be returned will be taken from the list
in the order given; the provided list is not modified.
Examples
========
>>> from sympy.utilities.randtest import _randint
>>> ri = _randint()
>>> ri(1, 1000) # doctest: +SKIP
999
>>> ri = _randint(3)
>>> ri(1, 1000) # doctest: +SKIP
238
>>> ri = _randint([0, 5, 1, 2, 4])
>>> ri(1, 3), ri(1, 3)
(1, 2)
"""
if seed is None:
return random.randint
elif isinstance(seed, int):
return random.Random(seed).randint
elif is_sequence(seed):
seed = list(seed) # make a copy
seed.reverse()
def give(a, b, seq=seed):
a, b = as_int(a), as_int(b)
w = b - a
if w < 0:
raise ValueError('_randint got empty range')
try:
x = seq.pop()
except AttributeError:
raise ValueError('_randint expects a list-like sequence')
except IndexError:
raise ValueError('_randint sequence was too short')
if a <= x <= b:
return x
else:
return give(a, b, seq)
return give
else:
raise ValueError('_randint got an unexpected seed')
| 5,449 | 29.617978 | 78 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/exceptions.py
|
"""
General SymPy exceptions and warnings.
"""
from __future__ import print_function, division
import warnings
from sympy.utilities.misc import filldedent
class SymPyDeprecationWarning(DeprecationWarning):
r"""A warning for deprecated features of SymPy.
This class is expected to be used with the warnings.warn function (note
that one has to explicitly turn on deprecation warnings):
>>> import warnings
>>> from sympy.utilities.exceptions import SymPyDeprecationWarning
>>> warnings.simplefilter(
... "always", SymPyDeprecationWarning)
>>> warnings.warn(
... SymPyDeprecationWarning(feature="Old deprecated thing",
... issue=1065, deprecated_since_version="1.0")) #doctest:+SKIP
__main__:3: SymPyDeprecationWarning:
Old deprecated thing has been deprecated since SymPy 1.0. See
https://github.com/sympy/sympy/issues/1065 for more info.
>>> SymPyDeprecationWarning(feature="Old deprecated thing",
... issue=1065, deprecated_since_version="1.1").warn() #doctest:+SKIP
__main__:1: SymPyDeprecationWarning:
Old deprecated thing has been deprecated since SymPy 1.1.
See https://github.com/sympy/sympy/issues/1065 for more info.
Three arguments to this class are required: ``feature``, ``issue`` and
``deprecated_since_version``.
The ``issue`` flag should be an integer referencing for a "Deprecation
Removal" issue in the SymPy issue tracker. See
https://github.com/sympy/sympy/wiki/Deprecating-policy.
>>> SymPyDeprecationWarning(
... feature="Old feature",
... useinstead="new feature",
... issue=5241,
... deprecated_since_version="1.1")
Old feature has been deprecated since SymPy 1.1. Use new feature
instead. See https://github.com/sympy/sympy/issues/5241 for more info.
Every formal deprecation should have an associated issue in the GitHub
issue tracker. All such issues should have the DeprecationRemoval
tag.
Additionally, each formal deprecation should mark the first release for
which it was deprecated. Use the ``deprecated_since_version`` flag for
this.
>>> SymPyDeprecationWarning(
... feature="Old feature",
... useinstead="new feature",
... deprecated_since_version="0.7.2",
... issue=1065)
Old feature has been deprecated since SymPy 0.7.2. Use new feature
instead. See https://github.com/sympy/sympy/issues/1065 for more info.
To provide additional information, create an instance of this
class in this way:
>>> SymPyDeprecationWarning(
... feature="Such and such",
... last_supported_version="1.2.3",
... useinstead="this other feature",
... issue=1065,
... deprecated_since_version="1.1")
Such and such has been deprecated since SymPy 1.1. It will be last
supported in SymPy version 1.2.3. Use this other feature instead. See
https://github.com/sympy/sympy/issues/1065 for more info.
Note that the text in ``feature`` begins a sentence, so if it begins with
a plain English word, the first letter of that word should be capitalized.
Either (or both) of the arguments ``last_supported_version`` and
``useinstead`` can be omitted. In this case the corresponding sentence
will not be shown:
>>> SymPyDeprecationWarning(feature="Such and such",
... useinstead="this other feature", issue=1065,
... deprecated_since_version="1.1")
Such and such has been deprecated since SymPy 1.1. Use this other
feature instead. See https://github.com/sympy/sympy/issues/1065 for
more info.
You can still provide the argument value. If it is a string, it
will be appended to the end of the message:
>>> SymPyDeprecationWarning(
... feature="Such and such",
... useinstead="this other feature",
... value="Contact the developers for further information.",
... issue=1065,
... deprecated_since_version="1.1")
Such and such has been deprecated since SymPy 1.1. Use this other
feature instead. See https://github.com/sympy/sympy/issues/1065 for
more info. Contact the developers for further information.
If, however, the argument value does not hold a string, a string
representation of the object will be appended to the message:
>>> SymPyDeprecationWarning(
... feature="Such and such",
... useinstead="this other feature",
... value=[1,2,3],
... issue=1065,
... deprecated_since_version="1.1")
Such and such has been deprecated since SymPy 1.1. Use this other
feature instead. See https://github.com/sympy/sympy/issues/1065 for
more info. ([1, 2, 3])
Note that it may be necessary to go back through all the deprecations
before a release to make sure that the version number is correct. So just
use what you believe will be the next release number (this usually means
bumping the minor number by one).
To mark a function as deprecated, you can use the decorator
@deprecated.
See Also
========
sympy.core.decorators.deprecated
"""
def __init__(self, value=None, feature=None, last_supported_version=None,
useinstead=None, issue=None, deprecated_since_version=None):
self.fullMessage = ""
if not feature:
raise ValueError("feature is required argument of SymPyDeprecationWarning")
if not deprecated_since_version:
raise ValueError("deprecated_since_version is a required argument of SymPyDeprecationWarning")
self.fullMessage = "%s has been deprecated since SymPy %s. " % \
(feature, deprecated_since_version)
if last_supported_version:
self.fullMessage += ("It will be last supported in SymPy "
"version %s. ") % last_supported_version
if useinstead:
self.fullMessage += "Use %s instead. " % useinstead
if not issue:
raise ValueError("""\
The issue argument of SymPyDeprecationWarning is required.
This should be a separate issue with the "Deprecation Removal" label. See
https://github.com/sympy/sympy/wiki/Deprecating-policy.\
""")
self.fullMessage += ("See "
"https://github.com/sympy/sympy/issues/%d for more "
"info. ") % issue
if value:
if not isinstance(value, str):
value = "(%s)" % repr(value)
value = " " + value
else:
value = ""
self.fullMessage += value
def __str__(self):
return '\n%s\n' % filldedent(self.fullMessage)
def warn(self, stacklevel=2):
# the next line is what the user would see after the error is printed
# if stacklevel was set to 1. If you are writing a wrapper around this,
# increase the stacklevel accordingly.
warnings.warn(self, stacklevel=stacklevel)
# Python by default hides DeprecationWarnings, which we do not want.
warnings.simplefilter("once", SymPyDeprecationWarning)
| 7,088 | 37.318919 | 106 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/codegen.py
|
"""
module for generating C, C++, Fortran77, Fortran90, Julia, Rust
and Octave/Matlab routines that evaluate sympy expressions.
This module is work in progress.
Only the milestones with a '+' character in the list below have been completed.
--- How is sympy.utilities.codegen different from sympy.printing.ccode? ---
We considered the idea to extend the printing routines for sympy functions in
such a way that it prints complete compilable code, but this leads to a few
unsurmountable issues that can only be tackled with dedicated code generator:
- For C, one needs both a code and a header file, while the printing routines
generate just one string. This code generator can be extended to support
.pyf files for f2py.
- SymPy functions are not concerned with programming-technical issues, such
as input, output and input-output arguments. Other examples are contiguous
or non-contiguous arrays, including headers of other libraries such as gsl
or others.
- It is highly interesting to evaluate several sympy functions in one C
routine, eventually sharing common intermediate results with the help
of the cse routine. This is more than just printing.
- From the programming perspective, expressions with constants should be
evaluated in the code generator as much as possible. This is different
for printing.
--- Basic assumptions ---
* A generic Routine data structure describes the routine that must be
translated into C/Fortran/... code. This data structure covers all
features present in one or more of the supported languages.
* Descendants from the CodeGen class transform multiple Routine instances
into compilable code. Each derived class translates into a specific
language.
* In many cases, one wants a simple workflow. The friendly functions in the
last part are a simple api on top of the Routine/CodeGen stuff. They are
easier to use, but are less powerful.
--- Milestones ---
+ First working version with scalar input arguments, generating C code,
tests
+ Friendly functions that are easier to use than the rigorous
Routine/CodeGen workflow.
+ Integer and Real numbers as input and output
+ Output arguments
+ InputOutput arguments
+ Sort input/output arguments properly
+ Contiguous array arguments (numpy matrices)
+ Also generate .pyf code for f2py (in autowrap module)
+ Isolate constants and evaluate them beforehand in double precision
+ Fortran 90
+ Octave/Matlab
- Common Subexpression Elimination
- User defined comments in the generated code
- Optional extra include lines for libraries/objects that can eval special
functions
- Test other C compilers and libraries: gcc, tcc, libtcc, gcc+gsl, ...
- Contiguous array arguments (sympy matrices)
- Non-contiguous array arguments (sympy matrices)
- ccode must raise an error when it encounters something that can not be
translated into c. ccode(integrate(sin(x)/x, x)) does not make sense.
- Complex numbers as input and output
- A default complex datatype
- Include extra information in the header: date, user, hostname, sha1
hash, ...
- Fortran 77
- C++
- Python
- Julia
- Rust
- ...
"""
from __future__ import print_function, division
import os
import textwrap
from sympy import __version__ as sympy_version
from sympy.core import Symbol, S, Expr, Tuple, Equality, Function, Basic
from sympy.core.compatibility import is_sequence, StringIO, string_types
from sympy.printing.codeprinter import AssignmentError
from sympy.printing.ccode import c_code_printers
from sympy.printing.fcode import FCodePrinter
from sympy.printing.julia import JuliaCodePrinter
from sympy.printing.octave import OctaveCodePrinter
from sympy.printing.rust import RustCodePrinter
from sympy.tensor import Idx, Indexed, IndexedBase
from sympy.matrices import (MatrixSymbol, ImmutableMatrix, MatrixBase,
MatrixExpr, MatrixSlice)
__all__ = [
# description of routines
"Routine", "DataType", "default_datatypes", "get_default_datatype",
"Argument", "InputArgument", "Result",
# routines -> code
"CodeGen", "CCodeGen", "FCodeGen", "JuliaCodeGen", "OctaveCodeGen",
"RustCodeGen",
# friendly functions
"codegen", "make_routine",
]
#
# Description of routines
#
class Routine(object):
"""Generic description of evaluation routine for set of expressions.
A CodeGen class can translate instances of this class into code in a
particular language. The routine specification covers all the features
present in these languages. The CodeGen part must raise an exception
when certain features are not present in the target language. For
example, multiple return values are possible in Python, but not in C or
Fortran. Another example: Fortran and Python support complex numbers,
while C does not.
"""
def __init__(self, name, arguments, results, local_vars, global_vars):
"""Initialize a Routine instance.
Parameters
==========
name : string
Name of the routine.
arguments : list of Arguments
These are things that appear in arguments of a routine, often
appearing on the right-hand side of a function call. These are
commonly InputArguments but in some languages, they can also be
OutputArguments or InOutArguments (e.g., pass-by-reference in C
code).
results : list of Results
These are the return values of the routine, often appearing on
the left-hand side of a function call. The difference between
Results and OutputArguments and when you should use each is
language-specific.
local_vars : list of Symbols
These are used internally by the routine.
global_vars : list of Symbols
Variables which will not be passed into the function.
"""
# extract all input symbols and all symbols appearing in an expression
input_symbols = set([])
symbols = set([])
for arg in arguments:
if isinstance(arg, OutputArgument):
symbols.update(arg.expr.free_symbols)
elif isinstance(arg, InputArgument):
input_symbols.add(arg.name)
elif isinstance(arg, InOutArgument):
input_symbols.add(arg.name)
symbols.update(arg.expr.free_symbols)
else:
raise ValueError("Unknown Routine argument: %s" % arg)
for r in results:
if not isinstance(r, Result):
raise ValueError("Unknown Routine result: %s" % r)
symbols.update(r.expr.free_symbols)
symbols = set([s.label if isinstance(s, Idx) else s for s in symbols])
# Check that all symbols in the expressions are covered by
# InputArguments/InOutArguments---subset because user could
# specify additional (unused) InputArguments or local_vars.
notcovered = symbols.difference(
input_symbols.union(local_vars).union(global_vars))
if notcovered != set([]):
raise ValueError("Symbols needed for output are not in input " +
", ".join([str(x) for x in notcovered]))
self.name = name
self.arguments = arguments
self.results = results
self.local_vars = local_vars
self.global_vars = global_vars
def __str__(self):
return self.__class__.__name__ + "({name!r}, {arguments}, {results}, {local_vars}, {global_vars})".format(**self.__dict__)
__repr__ = __str__
@property
def variables(self):
"""Returns a set of all variables possibly used in the routine.
For routines with unnamed return values, the dummies that may or
may not be used will be included in the set.
"""
v = set(self.local_vars)
for arg in self.arguments:
v.add(arg.name)
for res in self.results:
v.add(res.result_var)
return v
@property
def result_variables(self):
"""Returns a list of OutputArgument, InOutArgument and Result.
If return values are present, they are at the end ot the list.
"""
args = [arg for arg in self.arguments if isinstance(
arg, (OutputArgument, InOutArgument))]
args.extend(self.results)
return args
class DataType(object):
"""Holds strings for a certain datatype in different languages."""
def __init__(self, cname, fname, pyname, jlname, octname, rsname):
self.cname = cname
self.fname = fname
self.pyname = pyname
self.jlname = jlname
self.octname = octname
self.rsname = rsname
default_datatypes = {
"int": DataType("int", "INTEGER*4", "int", "", "", "i32"),
"float": DataType("double", "REAL*8", "float", "", "", "f64"),
}
def get_default_datatype(expr):
"""Derives an appropriate datatype based on the expression."""
if expr.is_integer:
return default_datatypes["int"]
elif isinstance(expr, MatrixBase):
for element in expr:
if not element.is_integer:
return default_datatypes["float"]
return default_datatypes["int"]
else:
return default_datatypes["float"]
class Variable(object):
"""Represents a typed variable."""
def __init__(self, name, datatype=None, dimensions=None, precision=None):
"""Return a new variable.
Parameters
==========
name : Symbol or MatrixSymbol
datatype : optional
When not given, the data type will be guessed based on the
assumptions on the symbol argument.
dimension : sequence containing tupes, optional
If present, the argument is interpreted as an array, where this
sequence of tuples specifies (lower, upper) bounds for each
index of the array.
precision : int, optional
Controls the precision of floating point constants.
"""
if not isinstance(name, (Symbol, MatrixSymbol)):
raise TypeError("The first argument must be a sympy symbol.")
if datatype is None:
datatype = get_default_datatype(name)
elif not isinstance(datatype, DataType):
raise TypeError("The (optional) `datatype' argument must be an "
"instance of the DataType class.")
if dimensions and not isinstance(dimensions, (tuple, list)):
raise TypeError(
"The dimension argument must be a sequence of tuples")
self._name = name
self._datatype = {
'C': datatype.cname,
'FORTRAN': datatype.fname,
'JULIA': datatype.jlname,
'OCTAVE': datatype.octname,
'PYTHON': datatype.pyname,
'RUST': datatype.rsname,
}
self.dimensions = dimensions
self.precision = precision
def __str__(self):
return "%s(%r)" % (self.__class__.__name__, self.name)
__repr__ = __str__
@property
def name(self):
return self._name
def get_datatype(self, language):
"""Returns the datatype string for the requested language.
Examples
========
>>> from sympy import Symbol
>>> from sympy.utilities.codegen import Variable
>>> x = Variable(Symbol('x'))
>>> x.get_datatype('c')
'double'
>>> x.get_datatype('fortran')
'REAL*8'
"""
try:
return self._datatype[language.upper()]
except KeyError:
raise CodeGenError("Has datatypes for languages: %s" %
", ".join(self._datatype))
class Argument(Variable):
"""An abstract Argument data structure: a name and a data type.
This structure is refined in the descendants below.
"""
pass
class InputArgument(Argument):
pass
class ResultBase(object):
"""Base class for all "outgoing" information from a routine.
Objects of this class stores a sympy expression, and a sympy object
representing a result variable that will be used in the generated code
only if necessary.
"""
def __init__(self, expr, result_var):
self.expr = expr
self.result_var = result_var
def __str__(self):
return "%s(%r, %r)" % (self.__class__.__name__, self.expr,
self.result_var)
__repr__ = __str__
class OutputArgument(Argument, ResultBase):
"""OutputArgument are always initialized in the routine."""
def __init__(self, name, result_var, expr, datatype=None, dimensions=None, precision=None):
"""Return a new variable.
Parameters
==========
name : Symbol, MatrixSymbol
The name of this variable. When used for code generation, this
might appear, for example, in the prototype of function in the
argument list.
result_var : Symbol, Indexed
Something that can be used to assign a value to this variable.
Typically the same as `name` but for Indexed this should be e.g.,
"y[i]" whereas `name` should be the Symbol "y".
expr : object
The expression that should be output, typically a SymPy
expression.
datatype : optional
When not given, the data type will be guessed based on the
assumptions on the symbol argument.
dimension : sequence containing tupes, optional
If present, the argument is interpreted as an array, where this
sequence of tuples specifies (lower, upper) bounds for each
index of the array.
precision : int, optional
Controls the precision of floating point constants.
"""
Argument.__init__(self, name, datatype, dimensions, precision)
ResultBase.__init__(self, expr, result_var)
def __str__(self):
return "%s(%r, %r, %r)" % (self.__class__.__name__, self.name, self.expr,
self.result_var)
__repr__ = __str__
class InOutArgument(Argument, ResultBase):
"""InOutArgument are never initialized in the routine."""
def __init__(self, name, result_var, expr, datatype=None, dimensions=None, precision=None):
if not datatype:
datatype = get_default_datatype(expr)
Argument.__init__(self, name, datatype, dimensions, precision)
ResultBase.__init__(self, expr, result_var)
__init__.__doc__ = OutputArgument.__init__.__doc__
def __str__(self):
return "%s(%r, %r, %r)" % (self.__class__.__name__, self.name, self.expr,
self.result_var)
__repr__ = __str__
class Result(Variable, ResultBase):
"""An expression for a return value.
The name result is used to avoid conflicts with the reserved word
"return" in the python language. It is also shorter than ReturnValue.
These may or may not need a name in the destination (e.g., "return(x*y)"
might return a value without ever naming it).
"""
def __init__(self, expr, name=None, result_var=None, datatype=None,
dimensions=None, precision=None):
"""Initialize a return value.
Parameters
==========
expr : SymPy expression
name : Symbol, MatrixSymbol, optional
The name of this return variable. When used for code generation,
this might appear, for example, in the prototype of function in a
list of return values. A dummy name is generated if omitted.
result_var : Symbol, Indexed, optional
Something that can be used to assign a value to this variable.
Typically the same as `name` but for Indexed this should be e.g.,
"y[i]" whereas `name` should be the Symbol "y". Defaults to
`name` if omitted.
datatype : optional
When not given, the data type will be guessed based on the
assumptions on the symbol argument.
dimension : sequence containing tupes, optional
If present, this variable is interpreted as an array,
where this sequence of tuples specifies (lower, upper)
bounds for each index of the array.
precision : int, optional
Controls the precision of floating point constants.
"""
# Basic because it is the base class for all types of expressions
if not isinstance(expr, (Basic, MatrixBase)):
raise TypeError("The first argument must be a sympy expression.")
if name is None:
name = 'result_%d' % abs(hash(expr))
if isinstance(name, string_types):
if isinstance(expr, (MatrixBase, MatrixExpr)):
name = MatrixSymbol(name, *expr.shape)
else:
name = Symbol(name)
if result_var is None:
result_var = name
Variable.__init__(self, name, datatype=datatype,
dimensions=dimensions, precision=precision)
ResultBase.__init__(self, expr, result_var)
#
# Transformation of routine objects into code
#
class CodeGen(object):
"""Abstract class for the code generators."""
printer = None # will be set to an instance of a CodePrinter subclass
def _indent_code(self, codelines):
return self.printer.indent_code(codelines)
def _printer_method_with_settings(self, method, settings=None, *args, **kwargs):
settings = settings or {}
ori = {k: self.printer._settings[k] for k in settings}
for k, v in settings.items():
self.printer._settings[k] = v
result = getattr(self.printer, method)(*args, **kwargs)
for k, v in ori.items():
self.printer._settings[k] = v
return result
def _get_symbol(self, s):
"""Returns the symbol as fcode prints it."""
if self.printer._settings['human']:
expr_str = self.printer.doprint(s)
else:
constants, not_supported, expr_str = self.printer.doprint(s)
if constants or not_supported:
raise ValueError("Failed to print %s" % str(s))
return expr_str.strip()
def __init__(self, project="project"):
"""Initialize a code generator.
Derived classes will offer more options that affect the generated
code.
"""
self.project = project
def routine(self, name, expr, argument_sequence, global_vars):
"""Creates an Routine object that is appropriate for this language.
This implementation is appropriate for at least C/Fortran. Subclasses
can override this if necessary.
Here, we assume at most one return value (the l-value) which must be
scalar. Additional outputs are OutputArguments (e.g., pointers on
right-hand-side or pass-by-reference). Matrices are always returned
via OutputArguments. If ``argument_sequence`` is None, arguments will
be ordered alphabetically, but with all InputArguments first, and then
OutputArgument and InOutArguments.
"""
if is_sequence(expr) and not isinstance(expr, (MatrixBase, MatrixExpr)):
if not expr:
raise ValueError("No expression given")
expressions = Tuple(*expr)
else:
expressions = Tuple(expr)
# local variables
local_vars = {i.label for i in expressions.atoms(Idx)}
# global variables
global_vars = set() if global_vars is None else set(global_vars)
# symbols that should be arguments
symbols = expressions.free_symbols - local_vars - global_vars
new_symbols = set([])
new_symbols.update(symbols)
for symbol in symbols:
if isinstance(symbol, Idx):
new_symbols.remove(symbol)
new_symbols.update(symbol.args[1].free_symbols)
symbols = new_symbols
# Decide whether to use output argument or return value
return_val = []
output_args = []
for expr in expressions:
if isinstance(expr, Equality):
out_arg = expr.lhs
expr = expr.rhs
if isinstance(out_arg, Indexed):
dims = tuple([ (S.Zero, dim - 1) for dim in out_arg.shape])
symbol = out_arg.base.label
elif isinstance(out_arg, Symbol):
dims = []
symbol = out_arg
elif isinstance(out_arg, MatrixSymbol):
dims = tuple([ (S.Zero, dim - 1) for dim in out_arg.shape])
symbol = out_arg
else:
raise CodeGenError("Only Indexed, Symbol, or MatrixSymbol "
"can define output arguments.")
if expr.has(symbol):
output_args.append(
InOutArgument(symbol, out_arg, expr, dimensions=dims))
else:
output_args.append(
OutputArgument(symbol, out_arg, expr, dimensions=dims))
# avoid duplicate arguments
symbols.remove(symbol)
elif isinstance(expr, (ImmutableMatrix, MatrixSlice)):
# Create a "dummy" MatrixSymbol to use as the Output arg
out_arg = MatrixSymbol('out_%s' % abs(hash(expr)), *expr.shape)
dims = tuple([(S.Zero, dim - 1) for dim in out_arg.shape])
output_args.append(
OutputArgument(out_arg, out_arg, expr, dimensions=dims))
else:
return_val.append(Result(expr))
arg_list = []
# setup input argument list
array_symbols = {}
for array in expressions.atoms(Indexed):
array_symbols[array.base.label] = array
for array in expressions.atoms(MatrixSymbol):
array_symbols[array] = array
for symbol in sorted(symbols, key=str):
if symbol in array_symbols:
dims = []
array = array_symbols[symbol]
for dim in array.shape:
dims.append((S.Zero, dim - 1))
metadata = {'dimensions': dims}
else:
metadata = {}
arg_list.append(InputArgument(symbol, **metadata))
output_args.sort(key=lambda x: str(x.name))
arg_list.extend(output_args)
if argument_sequence is not None:
# if the user has supplied IndexedBase instances, we'll accept that
new_sequence = []
for arg in argument_sequence:
if isinstance(arg, IndexedBase):
new_sequence.append(arg.label)
else:
new_sequence.append(arg)
argument_sequence = new_sequence
missing = [x for x in arg_list if x.name not in argument_sequence]
if missing:
msg = "Argument list didn't specify: {0} "
msg = msg.format(", ".join([str(m.name) for m in missing]))
raise CodeGenArgumentListError(msg, missing)
# create redundant arguments to produce the requested sequence
name_arg_dict = {x.name: x for x in arg_list}
new_args = []
for symbol in argument_sequence:
try:
new_args.append(name_arg_dict[symbol])
except KeyError:
new_args.append(InputArgument(symbol))
arg_list = new_args
return Routine(name, arg_list, return_val, local_vars, global_vars)
def write(self, routines, prefix, to_files=False, header=True, empty=True):
"""Writes all the source code files for the given routines.
The generated source is returned as a list of (filename, contents)
tuples, or is written to files (see below). Each filename consists
of the given prefix, appended with an appropriate extension.
Parameters
==========
routines : list
A list of Routine instances to be written
prefix : string
The prefix for the output files
to_files : bool, optional
When True, the output is written to files. Otherwise, a list
of (filename, contents) tuples is returned. [default: False]
header : bool, optional
When True, a header comment is included on top of each source
file. [default: True]
empty : bool, optional
When True, empty lines are included to structure the source
files. [default: True]
"""
if to_files:
for dump_fn in self.dump_fns:
filename = "%s.%s" % (prefix, dump_fn.extension)
with open(filename, "w") as f:
dump_fn(self, routines, f, prefix, header, empty)
else:
result = []
for dump_fn in self.dump_fns:
filename = "%s.%s" % (prefix, dump_fn.extension)
contents = StringIO()
dump_fn(self, routines, contents, prefix, header, empty)
result.append((filename, contents.getvalue()))
return result
def dump_code(self, routines, f, prefix, header=True, empty=True):
"""Write the code by calling language specific methods.
The generated file contains all the definitions of the routines in
low-level code and refers to the header file if appropriate.
Parameters
==========
routines : list
A list of Routine instances.
f : file-like
Where to write the file.
prefix : string
The filename prefix, used to refer to the proper header file.
Only the basename of the prefix is used.
header : bool, optional
When True, a header comment is included on top of each source
file. [default : True]
empty : bool, optional
When True, empty lines are included to structure the source
files. [default : True]
"""
code_lines = self._preprocessor_statements(prefix)
for routine in routines:
if empty:
code_lines.append("\n")
code_lines.extend(self._get_routine_opening(routine))
code_lines.extend(self._declare_arguments(routine))
code_lines.extend(self._declare_globals(routine))
code_lines.extend(self._declare_locals(routine))
if empty:
code_lines.append("\n")
code_lines.extend(self._call_printer(routine))
if empty:
code_lines.append("\n")
code_lines.extend(self._get_routine_ending(routine))
code_lines = self._indent_code(''.join(code_lines))
if header:
code_lines = ''.join(self._get_header() + [code_lines])
if code_lines:
f.write(code_lines)
class CodeGenError(Exception):
pass
class CodeGenArgumentListError(Exception):
@property
def missing_args(self):
return self.args[1]
header_comment = """Code generated with sympy %(version)s
See http://www.sympy.org/ for more information.
This file is part of '%(project)s'
"""
class CCodeGen(CodeGen):
"""Generator for C code.
The .write() method inherited from CodeGen will output a code file and
an interface file, <prefix>.c and <prefix>.h respectively.
"""
code_extension = "c"
interface_extension = "h"
standard = 'c99'
def __init__(self, project="project", printer=None,
preprocessor_statements=None):
super(CCodeGen, self).__init__(project=project)
self.printer = printer or c_code_printers[self.standard.lower()]()
self.preprocessor_statements = preprocessor_statements
if preprocessor_statements is None:
self.preprocessor_statements = ['#include <math.h>']
def _get_header(self):
"""Writes a common header for the generated files."""
code_lines = []
code_lines.append("/" + "*"*78 + '\n')
tmp = header_comment % {"version": sympy_version,
"project": self.project}
for line in tmp.splitlines():
code_lines.append(" *%s*\n" % line.center(76))
code_lines.append(" " + "*"*78 + "/\n")
return code_lines
def get_prototype(self, routine):
"""Returns a string for the function prototype of the routine.
If the routine has multiple result objects, an CodeGenError is
raised.
See: http://en.wikipedia.org/wiki/Function_prototype
"""
if len(routine.results) > 1:
raise CodeGenError("C only supports a single or no return value.")
elif len(routine.results) == 1:
ctype = routine.results[0].get_datatype('C')
else:
ctype = "void"
type_args = []
for arg in routine.arguments:
name = self.printer.doprint(arg.name)
if arg.dimensions or isinstance(arg, ResultBase):
type_args.append((arg.get_datatype('C'), "*%s" % name))
else:
type_args.append((arg.get_datatype('C'), name))
arguments = ", ".join([ "%s %s" % t for t in type_args])
return "%s %s(%s)" % (ctype, routine.name, arguments)
def _preprocessor_statements(self, prefix):
code_lines = []
code_lines.append('#include "{}.h"'.format(os.path.basename(prefix)))
code_lines.extend(self.preprocessor_statements)
code_lines = ['{}\n'.format(l) for l in code_lines]
return code_lines
def _get_routine_opening(self, routine):
prototype = self.get_prototype(routine)
return ["%s {\n" % prototype]
def _declare_arguments(self, routine):
# arguments are declared in prototype
return []
def _declare_globals(self, routine):
# global variables are not explicitly declared within C functions
return []
def _declare_locals(self, routine):
# loop variables are declared in loop statement
return []
def _call_printer(self, routine):
code_lines = []
# Compose a list of symbols to be dereferenced in the function
# body. These are the arguments that were passed by a reference
# pointer, excluding arrays.
dereference = []
for arg in routine.arguments:
if isinstance(arg, ResultBase) and not arg.dimensions:
dereference.append(arg.name)
return_val = None
for result in routine.result_variables:
if isinstance(result, Result):
assign_to = routine.name + "_result"
t = result.get_datatype('c')
code_lines.append("{0} {1};\n".format(t, str(assign_to)))
return_val = assign_to
else:
assign_to = result.result_var
try:
constants, not_c, c_expr = self._printer_method_with_settings(
'doprint', dict(human=False, dereference=dereference),
result.expr, assign_to=assign_to)
except AssignmentError:
assign_to = result.result_var
code_lines.append(
"%s %s;\n" % (result.get_datatype('c'), str(assign_to)))
constants, not_c, c_expr = self._printer_method_with_settings(
'doprint', dict(human=False, dereference=dereference),
result.expr, assign_to=assign_to)
for name, value in sorted(constants, key=str):
code_lines.append("double const %s = %s;\n" % (name, value))
code_lines.append("%s\n" % c_expr)
if return_val:
code_lines.append(" return %s;\n" % return_val)
return code_lines
def _get_routine_ending(self, routine):
return ["}\n"]
def dump_c(self, routines, f, prefix, header=True, empty=True):
self.dump_code(routines, f, prefix, header, empty)
dump_c.extension = code_extension
dump_c.__doc__ = CodeGen.dump_code.__doc__
def dump_h(self, routines, f, prefix, header=True, empty=True):
"""Writes the C header file.
This file contains all the function declarations.
Parameters
==========
routines : list
A list of Routine instances.
f : file-like
Where to write the file.
prefix : string
The filename prefix, used to construct the include guards.
Only the basename of the prefix is used.
header : bool, optional
When True, a header comment is included on top of each source
file. [default : True]
empty : bool, optional
When True, empty lines are included to structure the source
files. [default : True]
"""
if header:
print(''.join(self._get_header()), file=f)
guard_name = "%s__%s__H" % (self.project.replace(
" ", "_").upper(), prefix.replace("/", "_").upper())
# include guards
if empty:
print(file=f)
print("#ifndef %s" % guard_name, file=f)
print("#define %s" % guard_name, file=f)
if empty:
print(file=f)
# declaration of the function prototypes
for routine in routines:
prototype = self.get_prototype(routine)
print("%s;" % prototype, file=f)
# end if include guards
if empty:
print(file=f)
print("#endif", file=f)
if empty:
print(file=f)
dump_h.extension = interface_extension
# This list of dump functions is used by CodeGen.write to know which dump
# functions it has to call.
dump_fns = [dump_c, dump_h]
class C89CodeGen(CCodeGen):
standard = 'C89'
class C99CodeGen(CCodeGen):
standard = 'C99'
class FCodeGen(CodeGen):
"""Generator for Fortran 95 code
The .write() method inherited from CodeGen will output a code file and
an interface file, <prefix>.f90 and <prefix>.h respectively.
"""
code_extension = "f90"
interface_extension = "h"
def __init__(self, project='project', printer=None):
super(FCodeGen, self).__init__(project)
self.printer = printer or FCodePrinter()
def _get_header(self):
"""Writes a common header for the generated files."""
code_lines = []
code_lines.append("!" + "*"*78 + '\n')
tmp = header_comment % {"version": sympy_version,
"project": self.project}
for line in tmp.splitlines():
code_lines.append("!*%s*\n" % line.center(76))
code_lines.append("!" + "*"*78 + '\n')
return code_lines
def _preprocessor_statements(self, prefix):
return []
def _get_routine_opening(self, routine):
"""Returns the opening statements of the fortran routine."""
code_list = []
if len(routine.results) > 1:
raise CodeGenError(
"Fortran only supports a single or no return value.")
elif len(routine.results) == 1:
result = routine.results[0]
code_list.append(result.get_datatype('fortran'))
code_list.append("function")
else:
code_list.append("subroutine")
args = ", ".join("%s" % self._get_symbol(arg.name)
for arg in routine.arguments)
call_sig = "{0}({1})\n".format(routine.name, args)
# Fortran 95 requires all lines be less than 132 characters, so wrap
# this line before appending.
call_sig = ' &\n'.join(textwrap.wrap(call_sig,
width=60,
break_long_words=False)) + '\n'
code_list.append(call_sig)
code_list = [' '.join(code_list)]
code_list.append('implicit none\n')
return code_list
def _declare_arguments(self, routine):
# argument type declarations
code_list = []
array_list = []
scalar_list = []
for arg in routine.arguments:
if isinstance(arg, InputArgument):
typeinfo = "%s, intent(in)" % arg.get_datatype('fortran')
elif isinstance(arg, InOutArgument):
typeinfo = "%s, intent(inout)" % arg.get_datatype('fortran')
elif isinstance(arg, OutputArgument):
typeinfo = "%s, intent(out)" % arg.get_datatype('fortran')
else:
raise CodeGenError("Unkown Argument type: %s" % type(arg))
fprint = self._get_symbol
if arg.dimensions:
# fortran arrays start at 1
dimstr = ", ".join(["%s:%s" % (
fprint(dim[0] + 1), fprint(dim[1] + 1))
for dim in arg.dimensions])
typeinfo += ", dimension(%s)" % dimstr
array_list.append("%s :: %s\n" % (typeinfo, fprint(arg.name)))
else:
scalar_list.append("%s :: %s\n" % (typeinfo, fprint(arg.name)))
# scalars first, because they can be used in array declarations
code_list.extend(scalar_list)
code_list.extend(array_list)
return code_list
def _declare_globals(self, routine):
# Global variables not explicitly declared within Fortran 90 functions.
# Note: a future F77 mode may need to generate "common" blocks.
return []
def _declare_locals(self, routine):
code_list = []
for var in sorted(routine.local_vars, key=str):
typeinfo = get_default_datatype(var)
code_list.append("%s :: %s\n" % (
typeinfo.fname, self._get_symbol(var)))
return code_list
def _get_routine_ending(self, routine):
"""Returns the closing statements of the fortran routine."""
if len(routine.results) == 1:
return ["end function\n"]
else:
return ["end subroutine\n"]
def get_interface(self, routine):
"""Returns a string for the function interface.
The routine should have a single result object, which can be None.
If the routine has multiple result objects, a CodeGenError is
raised.
See: http://en.wikipedia.org/wiki/Function_prototype
"""
prototype = [ "interface\n" ]
prototype.extend(self._get_routine_opening(routine))
prototype.extend(self._declare_arguments(routine))
prototype.extend(self._get_routine_ending(routine))
prototype.append("end interface\n")
return "".join(prototype)
def _call_printer(self, routine):
declarations = []
code_lines = []
for result in routine.result_variables:
if isinstance(result, Result):
assign_to = routine.name
elif isinstance(result, (OutputArgument, InOutArgument)):
assign_to = result.result_var
constants, not_fortran, f_expr = self._printer_method_with_settings(
'doprint', dict(human=False, source_format='free'),
result.expr, assign_to=assign_to)
for obj, v in sorted(constants, key=str):
t = get_default_datatype(obj)
declarations.append(
"%s, parameter :: %s = %s\n" % (t.fname, obj, v))
for obj in sorted(not_fortran, key=str):
t = get_default_datatype(obj)
if isinstance(obj, Function):
name = obj.func
else:
name = obj
declarations.append("%s :: %s\n" % (t.fname, name))
code_lines.append("%s\n" % f_expr)
return declarations + code_lines
def _indent_code(self, codelines):
return self._printer_method_with_settings(
'indent_code', dict(human=False, source_format='free'), codelines)
def dump_f95(self, routines, f, prefix, header=True, empty=True):
# check that symbols are unique with ignorecase
for r in routines:
lowercase = {str(x).lower() for x in r.variables}
orig_case = {str(x) for x in r.variables}
if len(lowercase) < len(orig_case):
raise CodeGenError("Fortran ignores case. Got symbols: %s" %
(", ".join([str(var) for var in r.variables])))
self.dump_code(routines, f, prefix, header, empty)
dump_f95.extension = code_extension
dump_f95.__doc__ = CodeGen.dump_code.__doc__
def dump_h(self, routines, f, prefix, header=True, empty=True):
"""Writes the interface to a header file.
This file contains all the function declarations.
Parameters
==========
routines : list
A list of Routine instances.
f : file-like
Where to write the file.
prefix : string
The filename prefix.
header : bool, optional
When True, a header comment is included on top of each source
file. [default : True]
empty : bool, optional
When True, empty lines are included to structure the source
files. [default : True]
"""
if header:
print(''.join(self._get_header()), file=f)
if empty:
print(file=f)
# declaration of the function prototypes
for routine in routines:
prototype = self.get_interface(routine)
f.write(prototype)
if empty:
print(file=f)
dump_h.extension = interface_extension
# This list of dump functions is used by CodeGen.write to know which dump
# functions it has to call.
dump_fns = [dump_f95, dump_h]
class JuliaCodeGen(CodeGen):
"""Generator for Julia code.
The .write() method inherited from CodeGen will output a code file
<prefix>.jl.
"""
code_extension = "jl"
def __init__(self, project='project', printer=None):
super(JuliaCodeGen, self).__init__(project)
self.printer = printer or JuliaCodePrinter()
def routine(self, name, expr, argument_sequence, global_vars):
"""Specialized Routine creation for Julia."""
if is_sequence(expr) and not isinstance(expr, (MatrixBase, MatrixExpr)):
if not expr:
raise ValueError("No expression given")
expressions = Tuple(*expr)
else:
expressions = Tuple(expr)
# local variables
local_vars = {i.label for i in expressions.atoms(Idx)}
# global variables
global_vars = set() if global_vars is None else set(global_vars)
# symbols that should be arguments
old_symbols = expressions.free_symbols - local_vars - global_vars
symbols = set([])
for s in old_symbols:
if isinstance(s, Idx):
symbols.update(s.args[1].free_symbols)
else:
symbols.add(s)
# Julia supports multiple return values
return_vals = []
output_args = []
for (i, expr) in enumerate(expressions):
if isinstance(expr, Equality):
out_arg = expr.lhs
expr = expr.rhs
symbol = out_arg
if isinstance(out_arg, Indexed):
dims = tuple([ (S.One, dim) for dim in out_arg.shape])
symbol = out_arg.base.label
output_args.append(InOutArgument(symbol, out_arg, expr, dimensions=dims))
if not isinstance(out_arg, (Indexed, Symbol, MatrixSymbol)):
raise CodeGenError("Only Indexed, Symbol, or MatrixSymbol "
"can define output arguments.")
return_vals.append(Result(expr, name=symbol, result_var=out_arg))
if not expr.has(symbol):
# this is a pure output: remove from the symbols list, so
# it doesn't become an input.
symbols.remove(symbol)
else:
# we have no name for this output
return_vals.append(Result(expr, name='out%d' % (i+1)))
# setup input argument list
output_args.sort(key=lambda x: str(x.name))
arg_list = list(output_args)
array_symbols = {}
for array in expressions.atoms(Indexed):
array_symbols[array.base.label] = array
for array in expressions.atoms(MatrixSymbol):
array_symbols[array] = array
for symbol in sorted(symbols, key=str):
arg_list.append(InputArgument(symbol))
if argument_sequence is not None:
# if the user has supplied IndexedBase instances, we'll accept that
new_sequence = []
for arg in argument_sequence:
if isinstance(arg, IndexedBase):
new_sequence.append(arg.label)
else:
new_sequence.append(arg)
argument_sequence = new_sequence
missing = [x for x in arg_list if x.name not in argument_sequence]
if missing:
msg = "Argument list didn't specify: {0} "
msg = msg.format(", ".join([str(m.name) for m in missing]))
raise CodeGenArgumentListError(msg, missing)
# create redundant arguments to produce the requested sequence
name_arg_dict = {x.name: x for x in arg_list}
new_args = []
for symbol in argument_sequence:
try:
new_args.append(name_arg_dict[symbol])
except KeyError:
new_args.append(InputArgument(symbol))
arg_list = new_args
return Routine(name, arg_list, return_vals, local_vars, global_vars)
def _get_header(self):
"""Writes a common header for the generated files."""
code_lines = []
tmp = header_comment % {"version": sympy_version,
"project": self.project}
for line in tmp.splitlines():
if line == '':
code_lines.append("#\n")
else:
code_lines.append("# %s\n" % line)
return code_lines
def _preprocessor_statements(self, prefix):
return []
def _get_routine_opening(self, routine):
"""Returns the opening statements of the routine."""
code_list = []
code_list.append("function ")
# Inputs
args = []
for i, arg in enumerate(routine.arguments):
if isinstance(arg, OutputArgument):
raise CodeGenError("Julia: invalid argument of type %s" %
str(type(arg)))
if isinstance(arg, (InputArgument, InOutArgument)):
args.append("%s" % self._get_symbol(arg.name))
args = ", ".join(args)
code_list.append("%s(%s)\n" % (routine.name, args))
code_list = [ "".join(code_list) ]
return code_list
def _declare_arguments(self, routine):
return []
def _declare_globals(self, routine):
return []
def _declare_locals(self, routine):
return []
def _get_routine_ending(self, routine):
outs = []
for result in routine.results:
if isinstance(result, Result):
# Note: name not result_var; want `y` not `y[i]` for Indexed
s = self._get_symbol(result.name)
else:
raise CodeGenError("unexpected object in Routine results")
outs.append(s)
return ["return " + ", ".join(outs) + "\nend\n"]
def _call_printer(self, routine):
declarations = []
code_lines = []
for i, result in enumerate(routine.results):
if isinstance(result, Result):
assign_to = result.result_var
else:
raise CodeGenError("unexpected object in Routine results")
constants, not_supported, jl_expr = self._printer_method_with_settings(
'doprint', dict(human=False), result.expr, assign_to=assign_to)
for obj, v in sorted(constants, key=str):
declarations.append(
"%s = %s\n" % (obj, v))
for obj in sorted(not_supported, key=str):
if isinstance(obj, Function):
name = obj.func
else:
name = obj
declarations.append(
"# unsupported: %s\n" % (name))
code_lines.append("%s\n" % (jl_expr))
return declarations + code_lines
def _indent_code(self, codelines):
# Note that indenting seems to happen twice, first
# statement-by-statement by JuliaPrinter then again here.
p = JuliaCodePrinter({'human': False})
return p.indent_code(codelines)
def dump_jl(self, routines, f, prefix, header=True, empty=True):
self.dump_code(routines, f, prefix, header, empty)
dump_jl.extension = code_extension
dump_jl.__doc__ = CodeGen.dump_code.__doc__
# This list of dump functions is used by CodeGen.write to know which dump
# functions it has to call.
dump_fns = [dump_jl]
class OctaveCodeGen(CodeGen):
"""Generator for Octave code.
The .write() method inherited from CodeGen will output a code file
<prefix>.m.
Octave .m files usually contain one function. That function name should
match the filename (``prefix``). If you pass multiple ``name_expr`` pairs,
the latter ones are presumed to be private functions accessed by the
primary function.
You should only pass inputs to ``argument_sequence``: outputs are ordered
according to their order in ``name_expr``.
"""
code_extension = "m"
def __init__(self, project='project', printer=None):
super(OctaveCodeGen, self).__init__(project)
self.printer = printer or OctaveCodePrinter()
def routine(self, name, expr, argument_sequence, global_vars):
"""Specialized Routine creation for Octave."""
# FIXME: this is probably general enough for other high-level
# languages, perhaps its the C/Fortran one that is specialized!
if is_sequence(expr) and not isinstance(expr, (MatrixBase, MatrixExpr)):
if not expr:
raise ValueError("No expression given")
expressions = Tuple(*expr)
else:
expressions = Tuple(expr)
# local variables
local_vars = {i.label for i in expressions.atoms(Idx)}
# global variables
global_vars = set() if global_vars is None else set(global_vars)
# symbols that should be arguments
old_symbols = expressions.free_symbols - local_vars - global_vars
symbols = set([])
for s in old_symbols:
if isinstance(s, Idx):
symbols.update(s.args[1].free_symbols)
else:
symbols.add(s)
# Octave supports multiple return values
return_vals = []
for (i, expr) in enumerate(expressions):
if isinstance(expr, Equality):
out_arg = expr.lhs
expr = expr.rhs
symbol = out_arg
if isinstance(out_arg, Indexed):
symbol = out_arg.base.label
if not isinstance(out_arg, (Indexed, Symbol, MatrixSymbol)):
raise CodeGenError("Only Indexed, Symbol, or MatrixSymbol "
"can define output arguments.")
return_vals.append(Result(expr, name=symbol, result_var=out_arg))
if not expr.has(symbol):
# this is a pure output: remove from the symbols list, so
# it doesn't become an input.
symbols.remove(symbol)
else:
# we have no name for this output
return_vals.append(Result(expr, name='out%d' % (i+1)))
# setup input argument list
arg_list = []
array_symbols = {}
for array in expressions.atoms(Indexed):
array_symbols[array.base.label] = array
for array in expressions.atoms(MatrixSymbol):
array_symbols[array] = array
for symbol in sorted(symbols, key=str):
arg_list.append(InputArgument(symbol))
if argument_sequence is not None:
# if the user has supplied IndexedBase instances, we'll accept that
new_sequence = []
for arg in argument_sequence:
if isinstance(arg, IndexedBase):
new_sequence.append(arg.label)
else:
new_sequence.append(arg)
argument_sequence = new_sequence
missing = [x for x in arg_list if x.name not in argument_sequence]
if missing:
msg = "Argument list didn't specify: {0} "
msg = msg.format(", ".join([str(m.name) for m in missing]))
raise CodeGenArgumentListError(msg, missing)
# create redundant arguments to produce the requested sequence
name_arg_dict = {x.name: x for x in arg_list}
new_args = []
for symbol in argument_sequence:
try:
new_args.append(name_arg_dict[symbol])
except KeyError:
new_args.append(InputArgument(symbol))
arg_list = new_args
return Routine(name, arg_list, return_vals, local_vars, global_vars)
def _get_header(self):
"""Writes a common header for the generated files."""
code_lines = []
tmp = header_comment % {"version": sympy_version,
"project": self.project}
for line in tmp.splitlines():
if line == '':
code_lines.append("%\n")
else:
code_lines.append("%% %s\n" % line)
return code_lines
def _preprocessor_statements(self, prefix):
return []
def _get_routine_opening(self, routine):
"""Returns the opening statements of the routine."""
code_list = []
code_list.append("function ")
# Outputs
outs = []
for i, result in enumerate(routine.results):
if isinstance(result, Result):
# Note: name not result_var; want `y` not `y(i)` for Indexed
s = self._get_symbol(result.name)
else:
raise CodeGenError("unexpected object in Routine results")
outs.append(s)
if len(outs) > 1:
code_list.append("[" + (", ".join(outs)) + "]")
else:
code_list.append("".join(outs))
code_list.append(" = ")
# Inputs
args = []
for i, arg in enumerate(routine.arguments):
if isinstance(arg, (OutputArgument, InOutArgument)):
raise CodeGenError("Octave: invalid argument of type %s" %
str(type(arg)))
if isinstance(arg, InputArgument):
args.append("%s" % self._get_symbol(arg.name))
args = ", ".join(args)
code_list.append("%s(%s)\n" % (routine.name, args))
code_list = [ "".join(code_list) ]
return code_list
def _declare_arguments(self, routine):
return []
def _declare_globals(self, routine):
if not routine.global_vars:
return []
s = " ".join(sorted([self._get_symbol(g) for g in routine.global_vars]))
return ["global " + s + "\n"]
def _declare_locals(self, routine):
return []
def _get_routine_ending(self, routine):
return ["end\n"]
def _call_printer(self, routine):
declarations = []
code_lines = []
for i, result in enumerate(routine.results):
if isinstance(result, Result):
assign_to = result.result_var
else:
raise CodeGenError("unexpected object in Routine results")
constants, not_supported, oct_expr = self._printer_method_with_settings(
'doprint', dict(human=False), result.expr, assign_to=assign_to)
for obj, v in sorted(constants, key=str):
declarations.append(
" %s = %s; %% constant\n" % (obj, v))
for obj in sorted(not_supported, key=str):
if isinstance(obj, Function):
name = obj.func
else:
name = obj
declarations.append(
" %% unsupported: %s\n" % (name))
code_lines.append("%s\n" % (oct_expr))
return declarations + code_lines
def _indent_code(self, codelines):
return self._printer_method_with_settings(
'indent_code', dict(human=False), codelines)
def dump_m(self, routines, f, prefix, header=True, empty=True, inline=True):
# Note used to call self.dump_code() but we need more control for header
code_lines = self._preprocessor_statements(prefix)
for i, routine in enumerate(routines):
if i > 0:
if empty:
code_lines.append("\n")
code_lines.extend(self._get_routine_opening(routine))
if i == 0:
if routine.name != prefix:
raise ValueError('Octave function name should match prefix')
if header:
code_lines.append("%" + prefix.upper() +
" Autogenerated by sympy\n")
code_lines.append(''.join(self._get_header()))
code_lines.extend(self._declare_arguments(routine))
code_lines.extend(self._declare_globals(routine))
code_lines.extend(self._declare_locals(routine))
if empty:
code_lines.append("\n")
code_lines.extend(self._call_printer(routine))
if empty:
code_lines.append("\n")
code_lines.extend(self._get_routine_ending(routine))
code_lines = self._indent_code(''.join(code_lines))
if code_lines:
f.write(code_lines)
dump_m.extension = code_extension
dump_m.__doc__ = CodeGen.dump_code.__doc__
# This list of dump functions is used by CodeGen.write to know which dump
# functions it has to call.
dump_fns = [dump_m]
class RustCodeGen(CodeGen):
"""Generator for Rust code.
The .write() method inherited from CodeGen will output a code file
<prefix>.rs
"""
code_extension = "rs"
def __init__(self, project="project", printer=None):
super(RustCodeGen, self).__init__(project=project)
self.printer = printer or RustCodePrinter()
def routine(self, name, expr, argument_sequence, global_vars):
"""Specialized Routine creation for Rust."""
if is_sequence(expr) and not isinstance(expr, (MatrixBase, MatrixExpr)):
if not expr:
raise ValueError("No expression given")
expressions = Tuple(*expr)
else:
expressions = Tuple(expr)
# local variables
local_vars = set([i.label for i in expressions.atoms(Idx)])
# global variables
global_vars = set() if global_vars is None else set(global_vars)
# symbols that should be arguments
symbols = expressions.free_symbols - local_vars - global_vars
# Rust supports multiple return values
return_vals = []
output_args = []
for (i, expr) in enumerate(expressions):
if isinstance(expr, Equality):
out_arg = expr.lhs
expr = expr.rhs
symbol = out_arg
if isinstance(out_arg, Indexed):
dims = tuple([ (S.One, dim) for dim in out_arg.shape])
symbol = out_arg.base.label
output_args.append(InOutArgument(symbol, out_arg, expr, dimensions=dims))
if not isinstance(out_arg, (Indexed, Symbol, MatrixSymbol)):
raise CodeGenError("Only Indexed, Symbol, or MatrixSymbol "
"can define output arguments.")
return_vals.append(Result(expr, name=symbol, result_var=out_arg))
if not expr.has(symbol):
# this is a pure output: remove from the symbols list, so
# it doesn't become an input.
symbols.remove(symbol)
else:
# we have no name for this output
return_vals.append(Result(expr, name='out%d' % (i+1)))
# setup input argument list
output_args.sort(key=lambda x: str(x.name))
arg_list = list(output_args)
array_symbols = {}
for array in expressions.atoms(Indexed):
array_symbols[array.base.label] = array
for array in expressions.atoms(MatrixSymbol):
array_symbols[array] = array
for symbol in sorted(symbols, key=str):
arg_list.append(InputArgument(symbol))
if argument_sequence is not None:
# if the user has supplied IndexedBase instances, we'll accept that
new_sequence = []
for arg in argument_sequence:
if isinstance(arg, IndexedBase):
new_sequence.append(arg.label)
else:
new_sequence.append(arg)
argument_sequence = new_sequence
missing = [x for x in arg_list if x.name not in argument_sequence]
if missing:
msg = "Argument list didn't specify: {0} "
msg = msg.format(", ".join([str(m.name) for m in missing]))
raise CodeGenArgumentListError(msg, missing)
# create redundant arguments to produce the requested sequence
name_arg_dict = dict([(x.name, x) for x in arg_list])
new_args = []
for symbol in argument_sequence:
try:
new_args.append(name_arg_dict[symbol])
except KeyError:
new_args.append(InputArgument(symbol))
arg_list = new_args
return Routine(name, arg_list, return_vals, local_vars, global_vars)
def _get_header(self):
"""Writes a common header for the generated files."""
code_lines = []
code_lines.append("/*\n")
tmp = header_comment % {"version": sympy_version,
"project": self.project}
for line in tmp.splitlines():
code_lines.append((" *%s" % line.center(76)).rstrip() + "\n")
code_lines.append(" */\n")
return code_lines
def get_prototype(self, routine):
"""Returns a string for the function prototype of the routine.
If the routine has multiple result objects, an CodeGenError is
raised.
See: http://en.wikipedia.org/wiki/Function_prototype
"""
results = [i.get_datatype('Rust') for i in routine.results]
if len(results) == 1:
rstype = " -> " + results[0]
elif len(routine.results) > 1:
rstype = " -> (" + ", ".join(results) + ")"
else:
rstype = ""
type_args = []
for arg in routine.arguments:
name = self.printer.doprint(arg.name)
if arg.dimensions or isinstance(arg, ResultBase):
type_args.append(("*%s" % name, arg.get_datatype('Rust')))
else:
type_args.append((name, arg.get_datatype('Rust')))
arguments = ", ".join([ "%s: %s" % t for t in type_args])
return "fn %s(%s)%s" % (routine.name, arguments, rstype)
def _preprocessor_statements(self, prefix):
code_lines = []
# code_lines.append("use std::f64::consts::*;\n")
return code_lines
def _get_routine_opening(self, routine):
prototype = self.get_prototype(routine)
return ["%s {\n" % prototype]
def _declare_arguments(self, routine):
# arguments are declared in prototype
return []
def _declare_globals(self, routine):
# global variables are not explicitly declared within C functions
return []
def _declare_locals(self, routine):
# loop variables are declared in loop statement
return []
def _call_printer(self, routine):
code_lines = []
declarations = []
returns = []
# Compose a list of symbols to be dereferenced in the function
# body. These are the arguments that were passed by a reference
# pointer, excluding arrays.
dereference = []
for arg in routine.arguments:
if isinstance(arg, ResultBase) and not arg.dimensions:
dereference.append(arg.name)
for i, result in enumerate(routine.results):
if isinstance(result, Result):
assign_to = result.result_var
returns.append(str(result.result_var))
else:
raise CodeGenError("unexpected object in Routine results")
constants, not_supported, rs_expr = self._printer_method_with_settings(
'doprint', dict(human=False), result.expr, assign_to=assign_to)
for name, value in sorted(constants, key=str):
declarations.append("const %s: f64 = %s;\n" % (name, value))
for obj in sorted(not_supported, key=str):
if isinstance(obj, Function):
name = obj.func
else:
name = obj
declarations.append("// unsupported: %s\n" % (name))
code_lines.append("let %s\n" % rs_expr);
if len(returns) > 1:
returns = ['(' + ', '.join(returns) + ')']
returns.append('\n')
return declarations + code_lines + returns
def _get_routine_ending(self, routine):
return ["}\n"]
def dump_rs(self, routines, f, prefix, header=True, empty=True):
self.dump_code(routines, f, prefix, header, empty)
dump_rs.extension = code_extension
dump_rs.__doc__ = CodeGen.dump_code.__doc__
# This list of dump functions is used by CodeGen.write to know which dump
# functions it has to call.
dump_fns = [dump_rs]
def get_code_generator(language, project=None, standard=None):
if language == 'C':
if standard is None:
pass
elif standard.lower() == 'c89':
language = 'C89'
elif standard.lower() == 'c99':
language = 'C99'
CodeGenClass = {"C": CCodeGen, "C89": C89CodeGen, "C99": C99CodeGen,
"F95": FCodeGen, "JULIA": JuliaCodeGen,
"OCTAVE": OctaveCodeGen,
"RUST": RustCodeGen}.get(language.upper())
if CodeGenClass is None:
raise ValueError("Language '%s' is not supported." % language)
return CodeGenClass(project)
#
# Friendly functions
#
def codegen(name_expr, language=None, prefix=None, project="project",
to_files=False, header=True, empty=True, argument_sequence=None,
global_vars=None, standard=None, code_gen=None):
"""Generate source code for expressions in a given language.
Parameters
==========
name_expr : tuple, or list of tuples
A single (name, expression) tuple or a list of (name, expression)
tuples. Each tuple corresponds to a routine. If the expression is
an equality (an instance of class Equality) the left hand side is
considered an output argument. If expression is an iterable, then
the routine will have multiple outputs.
language : string,
A string that indicates the source code language. This is case
insensitive. Currently, 'C', 'F95' and 'Octave' are supported.
'Octave' generates code compatible with both Octave and Matlab.
prefix : string, optional
A prefix for the names of the files that contain the source code.
Language-dependent suffixes will be appended. If omitted, the name
of the first name_expr tuple is used.
project : string, optional
A project name, used for making unique preprocessor instructions.
[default: "project"]
to_files : bool, optional
When True, the code will be written to one or more files with the
given prefix, otherwise strings with the names and contents of
these files are returned. [default: False]
header : bool, optional
When True, a header is written on top of each source file.
[default: True]
empty : bool, optional
When True, empty lines are used to structure the code.
[default: True]
argument_sequence : iterable, optional
Sequence of arguments for the routine in a preferred order. A
CodeGenError is raised if required arguments are missing.
Redundant arguments are used without warning. If omitted,
arguments will be ordered alphabetically, but with all input
aguments first, and then output or in-out arguments.
global_vars : iterable, optional
Sequence of global variables used by the routine. Variables
listed here will not show up as function arguments.
standard : string
code_gen : CodeGen instance
An instance of a CodeGen subclass. Overrides ``language``.
Examples
========
>>> from sympy.utilities.codegen import codegen
>>> from sympy.abc import x, y, z
>>> [(c_name, c_code), (h_name, c_header)] = codegen(
... ("f", x+y*z), "C89", "test", header=False, empty=False)
>>> print(c_name)
test.c
>>> print(c_code)
#include "test.h"
#include <math.h>
double f(double x, double y, double z) {
double f_result;
f_result = x + y*z;
return f_result;
}
<BLANKLINE>
>>> print(h_name)
test.h
>>> print(c_header)
#ifndef PROJECT__TEST__H
#define PROJECT__TEST__H
double f(double x, double y, double z);
#endif
<BLANKLINE>
Another example using Equality objects to give named outputs. Here the
filename (prefix) is taken from the first (name, expr) pair.
>>> from sympy.abc import f, g
>>> from sympy import Eq
>>> [(c_name, c_code), (h_name, c_header)] = codegen(
... [("myfcn", x + y), ("fcn2", [Eq(f, 2*x), Eq(g, y)])],
... "C99", header=False, empty=False)
>>> print(c_name)
myfcn.c
>>> print(c_code)
#include "myfcn.h"
#include <math.h>
double myfcn(double x, double y) {
double myfcn_result;
myfcn_result = x + y;
return myfcn_result;
}
void fcn2(double x, double y, double *f, double *g) {
(*f) = 2*x;
(*g) = y;
}
<BLANKLINE>
If the generated function(s) will be part of a larger project where various
global variables have been defined, the 'global_vars' option can be used
to remove the specified variables from the function signature
>>> from sympy.utilities.codegen import codegen
>>> from sympy.abc import x, y, z
>>> [(f_name, f_code), header] = codegen(
... ("f", x+y*z), "F95", header=False, empty=False,
... argument_sequence=(x, y), global_vars=(z,))
>>> print(f_code)
REAL*8 function f(x, y)
implicit none
REAL*8, intent(in) :: x
REAL*8, intent(in) :: y
f = x + y*z
end function
<BLANKLINE>
"""
# Initialize the code generator.
if language is None:
if code_gen is None:
raise ValueError("Need either language or code_gen")
else:
if code_gen is not None:
raise ValueError("You cannot specify both language and code_gen.")
code_gen = get_code_generator(language, project, standard)
if isinstance(name_expr[0], string_types):
# single tuple is given, turn it into a singleton list with a tuple.
name_expr = [name_expr]
if prefix is None:
prefix = name_expr[0][0]
# Construct Routines appropriate for this code_gen from (name, expr) pairs.
routines = []
for name, expr in name_expr:
routines.append(code_gen.routine(name, expr, argument_sequence,
global_vars))
# Write the code.
return code_gen.write(routines, prefix, to_files, header, empty)
def make_routine(name, expr, argument_sequence=None,
global_vars=None, language="F95"):
"""A factory that makes an appropriate Routine from an expression.
Parameters
==========
name : string
The name of this routine in the generated code.
expr : expression or list/tuple of expressions
A SymPy expression that the Routine instance will represent. If
given a list or tuple of expressions, the routine will be
considered to have multiple return values and/or output arguments.
argument_sequence : list or tuple, optional
List arguments for the routine in a preferred order. If omitted,
the results are language dependent, for example, alphabetical order
or in the same order as the given expressions.
global_vars : iterable, optional
Sequence of global variables used by the routine. Variables
listed here will not show up as function arguments.
language : string, optional
Specify a target language. The Routine itself should be
language-agnostic but the precise way one is created, error
checking, etc depend on the language. [default: "F95"].
A decision about whether to use output arguments or return values is made
depending on both the language and the particular mathematical expressions.
For an expression of type Equality, the left hand side is typically made
into an OutputArgument (or perhaps an InOutArgument if appropriate).
Otherwise, typically, the calculated expression is made a return values of
the routine.
Examples
========
>>> from sympy.utilities.codegen import make_routine
>>> from sympy.abc import x, y, f, g
>>> from sympy import Eq
>>> r = make_routine('test', [Eq(f, 2*x), Eq(g, x + y)])
>>> [arg.result_var for arg in r.results]
[]
>>> [arg.name for arg in r.arguments]
[x, y, f, g]
>>> [arg.name for arg in r.result_variables]
[f, g]
>>> r.local_vars
set()
Another more complicated example with a mixture of specified and
automatically-assigned names. Also has Matrix output.
>>> from sympy import Matrix
>>> r = make_routine('fcn', [x*y, Eq(f, 1), Eq(g, x + g), Matrix([[x, 2]])])
>>> [arg.result_var for arg in r.results] # doctest: +SKIP
[result_5397460570204848505]
>>> [arg.expr for arg in r.results]
[x*y]
>>> [arg.name for arg in r.arguments] # doctest: +SKIP
[x, y, f, g, out_8598435338387848786]
We can examine the various arguments more closely:
>>> from sympy.utilities.codegen import (InputArgument, OutputArgument,
... InOutArgument)
>>> [a.name for a in r.arguments if isinstance(a, InputArgument)]
[x, y]
>>> [a.name for a in r.arguments if isinstance(a, OutputArgument)] # doctest: +SKIP
[f, out_8598435338387848786]
>>> [a.expr for a in r.arguments if isinstance(a, OutputArgument)]
[1, Matrix([[x, 2]])]
>>> [a.name for a in r.arguments if isinstance(a, InOutArgument)]
[g]
>>> [a.expr for a in r.arguments if isinstance(a, InOutArgument)]
[g + x]
"""
# initialize a new code generator
code_gen = get_code_generator(language)
return code_gen.routine(name, expr, argument_sequence, global_vars)
| 76,207 | 34.998111 | 130 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/autowrap.py
|
"""Module for compiling codegen output, and wrap the binary for use in
python.
.. note:: To use the autowrap module it must first be imported
>>> from sympy.utilities.autowrap import autowrap
This module provides a common interface for different external backends, such
as f2py, fwrap, Cython, SWIG(?) etc. (Currently only f2py and Cython are
implemented) The goal is to provide access to compiled binaries of acceptable
performance with a one-button user interface, i.e.
>>> from sympy.abc import x,y
>>> expr = ((x - y)**(25)).expand()
>>> binary_callable = autowrap(expr)
>>> binary_callable(1, 2)
-1.0
The callable returned from autowrap() is a binary python function, not a
SymPy object. If it is desired to use the compiled function in symbolic
expressions, it is better to use binary_function() which returns a SymPy
Function object. The binary callable is attached as the _imp_ attribute and
invoked when a numerical evaluation is requested with evalf(), or with
lambdify().
>>> from sympy.utilities.autowrap import binary_function
>>> f = binary_function('f', expr)
>>> 2*f(x, y) + y
y + 2*f(x, y)
>>> (2*f(x, y) + y).evalf(2, subs={x: 1, y:2})
0.e-110
The idea is that a SymPy user will primarily be interested in working with
mathematical expressions, and should not have to learn details about wrapping
tools in order to evaluate expressions numerically, even if they are
computationally expensive.
When is this useful?
1) For computations on large arrays, Python iterations may be too slow,
and depending on the mathematical expression, it may be difficult to
exploit the advanced index operations provided by NumPy.
2) For *really* long expressions that will be called repeatedly, the
compiled binary should be significantly faster than SymPy's .evalf()
3) If you are generating code with the codegen utility in order to use
it in another project, the automatic python wrappers let you test the
binaries immediately from within SymPy.
4) To create customized ufuncs for use with numpy arrays.
See *ufuncify*.
When is this module NOT the best approach?
1) If you are really concerned about speed or memory optimizations,
you will probably get better results by working directly with the
wrapper tools and the low level code. However, the files generated
by this utility may provide a useful starting point and reference
code. Temporary files will be left intact if you supply the keyword
tempdir="path/to/files/".
2) If the array computation can be handled easily by numpy, and you
don't need the binaries for another project.
"""
from __future__ import print_function, division
import sys
import os
import shutil
import tempfile
from subprocess import STDOUT, CalledProcessError, check_output
from string import Template
from warnings import warn
from sympy.core.cache import cacheit
from sympy.core.compatibility import range, iterable
from sympy.core.function import Lambda
from sympy.core.relational import Eq
from sympy.core.symbol import Dummy, Symbol
from sympy.tensor.indexed import Idx, IndexedBase
from sympy.utilities.codegen import (make_routine, get_code_generator,
OutputArgument, InOutArgument,
InputArgument, CodeGenArgumentListError,
Result, ResultBase, C99CodeGen)
from sympy.utilities.lambdify import implemented_function
from sympy.utilities.decorator import doctest_depends_on
_doctest_depends_on = {'exe': ('f2py', 'gfortran', 'gcc'),
'modules': ('numpy',)}
class CodeWrapError(Exception):
pass
class CodeWrapper(object):
"""Base Class for code wrappers"""
_filename = "wrapped_code"
_module_basename = "wrapper_module"
_module_counter = 0
@property
def filename(self):
return "%s_%s" % (self._filename, CodeWrapper._module_counter)
@property
def module_name(self):
return "%s_%s" % (self._module_basename, CodeWrapper._module_counter)
def __init__(self, generator, filepath=None, flags=[], verbose=False):
"""
generator -- the code generator to use
"""
self.generator = generator
self.filepath = filepath
self.flags = flags
self.quiet = not verbose
@property
def include_header(self):
return bool(self.filepath)
@property
def include_empty(self):
return bool(self.filepath)
def _generate_code(self, main_routine, routines):
routines.append(main_routine)
self.generator.write(
routines, self.filename, True, self.include_header,
self.include_empty)
def wrap_code(self, routine, helpers=[]):
workdir = self.filepath or tempfile.mkdtemp("_sympy_compile")
if not os.access(workdir, os.F_OK):
os.mkdir(workdir)
oldwork = os.getcwd()
os.chdir(workdir)
try:
sys.path.append(workdir)
self._generate_code(routine, helpers)
self._prepare_files(routine)
self._process_files(routine)
mod = __import__(self.module_name)
finally:
sys.path.remove(workdir)
CodeWrapper._module_counter += 1
os.chdir(oldwork)
if not self.filepath:
try:
shutil.rmtree(workdir)
except OSError:
# Could be some issues on Windows
pass
return self._get_wrapped_function(mod, routine.name)
def _process_files(self, routine):
command = self.command
command.extend(self.flags)
try:
retoutput = check_output(command, stderr=STDOUT)
except CalledProcessError as e:
raise CodeWrapError(
"Error while executing command: %s. Command output is:\n%s" % (
" ".join(command), e.output.decode()))
if not self.quiet:
print(retoutput)
class DummyWrapper(CodeWrapper):
"""Class used for testing independent of backends """
template = """# dummy module for testing of SymPy
def %(name)s():
return "%(expr)s"
%(name)s.args = "%(args)s"
%(name)s.returns = "%(retvals)s"
"""
def _prepare_files(self, routine):
return
def _generate_code(self, routine, helpers):
with open('%s.py' % self.module_name, 'w') as f:
printed = ", ".join(
[str(res.expr) for res in routine.result_variables])
# convert OutputArguments to return value like f2py
args = filter(lambda x: not isinstance(
x, OutputArgument), routine.arguments)
retvals = []
for val in routine.result_variables:
if isinstance(val, Result):
retvals.append('nameless')
else:
retvals.append(val.result_var)
print(DummyWrapper.template % {
'name': routine.name,
'expr': printed,
'args': ", ".join([str(a.name) for a in args]),
'retvals': ", ".join([str(val) for val in retvals])
}, end="", file=f)
def _process_files(self, routine):
return
@classmethod
def _get_wrapped_function(cls, mod, name):
return getattr(mod, name)
class CythonCodeWrapper(CodeWrapper):
"""Wrapper that uses Cython"""
setup_template = """\
try:
from setuptools import setup
from setuptools import Extension
except ImportError:
from distutils.core import setup
from distutils.extension import Extension
from Cython.Build import cythonize
cy_opts = {cythonize_options}
{np_import}
ext_mods = [Extension(
{ext_args},
include_dirs={include_dirs},
library_dirs={library_dirs},
libraries={libraries},
extra_compile_args={extra_compile_args},
extra_link_args={extra_link_args}
)]
setup(ext_modules=cythonize(ext_mods, **cy_opts))
"""
pyx_imports = (
"import numpy as np\n"
"cimport numpy as np\n\n")
pyx_header = (
"cdef extern from '{header_file}.h':\n"
" {prototype}\n\n")
pyx_func = (
"def {name}_c({arg_string}):\n"
"\n"
"{declarations}"
"{body}")
std_compile_flag = '-std=c99'
def __init__(self, *args, **kwargs):
"""Instantiates a Cython code wrapper.
The following optional parameters get passed to ``distutils.Extension``
for building the Python extension module. Read its documentation to
learn more.
Parameters
==========
include_dirs : [list of strings]
A list of directories to search for C/C++ header files (in Unix
form for portability).
library_dirs : [list of strings]
A list of directories to search for C/C++ libraries at link time.
libraries : [list of strings]
A list of library names (not filenames or paths) to link against.
extra_compile_args : [list of strings]
Any extra platform- and compiler-specific information to use when
compiling the source files in 'sources'. For platforms and
compilers where "command line" makes sense, this is typically a
list of command-line arguments, but for other platforms it could be
anything. Note that the attribute ``std_compile_flag`` will be
appended to this list.
extra_link_args : [list of strings]
Any extra platform- and compiler-specific information to use when
linking object files together to create the extension (or to create
a new static Python interpreter). Similar interpretation as for
'extra_compile_args'.
cythonize_options : [dictionary]
Keyword arguments passed on to cythonize.
"""
self._include_dirs = kwargs.pop('include_dirs', [])
self._library_dirs = kwargs.pop('library_dirs', [])
self._libraries = kwargs.pop('libraries', [])
self._extra_compile_args = kwargs.pop('extra_compile_args', [])
self._extra_compile_args.append(self.std_compile_flag)
self._extra_link_args = kwargs.pop('extra_link_args', [])
self._cythonize_options = kwargs.pop('cythonize_options', {})
self._need_numpy = False
super(CythonCodeWrapper, self).__init__(*args, **kwargs)
@property
def command(self):
command = [sys.executable, "setup.py", "build_ext", "--inplace"]
return command
def _prepare_files(self, routine, build_dir=os.curdir):
# NOTE : build_dir is used for testing purposes.
pyxfilename = self.module_name + '.pyx'
codefilename = "%s.%s" % (self.filename, self.generator.code_extension)
# pyx
with open(pyxfilename, 'w') as f:
self.dump_pyx([routine], f, self.filename)
# setup.py
ext_args = [repr(self.module_name), repr([pyxfilename, codefilename])]
if self._need_numpy:
np_import = 'import numpy as np\n'
self._include_dirs.append('np.get_include()')
else:
np_import = ''
with open(os.path.join(build_dir, 'setup.py'), 'w') as f:
includes = str(self._include_dirs).replace("'np.get_include()'",
'np.get_include()')
f.write(self.setup_template.format(
ext_args=", ".join(ext_args),
np_import=np_import,
include_dirs=includes,
library_dirs=self._library_dirs,
libraries=self._libraries,
extra_compile_args=self._extra_compile_args,
extra_link_args=self._extra_link_args,
cythonize_options=self._cythonize_options
))
@classmethod
def _get_wrapped_function(cls, mod, name):
return getattr(mod, name + '_c')
def dump_pyx(self, routines, f, prefix):
"""Write a Cython file with python wrappers
This file contains all the definitions of the routines in c code and
refers to the header file.
Arguments
---------
routines
List of Routine instances
f
File-like object to write the file to
prefix
The filename prefix, used to refer to the proper header file.
Only the basename of the prefix is used.
"""
headers = []
functions = []
for routine in routines:
prototype = self.generator.get_prototype(routine)
# C Function Header Import
headers.append(self.pyx_header.format(header_file=prefix,
prototype=prototype))
# Partition the C function arguments into categories
py_rets, py_args, py_loc, py_inf = self._partition_args(routine.arguments)
# Function prototype
name = routine.name
arg_string = ", ".join(self._prototype_arg(arg) for arg in py_args)
# Local Declarations
local_decs = []
for arg, val in py_inf.items():
proto = self._prototype_arg(arg)
mat, ind = val
local_decs.append(" cdef {0} = {1}.shape[{2}]".format(proto, mat, ind))
local_decs.extend([" cdef {0}".format(self._declare_arg(a)) for a in py_loc])
declarations = "\n".join(local_decs)
if declarations:
declarations = declarations + "\n"
# Function Body
args_c = ", ".join([self._call_arg(a) for a in routine.arguments])
rets = ", ".join([str(r.name) for r in py_rets])
if routine.results:
body = ' return %s(%s)' % (routine.name, args_c)
if rets:
body = body + ', ' + rets
else:
body = ' %s(%s)\n' % (routine.name, args_c)
body = body + ' return ' + rets
functions.append(self.pyx_func.format(name=name, arg_string=arg_string,
declarations=declarations, body=body))
# Write text to file
if self._need_numpy:
# Only import numpy if required
f.write(self.pyx_imports)
f.write('\n'.join(headers))
f.write('\n'.join(functions))
def _partition_args(self, args):
"""Group function arguments into categories."""
py_args = []
py_returns = []
py_locals = []
py_inferred = {}
for arg in args:
if isinstance(arg, OutputArgument):
py_returns.append(arg)
py_locals.append(arg)
elif isinstance(arg, InOutArgument):
py_returns.append(arg)
py_args.append(arg)
else:
py_args.append(arg)
# Find arguments that are array dimensions. These can be inferred
# locally in the Cython code.
if isinstance(arg, (InputArgument, InOutArgument)) and arg.dimensions:
dims = [d[1] + 1 for d in arg.dimensions]
sym_dims = [(i, d) for (i, d) in enumerate(dims) if
isinstance(d, Symbol)]
for (i, d) in sym_dims:
py_inferred[d] = (arg.name, i)
for arg in args:
if arg.name in py_inferred:
py_inferred[arg] = py_inferred.pop(arg.name)
# Filter inferred arguments from py_args
py_args = [a for a in py_args if a not in py_inferred]
return py_returns, py_args, py_locals, py_inferred
def _prototype_arg(self, arg):
mat_dec = "np.ndarray[{mtype}, ndim={ndim}] {name}"
np_types = {'double': 'np.double_t',
'int': 'np.int_t'}
t = arg.get_datatype('c')
if arg.dimensions:
self._need_numpy = True
ndim = len(arg.dimensions)
mtype = np_types[t]
return mat_dec.format(mtype=mtype, ndim=ndim, name=arg.name)
else:
return "%s %s" % (t, str(arg.name))
def _declare_arg(self, arg):
proto = self._prototype_arg(arg)
if arg.dimensions:
shape = '(' + ','.join(str(i[1] + 1) for i in arg.dimensions) + ')'
return proto + " = np.empty({shape})".format(shape=shape)
else:
return proto + " = 0"
def _call_arg(self, arg):
if arg.dimensions:
t = arg.get_datatype('c')
return "<{0}*> {1}.data".format(t, arg.name)
elif isinstance(arg, ResultBase):
return "&{0}".format(arg.name)
else:
return str(arg.name)
class F2PyCodeWrapper(CodeWrapper):
"""Wrapper that uses f2py"""
def __init__(self, *args, **kwargs):
ext_keys = ['include_dirs', 'library_dirs', 'libraries',
'extra_compile_args', 'extra_link_args']
msg = ('The compilation option kwarg {} is not supported with the f2py '
'backend.')
for k in ext_keys:
if k in kwargs.keys():
warn(msg.format(k))
kwargs.pop(k, None)
super(F2PyCodeWrapper, self).__init__(*args, **kwargs)
@property
def command(self):
filename = self.filename + '.' + self.generator.code_extension
args = ['-c', '-m', self.module_name, filename]
command = [sys.executable, "-c", "import numpy.f2py as f2py2e;f2py2e.main()"]+args
return command
def _prepare_files(self, routine):
pass
@classmethod
def _get_wrapped_function(cls, mod, name):
return getattr(mod, name)
# Here we define a lookup of backends -> tuples of languages. For now, each
# tuple is of length 1, but if a backend supports more than one language,
# the most preferable language is listed first.
_lang_lookup = {'CYTHON': ('C99', 'C89', 'C'),
'F2PY': ('F95',),
'NUMPY': ('C99', 'C89', 'C'),
'DUMMY': ('F95',)} # Dummy here just for testing
def _infer_language(backend):
"""For a given backend, return the top choice of language"""
langs = _lang_lookup.get(backend.upper(), False)
if not langs:
raise ValueError("Unrecognized backend: " + backend)
return langs[0]
def _validate_backend_language(backend, language):
"""Throws error if backend and language are incompatible"""
langs = _lang_lookup.get(backend.upper(), False)
if not langs:
raise ValueError("Unrecognized backend: " + backend)
if language.upper() not in langs:
raise ValueError(("Backend {0} and language {1} are "
"incompatible").format(backend, language))
@cacheit
@doctest_depends_on(exe=('f2py', 'gfortran'), modules=('numpy',))
def autowrap(expr, language=None, backend='f2py', tempdir=None, args=None,
flags=None, verbose=False, helpers=None, code_gen=None, **kwargs):
"""Generates python callable binaries based on the math expression.
Parameters
----------
expr
The SymPy expression that should be wrapped as a binary routine.
language : string, optional
If supplied, (options: 'C' or 'F95'), specifies the language of the
generated code. If ``None`` [default], the language is inferred based
upon the specified backend.
backend : string, optional
Backend used to wrap the generated code. Either 'f2py' [default],
or 'cython'.
tempdir : string, optional
Path to directory for temporary files. If this argument is supplied,
the generated code and the wrapper input files are left intact in the
specified path.
args : iterable, optional
An ordered iterable of symbols. Specifies the argument sequence for the
function.
flags : iterable, optional
Additional option flags that will be passed to the backend.
verbose : bool, optional
If True, autowrap will not mute the command line backends. This can be
helpful for debugging.
helpers : iterable, optional
Used to define auxillary expressions needed for the main expr. If the
main expression needs to call a specialized function it should be put
in the ``helpers`` iterable. Autowrap will then make sure that the
compiled main expression can link to the helper routine. Items should
be tuples with (<funtion_name>, <sympy_expression>, <arguments>). It
is mandatory to supply an argument sequence to helper routines.
code_gen : CodeGen instance
An instance of a CodeGen subclass. Overrides ``language``.
include_dirs : [string]
A list of directories to search for C/C++ header files (in Unix form
for portability).
library_dirs : [string]
A list of directories to search for C/C++ libraries at link time.
libraries : [string]
A list of library names (not filenames or paths) to link against.
extra_compile_args : [string]
Any extra platform- and compiler-specific information to use when
compiling the source files in 'sources'. For platforms and compilers
where "command line" makes sense, this is typically a list of
command-line arguments, but for other platforms it could be anything.
extra_link_args : [string]
Any extra platform- and compiler-specific information to use when
linking object files together to create the extension (or to create a
new static Python interpreter). Similar interpretation as for
'extra_compile_args'.
Examples
--------
>>> from sympy.abc import x, y, z
>>> from sympy.utilities.autowrap import autowrap
>>> expr = ((x - y + z)**(13)).expand()
>>> binary_func = autowrap(expr)
>>> binary_func(1, 4, 2)
-1.0
"""
if language:
if not isinstance(language, type):
_validate_backend_language(backend, language)
else:
language = _infer_language(backend)
helpers = [helpers] if helpers else ()
args = list(args) if iterable(args, exclude=set) else args
if code_gen is None:
code_gen = get_code_generator(language, "autowrap")
CodeWrapperClass = {
'F2PY': F2PyCodeWrapper,
'CYTHON': CythonCodeWrapper,
'DUMMY': DummyWrapper
}[backend.upper()]
code_wrapper = CodeWrapperClass(code_gen, tempdir, flags if flags else (),
verbose, **kwargs)
helps = []
for name_h, expr_h, args_h in helpers:
helps.append(make_routine(name_h, expr_h, args_h))
for name_h, expr_h, args_h in helpers:
if expr.has(expr_h):
name_h = binary_function(name_h, expr_h, backend='dummy')
expr = expr.subs(expr_h, name_h(*args_h))
try:
routine = make_routine('autofunc', expr, args)
except CodeGenArgumentListError as e:
# if all missing arguments are for pure output, we simply attach them
# at the end and try again, because the wrappers will silently convert
# them to return values anyway.
new_args = []
for missing in e.missing_args:
if not isinstance(missing, OutputArgument):
raise
new_args.append(missing.name)
routine = make_routine('autofunc', expr, args + new_args)
return code_wrapper.wrap_code(routine, helpers=helps)
@doctest_depends_on(exe=('f2py', 'gfortran'), modules=('numpy',))
def binary_function(symfunc, expr, **kwargs):
"""Returns a sympy function with expr as binary implementation
This is a convenience function that automates the steps needed to
autowrap the SymPy expression and attaching it to a Function object
with implemented_function().
Parameters
----------
symfunc : sympy Function
The function to bind the callable to.
expr : sympy Expression
The expression used to generate the function.
kwargs : dict
Any kwargs accepted by autowrap.
Examples
--------
>>> from sympy.abc import x, y
>>> from sympy.utilities.autowrap import binary_function
>>> expr = ((x - y)**(25)).expand()
>>> f = binary_function('f', expr)
>>> type(f)
<class 'sympy.core.function.UndefinedFunction'>
>>> 2*f(x, y)
2*f(x, y)
>>> f(x, y).evalf(2, subs={x: 1, y: 2})
-1.0
"""
binary = autowrap(expr, **kwargs)
return implemented_function(symfunc, binary)
#################################################################
# UFUNCIFY #
#################################################################
_ufunc_top = Template("""\
#include "Python.h"
#include "math.h"
#include "numpy/ndarraytypes.h"
#include "numpy/ufuncobject.h"
#include "numpy/halffloat.h"
#include ${include_file}
static PyMethodDef ${module}Methods[] = {
{NULL, NULL, 0, NULL}
};""")
_ufunc_outcalls = Template("*((double *)out${outnum}) = ${funcname}(${call_args});")
_ufunc_body = Template("""\
static void ${funcname}_ufunc(char **args, npy_intp *dimensions, npy_intp* steps, void* data)
{
npy_intp i;
npy_intp n = dimensions[0];
${declare_args}
${declare_steps}
for (i = 0; i < n; i++) {
${outcalls}
${step_increments}
}
}
PyUFuncGenericFunction ${funcname}_funcs[1] = {&${funcname}_ufunc};
static char ${funcname}_types[${n_types}] = ${types}
static void *${funcname}_data[1] = {NULL};""")
_ufunc_bottom = Template("""\
#if PY_VERSION_HEX >= 0x03000000
static struct PyModuleDef moduledef = {
PyModuleDef_HEAD_INIT,
"${module}",
NULL,
-1,
${module}Methods,
NULL,
NULL,
NULL,
NULL
};
PyMODINIT_FUNC PyInit_${module}(void)
{
PyObject *m, *d;
${function_creation}
m = PyModule_Create(&moduledef);
if (!m) {
return NULL;
}
import_array();
import_umath();
d = PyModule_GetDict(m);
${ufunc_init}
return m;
}
#else
PyMODINIT_FUNC init${module}(void)
{
PyObject *m, *d;
${function_creation}
m = Py_InitModule("${module}", ${module}Methods);
if (m == NULL) {
return;
}
import_array();
import_umath();
d = PyModule_GetDict(m);
${ufunc_init}
}
#endif\
""")
_ufunc_init_form = Template("""\
ufunc${ind} = PyUFunc_FromFuncAndData(${funcname}_funcs, ${funcname}_data, ${funcname}_types, 1, ${n_in}, ${n_out},
PyUFunc_None, "${module}", ${docstring}, 0);
PyDict_SetItemString(d, "${funcname}", ufunc${ind});
Py_DECREF(ufunc${ind});""")
_ufunc_setup = Template("""\
def configuration(parent_package='', top_path=None):
import numpy
from numpy.distutils.misc_util import Configuration
config = Configuration('',
parent_package,
top_path)
config.add_extension('${module}', sources=['${module}.c', '${filename}.c'])
return config
if __name__ == "__main__":
from numpy.distutils.core import setup
setup(configuration=configuration)""")
class UfuncifyCodeWrapper(CodeWrapper):
"""Wrapper for Ufuncify"""
def __init__(self, *args, **kwargs):
ext_keys = ['include_dirs', 'library_dirs', 'libraries',
'extra_compile_args', 'extra_link_args']
msg = ('The compilation option kwarg {} is not supported with the numpy'
' backend.')
for k in ext_keys:
if k in kwargs.keys():
warn(msg.format(k))
kwargs.pop(k, None)
super(UfuncifyCodeWrapper, self).__init__(*args, **kwargs)
@property
def command(self):
command = [sys.executable, "setup.py", "build_ext", "--inplace"]
return command
def wrap_code(self, routines, helpers=None):
# This routine overrides CodeWrapper because we can't assume funcname == routines[0].name
# Therefore we have to break the CodeWrapper private API.
# There isn't an obvious way to extend multi-expr support to
# the other autowrap backends, so we limit this change to ufuncify.
helpers = helpers if helpers is not None else []
# We just need a consistent name
funcname = 'wrapped_' + str(id(routines) + id(helpers))
workdir = self.filepath or tempfile.mkdtemp("_sympy_compile")
if not os.access(workdir, os.F_OK):
os.mkdir(workdir)
oldwork = os.getcwd()
os.chdir(workdir)
try:
sys.path.append(workdir)
self._generate_code(routines, helpers)
self._prepare_files(routines, funcname)
self._process_files(routines)
mod = __import__(self.module_name)
finally:
sys.path.remove(workdir)
CodeWrapper._module_counter += 1
os.chdir(oldwork)
if not self.filepath:
try:
shutil.rmtree(workdir)
except OSError:
# Could be some issues on Windows
pass
return self._get_wrapped_function(mod, funcname)
def _generate_code(self, main_routines, helper_routines):
all_routines = main_routines + helper_routines
self.generator.write(
all_routines, self.filename, True, self.include_header,
self.include_empty)
def _prepare_files(self, routines, funcname):
# C
codefilename = self.module_name + '.c'
with open(codefilename, 'w') as f:
self.dump_c(routines, f, self.filename, funcname=funcname)
# setup.py
with open('setup.py', 'w') as f:
self.dump_setup(f)
@classmethod
def _get_wrapped_function(cls, mod, name):
return getattr(mod, name)
def dump_setup(self, f):
setup = _ufunc_setup.substitute(module=self.module_name,
filename=self.filename)
f.write(setup)
def dump_c(self, routines, f, prefix, funcname=None):
"""Write a C file with python wrappers
This file contains all the definitions of the routines in c code.
Arguments
---------
routines
List of Routine instances
f
File-like object to write the file to
prefix
The filename prefix, used to name the imported module.
funcname
Name of the main function to be returned.
"""
if (funcname is None) and (len(routines) == 1):
funcname = routines[0].name
elif funcname is None:
msg = 'funcname must be specified for multiple output routines'
raise ValueError(msg)
functions = []
function_creation = []
ufunc_init = []
module = self.module_name
include_file = "\"{0}.h\"".format(prefix)
top = _ufunc_top.substitute(include_file=include_file, module=module)
name = funcname
# Partition the C function arguments into categories
# Here we assume all routines accept the same arguments
r_index = 0
py_in, _ = self._partition_args(routines[0].arguments)
n_in = len(py_in)
n_out = len(routines)
# Declare Args
form = "char *{0}{1} = args[{2}];"
arg_decs = [form.format('in', i, i) for i in range(n_in)]
arg_decs.extend([form.format('out', i, i+n_in) for i in range(n_out)])
declare_args = '\n '.join(arg_decs)
# Declare Steps
form = "npy_intp {0}{1}_step = steps[{2}];"
step_decs = [form.format('in', i, i) for i in range(n_in)]
step_decs.extend([form.format('out', i, i+n_in) for i in range(n_out)])
declare_steps = '\n '.join(step_decs)
# Call Args
form = "*(double *)in{0}"
call_args = ', '.join([form.format(a) for a in range(n_in)])
# Step Increments
form = "{0}{1} += {0}{1}_step;"
step_incs = [form.format('in', i) for i in range(n_in)]
step_incs.extend([form.format('out', i, i) for i in range(n_out)])
step_increments = '\n '.join(step_incs)
# Types
n_types = n_in + n_out
types = "{" + ', '.join(["NPY_DOUBLE"]*n_types) + "};"
# Docstring
docstring = '"Created in SymPy with Ufuncify"'
# Function Creation
function_creation.append("PyObject *ufunc{0};".format(r_index))
# Ufunc initialization
init_form = _ufunc_init_form.substitute(module=module,
funcname=name,
docstring=docstring,
n_in=n_in, n_out=n_out,
ind=r_index)
ufunc_init.append(init_form)
outcalls = [_ufunc_outcalls.substitute(
outnum=i, call_args=call_args, funcname=routines[i].name) for i in
range(n_out)]
body = _ufunc_body.substitute(module=module, funcname=name,
declare_args=declare_args,
declare_steps=declare_steps,
call_args=call_args,
step_increments=step_increments,
n_types=n_types, types=types,
outcalls='\n '.join(outcalls))
functions.append(body)
body = '\n\n'.join(functions)
ufunc_init = '\n '.join(ufunc_init)
function_creation = '\n '.join(function_creation)
bottom = _ufunc_bottom.substitute(module=module,
ufunc_init=ufunc_init,
function_creation=function_creation)
text = [top, body, bottom]
f.write('\n\n'.join(text))
def _partition_args(self, args):
"""Group function arguments into categories."""
py_in = []
py_out = []
for arg in args:
if isinstance(arg, OutputArgument):
py_out.append(arg)
elif isinstance(arg, InOutArgument):
raise ValueError("Ufuncify doesn't support InOutArguments")
else:
py_in.append(arg)
return py_in, py_out
@cacheit
@doctest_depends_on(exe=('f2py', 'gfortran', 'gcc'), modules=('numpy',))
def ufuncify(args, expr, language=None, backend='numpy', tempdir=None,
flags=None, verbose=False, helpers=None, **kwargs):
"""Generates a binary function that supports broadcasting on numpy arrays.
Parameters
----------
args : iterable
Either a Symbol or an iterable of symbols. Specifies the argument
sequence for the function.
expr
A SymPy expression that defines the element wise operation.
language : string, optional
If supplied, (options: 'C' or 'F95'), specifies the language of the
generated code. If ``None`` [default], the language is inferred based
upon the specified backend.
backend : string, optional
Backend used to wrap the generated code. Either 'numpy' [default],
'cython', or 'f2py'.
tempdir : string, optional
Path to directory for temporary files. If this argument is supplied,
the generated code and the wrapper input files are left intact in
the specified path.
flags : iterable, optional
Additional option flags that will be passed to the backend.
verbose : bool, optional
If True, autowrap will not mute the command line backends. This can
be helpful for debugging.
helpers : iterable, optional
Used to define auxillary expressions needed for the main expr. If
the main expression needs to call a specialized function it should
be put in the ``helpers`` iterable. Autowrap will then make sure
that the compiled main expression can link to the helper routine.
Items should be tuples with (<funtion_name>, <sympy_expression>,
<arguments>). It is mandatory to supply an argument sequence to
helper routines.
kwargs : dict
These kwargs will be passed to autowrap if the `f2py` or `cython`
backend is used and ignored if the `numpy` backend is used.
Note
----
The default backend ('numpy') will create actual instances of
``numpy.ufunc``. These support ndimensional broadcasting, and implicit type
conversion. Use of the other backends will result in a "ufunc-like"
function, which requires equal length 1-dimensional arrays for all
arguments, and will not perform any type conversions.
References
----------
[1] http://docs.scipy.org/doc/numpy/reference/ufuncs.html
Examples
========
>>> from sympy.utilities.autowrap import ufuncify
>>> from sympy.abc import x, y
>>> import numpy as np
>>> f = ufuncify((x, y), y + x**2)
>>> type(f)
<class 'numpy.ufunc'>
>>> f([1, 2, 3], 2)
array([ 3., 6., 11.])
>>> f(np.arange(5), 3)
array([ 3., 4., 7., 12., 19.])
For the 'f2py' and 'cython' backends, inputs are required to be equal length
1-dimensional arrays. The 'f2py' backend will perform type conversion, but
the Cython backend will error if the inputs are not of the expected type.
>>> f_fortran = ufuncify((x, y), y + x**2, backend='f2py')
>>> f_fortran(1, 2)
array([ 3.])
>>> f_fortran(np.array([1, 2, 3]), np.array([1.0, 2.0, 3.0]))
array([ 2., 6., 12.])
>>> f_cython = ufuncify((x, y), y + x**2, backend='Cython')
>>> f_cython(1, 2) # doctest: +ELLIPSIS
Traceback (most recent call last):
...
TypeError: Argument '_x' has incorrect type (expected numpy.ndarray, got int)
>>> f_cython(np.array([1.0]), np.array([2.0]))
array([ 3.])
"""
if isinstance(args, Symbol):
args = (args,)
else:
args = tuple(args)
if language:
_validate_backend_language(backend, language)
else:
language = _infer_language(backend)
helpers = helpers if helpers else ()
flags = flags if flags else ()
if backend.upper() == 'NUMPY':
# maxargs is set by numpy compile-time constant NPY_MAXARGS
# If a future version of numpy modifies or removes this restriction
# this variable should be changed or removed
maxargs = 32
helps = []
for name, expr, args in helpers:
helps.append(make_routine(name, expr, args))
code_wrapper = UfuncifyCodeWrapper(C99CodeGen("ufuncify"), tempdir,
flags, verbose)
if not isinstance(expr, (list, tuple)):
expr = [expr]
if len(expr) == 0:
raise ValueError('Expression iterable has zero length')
if (len(expr) + len(args)) > maxargs:
msg = ('Cannot create ufunc with more than {0} total arguments: '
'got {1} in, {2} out')
raise ValueError(msg.format(maxargs, len(args), len(expr)))
routines = [make_routine('autofunc{}'.format(idx), exprx, args) for
idx, exprx in enumerate(expr)]
return code_wrapper.wrap_code(routines, helpers=helps)
else:
# Dummies are used for all added expressions to prevent name clashes
# within the original expression.
y = IndexedBase(Dummy())
m = Dummy(integer=True)
i = Idx(Dummy(integer=True), m)
f = implemented_function(Dummy().name, Lambda(args, expr))
# For each of the args create an indexed version.
indexed_args = [IndexedBase(Dummy(str(a))) for a in args]
# Order the arguments (out, args, dim)
args = [y] + indexed_args + [m]
args_with_indices = [a[i] for a in indexed_args]
return autowrap(Eq(y[i], f(*args_with_indices)), language, backend,
tempdir, args, flags, verbose, helpers, **kwargs)
| 40,243 | 35.685506 | 115 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/pkgdata.py
|
"""
pkgdata is a simple, extensible way for a package to acquire data file
resources.
The getResource function is equivalent to the standard idioms, such as
the following minimal implementation::
import sys, os
def getResource(identifier, pkgname=__name__):
pkgpath = os.path.dirname(sys.modules[pkgname].__file__)
path = os.path.join(pkgpath, identifier)
return open(os.path.normpath(path), mode='rb')
When a __loader__ is present on the module given by __name__, it will defer
getResource to its get_data implementation and return it as a file-like
object (such as StringIO).
"""
from __future__ import print_function, division
import sys
import os
from sympy.core.compatibility import cStringIO as StringIO
def get_resource(identifier, pkgname=__name__):
"""
Acquire a readable object for a given package name and identifier.
An IOError will be raised if the resource can not be found.
For example::
mydata = get_resource('mypkgdata.jpg').read()
Note that the package name must be fully qualified, if given, such
that it would be found in sys.modules.
In some cases, getResource will return a real file object. In that
case, it may be useful to use its name attribute to get the path
rather than use it as a file-like object. For example, you may
be handing data off to a C API.
"""
mod = sys.modules[pkgname]
fn = getattr(mod, '__file__', None)
if fn is None:
raise IOError("%r has no __file__!")
path = os.path.join(os.path.dirname(fn), identifier)
loader = getattr(mod, '__loader__', None)
if loader is not None:
try:
data = loader.get_data(path)
except (IOError,AttributeError):
pass
else:
return StringIO(data.decode('utf-8'))
return open(os.path.normpath(path), 'rb')
| 1,872 | 30.745763 | 75 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/misc.py
|
"""Miscellaneous stuff that doesn't really fit anywhere else."""
from __future__ import print_function, division
import sys
import os
import re as _re
from textwrap import fill, dedent
from sympy.core.compatibility import get_function_name, range
class Undecidable(ValueError):
# an error to be raised when a decision cannot be made definitively
# where a definitive answer is needed
pass
def filldedent(s, w=70):
"""
Strips leading and trailing empty lines from a copy of `s`, then dedents,
fills and returns it.
Empty line stripping serves to deal with docstrings like this one that
start with a newline after the initial triple quote, inserting an empty
line at the beginning of the string."""
return '\n' + fill(dedent(str(s)).strip('\n'), width=w)
def rawlines(s):
"""Return a cut-and-pastable string that, when printed, is equivalent
to the input. The string returned is formatted so it can be indented
nicely within tests; in some cases it is wrapped in the dedent
function which has to be imported from textwrap.
Examples
========
Note: because there are characters in the examples below that need
to be escaped because they are themselves within a triple quoted
docstring, expressions below look more complicated than they would
be if they were printed in an interpreter window.
>>> from sympy.utilities.misc import rawlines
>>> from sympy import TableForm
>>> s = str(TableForm([[1, 10]], headings=(None, ['a', 'bee'])))
>>> print(rawlines(s))
(
'a bee\\n'
'-----\\n'
'1 10 '
)
>>> print(rawlines('''this
... that'''))
dedent('''\\
this
that''')
>>> print(rawlines('''this
... that
... '''))
dedent('''\\
this
that
''')
>>> s = \"\"\"this
... is a triple '''
... \"\"\"
>>> print(rawlines(s))
dedent(\"\"\"\\
this
is a triple '''
\"\"\")
>>> print(rawlines('''this
... that
... '''))
(
'this\\n'
'that\\n'
' '
)
"""
lines = s.split('\n')
if len(lines) == 1:
return repr(lines[0])
triple = ["'''" in s, '"""' in s]
if any(li.endswith(' ') for li in lines) or '\\' in s or all(triple):
rv = ["("]
# add on the newlines
trailing = s.endswith('\n')
last = len(lines) - 1
for i, li in enumerate(lines):
if i != last or trailing:
rv.append(repr(li)[:-1] + '\\n\'')
else:
rv.append(repr(li))
return '\n '.join(rv) + '\n)'
else:
rv = '\n '.join(lines)
if triple[0]:
return 'dedent("""\\\n %s""")' % rv
else:
return "dedent('''\\\n %s''')" % rv
size = getattr(sys, "maxint", None)
if size is None: # Python 3 doesn't have maxint
size = sys.maxsize
if size > 2**32:
ARCH = "64-bit"
else:
ARCH = "32-bit"
# XXX: PyPy doesn't support hash randomization
HASH_RANDOMIZATION = getattr(sys.flags, 'hash_randomization', False)
_debug_tmp = []
_debug_iter = 0
def debug_decorator(func):
"""If SYMPY_DEBUG is True, it will print a nice execution tree with
arguments and results of all decorated functions, else do nothing.
"""
from sympy import SYMPY_DEBUG
if not SYMPY_DEBUG:
return func
def maketree(f, *args, **kw):
global _debug_tmp
global _debug_iter
oldtmp = _debug_tmp
_debug_tmp = []
_debug_iter += 1
def tree(subtrees):
def indent(s, type=1):
x = s.split("\n")
r = "+-%s\n" % x[0]
for a in x[1:]:
if a == "":
continue
if type == 1:
r += "| %s\n" % a
else:
r += " %s\n" % a
return r
if len(subtrees) == 0:
return ""
f = []
for a in subtrees[:-1]:
f.append(indent(a))
f.append(indent(subtrees[-1], 2))
return ''.join(f)
# If there is a bug and the algorithm enters an infinite loop, enable the
# following lines. It will print the names and parameters of all major functions
# that are called, *before* they are called
#from sympy.core.compatibility import reduce
#print("%s%s %s%s" % (_debug_iter, reduce(lambda x, y: x + y, \
# map(lambda x: '-', range(1, 2 + _debug_iter))), get_function_name(f), args))
r = f(*args, **kw)
_debug_iter -= 1
s = "%s%s = %s\n" % (get_function_name(f), args, r)
if _debug_tmp != []:
s += tree(_debug_tmp)
_debug_tmp = oldtmp
_debug_tmp.append(s)
if _debug_iter == 0:
print((_debug_tmp[0]))
_debug_tmp = []
return r
def decorated(*args, **kwargs):
return maketree(func, *args, **kwargs)
return decorated
def debug(*args):
"""
Print ``*args`` if SYMPY_DEBUG is True, else do nothing.
"""
from sympy import SYMPY_DEBUG
if SYMPY_DEBUG:
print(*args, file=sys.stderr)
def find_executable(executable, path=None):
"""Try to find 'executable' in the directories listed in 'path' (a
string listing directories separated by 'os.pathsep'; defaults to
os.environ['PATH']). Returns the complete filename or None if not
found
"""
if path is None:
path = os.environ['PATH']
paths = path.split(os.pathsep)
extlist = ['']
if os.name == 'os2':
(base, ext) = os.path.splitext(executable)
# executable files on OS/2 can have an arbitrary extension, but
# .exe is automatically appended if no dot is present in the name
if not ext:
executable = executable + ".exe"
elif sys.platform == 'win32':
pathext = os.environ['PATHEXT'].lower().split(os.pathsep)
(base, ext) = os.path.splitext(executable)
if ext.lower() not in pathext:
extlist = pathext
for ext in extlist:
execname = executable + ext
if os.path.isfile(execname):
return execname
else:
for p in paths:
f = os.path.join(p, execname)
if os.path.isfile(f):
return f
else:
return None
def func_name(x):
'''Return function name of `x` (if defined) else the `type(x)`.
See Also
========
sympy.core.compatibility get_function_name
'''
typ = type(x)
if str(typ).startswith("<type '"):
typ = str(typ).split("'")[1].split("'")[0]
return getattr(getattr(x, 'func', x), '__name__', typ)
def _replace(reps):
"""Return a function that can make the replacements, given in
``reps``, on a string. The replacements should be given as mapping.
Examples
========
>>> from sympy.utilities.misc import _replace
>>> f = _replace(dict(foo='bar', d='t'))
>>> f('food')
'bart'
>>> f = _replace({})
>>> f('food')
'food'
"""
if not reps:
return lambda x: x
D = lambda match: reps[match.group(0)]
pattern = _re.compile("|".join(
[_re.escape(k) for k, v in reps.items()]), _re.M)
return lambda string: pattern.sub(D, string)
def replace(string, *reps):
"""Return ``string`` with all keys in ``reps`` replaced with
their corresponding values, longer strings first, irrespective
of the order they are given. ``reps`` may be passed as tuples
or a single mapping.
Examples
========
>>> from sympy.utilities.misc import replace
>>> replace('foo', {'oo': 'ar', 'f': 'b'})
'bar'
>>> replace("spamham sha", ("spam", "eggs"), ("sha","md5"))
'eggsham md5'
There is no guarantee that a unique answer will be
obtained if keys in a mapping overlap (i.e. are the same
length and have some identical sequence at the
beginning/end):
>>> reps = [
... ('ab', 'x'),
... ('bc', 'y')]
>>> replace('abc', *reps) in ('xc', 'ay')
True
References
==========
.. [1] http://stackoverflow.com/questions/6116978/python-replace-multiple-strings
"""
if len(reps) == 1:
kv = reps[0]
if type(kv) is dict:
reps = kv
else:
return string.replace(*kv)
else:
reps = dict(reps)
return _replace(reps)(string)
def translate(s, a, b=None, c=None):
"""Return ``s`` where characters have been replaced or deleted.
SYNTAX
======
translate(s, None, deletechars):
all characters in ``deletechars`` are deleted
translate(s, map [,deletechars]):
all characters in ``deletechars`` (if provided) are deleted
then the replacements defined by map are made; if the keys
of map are strings then the longer ones are handled first.
Multicharacter deletions should have a value of ''.
translate(s, oldchars, newchars, deletechars)
all characters in ``deletechars`` are deleted
then each character in ``oldchars`` is replaced with the
corresponding character in ``newchars``
Examples
========
>>> from sympy.utilities.misc import translate
>>> from sympy.core.compatibility import unichr
>>> abc = 'abc'
>>> translate(abc, None, 'a')
'bc'
>>> translate(abc, {'a': 'x'}, 'c')
'xb'
>>> translate(abc, {'abc': 'x', 'a': 'y'})
'x'
>>> translate('abcd', 'ac', 'AC', 'd')
'AbC'
There is no guarantee that a unique answer will be
obtained if keys in a mapping overlap are the same
length and have some identical sequences at the
beginning/end:
>>> translate(abc, {'ab': 'x', 'bc': 'y'}) in ('xc', 'ay')
True
"""
from sympy.core.compatibility import maketrans, PY3
mr = {}
if a is None:
assert c is None
if not b:
return s
c = b
a = b = ''
else:
if type(a) is dict:
short = {}
for k in list(a.keys()):
if (len(k) == 1 and len(a[k]) == 1):
short[k] = a.pop(k)
mr = a
c = b
if short:
a, b = [''.join(i) for i in list(zip(*short.items()))]
else:
a = b = ''
else:
assert len(a) == len(b)
if PY3:
if c:
s = s.translate(maketrans('', '', c))
s = replace(s, mr)
return s.translate(maketrans(a, b))
else:
# when support for Python 2 is dropped, this if-else-block
# can be replaced with the if-clause
if c:
c = list(c)
rem = {}
for i in range(-1, -1 - len(c), -1):
if ord(c[i]) > 255:
rem[c[i]] = ''
c.pop(i)
s = s.translate(None, ''.join(c))
s = replace(s, rem)
if a:
a = list(a)
b = list(b)
for i in range(-1, -1 - len(a), -1):
if ord(a[i]) > 255 or ord(b[i]) > 255:
mr[a.pop(i)] = b.pop(i)
a = ''.join(a)
b = ''.join(b)
s = replace(s, mr)
table = maketrans(a, b)
# s may have become unicode which uses the py3 syntax for translate
if type(table) is str and type(s) is str:
s = s.translate(table)
else:
s = s.translate(dict(
[(i, ord(c)) for i, c in enumerate(table)]))
return s
| 11,718 | 28.079404 | 89 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/timeutils.py
|
"""Simple tools for timing functions' execution, when IPython is not available. """
from __future__ import print_function, division
import timeit
import math
from sympy.core.compatibility import range
_scales = [1e0, 1e3, 1e6, 1e9]
_units = [u's', u'ms', u'\N{GREEK SMALL LETTER MU}s', u'ns']
def timed(func, setup="pass", limit=None):
"""Adaptively measure execution time of a function. """
timer = timeit.Timer(func, setup=setup)
repeat, number = 3, 1
for i in range(1, 10):
if timer.timeit(number) >= 0.2:
break
elif limit is not None and number >= limit:
break
else:
number *= 10
time = min(timer.repeat(repeat, number)) / number
if time > 0.0:
order = min(-int(math.floor(math.log10(time)) // 3), 3)
else:
order = 3
return (number, time, time*_scales[order], _units[order])
# Code for doing inline timings of recursive algorithms.
def __do_timings():
import os
res = os.getenv('SYMPY_TIMINGS', '')
res = [x.strip() for x in res.split(',')]
return set(res)
_do_timings = __do_timings()
_timestack = None
def _print_timestack(stack, level=1):
print('-'*level, '%.2f %s%s' % (stack[2], stack[0], stack[3]))
for s in stack[1]:
_print_timestack(s, level + 1)
def timethis(name):
def decorator(func):
global _do_timings
if not name in _do_timings:
return func
def wrapper(*args, **kwargs):
from time import time
global _timestack
oldtimestack = _timestack
_timestack = [func.func_name, [], 0, args]
t1 = time()
r = func(*args, **kwargs)
t2 = time()
_timestack[2] = t2 - t1
if oldtimestack is not None:
oldtimestack[1].append(_timestack)
_timestack = oldtimestack
else:
_print_timestack(_timestack)
_timestack = None
return r
return wrapper
return decorator
| 2,063 | 25.126582 | 83 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/lambdify.py
|
"""
This module provides convenient functions to transform sympy expressions to
lambda functions which can be used to calculate numerical values very fast.
"""
from __future__ import print_function, division
from functools import wraps
import inspect
import textwrap
from sympy.core.compatibility import (exec_, is_sequence, iterable,
NotIterable, string_types, range, builtins, integer_types)
from sympy.utilities.decorator import doctest_depends_on
# These are the namespaces the lambda functions will use.
MATH = {}
MPMATH = {}
NUMPY = {}
TENSORFLOW = {}
SYMPY = {}
NUMEXPR = {}
# Default namespaces, letting us define translations that can't be defined
# by simple variable maps, like I => 1j
# These are separate from the names above because the above names are modified
# throughout this file, whereas these should remain unmodified.
MATH_DEFAULT = {}
MPMATH_DEFAULT = {}
NUMPY_DEFAULT = {"I": 1j}
TENSORFLOW_DEFAULT = {}
SYMPY_DEFAULT = {}
NUMEXPR_DEFAULT = {}
# Mappings between sympy and other modules function names.
MATH_TRANSLATIONS = {
"ceiling": "ceil",
"E": "e",
"ln": "log",
}
MPMATH_TRANSLATIONS = {
"Abs": "fabs",
"elliptic_k": "ellipk",
"elliptic_f": "ellipf",
"elliptic_e": "ellipe",
"elliptic_pi": "ellippi",
"ceiling": "ceil",
"chebyshevt": "chebyt",
"chebyshevu": "chebyu",
"E": "e",
"I": "j",
"ln": "log",
#"lowergamma":"lower_gamma",
"oo": "inf",
#"uppergamma":"upper_gamma",
"LambertW": "lambertw",
"MutableDenseMatrix": "matrix",
"ImmutableDenseMatrix": "matrix",
"conjugate": "conj",
"dirichlet_eta": "altzeta",
"Ei": "ei",
"Shi": "shi",
"Chi": "chi",
"Si": "si",
"Ci": "ci"
}
NUMPY_TRANSLATIONS = {
"acos": "arccos",
"acosh": "arccosh",
"arg": "angle",
"asin": "arcsin",
"asinh": "arcsinh",
"atan": "arctan",
"atan2": "arctan2",
"atanh": "arctanh",
"ceiling": "ceil",
"E": "e",
"im": "imag",
"ln": "log",
"Mod": "mod",
"oo": "inf",
"re": "real",
"SparseMatrix": "array",
"ImmutableSparseMatrix": "array",
"Matrix": "array",
"MutableDenseMatrix": "array",
"ImmutableDenseMatrix": "array",
}
TENSORFLOW_TRANSLATIONS = {
"Abs": "abs",
"ceiling": "ceil",
"im": "imag",
"ln": "log",
"Mod": "mod",
"conjugate": "conj",
"re": "real",
}
NUMEXPR_TRANSLATIONS = {}
# Available modules:
MODULES = {
"math": (MATH, MATH_DEFAULT, MATH_TRANSLATIONS, ("from math import *",)),
"mpmath": (MPMATH, MPMATH_DEFAULT, MPMATH_TRANSLATIONS, ("from mpmath import *",)),
"numpy": (NUMPY, NUMPY_DEFAULT, NUMPY_TRANSLATIONS, ("import_module('numpy')",)),
"tensorflow": (TENSORFLOW, TENSORFLOW_DEFAULT, TENSORFLOW_TRANSLATIONS, ("import_module('tensorflow')",)),
"sympy": (SYMPY, SYMPY_DEFAULT, {}, (
"from sympy.functions import *",
"from sympy.matrices import *",
"from sympy import Integral, pi, oo, nan, zoo, E, I",)),
"numexpr" : (NUMEXPR, NUMEXPR_DEFAULT, NUMEXPR_TRANSLATIONS,
("import_module('numexpr')", )),
}
def _import(module, reload="False"):
"""
Creates a global translation dictionary for module.
The argument module has to be one of the following strings: "math",
"mpmath", "numpy", "sympy", "tensorflow".
These dictionaries map names of python functions to their equivalent in
other modules.
"""
from sympy.external import import_module
try:
namespace, namespace_default, translations, import_commands = MODULES[
module]
except KeyError:
raise NameError(
"'%s' module can't be used for lambdification" % module)
# Clear namespace or exit
if namespace != namespace_default:
# The namespace was already generated, don't do it again if not forced.
if reload:
namespace.clear()
namespace.update(namespace_default)
else:
return
for import_command in import_commands:
if import_command.startswith('import_module'):
module = eval(import_command)
if module is not None:
namespace.update(module.__dict__)
continue
else:
try:
exec_(import_command, {}, namespace)
continue
except ImportError:
pass
raise ImportError(
"can't import '%s' with '%s' command" % (module, import_command))
# Add translated names to namespace
for sympyname, translation in translations.items():
namespace[sympyname] = namespace[translation]
# For computing the modulus of a sympy expression we use the builtin abs
# function, instead of the previously used fabs function for all
# translation modules. This is because the fabs function in the math
# module does not accept complex valued arguments. (see issue 9474). The
# only exception, where we don't use the builtin abs function is the
# mpmath translation module, because mpmath.fabs returns mpf objects in
# contrast to abs().
if 'Abs' not in namespace:
namespace['Abs'] = abs
@doctest_depends_on(modules=('numpy'))
def lambdify(args, expr, modules=None, printer=None, use_imps=True,
dummify=True):
"""
Returns a lambda function for fast calculation of numerical values.
If not specified differently by the user, ``modules`` defaults to
``["numpy"]`` if NumPy is installed, and ``["math", "mpmath", "sympy"]``
if it isn't, that is, SymPy functions are replaced as far as possible by
either ``numpy`` functions if available, and Python's standard library
``math``, or ``mpmath`` functions otherwise. To change this behavior, the
"modules" argument can be used. It accepts:
- the strings "math", "mpmath", "numpy", "numexpr", "sympy", "tensorflow"
- any modules (e.g. math)
- dictionaries that map names of sympy functions to arbitrary functions
- lists that contain a mix of the arguments above, with higher priority
given to entries appearing first.
.. warning::
Note that this function uses ``eval``, and thus shouldn't be used on
unsanitized input.
The default behavior is to substitute all arguments in the provided
expression with dummy symbols. This allows for applied functions (e.g.
f(t)) to be supplied as arguments. Call the function with dummify=False if
dummy substitution is unwanted (and `args` is not a string). If you want
to view the lambdified function or provide "sympy" as the module, you
should probably set dummify=False.
For functions involving large array calculations, numexpr can provide a
significant speedup over numpy. Please note that the available functions
for numexpr are more limited than numpy but can be expanded with
implemented_function and user defined subclasses of Function. If specified,
numexpr may be the only option in modules. The official list of numexpr
functions can be found at:
https://github.com/pydata/numexpr#supported-functions
In previous releases ``lambdify`` replaced ``Matrix`` with ``numpy.matrix``
by default. As of release 1.0 ``numpy.array`` is the default.
To get the old default behavior you must pass in ``[{'ImmutableDenseMatrix':
numpy.matrix}, 'numpy']`` to the ``modules`` kwarg.
>>> from sympy import lambdify, Matrix
>>> from sympy.abc import x, y
>>> import numpy
>>> array2mat = [{'ImmutableDenseMatrix': numpy.matrix}, 'numpy']
>>> f = lambdify((x, y), Matrix([x, y]), modules=array2mat)
>>> f(1, 2)
matrix([[1],
[2]])
Usage
=====
(1) Use one of the provided modules:
>>> from sympy import sin, tan, gamma
>>> from sympy.utilities.lambdify import lambdastr
>>> from sympy.abc import x, y
>>> f = lambdify(x, sin(x), "math")
Attention: Functions that are not in the math module will throw a name
error when the lambda function is evaluated! So this would
be better:
>>> f = lambdify(x, sin(x)*gamma(x), ("math", "mpmath", "sympy"))
(2) Use some other module:
>>> import numpy
>>> f = lambdify((x,y), tan(x*y), numpy)
Attention: There are naming differences between numpy and sympy. So if
you simply take the numpy module, e.g. sympy.atan will not be
translated to numpy.arctan. Use the modified module instead
by passing the string "numpy":
>>> f = lambdify((x,y), tan(x*y), "numpy")
>>> f(1, 2)
-2.18503986326
>>> from numpy import array
>>> f(array([1, 2, 3]), array([2, 3, 5]))
[-2.18503986 -0.29100619 -0.8559934 ]
(3) Use a dictionary defining custom functions:
>>> def my_cool_function(x): return 'sin(%s) is cool' % x
>>> myfuncs = {"sin" : my_cool_function}
>>> f = lambdify(x, sin(x), myfuncs); f(1)
'sin(1) is cool'
Examples
========
>>> from sympy.utilities.lambdify import implemented_function
>>> from sympy import sqrt, sin, Matrix
>>> from sympy import Function
>>> from sympy.abc import w, x, y, z
>>> f = lambdify(x, x**2)
>>> f(2)
4
>>> f = lambdify((x, y, z), [z, y, x])
>>> f(1,2,3)
[3, 2, 1]
>>> f = lambdify(x, sqrt(x))
>>> f(4)
2.0
>>> f = lambdify((x, y), sin(x*y)**2)
>>> f(0, 5)
0.0
>>> row = lambdify((x, y), Matrix((x, x + y)).T, modules='sympy')
>>> row(1, 2)
Matrix([[1, 3]])
Tuple arguments are handled and the lambdified function should
be called with the same type of arguments as were used to create
the function.:
>>> f = lambdify((x, (y, z)), x + y)
>>> f(1, (2, 4))
3
A more robust way of handling this is to always work with flattened
arguments:
>>> from sympy.utilities.iterables import flatten
>>> args = w, (x, (y, z))
>>> vals = 1, (2, (3, 4))
>>> f = lambdify(flatten(args), w + x + y + z)
>>> f(*flatten(vals))
10
Functions present in `expr` can also carry their own numerical
implementations, in a callable attached to the ``_imp_``
attribute. Usually you attach this using the
``implemented_function`` factory:
>>> f = implemented_function(Function('f'), lambda x: x+1)
>>> func = lambdify(x, f(x))
>>> func(4)
5
``lambdify`` always prefers ``_imp_`` implementations to implementations
in other namespaces, unless the ``use_imps`` input parameter is False.
Usage with Tensorflow module:
>>> import tensorflow as tf
>>> f = Max(x, sin(x))
>>> func = lambdify(x, f, 'tensorflow')
>>> result = func(tf.constant(1.0))
>>> result # a tf.Tensor representing the result of the calculation
<tf.Tensor 'Maximum:0' shape=() dtype=float32>
>>> sess = tf.Session()
>>> sess.run(result) # compute result
1.0
>>> var = tf.Variable(1.0)
>>> sess.run(tf.global_variables_initializer())
>>> sess.run(func(var)) # also works for tf.Variable and tf.Placeholder
1.0
>>> tensor = tf.constant([[1.0, 2.0], [3.0, 4.0]]) # works with any shape tensor
>>> sess.run(func(tensor))
array([[ 1., 2.],
[ 3., 4.]], dtype=float32)
"""
from sympy.core.symbol import Symbol
from sympy.utilities.iterables import flatten
# If the user hasn't specified any modules, use what is available.
module_provided = True
if modules is None:
module_provided = False
try:
_import("numpy")
except ImportError:
# Use either numpy (if available) or python.math where possible.
# XXX: This leads to different behaviour on different systems and
# might be the reason for irreproducible errors.
modules = ["math", "mpmath", "sympy"]
else:
modules = ["numpy"]
# Get the needed namespaces.
namespaces = []
# First find any function implementations
if use_imps:
namespaces.append(_imp_namespace(expr))
# Check for dict before iterating
if isinstance(modules, (dict, str)) or not hasattr(modules, '__iter__'):
namespaces.append(modules)
else:
# consistency check
if _module_present('numexpr', modules) and len(modules) > 1:
raise TypeError("numexpr must be the only item in 'modules'")
namespaces += list(modules)
# fill namespace with first having highest priority
namespace = {}
for m in namespaces[::-1]:
buf = _get_namespace(m)
namespace.update(buf)
if hasattr(expr, "atoms"):
#Try if you can extract symbols from the expression.
#Move on if expr.atoms in not implemented.
syms = expr.atoms(Symbol)
for term in syms:
namespace.update({str(term): term})
if _module_present('mpmath',namespaces) and printer is None:
#XXX: This has to be done here because of circular imports
from sympy.printing.lambdarepr import MpmathPrinter as printer
if _module_present('numpy',namespaces) and printer is None:
#XXX: This has to be done here because of circular imports
from sympy.printing.lambdarepr import NumPyPrinter as printer
if _module_present('numexpr',namespaces) and printer is None:
#XXX: This has to be done here because of circular imports
from sympy.printing.lambdarepr import NumExprPrinter as printer
if _module_present('tensorflow',namespaces) and printer is None:
#XXX: This has to be done here because of circular imports
from sympy.printing.lambdarepr import TensorflowPrinter as printer
# Get the names of the args, for creating a docstring
if not iterable(args):
args = (args,)
names = []
# Grab the callers frame, for getting the names by inspection (if needed)
callers_local_vars = inspect.currentframe().f_back.f_locals.items()
for n, var in enumerate(args):
if hasattr(var, 'name'):
names.append(var.name)
else:
# It's an iterable. Try to get name by inspection of calling frame.
name_list = [var_name for var_name, var_val in callers_local_vars
if var_val is var]
if len(name_list) == 1:
names.append(name_list[0])
else:
# Cannot infer name with certainty. arg_# will have to do.
names.append('arg_' + str(n))
# Create lambda function.
lstr = lambdastr(args, expr, printer=printer, dummify=dummify)
flat = '__flatten_args__'
if flat in lstr:
namespace.update({flat: flatten})
# Provide lambda expression with builtins, and compatible implementation of range
namespace.update({'builtins':builtins, 'range':range})
func = eval(lstr, namespace)
# For numpy lambdify, wrap all input arguments in arrays.
# This is a fix for gh-11306.
if module_provided and _module_present('numpy',namespaces):
def array_wrap(funcarg):
@wraps(funcarg)
def wrapper(*argsx, **kwargsx):
asarray = namespace['asarray']
newargs = [asarray(i) if isinstance(i, integer_types + (float,
complex)) else i for i in argsx]
return funcarg(*newargs, **kwargsx)
return wrapper
func = array_wrap(func)
# Apply the docstring
sig = "func({0})".format(", ".join(str(i) for i in names))
sig = textwrap.fill(sig, subsequent_indent=' '*8)
expr_str = str(expr)
if len(expr_str) > 78:
expr_str = textwrap.wrap(expr_str, 75)[0] + '...'
func.__doc__ = ("Created with lambdify. Signature:\n\n{sig}\n\n"
"Expression:\n\n{expr}").format(sig=sig, expr=expr_str)
return func
def _module_present(modname, modlist):
if modname in modlist:
return True
for m in modlist:
if hasattr(m, '__name__') and m.__name__ == modname:
return True
return False
def _get_namespace(m):
"""
This is used by _lambdify to parse its arguments.
"""
if isinstance(m, str):
_import(m)
return MODULES[m][0]
elif isinstance(m, dict):
return m
elif hasattr(m, "__dict__"):
return m.__dict__
else:
raise TypeError("Argument must be either a string, dict or module but it is: %s" % m)
def lambdastr(args, expr, printer=None, dummify=False):
"""
Returns a string that can be evaluated to a lambda function.
Examples
========
>>> from sympy.abc import x, y, z
>>> from sympy.utilities.lambdify import lambdastr
>>> lambdastr(x, x**2)
'lambda x: (x**2)'
>>> lambdastr((x,y,z), [z,y,x])
'lambda x,y,z: ([z, y, x])'
Although tuples may not appear as arguments to lambda in Python 3,
lambdastr will create a lambda function that will unpack the original
arguments so that nested arguments can be handled:
>>> lambdastr((x, (y, z)), x + y)
'lambda _0,_1: (lambda x,y,z: (x + y))(*list(__flatten_args__([_0,_1])))'
"""
# Transforming everything to strings.
from sympy.matrices import DeferredVector
from sympy import Dummy, sympify, Symbol, Function, flatten
if printer is not None:
if inspect.isfunction(printer):
lambdarepr = printer
else:
if inspect.isclass(printer):
lambdarepr = lambda expr: printer().doprint(expr)
else:
lambdarepr = lambda expr: printer.doprint(expr)
else:
#XXX: This has to be done here because of circular imports
from sympy.printing.lambdarepr import lambdarepr
def sub_args(args, dummies_dict):
if isinstance(args, str):
return args
elif isinstance(args, DeferredVector):
return str(args)
elif iterable(args):
dummies = flatten([sub_args(a, dummies_dict) for a in args])
return ",".join(str(a) for a in dummies)
else:
#Sub in dummy variables for functions or symbols
if isinstance(args, (Function, Symbol)):
dummies = Dummy()
dummies_dict.update({args : dummies})
return str(dummies)
else:
return str(args)
def sub_expr(expr, dummies_dict):
try:
expr = sympify(expr).xreplace(dummies_dict)
except Exception:
if isinstance(expr, DeferredVector):
pass
elif isinstance(expr, dict):
k = [sub_expr(sympify(a), dummies_dict) for a in expr.keys()]
v = [sub_expr(sympify(a), dummies_dict) for a in expr.values()]
expr = dict(zip(k, v))
elif isinstance(expr, tuple):
expr = tuple(sub_expr(sympify(a), dummies_dict) for a in expr)
elif isinstance(expr, list):
expr = [sub_expr(sympify(a), dummies_dict) for a in expr]
return expr
# Transform args
def isiter(l):
return iterable(l, exclude=(str, DeferredVector, NotIterable))
if isiter(args) and any(isiter(i) for i in args):
from sympy.utilities.iterables import flatten
import re
dum_args = [str(Dummy(str(i))) for i in range(len(args))]
iter_args = ','.join([i if isiter(a) else i
for i, a in zip(dum_args, args)])
lstr = lambdastr(flatten(args), expr, printer=printer, dummify=dummify)
flat = '__flatten_args__'
rv = 'lambda %s: (%s)(*list(%s([%s])))' % (
','.join(dum_args), lstr, flat, iter_args)
if len(re.findall(r'\b%s\b' % flat, rv)) > 1:
raise ValueError('the name %s is reserved by lambdastr' % flat)
return rv
dummies_dict = {}
if dummify:
args = sub_args(args, dummies_dict)
else:
if isinstance(args, str):
pass
elif iterable(args, exclude=DeferredVector):
args = ",".join(str(a) for a in args)
# Transform expr
if dummify:
if isinstance(expr, str):
pass
else:
expr = sub_expr(expr, dummies_dict)
expr = lambdarepr(expr)
return "lambda %s: (%s)" % (args, expr)
def _imp_namespace(expr, namespace=None):
""" Return namespace dict with function implementations
We need to search for functions in anything that can be thrown at
us - that is - anything that could be passed as `expr`. Examples
include sympy expressions, as well as tuples, lists and dicts that may
contain sympy expressions.
Parameters
----------
expr : object
Something passed to lambdify, that will generate valid code from
``str(expr)``.
namespace : None or mapping
Namespace to fill. None results in new empty dict
Returns
-------
namespace : dict
dict with keys of implemented function names within `expr` and
corresponding values being the numerical implementation of
function
Examples
========
>>> from sympy.abc import x
>>> from sympy.utilities.lambdify import implemented_function, _imp_namespace
>>> from sympy import Function
>>> f = implemented_function(Function('f'), lambda x: x+1)
>>> g = implemented_function(Function('g'), lambda x: x*10)
>>> namespace = _imp_namespace(f(g(x)))
>>> sorted(namespace.keys())
['f', 'g']
"""
# Delayed import to avoid circular imports
from sympy.core.function import FunctionClass
if namespace is None:
namespace = {}
# tuples, lists, dicts are valid expressions
if is_sequence(expr):
for arg in expr:
_imp_namespace(arg, namespace)
return namespace
elif isinstance(expr, dict):
for key, val in expr.items():
# functions can be in dictionary keys
_imp_namespace(key, namespace)
_imp_namespace(val, namespace)
return namespace
# sympy expressions may be Functions themselves
func = getattr(expr, 'func', None)
if isinstance(func, FunctionClass):
imp = getattr(func, '_imp_', None)
if imp is not None:
name = expr.func.__name__
if name in namespace and namespace[name] != imp:
raise ValueError('We found more than one '
'implementation with name '
'"%s"' % name)
namespace[name] = imp
# and / or they may take Functions as arguments
if hasattr(expr, 'args'):
for arg in expr.args:
_imp_namespace(arg, namespace)
return namespace
def implemented_function(symfunc, implementation):
""" Add numerical ``implementation`` to function ``symfunc``.
``symfunc`` can be an ``UndefinedFunction`` instance, or a name string.
In the latter case we create an ``UndefinedFunction`` instance with that
name.
Be aware that this is a quick workaround, not a general method to create
special symbolic functions. If you want to create a symbolic function to be
used by all the machinery of SymPy you should subclass the ``Function``
class.
Parameters
----------
symfunc : ``str`` or ``UndefinedFunction`` instance
If ``str``, then create new ``UndefinedFunction`` with this as
name. If `symfunc` is a sympy function, attach implementation to it.
implementation : callable
numerical implementation to be called by ``evalf()`` or ``lambdify``
Returns
-------
afunc : sympy.FunctionClass instance
function with attached implementation
Examples
========
>>> from sympy.abc import x
>>> from sympy.utilities.lambdify import lambdify, implemented_function
>>> from sympy import Function
>>> f = implemented_function(Function('f'), lambda x: x+1)
>>> lam_f = lambdify(x, f(x))
>>> lam_f(4)
5
"""
# Delayed import to avoid circular imports
from sympy.core.function import UndefinedFunction
# if name, create function to hold implementation
if isinstance(symfunc, string_types):
symfunc = UndefinedFunction(symfunc)
elif not isinstance(symfunc, UndefinedFunction):
raise ValueError('symfunc should be either a string or'
' an UndefinedFunction instance.')
# We need to attach as a method because symfunc will be a class
symfunc._imp_ = staticmethod(implementation)
return symfunc
| 24,657 | 34.025568 | 110 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/iterables.py
|
from __future__ import print_function, division
from collections import defaultdict
from itertools import (
combinations, combinations_with_replacement, permutations,
product, product as cartes
)
import random
from operator import gt
from sympy.core import Basic
# this is the logical location of these functions
from sympy.core.compatibility import (
as_int, default_sort_key, is_sequence, iterable, ordered, range
)
from sympy.utilities.enumerative import (
multiset_partitions_taocp, list_visitor, MultisetPartitionTraverser)
def flatten(iterable, levels=None, cls=None):
"""
Recursively denest iterable containers.
>>> from sympy.utilities.iterables import flatten
>>> flatten([1, 2, 3])
[1, 2, 3]
>>> flatten([1, 2, [3]])
[1, 2, 3]
>>> flatten([1, [2, 3], [4, 5]])
[1, 2, 3, 4, 5]
>>> flatten([1.0, 2, (1, None)])
[1.0, 2, 1, None]
If you want to denest only a specified number of levels of
nested containers, then set ``levels`` flag to the desired
number of levels::
>>> ls = [[(-2, -1), (1, 2)], [(0, 0)]]
>>> flatten(ls, levels=1)
[(-2, -1), (1, 2), (0, 0)]
If cls argument is specified, it will only flatten instances of that
class, for example:
>>> from sympy.core import Basic
>>> class MyOp(Basic):
... pass
...
>>> flatten([MyOp(1, MyOp(2, 3))], cls=MyOp)
[1, 2, 3]
adapted from http://kogs-www.informatik.uni-hamburg.de/~meine/python_tricks
"""
if levels is not None:
if not levels:
return iterable
elif levels > 0:
levels -= 1
else:
raise ValueError(
"expected non-negative number of levels, got %s" % levels)
if cls is None:
reducible = lambda x: is_sequence(x, set)
else:
reducible = lambda x: isinstance(x, cls)
result = []
for el in iterable:
if reducible(el):
if hasattr(el, 'args'):
el = el.args
result.extend(flatten(el, levels=levels, cls=cls))
else:
result.append(el)
return result
def unflatten(iter, n=2):
"""Group ``iter`` into tuples of length ``n``. Raise an error if
the length of ``iter`` is not a multiple of ``n``.
"""
if n < 1 or len(iter) % n:
raise ValueError('iter length is not a multiple of %i' % n)
return list(zip(*(iter[i::n] for i in range(n))))
def reshape(seq, how):
"""Reshape the sequence according to the template in ``how``.
Examples
========
>>> from sympy.utilities import reshape
>>> seq = list(range(1, 9))
>>> reshape(seq, [4]) # lists of 4
[[1, 2, 3, 4], [5, 6, 7, 8]]
>>> reshape(seq, (4,)) # tuples of 4
[(1, 2, 3, 4), (5, 6, 7, 8)]
>>> reshape(seq, (2, 2)) # tuples of 4
[(1, 2, 3, 4), (5, 6, 7, 8)]
>>> reshape(seq, (2, [2])) # (i, i, [i, i])
[(1, 2, [3, 4]), (5, 6, [7, 8])]
>>> reshape(seq, ((2,), [2])) # etc....
[((1, 2), [3, 4]), ((5, 6), [7, 8])]
>>> reshape(seq, (1, [2], 1))
[(1, [2, 3], 4), (5, [6, 7], 8)]
>>> reshape(tuple(seq), ([[1], 1, (2,)],))
(([[1], 2, (3, 4)],), ([[5], 6, (7, 8)],))
>>> reshape(tuple(seq), ([1], 1, (2,)))
(([1], 2, (3, 4)), ([5], 6, (7, 8)))
>>> reshape(list(range(12)), [2, [3], {2}, (1, (3,), 1)])
[[0, 1, [2, 3, 4], {5, 6}, (7, (8, 9, 10), 11)]]
"""
m = sum(flatten(how))
n, rem = divmod(len(seq), m)
if m < 0 or rem:
raise ValueError('template must sum to positive number '
'that divides the length of the sequence')
i = 0
container = type(how)
rv = [None]*n
for k in range(len(rv)):
rv[k] = []
for hi in how:
if type(hi) is int:
rv[k].extend(seq[i: i + hi])
i += hi
else:
n = sum(flatten(hi))
hi_type = type(hi)
rv[k].append(hi_type(reshape(seq[i: i + n], hi)[0]))
i += n
rv[k] = container(rv[k])
return type(seq)(rv)
def group(seq, multiple=True):
"""
Splits a sequence into a list of lists of equal, adjacent elements.
Examples
========
>>> from sympy.utilities.iterables import group
>>> group([1, 1, 1, 2, 2, 3])
[[1, 1, 1], [2, 2], [3]]
>>> group([1, 1, 1, 2, 2, 3], multiple=False)
[(1, 3), (2, 2), (3, 1)]
>>> group([1, 1, 3, 2, 2, 1], multiple=False)
[(1, 2), (3, 1), (2, 2), (1, 1)]
See Also
========
multiset
"""
if not seq:
return []
current, groups = [seq[0]], []
for elem in seq[1:]:
if elem == current[-1]:
current.append(elem)
else:
groups.append(current)
current = [elem]
groups.append(current)
if multiple:
return groups
for i, current in enumerate(groups):
groups[i] = (current[0], len(current))
return groups
def multiset(seq):
"""Return the hashable sequence in multiset form with values being the
multiplicity of the item in the sequence.
Examples
========
>>> from sympy.utilities.iterables import multiset
>>> multiset('mississippi')
{'i': 4, 'm': 1, 'p': 2, 's': 4}
See Also
========
group
"""
rv = defaultdict(int)
for s in seq:
rv[s] += 1
return dict(rv)
def postorder_traversal(node, keys=None):
"""
Do a postorder traversal of a tree.
This generator recursively yields nodes that it has visited in a postorder
fashion. That is, it descends through the tree depth-first to yield all of
a node's children's postorder traversal before yielding the node itself.
Parameters
==========
node : sympy expression
The expression to traverse.
keys : (default None) sort key(s)
The key(s) used to sort args of Basic objects. When None, args of Basic
objects are processed in arbitrary order. If key is defined, it will
be passed along to ordered() as the only key(s) to use to sort the
arguments; if ``key`` is simply True then the default keys of
``ordered`` will be used (node count and default_sort_key).
Yields
======
subtree : sympy expression
All of the subtrees in the tree.
Examples
========
>>> from sympy.utilities.iterables import postorder_traversal
>>> from sympy.abc import w, x, y, z
The nodes are returned in the order that they are encountered unless key
is given; simply passing key=True will guarantee that the traversal is
unique.
>>> list(postorder_traversal(w + (x + y)*z)) # doctest: +SKIP
[z, y, x, x + y, z*(x + y), w, w + z*(x + y)]
>>> list(postorder_traversal(w + (x + y)*z, keys=True))
[w, z, x, y, x + y, z*(x + y), w + z*(x + y)]
"""
if isinstance(node, Basic):
args = node.args
if keys:
if keys != True:
args = ordered(args, keys, default=False)
else:
args = ordered(args)
for arg in args:
for subtree in postorder_traversal(arg, keys):
yield subtree
elif iterable(node):
for item in node:
for subtree in postorder_traversal(item, keys):
yield subtree
yield node
def interactive_traversal(expr):
"""Traverse a tree asking a user which branch to choose. """
from sympy.printing import pprint
RED, BRED = '\033[0;31m', '\033[1;31m'
GREEN, BGREEN = '\033[0;32m', '\033[1;32m'
YELLOW, BYELLOW = '\033[0;33m', '\033[1;33m'
BLUE, BBLUE = '\033[0;34m', '\033[1;34m'
MAGENTA, BMAGENTA = '\033[0;35m', '\033[1;35m'
CYAN, BCYAN = '\033[0;36m', '\033[1;36m'
END = '\033[0m'
def cprint(*args):
print("".join(map(str, args)) + END)
def _interactive_traversal(expr, stage):
if stage > 0:
print()
cprint("Current expression (stage ", BYELLOW, stage, END, "):")
print(BCYAN)
pprint(expr)
print(END)
if isinstance(expr, Basic):
if expr.is_Add:
args = expr.as_ordered_terms()
elif expr.is_Mul:
args = expr.as_ordered_factors()
else:
args = expr.args
elif hasattr(expr, "__iter__"):
args = list(expr)
else:
return expr
n_args = len(args)
if not n_args:
return expr
for i, arg in enumerate(args):
cprint(GREEN, "[", BGREEN, i, GREEN, "] ", BLUE, type(arg), END)
pprint(arg)
print
if n_args == 1:
choices = '0'
else:
choices = '0-%d' % (n_args - 1)
try:
choice = raw_input("Your choice [%s,f,l,r,d,?]: " % choices)
except EOFError:
result = expr
print()
else:
if choice == '?':
cprint(RED, "%s - select subexpression with the given index" %
choices)
cprint(RED, "f - select the first subexpression")
cprint(RED, "l - select the last subexpression")
cprint(RED, "r - select a random subexpression")
cprint(RED, "d - done\n")
result = _interactive_traversal(expr, stage)
elif choice in ['d', '']:
result = expr
elif choice == 'f':
result = _interactive_traversal(args[0], stage + 1)
elif choice == 'l':
result = _interactive_traversal(args[-1], stage + 1)
elif choice == 'r':
result = _interactive_traversal(random.choice(args), stage + 1)
else:
try:
choice = int(choice)
except ValueError:
cprint(BRED,
"Choice must be a number in %s range\n" % choices)
result = _interactive_traversal(expr, stage)
else:
if choice < 0 or choice >= n_args:
cprint(BRED, "Choice must be in %s range\n" % choices)
result = _interactive_traversal(expr, stage)
else:
result = _interactive_traversal(args[choice], stage + 1)
return result
return _interactive_traversal(expr, 0)
def ibin(n, bits=0, str=False):
"""Return a list of length ``bits`` corresponding to the binary value
of ``n`` with small bits to the right (last). If bits is omitted, the
length will be the number required to represent ``n``. If the bits are
desired in reversed order, use the [::-1] slice of the returned list.
If a sequence of all bits-length lists starting from [0, 0,..., 0]
through [1, 1, ..., 1] are desired, pass a non-integer for bits, e.g.
'all'.
If the bit *string* is desired pass ``str=True``.
Examples
========
>>> from sympy.utilities.iterables import ibin
>>> ibin(2)
[1, 0]
>>> ibin(2, 4)
[0, 0, 1, 0]
>>> ibin(2, 4)[::-1]
[0, 1, 0, 0]
If all lists corresponding to 0 to 2**n - 1, pass a non-integer
for bits:
>>> bits = 2
>>> for i in ibin(2, 'all'):
... print(i)
(0, 0)
(0, 1)
(1, 0)
(1, 1)
If a bit string is desired of a given length, use str=True:
>>> n = 123
>>> bits = 10
>>> ibin(n, bits, str=True)
'0001111011'
>>> ibin(n, bits, str=True)[::-1] # small bits left
'1101111000'
>>> list(ibin(3, 'all', str=True))
['000', '001', '010', '011', '100', '101', '110', '111']
"""
if not str:
try:
bits = as_int(bits)
return [1 if i == "1" else 0 for i in bin(n)[2:].rjust(bits, "0")]
except ValueError:
return variations(list(range(2)), n, repetition=True)
else:
try:
bits = as_int(bits)
return bin(n)[2:].rjust(bits, "0")
except ValueError:
return (bin(i)[2:].rjust(n, "0") for i in range(2**n))
def variations(seq, n, repetition=False):
"""Returns a generator of the n-sized variations of ``seq`` (size N).
``repetition`` controls whether items in ``seq`` can appear more than once;
Examples
========
variations(seq, n) will return N! / (N - n)! permutations without
repetition of seq's elements:
>>> from sympy.utilities.iterables import variations
>>> list(variations([1, 2], 2))
[(1, 2), (2, 1)]
variations(seq, n, True) will return the N**n permutations obtained
by allowing repetition of elements:
>>> list(variations([1, 2], 2, repetition=True))
[(1, 1), (1, 2), (2, 1), (2, 2)]
If you ask for more items than are in the set you get the empty set unless
you allow repetitions:
>>> list(variations([0, 1], 3, repetition=False))
[]
>>> list(variations([0, 1], 3, repetition=True))[:4]
[(0, 0, 0), (0, 0, 1), (0, 1, 0), (0, 1, 1)]
See Also
========
sympy.core.compatibility.permutations
sympy.core.compatibility.product
"""
if not repetition:
seq = tuple(seq)
if len(seq) < n:
return
for i in permutations(seq, n):
yield i
else:
if n == 0:
yield ()
else:
for i in product(seq, repeat=n):
yield i
def subsets(seq, k=None, repetition=False):
"""Generates all k-subsets (combinations) from an n-element set, seq.
A k-subset of an n-element set is any subset of length exactly k. The
number of k-subsets of an n-element set is given by binomial(n, k),
whereas there are 2**n subsets all together. If k is None then all
2**n subsets will be returned from shortest to longest.
Examples
========
>>> from sympy.utilities.iterables import subsets
subsets(seq, k) will return the n!/k!/(n - k)! k-subsets (combinations)
without repetition, i.e. once an item has been removed, it can no
longer be "taken":
>>> list(subsets([1, 2], 2))
[(1, 2)]
>>> list(subsets([1, 2]))
[(), (1,), (2,), (1, 2)]
>>> list(subsets([1, 2, 3], 2))
[(1, 2), (1, 3), (2, 3)]
subsets(seq, k, repetition=True) will return the (n - 1 + k)!/k!/(n - 1)!
combinations *with* repetition:
>>> list(subsets([1, 2], 2, repetition=True))
[(1, 1), (1, 2), (2, 2)]
If you ask for more items than are in the set you get the empty set unless
you allow repetitions:
>>> list(subsets([0, 1], 3, repetition=False))
[]
>>> list(subsets([0, 1], 3, repetition=True))
[(0, 0, 0), (0, 0, 1), (0, 1, 1), (1, 1, 1)]
"""
if k is None:
for k in range(len(seq) + 1):
for i in subsets(seq, k, repetition):
yield i
else:
if not repetition:
for i in combinations(seq, k):
yield i
else:
for i in combinations_with_replacement(seq, k):
yield i
def filter_symbols(iterator, exclude):
"""
Only yield elements from `iterator` that do not occur in `exclude`.
Parameters
==========
iterator : iterable
iterator to take elements from
exclude : iterable
elements to exclude
Returns
=======
iterator : iterator
filtered iterator
"""
exclude = set(exclude)
for s in iterator:
if s not in exclude:
yield s
def numbered_symbols(prefix='x', cls=None, start=0, exclude=[], *args, **assumptions):
"""
Generate an infinite stream of Symbols consisting of a prefix and
increasing subscripts provided that they do not occur in `exclude`.
Parameters
==========
prefix : str, optional
The prefix to use. By default, this function will generate symbols of
the form "x0", "x1", etc.
cls : class, optional
The class to use. By default, it uses Symbol, but you can also use Wild or Dummy.
start : int, optional
The start number. By default, it is 0.
Returns
=======
sym : Symbol
The subscripted symbols.
"""
exclude = set(exclude or [])
if cls is None:
# We can't just make the default cls=Symbol because it isn't
# imported yet.
from sympy import Symbol
cls = Symbol
while True:
name = '%s%s' % (prefix, start)
s = cls(name, *args, **assumptions)
if s not in exclude:
yield s
start += 1
def capture(func):
"""Return the printed output of func().
`func` should be a function without arguments that produces output with
print statements.
>>> from sympy.utilities.iterables import capture
>>> from sympy import pprint
>>> from sympy.abc import x
>>> def foo():
... print('hello world!')
...
>>> 'hello' in capture(foo) # foo, not foo()
True
>>> capture(lambda: pprint(2/x))
'2\\n-\\nx\\n'
"""
from sympy.core.compatibility import StringIO
import sys
stdout = sys.stdout
sys.stdout = file = StringIO()
try:
func()
finally:
sys.stdout = stdout
return file.getvalue()
def sift(seq, keyfunc):
"""
Sift the sequence, ``seq`` into a dictionary according to keyfunc.
OUTPUT: each element in expr is stored in a list keyed to the value
of keyfunc for the element.
Examples
========
>>> from sympy.utilities import sift
>>> from sympy.abc import x, y
>>> from sympy import sqrt, exp
>>> sift(range(5), lambda x: x % 2)
{0: [0, 2, 4], 1: [1, 3]}
sift() returns a defaultdict() object, so any key that has no matches will
give [].
>>> sift([x], lambda x: x.is_commutative)
{True: [x]}
>>> _[False]
[]
Sometimes you won't know how many keys you will get:
>>> sift([sqrt(x), exp(x), (y**x)**2],
... lambda x: x.as_base_exp()[0])
{E: [exp(x)], x: [sqrt(x)], y: [y**(2*x)]}
If you need to sort the sifted items it might be better to use
``ordered`` which can economically apply multiple sort keys
to a squence while sorting.
See Also
========
ordered
"""
m = defaultdict(list)
for i in seq:
m[keyfunc(i)].append(i)
return m
def take(iter, n):
"""Return ``n`` items from ``iter`` iterator. """
return [ value for _, value in zip(range(n), iter) ]
def dict_merge(*dicts):
"""Merge dictionaries into a single dictionary. """
merged = {}
for dict in dicts:
merged.update(dict)
return merged
def common_prefix(*seqs):
"""Return the subsequence that is a common start of sequences in ``seqs``.
>>> from sympy.utilities.iterables import common_prefix
>>> common_prefix(list(range(3)))
[0, 1, 2]
>>> common_prefix(list(range(3)), list(range(4)))
[0, 1, 2]
>>> common_prefix([1, 2, 3], [1, 2, 5])
[1, 2]
>>> common_prefix([1, 2, 3], [1, 3, 5])
[1]
"""
if any(not s for s in seqs):
return []
elif len(seqs) == 1:
return seqs[0]
i = 0
for i in range(min(len(s) for s in seqs)):
if not all(seqs[j][i] == seqs[0][i] for j in range(len(seqs))):
break
else:
i += 1
return seqs[0][:i]
def common_suffix(*seqs):
"""Return the subsequence that is a common ending of sequences in ``seqs``.
>>> from sympy.utilities.iterables import common_suffix
>>> common_suffix(list(range(3)))
[0, 1, 2]
>>> common_suffix(list(range(3)), list(range(4)))
[]
>>> common_suffix([1, 2, 3], [9, 2, 3])
[2, 3]
>>> common_suffix([1, 2, 3], [9, 7, 3])
[3]
"""
if any(not s for s in seqs):
return []
elif len(seqs) == 1:
return seqs[0]
i = 0
for i in range(-1, -min(len(s) for s in seqs) - 1, -1):
if not all(seqs[j][i] == seqs[0][i] for j in range(len(seqs))):
break
else:
i -= 1
if i == -1:
return []
else:
return seqs[0][i + 1:]
def prefixes(seq):
"""
Generate all prefixes of a sequence.
Examples
========
>>> from sympy.utilities.iterables import prefixes
>>> list(prefixes([1,2,3,4]))
[[1], [1, 2], [1, 2, 3], [1, 2, 3, 4]]
"""
n = len(seq)
for i in range(n):
yield seq[:i + 1]
def postfixes(seq):
"""
Generate all postfixes of a sequence.
Examples
========
>>> from sympy.utilities.iterables import postfixes
>>> list(postfixes([1,2,3,4]))
[[4], [3, 4], [2, 3, 4], [1, 2, 3, 4]]
"""
n = len(seq)
for i in range(n):
yield seq[n - i - 1:]
def topological_sort(graph, key=None):
r"""
Topological sort of graph's vertices.
Parameters
==========
``graph`` : ``tuple[list, list[tuple[T, T]]``
A tuple consisting of a list of vertices and a list of edges of
a graph to be sorted topologically.
``key`` : ``callable[T]`` (optional)
Ordering key for vertices on the same level. By default the natural
(e.g. lexicographic) ordering is used (in this case the base type
must implement ordering relations).
Examples
========
Consider a graph::
+---+ +---+ +---+
| 7 |\ | 5 | | 3 |
+---+ \ +---+ +---+
| _\___/ ____ _/ |
| / \___/ \ / |
V V V V |
+----+ +---+ |
| 11 | | 8 | |
+----+ +---+ |
| | \____ ___/ _ |
| \ \ / / \ |
V \ V V / V V
+---+ \ +---+ | +----+
| 2 | | | 9 | | | 10 |
+---+ | +---+ | +----+
\________/
where vertices are integers. This graph can be encoded using
elementary Python's data structures as follows::
>>> V = [2, 3, 5, 7, 8, 9, 10, 11]
>>> E = [(7, 11), (7, 8), (5, 11), (3, 8), (3, 10),
... (11, 2), (11, 9), (11, 10), (8, 9)]
To compute a topological sort for graph ``(V, E)`` issue::
>>> from sympy.utilities.iterables import topological_sort
>>> topological_sort((V, E))
[3, 5, 7, 8, 11, 2, 9, 10]
If specific tie breaking approach is needed, use ``key`` parameter::
>>> topological_sort((V, E), key=lambda v: -v)
[7, 5, 11, 3, 10, 8, 9, 2]
Only acyclic graphs can be sorted. If the input graph has a cycle,
then :py:exc:`ValueError` will be raised::
>>> topological_sort((V, E + [(10, 7)]))
Traceback (most recent call last):
...
ValueError: cycle detected
.. seealso:: http://en.wikipedia.org/wiki/Topological_sorting
"""
V, E = graph
L = []
S = set(V)
E = list(E)
for v, u in E:
S.discard(u)
if key is None:
key = lambda value: value
S = sorted(S, key=key, reverse=True)
while S:
node = S.pop()
L.append(node)
for u, v in list(E):
if u == node:
E.remove((u, v))
for _u, _v in E:
if v == _v:
break
else:
kv = key(v)
for i, s in enumerate(S):
ks = key(s)
if kv > ks:
S.insert(i, v)
break
else:
S.append(v)
if E:
raise ValueError("cycle detected")
else:
return L
def rotate_left(x, y):
"""
Left rotates a list x by the number of steps specified
in y.
Examples
========
>>> from sympy.utilities.iterables import rotate_left
>>> a = [0, 1, 2]
>>> rotate_left(a, 1)
[1, 2, 0]
"""
if len(x) == 0:
return []
y = y % len(x)
return x[y:] + x[:y]
def rotate_right(x, y):
"""
Right rotates a list x by the number of steps specified
in y.
Examples
========
>>> from sympy.utilities.iterables import rotate_right
>>> a = [0, 1, 2]
>>> rotate_right(a, 1)
[2, 0, 1]
"""
if len(x) == 0:
return []
y = len(x) - y % len(x)
return x[y:] + x[:y]
def multiset_combinations(m, n, g=None):
"""
Return the unique combinations of size ``n`` from multiset ``m``.
Examples
========
>>> from sympy.utilities.iterables import multiset_combinations
>>> from itertools import combinations
>>> [''.join(i) for i in multiset_combinations('baby', 3)]
['abb', 'aby', 'bby']
>>> def count(f, s): return len(list(f(s, 3)))
The number of combinations depends on the number of letters; the
number of unique combinations depends on how the letters are
repeated.
>>> s1 = 'abracadabra'
>>> s2 = 'banana tree'
>>> count(combinations, s1), count(multiset_combinations, s1)
(165, 23)
>>> count(combinations, s2), count(multiset_combinations, s2)
(165, 54)
"""
if g is None:
if type(m) is dict:
if n > sum(m.values()):
return
g = [[k, m[k]] for k in ordered(m)]
else:
m = list(m)
if n > len(m):
return
try:
m = multiset(m)
g = [(k, m[k]) for k in ordered(m)]
except TypeError:
m = list(ordered(m))
g = [list(i) for i in group(m, multiple=False)]
del m
if sum(v for k, v in g) < n or not n:
yield []
else:
for i, (k, v) in enumerate(g):
if v >= n:
yield [k]*n
v = n - 1
for v in range(min(n, v), 0, -1):
for j in multiset_combinations(None, n - v, g[i + 1:]):
rv = [k]*v + j
if len(rv) == n:
yield rv
def multiset_permutations(m, size=None, g=None):
"""
Return the unique permutations of multiset ``m``.
Examples
========
>>> from sympy.utilities.iterables import multiset_permutations
>>> from sympy import factorial
>>> [''.join(i) for i in multiset_permutations('aab')]
['aab', 'aba', 'baa']
>>> factorial(len('banana'))
720
>>> len(list(multiset_permutations('banana')))
60
"""
if g is None:
if type(m) is dict:
g = [[k, m[k]] for k in ordered(m)]
else:
m = list(ordered(m))
g = [list(i) for i in group(m, multiple=False)]
del m
do = [gi for gi in g if gi[1] > 0]
SUM = sum([gi[1] for gi in do])
if not do or size is not None and (size > SUM or size < 1):
if size < 1:
yield []
return
elif size == 1:
for k, v in do:
yield [k]
elif len(do) == 1:
k, v = do[0]
v = v if size is None else (size if size <= v else 0)
yield [k for i in range(v)]
elif all(v == 1 for k, v in do):
for p in permutations([k for k, v in do], size):
yield list(p)
else:
size = size if size is not None else SUM
for i, (k, v) in enumerate(do):
do[i][1] -= 1
for j in multiset_permutations(None, size - 1, do):
if j:
yield [k] + j
do[i][1] += 1
def _partition(seq, vector, m=None):
"""
Return the partion of seq as specified by the partition vector.
Examples
========
>>> from sympy.utilities.iterables import _partition
>>> _partition('abcde', [1, 0, 1, 2, 0])
[['b', 'e'], ['a', 'c'], ['d']]
Specifying the number of bins in the partition is optional:
>>> _partition('abcde', [1, 0, 1, 2, 0], 3)
[['b', 'e'], ['a', 'c'], ['d']]
The output of _set_partitions can be passed as follows:
>>> output = (3, [1, 0, 1, 2, 0])
>>> _partition('abcde', *output)
[['b', 'e'], ['a', 'c'], ['d']]
See Also
========
combinatorics.partitions.Partition.from_rgs()
"""
if m is None:
m = max(vector) + 1
elif type(vector) is int: # entered as m, vector
vector, m = m, vector
p = [[] for i in range(m)]
for i, v in enumerate(vector):
p[v].append(seq[i])
return p
def _set_partitions(n):
"""Cycle through all partions of n elements, yielding the
current number of partitions, ``m``, and a mutable list, ``q``
such that element[i] is in part q[i] of the partition.
NOTE: ``q`` is modified in place and generally should not be changed
between function calls.
Examples
========
>>> from sympy.utilities.iterables import _set_partitions, _partition
>>> for m, q in _set_partitions(3):
... print('%s %s %s' % (m, q, _partition('abc', q, m)))
1 [0, 0, 0] [['a', 'b', 'c']]
2 [0, 0, 1] [['a', 'b'], ['c']]
2 [0, 1, 0] [['a', 'c'], ['b']]
2 [0, 1, 1] [['a'], ['b', 'c']]
3 [0, 1, 2] [['a'], ['b'], ['c']]
Notes
=====
This algorithm is similar to, and solves the same problem as,
Algorithm 7.2.1.5H, from volume 4A of Knuth's The Art of Computer
Programming. Knuth uses the term "restricted growth string" where
this code refers to a "partition vector". In each case, the meaning is
the same: the value in the ith element of the vector specifies to
which part the ith set element is to be assigned.
At the lowest level, this code implements an n-digit big-endian
counter (stored in the array q) which is incremented (with carries) to
get the next partition in the sequence. A special twist is that a
digit is constrained to be at most one greater than the maximum of all
the digits to the left of it. The array p maintains this maximum, so
that the code can efficiently decide when a digit can be incremented
in place or whether it needs to be reset to 0 and trigger a carry to
the next digit. The enumeration starts with all the digits 0 (which
corresponds to all the set elements being assigned to the same 0th
part), and ends with 0123...n, which corresponds to each set element
being assigned to a different, singleton, part.
This routine was rewritten to use 0-based lists while trying to
preserve the beauty and efficiency of the original algorithm.
Reference
=========
Nijenhuis, Albert and Wilf, Herbert. (1978) Combinatorial Algorithms,
2nd Ed, p 91, algorithm "nexequ". Available online from
http://www.math.upenn.edu/~wilf/website/CombAlgDownld.html (viewed
November 17, 2012).
"""
p = [0]*n
q = [0]*n
nc = 1
yield nc, q
while nc != n:
m = n
while 1:
m -= 1
i = q[m]
if p[i] != 1:
break
q[m] = 0
i += 1
q[m] = i
m += 1
nc += m - n
p[0] += n - m
if i == nc:
p[nc] = 0
nc += 1
p[i - 1] -= 1
p[i] += 1
yield nc, q
def multiset_partitions(multiset, m=None):
"""
Return unique partitions of the given multiset (in list form).
If ``m`` is None, all multisets will be returned, otherwise only
partitions with ``m`` parts will be returned.
If ``multiset`` is an integer, a range [0, 1, ..., multiset - 1]
will be supplied.
Examples
========
>>> from sympy.utilities.iterables import multiset_partitions
>>> list(multiset_partitions([1, 2, 3, 4], 2))
[[[1, 2, 3], [4]], [[1, 2, 4], [3]], [[1, 2], [3, 4]],
[[1, 3, 4], [2]], [[1, 3], [2, 4]], [[1, 4], [2, 3]],
[[1], [2, 3, 4]]]
>>> list(multiset_partitions([1, 2, 3, 4], 1))
[[[1, 2, 3, 4]]]
Only unique partitions are returned and these will be returned in a
canonical order regardless of the order of the input:
>>> a = [1, 2, 2, 1]
>>> ans = list(multiset_partitions(a, 2))
>>> a.sort()
>>> list(multiset_partitions(a, 2)) == ans
True
>>> a = range(3, 1, -1)
>>> (list(multiset_partitions(a)) ==
... list(multiset_partitions(sorted(a))))
True
If m is omitted then all partitions will be returned:
>>> list(multiset_partitions([1, 1, 2]))
[[[1, 1, 2]], [[1, 1], [2]], [[1, 2], [1]], [[1], [1], [2]]]
>>> list(multiset_partitions([1]*3))
[[[1, 1, 1]], [[1], [1, 1]], [[1], [1], [1]]]
Counting
========
The number of partitions of a set is given by the bell number:
>>> from sympy import bell
>>> len(list(multiset_partitions(5))) == bell(5) == 52
True
The number of partitions of length k from a set of size n is given by the
Stirling Number of the 2nd kind:
>>> def S2(n, k):
... from sympy import Dummy, binomial, factorial, Sum
... if k > n:
... return 0
... j = Dummy()
... arg = (-1)**(k-j)*j**n*binomial(k,j)
... return 1/factorial(k)*Sum(arg,(j,0,k)).doit()
...
>>> S2(5, 2) == len(list(multiset_partitions(5, 2))) == 15
True
These comments on counting apply to *sets*, not multisets.
Notes
=====
When all the elements are the same in the multiset, the order
of the returned partitions is determined by the ``partitions``
routine. If one is counting partitions then it is better to use
the ``nT`` function.
See Also
========
partitions
sympy.combinatorics.partitions.Partition
sympy.combinatorics.partitions.IntegerPartition
sympy.functions.combinatorial.numbers.nT
"""
# This function looks at the supplied input and dispatches to
# several special-case routines as they apply.
if type(multiset) is int:
n = multiset
if m and m > n:
return
multiset = list(range(n))
if m == 1:
yield [multiset[:]]
return
# If m is not None, it can sometimes be faster to use
# MultisetPartitionTraverser.enum_range() even for inputs
# which are sets. Since the _set_partitions code is quite
# fast, this is only advantageous when the overall set
# partitions outnumber those with the desired number of parts
# by a large factor. (At least 60.) Such a switch is not
# currently implemented.
for nc, q in _set_partitions(n):
if m is None or nc == m:
rv = [[] for i in range(nc)]
for i in range(n):
rv[q[i]].append(multiset[i])
yield rv
return
if len(multiset) == 1 and type(multiset) is str:
multiset = [multiset]
if not has_variety(multiset):
# Only one component, repeated n times. The resulting
# partitions correspond to partitions of integer n.
n = len(multiset)
if m and m > n:
return
if m == 1:
yield [multiset[:]]
return
x = multiset[:1]
for size, p in partitions(n, m, size=True):
if m is None or size == m:
rv = []
for k in sorted(p):
rv.extend([x*k]*p[k])
yield rv
else:
multiset = list(ordered(multiset))
n = len(multiset)
if m and m > n:
return
if m == 1:
yield [multiset[:]]
return
# Split the information of the multiset into two lists -
# one of the elements themselves, and one (of the same length)
# giving the number of repeats for the corresponding element.
elements, multiplicities = zip(*group(multiset, False))
if len(elements) < len(multiset):
# General case - multiset with more than one distinct element
# and at least one element repeated more than once.
if m:
mpt = MultisetPartitionTraverser()
for state in mpt.enum_range(multiplicities, m-1, m):
yield list_visitor(state, elements)
else:
for state in multiset_partitions_taocp(multiplicities):
yield list_visitor(state, elements)
else:
# Set partitions case - no repeated elements. Pretty much
# same as int argument case above, with same possible, but
# currently unimplemented optimization for some cases when
# m is not None
for nc, q in _set_partitions(n):
if m is None or nc == m:
rv = [[] for i in range(nc)]
for i in range(n):
rv[q[i]].append(i)
yield [[multiset[j] for j in i] for i in rv]
def partitions(n, m=None, k=None, size=False):
"""Generate all partitions of positive integer, n.
Parameters
==========
``m`` : integer (default gives partitions of all sizes)
limits number of parts in partition (mnemonic: m, maximum parts)
``k`` : integer (default gives partitions number from 1 through n)
limits the numbers that are kept in the partition (mnemonic: k, keys)
``size`` : bool (default False, only partition is returned)
when ``True`` then (M, P) is returned where M is the sum of the
multiplicities and P is the generated partition.
Each partition is represented as a dictionary, mapping an integer
to the number of copies of that integer in the partition. For example,
the first partition of 4 returned is {4: 1}, "4: one of them".
Examples
========
>>> from sympy.utilities.iterables import partitions
The numbers appearing in the partition (the key of the returned dict)
are limited with k:
>>> for p in partitions(6, k=2): # doctest: +SKIP
... print(p)
{2: 3}
{1: 2, 2: 2}
{1: 4, 2: 1}
{1: 6}
The maximum number of parts in the partition (the sum of the values in
the returned dict) are limited with m (default value, None, gives
partitions from 1 through n):
>>> for p in partitions(6, m=2): # doctest: +SKIP
... print(p)
...
{6: 1}
{1: 1, 5: 1}
{2: 1, 4: 1}
{3: 2}
Note that the _same_ dictionary object is returned each time.
This is for speed: generating each partition goes quickly,
taking constant time, independent of n.
>>> [p for p in partitions(6, k=2)]
[{1: 6}, {1: 6}, {1: 6}, {1: 6}]
If you want to build a list of the returned dictionaries then
make a copy of them:
>>> [p.copy() for p in partitions(6, k=2)] # doctest: +SKIP
[{2: 3}, {1: 2, 2: 2}, {1: 4, 2: 1}, {1: 6}]
>>> [(M, p.copy()) for M, p in partitions(6, k=2, size=True)] # doctest: +SKIP
[(3, {2: 3}), (4, {1: 2, 2: 2}), (5, {1: 4, 2: 1}), (6, {1: 6})]
Reference:
modified from Tim Peter's version to allow for k and m values:
code.activestate.com/recipes/218332-generator-for-integer-partitions/
See Also
========
sympy.combinatorics.partitions.Partition
sympy.combinatorics.partitions.IntegerPartition
"""
if (
n <= 0 or
m is not None and m < 1 or
k is not None and k < 1 or
m and k and m*k < n):
# the empty set is the only way to handle these inputs
# and returning {} to represent it is consistent with
# the counting convention, e.g. nT(0) == 1.
if size:
yield 0, {}
else:
yield {}
return
if m is None:
m = n
else:
m = min(m, n)
if n == 0:
if size:
yield 1, {0: 1}
else:
yield {0: 1}
return
k = min(k or n, n)
n, m, k = as_int(n), as_int(m), as_int(k)
q, r = divmod(n, k)
ms = {k: q}
keys = [k] # ms.keys(), from largest to smallest
if r:
ms[r] = 1
keys.append(r)
room = m - q - bool(r)
if size:
yield sum(ms.values()), ms
else:
yield ms
while keys != [1]:
# Reuse any 1's.
if keys[-1] == 1:
del keys[-1]
reuse = ms.pop(1)
room += reuse
else:
reuse = 0
while 1:
# Let i be the smallest key larger than 1. Reuse one
# instance of i.
i = keys[-1]
newcount = ms[i] = ms[i] - 1
reuse += i
if newcount == 0:
del keys[-1], ms[i]
room += 1
# Break the remainder into pieces of size i-1.
i -= 1
q, r = divmod(reuse, i)
need = q + bool(r)
if need > room:
if not keys:
return
continue
ms[i] = q
keys.append(i)
if r:
ms[r] = 1
keys.append(r)
break
room -= need
if size:
yield sum(ms.values()), ms
else:
yield ms
def ordered_partitions(n, m=None, sort=True):
"""Generates ordered partitions of integer ``n``.
Parameters
==========
``m`` : integer (default gives partitions of all sizes) else only
those with size m. In addition, if ``m`` is not None then
partitions are generated *in place* (see examples).
``sort`` : bool (default True) controls whether partitions are
returned in sorted order when ``m`` is not None; when False,
the partitions are returned as fast as possible with elements
sorted, but when m|n the partitions will not be in
ascending lexicographical order.
Examples
========
>>> from sympy.utilities.iterables import ordered_partitions
All partitions of 5 in ascending lexicographical:
>>> for p in ordered_partitions(5):
... print(p)
[1, 1, 1, 1, 1]
[1, 1, 1, 2]
[1, 1, 3]
[1, 2, 2]
[1, 4]
[2, 3]
[5]
Only partitions of 5 with two parts:
>>> for p in ordered_partitions(5, 2):
... print(p)
[1, 4]
[2, 3]
When ``m`` is given, a given list objects will be used more than
once for speed reasons so you will not see the correct partitions
unless you make a copy of each as it is generated:
>>> [p for p in ordered_partitions(7, 3)]
[[1, 1, 1], [1, 1, 1], [1, 1, 1], [2, 2, 2]]
>>> [list(p) for p in ordered_partitions(7, 3)]
[[1, 1, 5], [1, 2, 4], [1, 3, 3], [2, 2, 3]]
When ``n`` is a multiple of ``m``, the elements are still sorted
but the partitions themselves will be *unordered* if sort is False;
the default is to return them in ascending lexicographical order.
>>> for p in ordered_partitions(6, 2):
... print(p)
[1, 5]
[2, 4]
[3, 3]
But if speed is more important than ordering, sort can be set to
False:
>>> for p in ordered_partitions(6, 2, sort=False):
... print(p)
[1, 5]
[3, 3]
[2, 4]
References
==========
.. [1] Generating Integer Partitions, [online],
Available: http://jeromekelleher.net/generating-integer-partitions.html
.. [2] Jerome Kelleher and Barry O'Sullivan, "Generating All
Partitions: A Comparison Of Two Encodings", [online],
Available: http://arxiv.org/pdf/0909.2331v2.pdf
"""
if n < 1 or m is not None and m < 1:
# the empty set is the only way to handle these inputs
# and returning {} to represent it is consistent with
# the counting convention, e.g. nT(0) == 1.
yield []
return
if m is None:
# The list `a`'s leading elements contain the partition in which
# y is the biggest element and x is either the same as y or the
# 2nd largest element; v and w are adjacent element indices
# to which x and y are being assigned, respectively.
a = [1]*n
y = -1
v = n
while v > 0:
v -= 1
x = a[v] + 1
while y >= 2 * x:
a[v] = x
y -= x
v += 1
w = v + 1
while x <= y:
a[v] = x
a[w] = y
yield a[:w + 1]
x += 1
y -= 1
a[v] = x + y
y = a[v] - 1
yield a[:w]
elif m == 1:
yield [n]
elif n == m:
yield [1]*n
else:
# recursively generate partitions of size m
for b in range(1, n//m + 1):
a = [b]*m
x = n - b*m
if not x:
if sort:
yield a
elif not sort and x <= m:
for ax in ordered_partitions(x, sort=False):
mi = len(ax)
a[-mi:] = [i + b for i in ax]
yield a
a[-mi:] = [b]*mi
else:
for mi in range(1, m):
for ax in ordered_partitions(x, mi, sort=True):
a[-mi:] = [i + b for i in ax]
yield a
a[-mi:] = [b]*mi
def binary_partitions(n):
"""
Generates the binary partition of n.
A binary partition consists only of numbers that are
powers of two. Each step reduces a 2**(k+1) to 2**k and
2**k. Thus 16 is converted to 8 and 8.
Reference: TAOCP 4, section 7.2.1.5, problem 64
Examples
========
>>> from sympy.utilities.iterables import binary_partitions
>>> for i in binary_partitions(5):
... print(i)
...
[4, 1]
[2, 2, 1]
[2, 1, 1, 1]
[1, 1, 1, 1, 1]
"""
from math import ceil, log
pow = int(2**(ceil(log(n, 2))))
sum = 0
partition = []
while pow:
if sum + pow <= n:
partition.append(pow)
sum += pow
pow >>= 1
last_num = len(partition) - 1 - (n & 1)
while last_num >= 0:
yield partition
if partition[last_num] == 2:
partition[last_num] = 1
partition.append(1)
last_num -= 1
continue
partition.append(1)
partition[last_num] >>= 1
x = partition[last_num + 1] = partition[last_num]
last_num += 1
while x > 1:
if x <= len(partition) - last_num - 1:
del partition[-x + 1:]
last_num += 1
partition[last_num] = x
else:
x >>= 1
yield [1]*n
def has_dups(seq):
"""Return True if there are any duplicate elements in ``seq``.
Examples
========
>>> from sympy.utilities.iterables import has_dups
>>> from sympy import Dict, Set
>>> has_dups((1, 2, 1))
True
>>> has_dups(range(3))
False
>>> all(has_dups(c) is False for c in (set(), Set(), dict(), Dict()))
True
"""
from sympy.core.containers import Dict
from sympy.sets.sets import Set
if isinstance(seq, (dict, set, Dict, Set)):
return False
uniq = set()
return any(True for s in seq if s in uniq or uniq.add(s))
def has_variety(seq):
"""Return True if there are any different elements in ``seq``.
Examples
========
>>> from sympy.utilities.iterables import has_variety
>>> has_variety((1, 2, 1))
True
>>> has_variety((1, 1, 1))
False
"""
for i, s in enumerate(seq):
if i == 0:
sentinel = s
else:
if s != sentinel:
return True
return False
def uniq(seq, result=None):
"""
Yield unique elements from ``seq`` as an iterator. The second
parameter ``result`` is used internally; it is not necessary to pass
anything for this.
Examples
========
>>> from sympy.utilities.iterables import uniq
>>> dat = [1, 4, 1, 5, 4, 2, 1, 2]
>>> type(uniq(dat)) in (list, tuple)
False
>>> list(uniq(dat))
[1, 4, 5, 2]
>>> list(uniq(x for x in dat))
[1, 4, 5, 2]
>>> list(uniq([[1], [2, 1], [1]]))
[[1], [2, 1]]
"""
try:
seen = set()
result = result or []
for i, s in enumerate(seq):
if not (s in seen or seen.add(s)):
yield s
except TypeError:
if s not in result:
yield s
result.append(s)
if hasattr(seq, '__getitem__'):
for s in uniq(seq[i + 1:], result):
yield s
else:
for s in uniq(seq, result):
yield s
def generate_bell(n):
"""Return permutations of [0, 1, ..., n - 1] such that each permutation
differs from the last by the exchange of a single pair of neighbors.
The ``n!`` permutations are returned as an iterator. In order to obtain
the next permutation from a random starting permutation, use the
``next_trotterjohnson`` method of the Permutation class (which generates
the same sequence in a different manner).
Examples
========
>>> from itertools import permutations
>>> from sympy.utilities.iterables import generate_bell
>>> from sympy import zeros, Matrix
This is the sort of permutation used in the ringing of physical bells,
and does not produce permutations in lexicographical order. Rather, the
permutations differ from each other by exactly one inversion, and the
position at which the swapping occurs varies periodically in a simple
fashion. Consider the first few permutations of 4 elements generated
by ``permutations`` and ``generate_bell``:
>>> list(permutations(range(4)))[:5]
[(0, 1, 2, 3), (0, 1, 3, 2), (0, 2, 1, 3), (0, 2, 3, 1), (0, 3, 1, 2)]
>>> list(generate_bell(4))[:5]
[(0, 1, 2, 3), (0, 1, 3, 2), (0, 3, 1, 2), (3, 0, 1, 2), (3, 0, 2, 1)]
Notice how the 2nd and 3rd lexicographical permutations have 3 elements
out of place whereas each "bell" permutation always has only two
elements out of place relative to the previous permutation (and so the
signature (+/-1) of a permutation is opposite of the signature of the
previous permutation).
How the position of inversion varies across the elements can be seen
by tracing out where the largest number appears in the permutations:
>>> m = zeros(4, 24)
>>> for i, p in enumerate(generate_bell(4)):
... m[:, i] = Matrix([j - 3 for j in list(p)]) # make largest zero
>>> m.print_nonzero('X')
[XXX XXXXXX XXXXXX XXX]
[XX XX XXXX XX XXXX XX XX]
[X XXXX XX XXXX XX XXXX X]
[ XXXXXX XXXXXX XXXXXX ]
See Also
========
sympy.combinatorics.Permutation.next_trotterjohnson
References
==========
* http://en.wikipedia.org/wiki/Method_ringing
* http://stackoverflow.com/questions/4856615/recursive-permutation/4857018
* http://programminggeeks.com/bell-algorithm-for-permutation/
* http://en.wikipedia.org/wiki/Steinhaus%E2%80%93Johnson%E2%80%93Trotter_algorithm
* Generating involutions, derangements, and relatives by ECO
Vincent Vajnovszki, DMTCS vol 1 issue 12, 2010
"""
n = as_int(n)
if n < 1:
raise ValueError('n must be a positive integer')
if n == 1:
yield (0,)
elif n == 2:
yield (0, 1)
yield (1, 0)
elif n == 3:
for li in [(0, 1, 2), (0, 2, 1), (2, 0, 1), (2, 1, 0), (1, 2, 0), (1, 0, 2)]:
yield li
else:
m = n - 1
op = [0] + [-1]*m
l = list(range(n))
while True:
yield tuple(l)
# find biggest element with op
big = None, -1 # idx, value
for i in range(n):
if op[i] and l[i] > big[1]:
big = i, l[i]
i, _ = big
if i is None:
break # there are no ops left
# swap it with neighbor in the indicated direction
j = i + op[i]
l[i], l[j] = l[j], l[i]
op[i], op[j] = op[j], op[i]
# if it landed at the end or if the neighbor in the same
# direction is bigger then turn off op
if j == 0 or j == m or l[j + op[j]] > l[j]:
op[j] = 0
# any element bigger to the left gets +1 op
for i in range(j):
if l[i] > l[j]:
op[i] = 1
# any element bigger to the right gets -1 op
for i in range(j + 1, n):
if l[i] > l[j]:
op[i] = -1
def generate_involutions(n):
"""
Generates involutions.
An involution is a permutation that when multiplied
by itself equals the identity permutation. In this
implementation the involutions are generated using
Fixed Points.
Alternatively, an involution can be considered as
a permutation that does not contain any cycles with
a length that is greater than two.
Reference:
http://mathworld.wolfram.com/PermutationInvolution.html
Examples
========
>>> from sympy.utilities.iterables import generate_involutions
>>> list(generate_involutions(3))
[(0, 1, 2), (0, 2, 1), (1, 0, 2), (2, 1, 0)]
>>> len(list(generate_involutions(4)))
10
"""
idx = list(range(n))
for p in permutations(idx):
for i in idx:
if p[p[i]] != i:
break
else:
yield p
def generate_derangements(perm):
"""
Routine to generate unique derangements.
TODO: This will be rewritten to use the
ECO operator approach once the permutations
branch is in master.
Examples
========
>>> from sympy.utilities.iterables import generate_derangements
>>> list(generate_derangements([0, 1, 2]))
[[1, 2, 0], [2, 0, 1]]
>>> list(generate_derangements([0, 1, 2, 3]))
[[1, 0, 3, 2], [1, 2, 3, 0], [1, 3, 0, 2], [2, 0, 3, 1], \
[2, 3, 0, 1], [2, 3, 1, 0], [3, 0, 1, 2], [3, 2, 0, 1], \
[3, 2, 1, 0]]
>>> list(generate_derangements([0, 1, 1]))
[]
See Also
========
sympy.functions.combinatorial.factorials.subfactorial
"""
p = multiset_permutations(perm)
indices = range(len(perm))
p0 = next(p)
for pi in p:
if all(pi[i] != p0[i] for i in indices):
yield pi
def necklaces(n, k, free=False):
"""
A routine to generate necklaces that may (free=True) or may not
(free=False) be turned over to be viewed. The "necklaces" returned
are comprised of ``n`` integers (beads) with ``k`` different
values (colors). Only unique necklaces are returned.
Examples
========
>>> from sympy.utilities.iterables import necklaces, bracelets
>>> def show(s, i):
... return ''.join(s[j] for j in i)
The "unrestricted necklace" is sometimes also referred to as a
"bracelet" (an object that can be turned over, a sequence that can
be reversed) and the term "necklace" is used to imply a sequence
that cannot be reversed. So ACB == ABC for a bracelet (rotate and
reverse) while the two are different for a necklace since rotation
alone cannot make the two sequences the same.
(mnemonic: Bracelets can be viewed Backwards, but Not Necklaces.)
>>> B = [show('ABC', i) for i in bracelets(3, 3)]
>>> N = [show('ABC', i) for i in necklaces(3, 3)]
>>> set(N) - set(B)
{'ACB'}
>>> list(necklaces(4, 2))
[(0, 0, 0, 0), (0, 0, 0, 1), (0, 0, 1, 1),
(0, 1, 0, 1), (0, 1, 1, 1), (1, 1, 1, 1)]
>>> [show('.o', i) for i in bracelets(4, 2)]
['....', '...o', '..oo', '.o.o', '.ooo', 'oooo']
References
==========
http://mathworld.wolfram.com/Necklace.html
"""
return uniq(minlex(i, directed=not free) for i in
variations(list(range(k)), n, repetition=True))
def bracelets(n, k):
"""Wrapper to necklaces to return a free (unrestricted) necklace."""
return necklaces(n, k, free=True)
def generate_oriented_forest(n):
"""
This algorithm generates oriented forests.
An oriented graph is a directed graph having no symmetric pair of directed
edges. A forest is an acyclic graph, i.e., it has no cycles. A forest can
also be described as a disjoint union of trees, which are graphs in which
any two vertices are connected by exactly one simple path.
Reference:
[1] T. Beyer and S.M. Hedetniemi: constant time generation of \
rooted trees, SIAM J. Computing Vol. 9, No. 4, November 1980
[2] http://stackoverflow.com/questions/1633833/oriented-forest-taocp-algorithm-in-python
Examples
========
>>> from sympy.utilities.iterables import generate_oriented_forest
>>> list(generate_oriented_forest(4))
[[0, 1, 2, 3], [0, 1, 2, 2], [0, 1, 2, 1], [0, 1, 2, 0], \
[0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 0, 1], [0, 1, 0, 0], [0, 0, 0, 0]]
"""
P = list(range(-1, n))
while True:
yield P[1:]
if P[n] > 0:
P[n] = P[P[n]]
else:
for p in range(n - 1, 0, -1):
if P[p] != 0:
target = P[p] - 1
for q in range(p - 1, 0, -1):
if P[q] == target:
break
offset = p - q
for i in range(p, n + 1):
P[i] = P[i - offset]
break
else:
break
def minlex(seq, directed=True, is_set=False, small=None):
"""
Return a tuple where the smallest element appears first; if
``directed`` is True (default) then the order is preserved, otherwise
the sequence will be reversed if that gives a smaller ordering.
If every element appears only once then is_set can be set to True
for more efficient processing.
If the smallest element is known at the time of calling, it can be
passed and the calculation of the smallest element will be omitted.
Examples
========
>>> from sympy.combinatorics.polyhedron import minlex
>>> minlex((1, 2, 0))
(0, 1, 2)
>>> minlex((1, 0, 2))
(0, 2, 1)
>>> minlex((1, 0, 2), directed=False)
(0, 1, 2)
>>> minlex('11010011000', directed=True)
'00011010011'
>>> minlex('11010011000', directed=False)
'00011001011'
"""
is_str = isinstance(seq, str)
seq = list(seq)
if small is None:
small = min(seq, key=default_sort_key)
if is_set:
i = seq.index(small)
if not directed:
n = len(seq)
p = (i + 1) % n
m = (i - 1) % n
if default_sort_key(seq[p]) > default_sort_key(seq[m]):
seq = list(reversed(seq))
i = n - i - 1
if i:
seq = rotate_left(seq, i)
best = seq
else:
count = seq.count(small)
if count == 1 and directed:
best = rotate_left(seq, seq.index(small))
else:
# if not directed, and not a set, we can't just
# pass this off to minlex with is_set True since
# peeking at the neighbor may not be sufficient to
# make the decision so we continue...
best = seq
for i in range(count):
seq = rotate_left(seq, seq.index(small, count != 1))
if seq < best:
best = seq
# it's cheaper to rotate now rather than search
# again for these in reversed order so we test
# the reverse now
if not directed:
seq = rotate_left(seq, 1)
seq = list(reversed(seq))
if seq < best:
best = seq
seq = list(reversed(seq))
seq = rotate_right(seq, 1)
# common return
if is_str:
return ''.join(best)
return tuple(best)
def runs(seq, op=gt):
"""Group the sequence into lists in which successive elements
all compare the same with the comparison operator, ``op``:
op(seq[i + 1], seq[i]) is True from all elements in a run.
Examples
========
>>> from sympy.utilities.iterables import runs
>>> from operator import ge
>>> runs([0, 1, 2, 2, 1, 4, 3, 2, 2])
[[0, 1, 2], [2], [1, 4], [3], [2], [2]]
>>> runs([0, 1, 2, 2, 1, 4, 3, 2, 2], op=ge)
[[0, 1, 2, 2], [1, 4], [3], [2, 2]]
"""
cycles = []
seq = iter(seq)
try:
run = [next(seq)]
except StopIteration:
return []
while True:
try:
ei = next(seq)
except StopIteration:
break
if op(ei, run[-1]):
run.append(ei)
continue
else:
cycles.append(run)
run = [ei]
if run:
cycles.append(run)
return cycles
def kbins(l, k, ordered=None):
"""
Return sequence ``l`` partitioned into ``k`` bins.
Examples
========
>>> from sympy.utilities.iterables import kbins
The default is to give the items in the same order, but grouped
into k partitions without any reordering:
>>> from __future__ import print_function
>>> for p in kbins(list(range(5)), 2):
... print(p)
...
[[0], [1, 2, 3, 4]]
[[0, 1], [2, 3, 4]]
[[0, 1, 2], [3, 4]]
[[0, 1, 2, 3], [4]]
The ``ordered`` flag which is either None (to give the simple partition
of the the elements) or is a 2 digit integer indicating whether the order of
the bins and the order of the items in the bins matters. Given::
A = [[0], [1, 2]]
B = [[1, 2], [0]]
C = [[2, 1], [0]]
D = [[0], [2, 1]]
the following values for ``ordered`` have the shown meanings::
00 means A == B == C == D
01 means A == B
10 means A == D
11 means A == A
>>> for ordered in [None, 0, 1, 10, 11]:
... print('ordered = %s' % ordered)
... for p in kbins(list(range(3)), 2, ordered=ordered):
... print(' %s' % p)
...
ordered = None
[[0], [1, 2]]
[[0, 1], [2]]
ordered = 0
[[0, 1], [2]]
[[0, 2], [1]]
[[0], [1, 2]]
ordered = 1
[[0], [1, 2]]
[[0], [2, 1]]
[[1], [0, 2]]
[[1], [2, 0]]
[[2], [0, 1]]
[[2], [1, 0]]
ordered = 10
[[0, 1], [2]]
[[2], [0, 1]]
[[0, 2], [1]]
[[1], [0, 2]]
[[0], [1, 2]]
[[1, 2], [0]]
ordered = 11
[[0], [1, 2]]
[[0, 1], [2]]
[[0], [2, 1]]
[[0, 2], [1]]
[[1], [0, 2]]
[[1, 0], [2]]
[[1], [2, 0]]
[[1, 2], [0]]
[[2], [0, 1]]
[[2, 0], [1]]
[[2], [1, 0]]
[[2, 1], [0]]
See Also
========
partitions, multiset_partitions
"""
def partition(lista, bins):
# EnricoGiampieri's partition generator from
# http://stackoverflow.com/questions/13131491/
# partition-n-items-into-k-bins-in-python-lazily
if len(lista) == 1 or bins == 1:
yield [lista]
elif len(lista) > 1 and bins > 1:
for i in range(1, len(lista)):
for part in partition(lista[i:], bins - 1):
if len([lista[:i]] + part) == bins:
yield [lista[:i]] + part
if ordered is None:
for p in partition(l, k):
yield p
elif ordered == 11:
for pl in multiset_permutations(l):
pl = list(pl)
for p in partition(pl, k):
yield p
elif ordered == 00:
for p in multiset_partitions(l, k):
yield p
elif ordered == 10:
for p in multiset_partitions(l, k):
for perm in permutations(p):
yield list(perm)
elif ordered == 1:
for kgot, p in partitions(len(l), k, size=True):
if kgot != k:
continue
for li in multiset_permutations(l):
rv = []
i = j = 0
li = list(li)
for size, multiplicity in sorted(p.items()):
for m in range(multiplicity):
j = i + size
rv.append(li[i: j])
i = j
yield rv
else:
raise ValueError(
'ordered must be one of 00, 01, 10 or 11, not %s' % ordered)
def permute_signs(t):
"""Return iterator in which the signs of non-zero elements
of t are permuted.
Examples
========
>>> from sympy.utilities.iterables import permute_signs
>>> list(permute_signs((0, 1, 2)))
[(0, 1, 2), (0, -1, 2), (0, 1, -2), (0, -1, -2)]
"""
for signs in cartes(*[(1, -1)]*(len(t) - t.count(0))):
signs = list(signs)
yield type(t)([i*signs.pop() if i else i for i in t])
def signed_permutations(t):
"""Return iterator in which the signs of non-zero elements
of t and the order of the elements are permuted.
Examples
========
>>> from sympy.utilities.iterables import signed_permutations
>>> list(signed_permutations((0, 1, 2)))
[(0, 1, 2), (0, -1, 2), (0, 1, -2), (0, -1, -2), (0, 2, 1),
(0, -2, 1), (0, 2, -1), (0, -2, -1), (1, 0, 2), (-1, 0, 2),
(1, 0, -2), (-1, 0, -2), (1, 2, 0), (-1, 2, 0), (1, -2, 0),
(-1, -2, 0), (2, 0, 1), (-2, 0, 1), (2, 0, -1), (-2, 0, -1),
(2, 1, 0), (-2, 1, 0), (2, -1, 0), (-2, -1, 0)]
"""
return (type(t)(i) for j in permutations(t)
for i in permute_signs(j))
| 65,711 | 27.935271 | 92 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/source.py
|
"""
This module adds several functions for interactive source code inspection.
"""
from __future__ import print_function, division
import inspect
def source(object):
"""
Prints the source code of a given object.
"""
print('In file: %s' % inspect.getsourcefile(object))
print(inspect.getsource(object))
def get_class(lookup_view):
"""
Convert a string version of a class name to the object.
For example, get_class('sympy.core.Basic') will return
class Basic located in module sympy.core
"""
if isinstance(lookup_view, str):
mod_name, func_name = get_mod_func(lookup_view)
if func_name != '':
lookup_view = getattr(
__import__(mod_name, {}, {}, ['*']), func_name)
if not callable(lookup_view):
raise AttributeError(
"'%s.%s' is not a callable." % (mod_name, func_name))
return lookup_view
def get_mod_func(callback):
"""
splits the string path to a class into a string path to the module
and the name of the class. For example:
>>> from sympy.utilities.source import get_mod_func
>>> get_mod_func('sympy.core.basic.Basic')
('sympy.core.basic', 'Basic')
"""
dot = callback.rfind('.')
if dot == -1:
return callback, ''
return callback[:dot], callback[dot + 1:]
| 1,368 | 26.38 | 74 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/enumerative.py
|
from __future__ import print_function, division
from sympy.core.compatibility import range
"""
Algorithms and classes to support enumerative combinatorics.
Currently just multiset partitions, but more could be added.
Terminology (following Knuth, algorithm 7.1.2.5M TAOCP)
*multiset* aaabbcccc has a *partition* aaabc | bccc
The submultisets, aaabc and bccc of the partition are called
*parts*, or sometimes *vectors*. (Knuth notes that multiset
partitions can be thought of as partitions of vectors of integers,
where the ith element of the vector gives the multiplicity of
element i.)
The values a, b and c are *components* of the multiset. These
correspond to elements of a set, but in a multiset can be present
with a multiplicity greater than 1.
The algorithm deserves some explanation.
Think of the part aaabc from the multiset above. If we impose an
ordering on the components of the multiset, we can represent a part
with a vector, in which the value of the first element of the vector
corresponds to the multiplicity of the first component in that
part. Thus, aaabc can be represented by the vector [3, 1, 1]. We
can also define an ordering on parts, based on the lexicographic
ordering of the vector (leftmost vector element, i.e., the element
with the smallest component number, is the most significant), so
that [3, 1, 1] > [3, 1, 0] and [3, 1, 1] > [2, 1, 4]. The ordering
on parts can be extended to an ordering on partitions: First, sort
the parts in each partition, left-to-right in decreasing order. Then
partition A is greater than partition B if A's leftmost/greatest
part is greater than B's leftmost part. If the leftmost parts are
equal, compare the second parts, and so on.
In this ordering, the greatest partion of a given multiset has only
one part. The least partition is the one in which the components
are spread out, one per part.
The enumeration algorithms in this file yield the partitions of the
argument multiset in decreasing order. The main data structure is a
stack of parts, corresponding to the current partition. An
important invariant is that the parts on the stack are themselves in
decreasing order. This data structure is decremented to find the
next smaller partition. Most often, decrementing the partition will
only involve adjustments to the smallest parts at the top of the
stack, much as adjacent integers *usually* differ only in their last
few digits.
Knuth's algorithm uses two main operations on parts:
Decrement - change the part so that it is smaller in the
(vector) lexicographic order, but reduced by the smallest amount possible.
For example, if the multiset has vector [5,
3, 1], and the bottom/greatest part is [4, 2, 1], this part would
decrement to [4, 2, 0], while [4, 0, 0] would decrement to [3, 3,
1]. A singleton part is never decremented -- [1, 0, 0] is not
decremented to [0, 3, 1]. Instead, the decrement operator needs
to fail for this case. In Knuth's psuedocode, the decrement
operator is step m5.
Spread unallocated multiplicity - Once a part has been decremented,
it cannot be the rightmost part in the partition. There is some
multiplicity that has not been allocated, and new parts must be
created above it in the stack to use up this multiplicity. To
maintain the invariant that the parts on the stack are in
decreasing order, these new parts must be less than or equal to
the decremented part.
For example, if the multiset is [5, 3, 1], and its most
significant part has just been decremented to [5, 3, 0], the
spread operation will add a new part so that the stack becomes
[[5, 3, 0], [0, 0, 1]]. If the most significant part (for the
same multiset) has been decremented to [2, 0, 0] the stack becomes
[[2, 0, 0], [2, 0, 0], [1, 3, 1]]. In the psuedocode, the spread
operation for one part is step m2. The complete spread operation
is a loop of steps m2 and m3.
In order to facilitate the spread operation, Knuth stores, for each
component of each part, not just the multiplicity of that component
in the part, but also the total multiplicity available for this
component in this part or any lesser part above it on the stack.
One added twist is that Knuth does not represent the part vectors as
arrays. Instead, he uses a sparse representation, in which a
component of a part is represented as a component number (c), plus
the multiplicity of the component in that part (v) as well as the
total multiplicity available for that component (u). This saves
time that would be spent skipping over zeros.
"""
class PartComponent(object):
"""Internal class used in support of the multiset partitions
enumerators and the associated visitor functions.
Represents one component of one part of the current partition.
A stack of these, plus an auxiliary frame array, f, represents a
partition of the multiset.
Knuth's psuedocode makes c, u, and v separate arrays.
"""
__slots__ = ('c', 'u', 'v')
def __init__(self):
self.c = 0 # Component number
self.u = 0 # The as yet unpartitioned amount in component c
# *before* it is allocated by this triple
self.v = 0 # Amount of c component in the current part
# (v<=u). An invariant of the representation is
# that the next higher triple for this component
# (if there is one) will have a value of u-v in
# its u attribute.
def __repr__(self):
"for debug/algorithm animation purposes"
return 'c:%d u:%d v:%d' % (self.c, self.u, self.v)
def __eq__(self, other):
"""Define value oriented equality, which is useful for testers"""
return (isinstance(other, self.__class__) and
self.c == other.c and
self.u == other.u and
self.v == other.v)
def __ne__(self, other):
"""Defined for consistency with __eq__"""
return not self.__eq__(other)
# This function tries to be a faithful implementation of algorithm
# 7.1.2.5M in Volume 4A, Combinatoral Algorithms, Part 1, of The Art
# of Computer Programming, by Donald Knuth. This includes using
# (mostly) the same variable names, etc. This makes for rather
# low-level Python.
# Changes from Knuth's psuedocode include
# - use PartComponent struct/object instead of 3 arrays
# - make the function a generator
# - map (with some difficulty) the GOTOs to Python control structures.
# - Knuth uses 1-based numbering for components, this code is 0-based
# - renamed variable l to lpart.
# - flag variable x takes on values True/False instead of 1/0
#
def multiset_partitions_taocp(multiplicities):
"""Enumerates partitions of a multiset.
Parameters
==========
multiplicities
list of integer multiplicities of the components of the multiset.
Yields
======
state
Internal data structure which encodes a particular partition.
This output is then usually processed by a vistor function
which combines the information from this data structure with
the components themselves to produce an actual partition.
Unless they wish to create their own visitor function, users will
have little need to look inside this data structure. But, for
reference, it is a 3-element list with components:
f
is a frame array, which is used to divide pstack into parts.
lpart
points to the base of the topmost part.
pstack
is an array of PartComponent objects.
The ``state`` output offers a peek into the internal data
structures of the enumeration function. The client should
treat this as read-only; any modification of the data
structure will cause unpredictable (and almost certainly
incorrect) results. Also, the components of ``state`` are
modified in place at each iteration. Hence, the visitor must
be called at each loop iteration. Accumulating the ``state``
instances and processing them later will not work.
Examples
========
>>> from sympy.utilities.enumerative import list_visitor
>>> from sympy.utilities.enumerative import multiset_partitions_taocp
>>> # variables components and multiplicities represent the multiset 'abb'
>>> components = 'ab'
>>> multiplicities = [1, 2]
>>> states = multiset_partitions_taocp(multiplicities)
>>> list(list_visitor(state, components) for state in states)
[[['a', 'b', 'b']],
[['a', 'b'], ['b']],
[['a'], ['b', 'b']],
[['a'], ['b'], ['b']]]
See Also
========
sympy.utilities.iterables.multiset_partitions: Takes a multiset
as input and directly yields multiset partitions. It
dispatches to a number of functions, including this one, for
implementation. Most users will find it more convenient to
use than multiset_partitions_taocp.
"""
# Important variables.
# m is the number of components, i.e., number of distinct elements
m = len(multiplicities)
# n is the cardinality, total number of elements whether or not distinct
n = sum(multiplicities)
# The main data structure, f segments pstack into parts. See
# list_visitor() for example code indicating how this internal
# state corresponds to a partition.
# Note: allocation of space for stack is conservative. Knuth's
# exercise 7.2.1.5.68 gives some indication of how to tighten this
# bound, but this is not implemented.
pstack = [PartComponent() for i in range(n * m + 1)]
f = [0] * (n + 1)
# Step M1 in Knuth (Initialize)
# Initial state - entire multiset in one part.
for j in range(m):
ps = pstack[j]
ps.c = j
ps.u = multiplicities[j]
ps.v = multiplicities[j]
# Other variables
f[0] = 0
a = 0
lpart = 0
f[1] = m
b = m # in general, current stack frame is from a to b - 1
while True:
while True:
# Step M2 (Subtract v from u)
j = a
k = b
x = False
while j < b:
pstack[k].u = pstack[j].u - pstack[j].v
if pstack[k].u == 0:
x = True
elif not x:
pstack[k].c = pstack[j].c
pstack[k].v = min(pstack[j].v, pstack[k].u)
x = pstack[k].u < pstack[j].v
k = k + 1
else: # x is True
pstack[k].c = pstack[j].c
pstack[k].v = pstack[k].u
k = k + 1
j = j + 1
# Note: x is True iff v has changed
# Step M3 (Push if nonzero.)
if k > b:
a = b
b = k
lpart = lpart + 1
f[lpart + 1] = b
# Return to M2
else:
break # Continue to M4
# M4 Visit a partition
state = [f, lpart, pstack]
yield state
# M5 (Decrease v)
while True:
j = b-1
while (pstack[j].v == 0):
j = j - 1
if j == a and pstack[j].v == 1:
# M6 (Backtrack)
if lpart == 0:
return
lpart = lpart - 1
b = a
a = f[lpart]
# Return to M5
else:
pstack[j].v = pstack[j].v - 1
for k in range(j + 1, b):
pstack[k].v = pstack[k].u
break # GOTO M2
# --------------- Visitor functions for multiset partitions ---------------
# A visitor takes the partition state generated by
# multiset_partitions_taocp or other enumerator, and produces useful
# output (such as the actual partition).
def factoring_visitor(state, primes):
"""Use with multiset_partitions_taocp to enumerate the ways a
number can be expressed as a product of factors. For this usage,
the exponents of the prime factors of a number are arguments to
the partition enumerator, while the corresponding prime factors
are input here.
Examples
========
To enumerate the factorings of a number we can think of the elements of the
partition as being the prime factors and the multiplicities as being their
exponents.
>>> from sympy.utilities.enumerative import factoring_visitor
>>> from sympy.utilities.enumerative import multiset_partitions_taocp
>>> from sympy import factorint
>>> primes, multiplicities = zip(*factorint(24).items())
>>> primes
(2, 3)
>>> multiplicities
(3, 1)
>>> states = multiset_partitions_taocp(multiplicities)
>>> list(factoring_visitor(state, primes) for state in states)
[[24], [8, 3], [12, 2], [4, 6], [4, 2, 3], [6, 2, 2], [2, 2, 2, 3]]
"""
f, lpart, pstack = state
factoring = []
for i in range(lpart + 1):
factor = 1
for ps in pstack[f[i]: f[i + 1]]:
if ps.v > 0:
factor *= primes[ps.c] ** ps.v
factoring.append(factor)
return factoring
def list_visitor(state, components):
"""Return a list of lists to represent the partition.
Examples
========
>>> from sympy.utilities.enumerative import list_visitor
>>> from sympy.utilities.enumerative import multiset_partitions_taocp
>>> states = multiset_partitions_taocp([1, 2, 1])
>>> s = next(states)
>>> list_visitor(s, 'abc') # for multiset 'a b b c'
[['a', 'b', 'b', 'c']]
>>> s = next(states)
>>> list_visitor(s, [1, 2, 3]) # for multiset '1 2 2 3
[[1, 2, 2], [3]]
"""
f, lpart, pstack = state
partition = []
for i in range(lpart+1):
part = []
for ps in pstack[f[i]:f[i+1]]:
if ps.v > 0:
part.extend([components[ps.c]] * ps.v)
partition.append(part)
return partition
class MultisetPartitionTraverser():
"""
Has methods to ``enumerate`` and ``count`` the partitions of a multiset.
This implements a refactored and extended version of Knuth's algorithm
7.1.2.5M [AOCP]_."
The enumeration methods of this class are generators and return
data structures which can be interpreted by the same visitor
functions used for the output of ``multiset_partitions_taocp``.
See Also
========
multiset_partitions_taocp
sympy.utilities.iterables.multiset_partititions
Examples
========
>>> from sympy.utilities.enumerative import MultisetPartitionTraverser
>>> m = MultisetPartitionTraverser()
>>> m.count_partitions([4,4,4,2])
127750
>>> m.count_partitions([3,3,3])
686
References
==========
.. [AOCP] Algorithm 7.1.2.5M in Volume 4A, Combinatoral Algorithms,
Part 1, of The Art of Computer Programming, by Donald Knuth.
.. [Factorisatio] On a Problem of Oppenheim concerning
"Factorisatio Numerorum" E. R. Canfield, Paul Erdos, Carl
Pomerance, JOURNAL OF NUMBER THEORY, Vol. 17, No. 1. August
1983. See section 7 for a description of an algorithm
similar to Knuth's.
.. [Yorgey] Generating Multiset Partitions, Brent Yorgey, The
Monad.Reader, Issue 8, September 2007.
"""
def __init__(self):
self.debug = False
# TRACING variables. These are useful for gathering
# statistics on the algorithm itself, but have no particular
# benefit to a user of the code.
self.k1 = 0
self.k2 = 0
self.p1 = 0
def db_trace(self, msg):
"""Useful for usderstanding/debugging the algorithms. Not
generally activated in end-user code."""
if self.debug:
letters = 'abcdefghijklmnopqrstuvwxyz'
state = [self.f, self.lpart, self.pstack]
print("DBG:", msg,
["".join(part) for part in list_visitor(state, letters)],
animation_visitor(state))
#
# Helper methods for enumeration
#
def _initialize_enumeration(self, multiplicities):
"""Allocates and initializes the partition stack.
This is called from the enumeration/counting routines, so
there is no need to call it separately."""
num_components = len(multiplicities)
# cardinality is the total number of elements, whether or not distinct
cardinality = sum(multiplicities)
# pstack is the partition stack, which is segmented by
# f into parts.
self.pstack = [PartComponent() for i in
range(num_components * cardinality + 1)]
self.f = [0] * (cardinality + 1)
# Initial state - entire multiset in one part.
for j in range(num_components):
ps = self.pstack[j]
ps.c = j
ps.u = multiplicities[j]
ps.v = multiplicities[j]
self.f[0] = 0
self.f[1] = num_components
self.lpart = 0
# The decrement_part() method corresponds to step M5 in Knuth's
# algorithm. This is the base version for enum_all(). Modified
# versions of this method are needed if we want to restrict
# sizes of the partitions produced.
def decrement_part(self, part):
"""Decrements part (a subrange of pstack), if possible, returning
True iff the part was successfully decremented.
If you think of the v values in the part as a multi-digit
integer (least significant digit on the right) this is
basically decrementing that integer, but with the extra
constraint that the leftmost digit cannot be decremented to 0.
Parameters
==========
part
The part, represented as a list of PartComponent objects,
which is to be decremented.
"""
plen = len(part)
for j in range(plen - 1, -1, -1):
if (j == 0 and part[j].v > 1) or (j > 0 and part[j].v > 0):
# found val to decrement
part[j].v -= 1
# Reset trailing parts back to maximum
for k in range(j + 1, plen):
part[k].v = part[k].u
return True
return False
# Version to allow number of parts to be bounded from above.
# Corresponds to (a modified) step M5.
def decrement_part_small(self, part, ub):
"""Decrements part (a subrange of pstack), if possible, returning
True iff the part was successfully decremented.
Parameters
==========
part
part to be decremented (topmost part on the stack)
ub
the maximum number of parts allowed in a partition
returned by the calling traversal.
Notes
=====
The goal of this modification of the ordinary decrement method
is to fail (meaning that the subtree rooted at this part is to
be skipped) when it can be proved that this part can only have
child partitions which are larger than allowed by ``ub``. If a
decision is made to fail, it must be accurate, otherwise the
enumeration will miss some partitions. But, it is OK not to
capture all the possible failures -- if a part is passed that
shouldn't be, the resulting too-large partitions are filtered
by the enumeration one level up. However, as is usual in
constrained enumerations, failing early is advantageous.
The tests used by this method catch the most common cases,
although this implementation is by no means the last word on
this problem. The tests include:
1) ``lpart`` must be less than ``ub`` by at least 2. This is because
once a part has been decremented, the partition
will gain at least one child in the spread step.
2) If the leading component of the part is about to be
decremented, check for how many parts will be added in
order to use up the unallocated multiplicity in that
leading component, and fail if this number is greater than
allowed by ``ub``. (See code for the exact expression.) This
test is given in the answer to Knuth's problem 7.2.1.5.69.
3) If there is *exactly* enough room to expand the leading
component by the above test, check the next component (if
it exists) once decrementing has finished. If this has
``v == 0``, this next component will push the expansion over the
limit by 1, so fail.
"""
if self.lpart >= ub - 1:
self.p1 += 1 # increment to keep track of usefulness of tests
return False
plen = len(part)
for j in range(plen - 1, -1, -1):
# Knuth's mod, (answer to problem 7.2.1.5.69)
if (j == 0) and (part[0].v - 1)*(ub - self.lpart) < part[0].u:
self.k1 += 1
return False
if (j == 0 and part[j].v > 1) or (j > 0 and part[j].v > 0):
# found val to decrement
part[j].v -= 1
# Reset trailing parts back to maximum
for k in range(j + 1, plen):
part[k].v = part[k].u
# Have now decremented part, but are we doomed to
# failure when it is expanded? Check one oddball case
# that turns out to be surprisingly common - exactly
# enough room to expand the leading component, but no
# room for the second component, which has v=0.
if (plen > 1 and (part[1].v == 0) and
(part[0].u - part[0].v) ==
((ub - self.lpart - 1) * part[0].v)):
self.k2 += 1
self.db_trace("Decrement fails test 3")
return False
return True
return False
def decrement_part_large(self, part, amt, lb):
"""Decrements part, while respecting size constraint.
A part can have no children which are of sufficient size (as
indicated by ``lb``) unless that part has sufficient
unallocated multiplicity. When enforcing the size constraint,
this method will decrement the part (if necessary) by an
amount needed to ensure sufficient unallocated multiplicity.
Returns True iff the part was successfully decremented.
Parameters
==========
part
part to be decremented (topmost part on the stack)
amt
Can only take values 0 or 1. A value of 1 means that the
part must be decremented, and then the size constraint is
enforced. A value of 0 means just to enforce the ``lb``
size constraint.
lb
The partitions produced by the calling enumeration must
have more parts than this value.
"""
if amt == 1:
# In this case we always need to increment, *before*
# enforcing the "sufficient unallocated multiplicity"
# constraint. Easiest for this is just to call the
# regular decrement method.
if not self.decrement_part(part):
return False
# Next, perform any needed additional decrementing to respect
# "sufficient unallocated multiplicity" (or fail if this is
# not possible).
min_unalloc = lb - self.lpart
if min_unalloc <= 0:
return True
total_mult = sum(pc.u for pc in part)
total_alloc = sum(pc.v for pc in part)
if total_mult <= min_unalloc:
return False
deficit = min_unalloc - (total_mult - total_alloc)
if deficit <= 0:
return True
for i in range(len(part) - 1, -1, -1):
if i == 0:
if part[0].v > deficit:
part[0].v -= deficit
return True
else:
return False # This shouldn't happen, due to above check
else:
if part[i].v >= deficit:
part[i].v -= deficit
return True
else:
deficit -= part[i].v
part[i].v = 0
def decrement_part_range(self, part, lb, ub):
"""Decrements part (a subrange of pstack), if possible, returning
True iff the part was successfully decremented.
Parameters
==========
part
part to be decremented (topmost part on the stack)
ub
the maximum number of parts allowed in a partition
returned by the calling traversal.
lb
The partitions produced by the calling enumeration must
have more parts than this value.
Notes
=====
Combines the constraints of _small and _large decrement
methods. If returns success, part has been decremented at
least once, but perhaps by quite a bit more if needed to meet
the lb constraint.
"""
# Constraint in the range case is just enforcing both the
# constraints from _small and _large cases. Note the 0 as the
# second argument to the _large call -- this is the signal to
# decrement only as needed to for constraint enforcement. The
# short circuiting and left-to-right order of the 'and'
# operator is important for this to work correctly.
return self.decrement_part_small(part, ub) and \
self.decrement_part_large(part, 0, lb)
def spread_part_multiplicity(self):
"""Returns True if a new part has been created, and
adjusts pstack, f and lpart as needed.
Notes
=====
Spreads unallocated multiplicity from the current top part
into a new part created above the current on the stack. This
new part is constrained to be less than or equal to the old in
terms of the part ordering.
This call does nothing (and returns False) if the current top
part has no unallocated multiplicity.
"""
j = self.f[self.lpart] # base of current top part
k = self.f[self.lpart + 1] # ub of current; potential base of next
base = k # save for later comparison
changed = False # Set to true when the new part (so far) is
# strictly less than (as opposed to less than
# or equal) to the old.
for j in range(self.f[self.lpart], self.f[self.lpart + 1]):
self.pstack[k].u = self.pstack[j].u - self.pstack[j].v
if self.pstack[k].u == 0:
changed = True
else:
self.pstack[k].c = self.pstack[j].c
if changed: # Put all available multiplicity in this part
self.pstack[k].v = self.pstack[k].u
else: # Still maintaining ordering constraint
if self.pstack[k].u < self.pstack[j].v:
self.pstack[k].v = self.pstack[k].u
changed = True
else:
self.pstack[k].v = self.pstack[j].v
k = k + 1
if k > base:
# Adjust for the new part on stack
self.lpart = self.lpart + 1
self.f[self.lpart + 1] = k
return True
return False
def top_part(self):
"""Return current top part on the stack, as a slice of pstack.
"""
return self.pstack[self.f[self.lpart]:self.f[self.lpart + 1]]
# Same interface and funtionality as multiset_partitions_taocp(),
# but some might find this refactored version easier to follow.
def enum_all(self, multiplicities):
"""Enumerate the partitions of a multiset.
Examples
========
>>> from sympy.utilities.enumerative import list_visitor
>>> from sympy.utilities.enumerative import MultisetPartitionTraverser
>>> m = MultisetPartitionTraverser()
>>> states = m.enum_all([2,2])
>>> list(list_visitor(state, 'ab') for state in states)
[[['a', 'a', 'b', 'b']],
[['a', 'a', 'b'], ['b']],
[['a', 'a'], ['b', 'b']],
[['a', 'a'], ['b'], ['b']],
[['a', 'b', 'b'], ['a']],
[['a', 'b'], ['a', 'b']],
[['a', 'b'], ['a'], ['b']],
[['a'], ['a'], ['b', 'b']],
[['a'], ['a'], ['b'], ['b']]]
See also
========
multiset_partitions_taocp():
which provides the same result as this method, but is
about twice as fast. Hence, enum_all is primarily useful
for testing. Also see the function for a discussion of
states and visitors.
"""
self._initialize_enumeration(multiplicities)
while True:
while self.spread_part_multiplicity():
pass
# M4 Visit a partition
state = [self.f, self.lpart, self.pstack]
yield state
# M5 (Decrease v)
while not self.decrement_part(self.top_part()):
# M6 (Backtrack)
if self.lpart == 0:
return
self.lpart -= 1
def enum_small(self, multiplicities, ub):
"""Enumerate multiset partitions with no more than ``ub`` parts.
Equivalent to enum_range(multiplicities, 0, ub)
See also
========
enum_all, enum_large, enum_range
Parameters
==========
multiplicities
list of multiplicities of the components of the multiset.
ub
Maximum number of parts
Examples
========
>>> from sympy.utilities.enumerative import list_visitor
>>> from sympy.utilities.enumerative import MultisetPartitionTraverser
>>> m = MultisetPartitionTraverser()
>>> states = m.enum_small([2,2], 2)
>>> list(list_visitor(state, 'ab') for state in states)
[[['a', 'a', 'b', 'b']],
[['a', 'a', 'b'], ['b']],
[['a', 'a'], ['b', 'b']],
[['a', 'b', 'b'], ['a']],
[['a', 'b'], ['a', 'b']]]
The implementation is based, in part, on the answer given to
exercise 69, in Knuth [AOCP]_.
"""
# Keep track of iterations which do not yield a partition.
# Clearly, we would like to keep this number small.
self.discarded = 0
if ub <= 0:
return
self._initialize_enumeration(multiplicities)
while True:
good_partition = True
while self.spread_part_multiplicity():
self.db_trace("spread 1")
if self.lpart >= ub:
self.discarded += 1
good_partition = False
self.db_trace(" Discarding")
self.lpart = ub - 2
break
# M4 Visit a partition
if good_partition:
state = [self.f, self.lpart, self.pstack]
yield state
# M5 (Decrease v)
while not self.decrement_part_small(self.top_part(), ub):
self.db_trace("Failed decrement, going to backtrack")
# M6 (Backtrack)
if self.lpart == 0:
return
self.lpart -= 1
self.db_trace("Backtracked to")
self.db_trace("decrement ok, about to expand")
def enum_large(self, multiplicities, lb):
"""Enumerate the partitions of a multiset with lb < num(parts)
Equivalent to enum_range(multiplicities, lb, sum(multiplicities))
See also
========
enum_all, enum_small, enum_range
Parameters
==========
multiplicities
list of multiplicities of the components of the multiset.
lb
Number of parts in the partition must be greater than
this lower bound.
Examples
========
>>> from sympy.utilities.enumerative import list_visitor
>>> from sympy.utilities.enumerative import MultisetPartitionTraverser
>>> m = MultisetPartitionTraverser()
>>> states = m.enum_large([2,2], 2)
>>> list(list_visitor(state, 'ab') for state in states)
[[['a', 'a'], ['b'], ['b']],
[['a', 'b'], ['a'], ['b']],
[['a'], ['a'], ['b', 'b']],
[['a'], ['a'], ['b'], ['b']]]
"""
self.discarded = 0
if lb >= sum(multiplicities):
return
self._initialize_enumeration(multiplicities)
self.decrement_part_large(self.top_part(), 0, lb)
while True:
good_partition = True
while self.spread_part_multiplicity():
if not self.decrement_part_large(self.top_part(), 0, lb):
# Failure here should be rare/impossible
self.discarded += 1
good_partition = False
break
# M4 Visit a partition
if good_partition:
state = [self.f, self.lpart, self.pstack]
yield state
# M5 (Decrease v)
while not self.decrement_part_large(self.top_part(), 1, lb):
# M6 (Backtrack)
if self.lpart == 0:
return
self.lpart -= 1
def enum_range(self, multiplicities, lb, ub):
"""Enumerate the partitions of a multiset with
``lb < num(parts) <= ub``.
In particular, if partitions with exactly ``k`` parts are
desired, call with ``(multiplicities, k - 1, k)``. This
method generalizes enum_all, enum_small, and enum_large.
Examples
========
>>> from sympy.utilities.enumerative import list_visitor
>>> from sympy.utilities.enumerative import MultisetPartitionTraverser
>>> m = MultisetPartitionTraverser()
>>> states = m.enum_range([2,2], 1, 2)
>>> list(list_visitor(state, 'ab') for state in states)
[[['a', 'a', 'b'], ['b']],
[['a', 'a'], ['b', 'b']],
[['a', 'b', 'b'], ['a']],
[['a', 'b'], ['a', 'b']]]
"""
# combine the constraints of the _large and _small
# enumerations.
self.discarded = 0
if ub <= 0 or lb >= sum(multiplicities):
return
self._initialize_enumeration(multiplicities)
self.decrement_part_large(self.top_part(), 0, lb)
while True:
good_partition = True
while self.spread_part_multiplicity():
self.db_trace("spread 1")
if not self.decrement_part_large(self.top_part(), 0, lb):
# Failure here - possible in range case?
self.db_trace(" Discarding (large cons)")
self.discarded += 1
good_partition = False
break
elif self.lpart >= ub:
self.discarded += 1
good_partition = False
self.db_trace(" Discarding small cons")
self.lpart = ub - 2
break
# M4 Visit a partition
if good_partition:
state = [self.f, self.lpart, self.pstack]
yield state
# M5 (Decrease v)
while not self.decrement_part_range(self.top_part(), lb, ub):
self.db_trace("Failed decrement, going to backtrack")
# M6 (Backtrack)
if self.lpart == 0:
return
self.lpart -= 1
self.db_trace("Backtracked to")
self.db_trace("decrement ok, about to expand")
def count_partitions_slow(self, multiplicities):
"""Returns the number of partitions of a multiset whose elements
have the multiplicities given in ``multiplicities``.
Primarily for comparison purposes. It follows the same path as
enumerate, and counts, rather than generates, the partitions.
See Also
========
count_partitions
Has the same calling interface, but is much faster.
"""
# number of partitions so far in the enumeration
self.pcount = 0
self._initialize_enumeration(multiplicities)
while True:
while self.spread_part_multiplicity():
pass
# M4 Visit (count) a partition
self.pcount += 1
# M5 (Decrease v)
while not self.decrement_part(self.top_part()):
# M6 (Backtrack)
if self.lpart == 0:
return self.pcount
self.lpart -= 1
def count_partitions(self, multiplicities):
"""Returns the number of partitions of a multiset whose components
have the multiplicities given in ``multiplicities``.
For larger counts, this method is much faster than calling one
of the enumerators and counting the result. Uses dynamic
programming to cut down on the number of nodes actually
explored. The dictionary used in order to accelerate the
counting process is stored in the ``MultisetPartitionTraverser``
object and persists across calls. If the the user does not
expect to call ``count_partitions`` for any additional
multisets, the object should be cleared to save memory. On
the other hand, the cache built up from one count run can
significantly speed up subsequent calls to ``count_partitions``,
so it may be advantageous not to clear the object.
Examples
========
>>> from sympy.utilities.enumerative import MultisetPartitionTraverser
>>> m = MultisetPartitionTraverser()
>>> m.count_partitions([9,8,2])
288716
>>> m.count_partitions([2,2])
9
>>> del m
Notes
=====
If one looks at the workings of Knuth's algorithm M [AOCP]_, it
can be viewed as a traversal of a binary tree of parts. A
part has (up to) two children, the left child resulting from
the spread operation, and the right child from the decrement
operation. The ordinary enumeration of multiset partitions is
an in-order traversal of this tree, and with the partitions
corresponding to paths from the root to the leaves. The
mapping from paths to partitions is a little complicated,
since the partition would contain only those parts which are
leaves or the parents of a spread link, not those which are
parents of a decrement link.
For counting purposes, it is sufficient to count leaves, and
this can be done with a recursive in-order traversal. The
number of leaves of a subtree rooted at a particular part is a
function only of that part itself, so memoizing has the
potential to speed up the counting dramatically.
This method follows a computational approach which is similar
to the hypothetical memoized recursive function, but with two
differences:
1) This method is iterative, borrowing its structure from the
other enumerations and maintaining an explicit stack of
parts which are in the process of being counted. (There
may be multisets which can be counted reasonably quickly by
this implementation, but which would overflow the default
Python recursion limit with a recursive implementation.)
2) Instead of using the part data structure directly, a more
compact key is constructed. This saves space, but more
importantly coalesces some parts which would remain
separate with physical keys.
Unlike the enumeration functions, there is currently no _range
version of count_partitions. If someone wants to stretch
their brain, it should be possible to construct one by
memoizing with a histogram of counts rather than a single
count, and combining the histograms.
"""
# number of partitions so far in the enumeration
self.pcount = 0
# dp_stack is list of lists of (part_key, start_count) pairs
self.dp_stack = []
# dp_map is map part_key-> count, where count represents the
# number of multiset which are descendants of a part with this
# key, **or any of its decrements**
# Thus, when we find a part in the map, we add its count
# value to the running total, cut off the enumeration, and
# backtrack
if not hasattr(self, 'dp_map'):
self.dp_map = {}
self._initialize_enumeration(multiplicities)
pkey = part_key(self.top_part())
self.dp_stack.append([(pkey, 0), ])
while True:
while self.spread_part_multiplicity():
pkey = part_key(self.top_part())
if pkey in self.dp_map:
# Already have a cached value for the count of the
# subtree rooted at this part. Add it to the
# running counter, and break out of the spread
# loop. The -1 below is to compensate for the
# leaf that this code path would otherwise find,
# and which gets incremented for below.
self.pcount += (self.dp_map[pkey] - 1)
self.lpart -= 1
break
else:
self.dp_stack.append([(pkey, self.pcount), ])
# M4 count a leaf partition
self.pcount += 1
# M5 (Decrease v)
while not self.decrement_part(self.top_part()):
# M6 (Backtrack)
for key, oldcount in self.dp_stack.pop():
self.dp_map[key] = self.pcount - oldcount
if self.lpart == 0:
return self.pcount
self.lpart -= 1
# At this point have successfully decremented the part on
# the stack and it does not appear in the cache. It needs
# to be added to the list at the top of dp_stack
pkey = part_key(self.top_part())
self.dp_stack[-1].append((pkey, self.pcount),)
def part_key(part):
"""Helper for MultisetPartitionTraverser.count_partitions that
creates a key for ``part``, that only includes information which can
affect the count for that part. (Any irrelevant information just
reduces the effectiveness of dynamic programming.)
Notes
=====
This member function is a candidate for future exploration. There
are likely symmetries that can be exploited to coalesce some
``part_key`` values, and thereby save space and improve
performance.
"""
# The component number is irrelevant for counting partitions, so
# leave it out of the memo key.
rval = []
for ps in part:
rval.append(ps.u)
rval.append(ps.v)
return tuple(rval)
| 43,446 | 36.747176 | 79 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/__init__.py
|
"""This module contains some general purpose utilities that are used across
SymPy.
"""
from .iterables import (flatten, group, take, subsets,
variations, numbered_symbols, cartes, capture, dict_merge,
postorder_traversal, interactive_traversal,
prefixes, postfixes, sift, topological_sort, unflatten,
has_dups, has_variety, reshape, default_sort_key, ordered)
from .misc import filldedent
from .lambdify import lambdify
from .source import source
from .decorator import threaded, xthreaded, public, memoize_property
from .runtests import test, doctest
from .timeutils import timed
| 603 | 27.761905 | 75 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/memoization.py
|
from __future__ import print_function, division
from sympy.core.decorators import wraps
from sympy.core.compatibility import range
def recurrence_memo(initial):
"""
Memo decorator for sequences defined by recurrence
See usage examples e.g. in the specfun/combinatorial module
"""
cache = initial
def decorator(f):
@wraps(f)
def g(n):
L = len(cache)
if n <= L - 1:
return cache[n]
for i in range(L, n + 1):
cache.append(f(i, cache))
return cache[-1]
return g
return decorator
def assoc_recurrence_memo(base_seq):
"""
Memo decorator for associated sequences defined by recurrence starting from base
base_seq(n) -- callable to get base sequence elements
XXX works only for Pn0 = base_seq(0) cases
XXX works only for m <= n cases
"""
cache = []
def decorator(f):
@wraps(f)
def g(n, m):
L = len(cache)
if n < L:
return cache[n][m]
for i in range(L, n + 1):
# get base sequence
F_i0 = base_seq(i)
F_i_cache = [F_i0]
cache.append(F_i_cache)
# XXX only works for m <= n cases
# generate assoc sequence
for j in range(1, i + 1):
F_ij = f(i, j, cache)
F_i_cache.append(F_ij)
return cache[n][m]
return g
return decorator
| 1,533 | 23.349206 | 84 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/magic.py
|
"""Functions that involve magic. """
from __future__ import print_function, division
def pollute(names, objects):
"""Pollute the global namespace with symbols -> objects mapping. """
from inspect import currentframe
frame = currentframe().f_back.f_back
try:
for name, obj in zip(names, objects):
frame.f_globals[name] = obj
finally:
del frame # break cyclic dependencies as stated in inspect docs
| 449 | 29 | 72 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/pytest.py
|
"""py.test hacks to support XFAIL/XPASS"""
from __future__ import print_function, division
import sys
import functools
import os
from sympy.core.compatibility import get_function_name
try:
import py
from py.test import skip, raises
USE_PYTEST = getattr(sys, '_running_pytest', False)
except ImportError:
USE_PYTEST = False
ON_TRAVIS = os.getenv('TRAVIS_BUILD_NUMBER', None)
if not USE_PYTEST:
def raises(expectedException, code=None):
"""
Tests that ``code`` raises the exception ``expectedException``.
``code`` may be a callable, such as a lambda expression or function
name.
If ``code`` is not given or None, ``raises`` will return a context
manager for use in ``with`` statements; the code to execute then
comes from the scope of the ``with``.
``raises()`` does nothing if the callable raises the expected exception,
otherwise it raises an AssertionError.
Examples
========
>>> from sympy.utilities.pytest import raises
>>> raises(ZeroDivisionError, lambda: 1/0)
>>> raises(ZeroDivisionError, lambda: 1/2)
Traceback (most recent call last):
...
AssertionError: DID NOT RAISE
>>> with raises(ZeroDivisionError):
... n = 1/0
>>> with raises(ZeroDivisionError):
... n = 1/2
Traceback (most recent call last):
...
AssertionError: DID NOT RAISE
Note that you cannot test multiple statements via
``with raises``:
>>> with raises(ZeroDivisionError):
... n = 1/0 # will execute and raise, aborting the ``with``
... n = 9999/0 # never executed
This is just what ``with`` is supposed to do: abort the
contained statement sequence at the first exception and let
the context manager deal with the exception.
To test multiple statements, you'll need a separate ``with``
for each:
>>> with raises(ZeroDivisionError):
... n = 1/0 # will execute and raise
>>> with raises(ZeroDivisionError):
... n = 9999/0 # will also execute and raise
"""
if code is None:
return RaisesContext(expectedException)
elif callable(code):
try:
code()
except expectedException:
return
raise AssertionError("DID NOT RAISE")
elif isinstance(code, str):
raise TypeError(
'\'raises(xxx, "code")\' has been phased out; '
'change \'raises(xxx, "expression")\' '
'to \'raises(xxx, lambda: expression)\', '
'\'raises(xxx, "statement")\' '
'to \'with raises(xxx): statement\'')
else:
raise TypeError(
'raises() expects a callable for the 2nd argument.')
class RaisesContext(object):
def __init__(self, expectedException):
self.expectedException = expectedException
def __enter__(self):
return None
def __exit__(self, exc_type, exc_value, traceback):
if exc_type is None:
raise AssertionError("DID NOT RAISE")
return issubclass(exc_type, self.expectedException)
class XFail(Exception):
pass
class XPass(Exception):
pass
class Skipped(Exception):
pass
def XFAIL(func):
def wrapper():
try:
func()
except Exception as e:
message = str(e)
if message != "Timeout":
raise XFail(get_function_name(func))
else:
raise Skipped("Timeout")
raise XPass(get_function_name(func))
wrapper = functools.update_wrapper(wrapper, func)
return wrapper
def skip(str):
raise Skipped(str)
def SKIP(reason):
"""Similar to :func:`skip`, but this is a decorator. """
def wrapper(func):
def func_wrapper():
raise Skipped(reason)
func_wrapper = functools.update_wrapper(func_wrapper, func)
return func_wrapper
return wrapper
def slow(func):
func._slow = True
def func_wrapper():
func()
func_wrapper = functools.update_wrapper(func_wrapper, func)
func_wrapper.__wrapped__ = func
return func_wrapper
else:
XFAIL = py.test.mark.xfail
slow = py.test.mark.slow
def SKIP(reason):
def skipping(func):
@functools.wraps(func)
def inner(*args, **kwargs):
skip(reason)
return inner
return skipping
| 4,768 | 27.90303 | 80 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/runtests.py
|
"""
This is our testing framework.
Goals:
* it should be compatible with py.test and operate very similarly
(or identically)
* doesn't require any external dependencies
* preferably all the functionality should be in this file only
* no magic, just import the test file and execute the test functions, that's it
* portable
"""
from __future__ import print_function, division
import os
import sys
import platform
import inspect
import traceback
import pdb
import re
import linecache
import time
from fnmatch import fnmatch
from timeit import default_timer as clock
import doctest as pdoctest # avoid clashing with our doctest() function
from doctest import DocTestFinder, DocTestRunner
import random
import subprocess
import signal
import stat
from sympy.core.cache import clear_cache
from sympy.core.compatibility import exec_, PY3, string_types, range
from sympy.utilities.misc import find_executable
from sympy.external import import_module
from sympy.utilities.exceptions import SymPyDeprecationWarning
IS_WINDOWS = (os.name == 'nt')
# emperically generated list of the proportion of time spent running
# an even split of tests. This should periodically be regenerated.
# A list of [.6, .1, .3] would mean that if the tests are evenly split
# into '1/3', '2/3', '3/3', the first split would take 60% of the time,
# the second 10% and the third 30%. These lists are normalized to sum
# to 1, so [60, 10, 30] has the same behavoir as [6, 1, 3] or [.6, .1, .3].
#
# This list can be generated with the code:
# from time import time
# import sympy
#
# delays, num_splits = [], 30
# for i in range(1, num_splits + 1):
# tic = time()
# sympy.test(split='{}/{}'.format(i, num_splits), time_balance=False)
# delays.append(time() - tic)
# tot = sum(delays)
# print([round(x / tot, 4) for x in delays]))
SPLIT_DENSITY = [0.2464, 0.0507, 0.0328, 0.0113, 0.0418, 0.012, 0.0269, 0.0095, 0.091, 0.0215, 0.001, 0.0023, 0.0116, 0.0137, 0.0041, 0.0039, 0.0145, 0.0172, 0.059, 0.0017, 0.0112, 0.0128, 0.0012, 0.0293, 0.0705, 0.0284, 0.1495, 0.0073, 0.0052, 0.0115]
SPLIT_DENSITY_SLOW = [0.3616, 0.0003, 0.0004, 0.0004, 0.0255, 0.0005, 0.0674, 0.0337, 0.1057, 0.0329, 0.0002, 0.0002, 0.0184, 0.0028, 0.0046, 0.0148, 0.0046, 0.0083, 0.0004, 0.0002, 0.0069, 0.0004, 0.0004, 0.0046, 0.0205, 0.1378, 0.1451, 0.0003, 0.0006, 0.0006]
class Skipped(Exception):
pass
# add more flags ??
future_flags = division.compiler_flag
def _indent(s, indent=4):
"""
Add the given number of space characters to the beginning of
every non-blank line in ``s``, and return the result.
If the string ``s`` is Unicode, it is encoded using the stdout
encoding and the ``backslashreplace`` error handler.
"""
# After a 2to3 run the below code is bogus, so wrap it with a version check
if not PY3:
if isinstance(s, unicode):
s = s.encode(pdoctest._encoding, 'backslashreplace')
# This regexp matches the start of non-blank lines:
return re.sub('(?m)^(?!$)', indent*' ', s)
pdoctest._indent = _indent
# ovverride reporter to maintain windows and python3
def _report_failure(self, out, test, example, got):
"""
Report that the given example failed.
"""
s = self._checker.output_difference(example, got, self.optionflags)
s = s.encode('raw_unicode_escape').decode('utf8', 'ignore')
out(self._failure_header(test, example) + s)
if PY3 and IS_WINDOWS:
DocTestRunner.report_failure = _report_failure
def convert_to_native_paths(lst):
"""
Converts a list of '/' separated paths into a list of
native (os.sep separated) paths and converts to lowercase
if the system is case insensitive.
"""
newlst = []
for i, rv in enumerate(lst):
rv = os.path.join(*rv.split("/"))
# on windows the slash after the colon is dropped
if sys.platform == "win32":
pos = rv.find(':')
if pos != -1:
if rv[pos + 1] != '\\':
rv = rv[:pos + 1] + '\\' + rv[pos + 1:]
newlst.append(sys_normcase(rv))
return newlst
def get_sympy_dir():
"""
Returns the root sympy directory and set the global value
indicating whether the system is case sensitive or not.
"""
global sys_case_insensitive
this_file = os.path.abspath(__file__)
sympy_dir = os.path.join(os.path.dirname(this_file), "..", "..")
sympy_dir = os.path.normpath(sympy_dir)
sys_case_insensitive = (os.path.isdir(sympy_dir) and
os.path.isdir(sympy_dir.lower()) and
os.path.isdir(sympy_dir.upper()))
return sys_normcase(sympy_dir)
def sys_normcase(f):
if sys_case_insensitive: # global defined after call to get_sympy_dir()
return f.lower()
return f
def setup_pprint():
from sympy import pprint_use_unicode, init_printing
# force pprint to be in ascii mode in doctests
pprint_use_unicode(False)
# hook our nice, hash-stable strprinter
init_printing(pretty_print=False)
def run_in_subprocess_with_hash_randomization(
function, function_args=(),
function_kwargs=None, command=sys.executable,
module='sympy.utilities.runtests', force=False):
"""
Run a function in a Python subprocess with hash randomization enabled.
If hash randomization is not supported by the version of Python given, it
returns False. Otherwise, it returns the exit value of the command. The
function is passed to sys.exit(), so the return value of the function will
be the return value.
The environment variable PYTHONHASHSEED is used to seed Python's hash
randomization. If it is set, this function will return False, because
starting a new subprocess is unnecessary in that case. If it is not set,
one is set at random, and the tests are run. Note that if this
environment variable is set when Python starts, hash randomization is
automatically enabled. To force a subprocess to be created even if
PYTHONHASHSEED is set, pass ``force=True``. This flag will not force a
subprocess in Python versions that do not support hash randomization (see
below), because those versions of Python do not support the ``-R`` flag.
``function`` should be a string name of a function that is importable from
the module ``module``, like "_test". The default for ``module`` is
"sympy.utilities.runtests". ``function_args`` and ``function_kwargs``
should be a repr-able tuple and dict, respectively. The default Python
command is sys.executable, which is the currently running Python command.
This function is necessary because the seed for hash randomization must be
set by the environment variable before Python starts. Hence, in order to
use a predetermined seed for tests, we must start Python in a separate
subprocess.
Hash randomization was added in the minor Python versions 2.6.8, 2.7.3,
3.1.5, and 3.2.3, and is enabled by default in all Python versions after
and including 3.3.0.
Examples
========
>>> from sympy.utilities.runtests import (
... run_in_subprocess_with_hash_randomization)
>>> # run the core tests in verbose mode
>>> run_in_subprocess_with_hash_randomization("_test",
... function_args=("core",),
... function_kwargs={'verbose': True}) # doctest: +SKIP
# Will return 0 if sys.executable supports hash randomization and tests
# pass, 1 if they fail, and False if it does not support hash
# randomization.
"""
# Note, we must return False everywhere, not None, as subprocess.call will
# sometimes return None.
# First check if the Python version supports hash randomization
# If it doesn't have this support, it won't reconize the -R flag
p = subprocess.Popen([command, "-RV"], stdout=subprocess.PIPE,
stderr=subprocess.STDOUT)
p.communicate()
if p.returncode != 0:
return False
hash_seed = os.getenv("PYTHONHASHSEED")
if not hash_seed:
os.environ["PYTHONHASHSEED"] = str(random.randrange(2**32))
else:
if not force:
return False
function_kwargs = function_kwargs or {}
# Now run the command
commandstring = ("import sys; from %s import %s;sys.exit(%s(*%s, **%s))" %
(module, function, function, repr(function_args),
repr(function_kwargs)))
try:
p = subprocess.Popen([command, "-R", "-c", commandstring])
p.communicate()
except KeyboardInterrupt:
p.wait()
finally:
# Put the environment variable back, so that it reads correctly for
# the current Python process.
if hash_seed is None:
del os.environ["PYTHONHASHSEED"]
else:
os.environ["PYTHONHASHSEED"] = hash_seed
return p.returncode
def run_all_tests(test_args=(), test_kwargs=None,
doctest_args=(), doctest_kwargs=None,
examples_args=(), examples_kwargs=None):
"""
Run all tests.
Right now, this runs the regular tests (bin/test), the doctests
(bin/doctest), the examples (examples/all.py), and the sage tests (see
sympy/external/tests/test_sage.py).
This is what ``setup.py test`` uses.
You can pass arguments and keyword arguments to the test functions that
support them (for now, test, doctest, and the examples). See the
docstrings of those functions for a description of the available options.
For example, to run the solvers tests with colors turned off:
>>> from sympy.utilities.runtests import run_all_tests
>>> run_all_tests(test_args=("solvers",),
... test_kwargs={"colors:False"}) # doctest: +SKIP
"""
tests_successful = True
test_kwargs = test_kwargs or {}
doctest_kwargs = doctest_kwargs or {}
examples_kwargs = examples_kwargs or {'quiet': True}
try:
# Regular tests
if not test(*test_args, **test_kwargs):
# some regular test fails, so set the tests_successful
# flag to false and continue running the doctests
tests_successful = False
# Doctests
print()
if not doctest(*doctest_args, **doctest_kwargs):
tests_successful = False
# Examples
print()
sys.path.append("examples")
from all import run_examples # examples/all.py
if not run_examples(*examples_args, **examples_kwargs):
tests_successful = False
# Sage tests
if sys.platform != "win32" and not PY3 and os.path.exists("bin/test"):
# run Sage tests; Sage currently doesn't support Windows or Python 3
# Only run Sage tests if 'bin/test' is present (it is missing from
# our release because everything in the 'bin' directory gets
# installed).
dev_null = open(os.devnull, 'w')
if subprocess.call("sage -v", shell=True, stdout=dev_null,
stderr=dev_null) == 0:
if subprocess.call("sage -python bin/test "
"sympy/external/tests/test_sage.py",
shell=True, cwd=os.path.dirname(os.path.dirname(os.path.dirname(__file__)))) != 0:
tests_successful = False
if tests_successful:
return
else:
# Return nonzero exit code
sys.exit(1)
except KeyboardInterrupt:
print()
print("DO *NOT* COMMIT!")
sys.exit(1)
def test(*paths, **kwargs):
"""
Run tests in the specified test_*.py files.
Tests in a particular test_*.py file are run if any of the given strings
in ``paths`` matches a part of the test file's path. If ``paths=[]``,
tests in all test_*.py files are run.
Notes:
- If sort=False, tests are run in random order (not default).
- Paths can be entered in native system format or in unix,
forward-slash format.
- Files that are on the blacklist can be tested by providing
their path; they are only excluded if no paths are given.
**Explanation of test results**
====== ===============================================================
Output Meaning
====== ===============================================================
. passed
F failed
X XPassed (expected to fail but passed)
f XFAILed (expected to fail and indeed failed)
s skipped
w slow
T timeout (e.g., when ``--timeout`` is used)
K KeyboardInterrupt (when running the slow tests with ``--slow``,
you can interrupt one of them without killing the test runner)
====== ===============================================================
Colors have no additional meaning and are used just to facilitate
interpreting the output.
Examples
========
>>> import sympy
Run all tests:
>>> sympy.test() # doctest: +SKIP
Run one file:
>>> sympy.test("sympy/core/tests/test_basic.py") # doctest: +SKIP
>>> sympy.test("_basic") # doctest: +SKIP
Run all tests in sympy/functions/ and some particular file:
>>> sympy.test("sympy/core/tests/test_basic.py",
... "sympy/functions") # doctest: +SKIP
Run all tests in sympy/core and sympy/utilities:
>>> sympy.test("/core", "/util") # doctest: +SKIP
Run specific test from a file:
>>> sympy.test("sympy/core/tests/test_basic.py",
... kw="test_equality") # doctest: +SKIP
Run specific test from any file:
>>> sympy.test(kw="subs") # doctest: +SKIP
Run the tests with verbose mode on:
>>> sympy.test(verbose=True) # doctest: +SKIP
Don't sort the test output:
>>> sympy.test(sort=False) # doctest: +SKIP
Turn on post-mortem pdb:
>>> sympy.test(pdb=True) # doctest: +SKIP
Turn off colors:
>>> sympy.test(colors=False) # doctest: +SKIP
Force colors, even when the output is not to a terminal (this is useful,
e.g., if you are piping to ``less -r`` and you still want colors)
>>> sympy.test(force_colors=False) # doctest: +SKIP
The traceback verboseness can be set to "short" or "no" (default is
"short")
>>> sympy.test(tb='no') # doctest: +SKIP
The ``split`` option can be passed to split the test run into parts. The
split currently only splits the test files, though this may change in the
future. ``split`` should be a string of the form 'a/b', which will run
part ``a`` of ``b``. For instance, to run the first half of the test suite:
>>> sympy.test(split='1/2') # doctest: +SKIP
The ``time_balance`` option can be passed in conjunction with ``split``.
If ``time_balance=True`` (the default for ``sympy.test``), sympy will attempt
to split the tests such that each split takes equal time. This heuristic
for balancing is based on pre-recorded test data.
>>> sympy.test(split='1/2', time_balance=True) # doctest: +SKIP
You can disable running the tests in a separate subprocess using
``subprocess=False``. This is done to support seeding hash randomization,
which is enabled by default in the Python versions where it is supported.
If subprocess=False, hash randomization is enabled/disabled according to
whether it has been enabled or not in the calling Python process.
However, even if it is enabled, the seed cannot be printed unless it is
called from a new Python process.
Hash randomization was added in the minor Python versions 2.6.8, 2.7.3,
3.1.5, and 3.2.3, and is enabled by default in all Python versions after
and including 3.3.0.
If hash randomization is not supported ``subprocess=False`` is used
automatically.
>>> sympy.test(subprocess=False) # doctest: +SKIP
To set the hash randomization seed, set the environment variable
``PYTHONHASHSEED`` before running the tests. This can be done from within
Python using
>>> import os
>>> os.environ['PYTHONHASHSEED'] = '42' # doctest: +SKIP
Or from the command line using
$ PYTHONHASHSEED=42 ./bin/test
If the seed is not set, a random seed will be chosen.
Note that to reproduce the same hash values, you must use both the same seed
as well as the same architecture (32-bit vs. 64-bit).
"""
subprocess = kwargs.pop("subprocess", True)
rerun = kwargs.pop("rerun", 0)
# count up from 0, do not print 0
print_counter = lambda i : (print("rerun %d" % (rerun-i))
if rerun-i else None)
if subprocess:
# loop backwards so last i is 0
for i in range(rerun, -1, -1):
print_counter(i)
ret = run_in_subprocess_with_hash_randomization("_test",
function_args=paths, function_kwargs=kwargs)
if ret is False:
break
val = not bool(ret)
# exit on the first failure or if done
if not val or i == 0:
return val
# rerun even if hash randomization is not supported
for i in range(rerun, -1, -1):
print_counter(i)
val = not bool(_test(*paths, **kwargs))
if not val or i == 0:
return val
def _test(*paths, **kwargs):
"""
Internal function that actually runs the tests.
All keyword arguments from ``test()`` are passed to this function except for
``subprocess``.
Returns 0 if tests passed and 1 if they failed. See the docstring of
``test()`` for more information.
"""
verbose = kwargs.get("verbose", False)
tb = kwargs.get("tb", "short")
kw = kwargs.get("kw", None) or ()
# ensure that kw is a tuple
if isinstance(kw, str):
kw = (kw, )
post_mortem = kwargs.get("pdb", False)
colors = kwargs.get("colors", True)
force_colors = kwargs.get("force_colors", False)
sort = kwargs.get("sort", True)
seed = kwargs.get("seed", None)
if seed is None:
seed = random.randrange(100000000)
timeout = kwargs.get("timeout", False)
slow = kwargs.get("slow", False)
enhance_asserts = kwargs.get("enhance_asserts", False)
split = kwargs.get('split', None)
time_balance = kwargs.get('time_balance', True)
blacklist = kwargs.get('blacklist', [])
blacklist = convert_to_native_paths(blacklist)
fast_threshold = kwargs.get('fast_threshold', None)
slow_threshold = kwargs.get('slow_threshold', None)
r = PyTestReporter(verbose=verbose, tb=tb, colors=colors,
force_colors=force_colors, split=split)
t = SymPyTests(r, kw, post_mortem, seed,
fast_threshold=fast_threshold,
slow_threshold=slow_threshold)
# Disable warnings for external modules
import sympy.external
sympy.external.importtools.WARN_OLD_VERSION = False
sympy.external.importtools.WARN_NOT_INSTALLED = False
# Show deprecation warnings
import warnings
warnings.simplefilter("error", SymPyDeprecationWarning)
warnings.filterwarnings('error', '.*', DeprecationWarning, module='sympy.*')
test_files = t.get_test_files('sympy')
not_blacklisted = [f for f in test_files
if not any(b in f for b in blacklist)]
if len(paths) == 0:
matched = not_blacklisted
else:
paths = convert_to_native_paths(paths)
matched = []
for f in not_blacklisted:
basename = os.path.basename(f)
for p in paths:
if p in f or fnmatch(basename, p):
matched.append(f)
break
density = None
if time_balance:
if slow:
density = SPLIT_DENSITY_SLOW
else:
density = SPLIT_DENSITY
if split:
matched = split_list(matched, split, density=density)
t._testfiles.extend(matched)
return int(not t.test(sort=sort, timeout=timeout,
slow=slow, enhance_asserts=enhance_asserts))
def doctest(*paths, **kwargs):
r"""
Runs doctests in all \*.py files in the sympy directory which match
any of the given strings in ``paths`` or all tests if paths=[].
Notes:
- Paths can be entered in native system format or in unix,
forward-slash format.
- Files that are on the blacklist can be tested by providing
their path; they are only excluded if no paths are given.
Examples
========
>>> import sympy
Run all tests:
>>> sympy.doctest() # doctest: +SKIP
Run one file:
>>> sympy.doctest("sympy/core/basic.py") # doctest: +SKIP
>>> sympy.doctest("polynomial.rst") # doctest: +SKIP
Run all tests in sympy/functions/ and some particular file:
>>> sympy.doctest("/functions", "basic.py") # doctest: +SKIP
Run any file having polynomial in its name, doc/src/modules/polynomial.rst,
sympy/functions/special/polynomials.py, and sympy/polys/polynomial.py:
>>> sympy.doctest("polynomial") # doctest: +SKIP
The ``split`` option can be passed to split the test run into parts. The
split currently only splits the test files, though this may change in the
future. ``split`` should be a string of the form 'a/b', which will run
part ``a`` of ``b``. Note that the regular doctests and the Sphinx
doctests are split independently. For instance, to run the first half of
the test suite:
>>> sympy.doctest(split='1/2') # doctest: +SKIP
The ``subprocess`` and ``verbose`` options are the same as with the function
``test()``. See the docstring of that function for more information.
"""
subprocess = kwargs.pop("subprocess", True)
rerun = kwargs.pop("rerun", 0)
# count up from 0, do not print 0
print_counter = lambda i : (print("rerun %d" % (rerun-i))
if rerun-i else None)
if subprocess:
# loop backwards so last i is 0
for i in range(rerun, -1, -1):
print_counter(i)
ret = run_in_subprocess_with_hash_randomization("_doctest",
function_args=paths, function_kwargs=kwargs)
if ret is False:
break
val = not bool(ret)
# exit on the first failure or if done
if not val or i == 0:
return val
# rerun even if hash randomization is not supported
for i in range(rerun, -1, -1):
print_counter(i)
val = not bool(_doctest(*paths, **kwargs))
if not val or i == 0:
return val
def _doctest(*paths, **kwargs):
"""
Internal function that actually runs the doctests.
All keyword arguments from ``doctest()`` are passed to this function
except for ``subprocess``.
Returns 0 if tests passed and 1 if they failed. See the docstrings of
``doctest()`` and ``test()`` for more information.
"""
normal = kwargs.get("normal", False)
verbose = kwargs.get("verbose", False)
colors = kwargs.get("colors", True)
force_colors = kwargs.get("force_colors", False)
blacklist = kwargs.get("blacklist", [])
split = kwargs.get('split', None)
blacklist.extend([
"doc/src/modules/plotting.rst", # generates live plots
"sympy/physics/gaussopt.py", # raises deprecation warning
"sympy/galgebra.py", # raises ImportError
"sympy/matrices/densearith.py", # raises deprecation warning
"sympy/matrices/densesolve.py", # raises deprecation warning
"sympy/matrices/densetools.py", # raises deprecation warning
"sympy/physics/unitsystems.py", # raises deprecation warning
])
if import_module('numpy') is None:
blacklist.extend([
"sympy/plotting/experimental_lambdify.py",
"sympy/plotting/plot_implicit.py",
"examples/advanced/autowrap_integrators.py",
"examples/advanced/autowrap_ufuncify.py",
"examples/intermediate/sample.py",
"examples/intermediate/mplot2d.py",
"examples/intermediate/mplot3d.py",
"doc/src/modules/numeric-computation.rst"
])
else:
if import_module('matplotlib') is None:
blacklist.extend([
"examples/intermediate/mplot2d.py",
"examples/intermediate/mplot3d.py"
])
else:
# Use a non-windowed backend, so that the tests work on Travis
import matplotlib
matplotlib.use('Agg')
# don't display matplotlib windows
from sympy.plotting.plot import unset_show
unset_show()
if import_module('pyglet') is None:
blacklist.extend(["sympy/plotting/pygletplot"])
if import_module('theano') is None:
blacklist.extend(["doc/src/modules/numeric-computation.rst"])
# disabled because of doctest failures in asmeurer's bot
blacklist.extend([
"sympy/utilities/autowrap.py",
"examples/advanced/autowrap_integrators.py",
"examples/advanced/autowrap_ufuncify.py"
])
# blacklist these modules until issue 4840 is resolved
blacklist.extend([
"sympy/conftest.py",
"sympy/utilities/benchmarking.py"
])
blacklist = convert_to_native_paths(blacklist)
# Disable warnings for external modules
import sympy.external
sympy.external.importtools.WARN_OLD_VERSION = False
sympy.external.importtools.WARN_NOT_INSTALLED = False
# Show deprecation warnings
import warnings
warnings.simplefilter("error", SymPyDeprecationWarning)
warnings.filterwarnings('error', '.*', DeprecationWarning, module='sympy.*')
r = PyTestReporter(verbose, split=split, colors=colors,\
force_colors=force_colors)
t = SymPyDocTests(r, normal)
test_files = t.get_test_files('sympy')
test_files.extend(t.get_test_files('examples', init_only=False))
not_blacklisted = [f for f in test_files
if not any(b in f for b in blacklist)]
if len(paths) == 0:
matched = not_blacklisted
else:
# take only what was requested...but not blacklisted items
# and allow for partial match anywhere or fnmatch of name
paths = convert_to_native_paths(paths)
matched = []
for f in not_blacklisted:
basename = os.path.basename(f)
for p in paths:
if p in f or fnmatch(basename, p):
matched.append(f)
break
if split:
matched = split_list(matched, split)
t._testfiles.extend(matched)
# run the tests and record the result for this *py portion of the tests
if t._testfiles:
failed = not t.test()
else:
failed = False
# N.B.
# --------------------------------------------------------------------
# Here we test *.rst files at or below doc/src. Code from these must
# be self supporting in terms of imports since there is no importing
# of necessary modules by doctest.testfile. If you try to pass *.py
# files through this they might fail because they will lack the needed
# imports and smarter parsing that can be done with source code.
#
test_files = t.get_test_files('doc/src', '*.rst', init_only=False)
test_files.sort()
not_blacklisted = [f for f in test_files
if not any(b in f for b in blacklist)]
if len(paths) == 0:
matched = not_blacklisted
else:
# Take only what was requested as long as it's not on the blacklist.
# Paths were already made native in *py tests so don't repeat here.
# There's no chance of having a *py file slip through since we
# only have *rst files in test_files.
matched = []
for f in not_blacklisted:
basename = os.path.basename(f)
for p in paths:
if p in f or fnmatch(basename, p):
matched.append(f)
break
if split:
matched = split_list(matched, split)
setup_pprint()
first_report = True
for rst_file in matched:
if not os.path.isfile(rst_file):
continue
old_displayhook = sys.displayhook
try:
out = sympytestfile(
rst_file, module_relative=False, encoding='utf-8',
optionflags=pdoctest.ELLIPSIS | pdoctest.NORMALIZE_WHITESPACE |
pdoctest.IGNORE_EXCEPTION_DETAIL)
finally:
# make sure we return to the original displayhook in case some
# doctest has changed that
sys.displayhook = old_displayhook
rstfailed, tested = out
if tested:
failed = rstfailed or failed
if first_report:
first_report = False
msg = 'rst doctests start'
if not t._testfiles:
r.start(msg=msg)
else:
r.write_center(msg)
print()
# use as the id, everything past the first 'sympy'
file_id = rst_file[rst_file.find('sympy') + len('sympy') + 1:]
print(file_id, end=" ")
# get at least the name out so it is know who is being tested
wid = r.terminal_width - len(file_id) - 1 # update width
test_file = '[%s]' % (tested)
report = '[%s]' % (rstfailed or 'OK')
print(''.join(
[test_file, ' '*(wid - len(test_file) - len(report)), report])
)
# the doctests for *py will have printed this message already if there was
# a failure, so now only print it if there was intervening reporting by
# testing the *rst as evidenced by first_report no longer being True.
if not first_report and failed:
print()
print("DO *NOT* COMMIT!")
return int(failed)
sp = re.compile(r'([0-9]+)/([1-9][0-9]*)')
def split_list(l, split, density=None):
"""
Splits a list into part a of b
split should be a string of the form 'a/b'. For instance, '1/3' would give
the split one of three.
If the length of the list is not divisible by the number of splits, the
last split will have more items.
`density` may be specified as a list. If specified,
tests will be balanced so that each split has as equal-as-possible
amount of mass according to `density`.
>>> from sympy.utilities.runtests import split_list
>>> a = list(range(10))
>>> split_list(a, '1/3')
[0, 1, 2]
>>> split_list(a, '2/3')
[3, 4, 5]
>>> split_list(a, '3/3')
[6, 7, 8, 9]
"""
m = sp.match(split)
if not m:
raise ValueError("split must be a string of the form a/b where a and b are ints")
i, t = map(int, m.groups())
if not density:
return l[(i - 1)*len(l)//t : i*len(l)//t]
# normalize density
tot = sum(density)
density = [x / tot for x in density]
def density_inv(x):
"""Interpolate the inverse to the cumulative
distribution function given by density"""
if x <= 0:
return 0
if x >= sum(density):
return 1
# find the first time the cumulative sum surpasses x
# and linearly interpolate
cumm = 0
for i, d in enumerate(density):
cumm += d
if cumm >= x:
break
frac = (d - (cumm - x)) / d
return (i + frac) / len(density)
lower_frac = density_inv((i - 1) / t)
higher_frac = density_inv(i / t)
return l[int(lower_frac*len(l)) : int(higher_frac*len(l))]
from collections import namedtuple
SymPyTestResults = namedtuple('TestResults', 'failed attempted')
def sympytestfile(filename, module_relative=True, name=None, package=None,
globs=None, verbose=None, report=True, optionflags=0,
extraglobs=None, raise_on_error=False,
parser=pdoctest.DocTestParser(), encoding=None):
"""
Test examples in the given file. Return (#failures, #tests).
Optional keyword arg ``module_relative`` specifies how filenames
should be interpreted:
- If ``module_relative`` is True (the default), then ``filename``
specifies a module-relative path. By default, this path is
relative to the calling module's directory; but if the
``package`` argument is specified, then it is relative to that
package. To ensure os-independence, ``filename`` should use
"/" characters to separate path segments, and should not
be an absolute path (i.e., it may not begin with "/").
- If ``module_relative`` is False, then ``filename`` specifies an
os-specific path. The path may be absolute or relative (to
the current working directory).
Optional keyword arg ``name`` gives the name of the test; by default
use the file's basename.
Optional keyword argument ``package`` is a Python package or the
name of a Python package whose directory should be used as the
base directory for a module relative filename. If no package is
specified, then the calling module's directory is used as the base
directory for module relative filenames. It is an error to
specify ``package`` if ``module_relative`` is False.
Optional keyword arg ``globs`` gives a dict to be used as the globals
when executing examples; by default, use {}. A copy of this dict
is actually used for each docstring, so that each docstring's
examples start with a clean slate.
Optional keyword arg ``extraglobs`` gives a dictionary that should be
merged into the globals that are used to execute examples. By
default, no extra globals are used.
Optional keyword arg ``verbose`` prints lots of stuff if true, prints
only failures if false; by default, it's true iff "-v" is in sys.argv.
Optional keyword arg ``report`` prints a summary at the end when true,
else prints nothing at the end. In verbose mode, the summary is
detailed, else very brief (in fact, empty if all tests passed).
Optional keyword arg ``optionflags`` or's together module constants,
and defaults to 0. Possible values (see the docs for details):
- DONT_ACCEPT_TRUE_FOR_1
- DONT_ACCEPT_BLANKLINE
- NORMALIZE_WHITESPACE
- ELLIPSIS
- SKIP
- IGNORE_EXCEPTION_DETAIL
- REPORT_UDIFF
- REPORT_CDIFF
- REPORT_NDIFF
- REPORT_ONLY_FIRST_FAILURE
Optional keyword arg ``raise_on_error`` raises an exception on the
first unexpected exception or failure. This allows failures to be
post-mortem debugged.
Optional keyword arg ``parser`` specifies a DocTestParser (or
subclass) that should be used to extract tests from the files.
Optional keyword arg ``encoding`` specifies an encoding that should
be used to convert the file to unicode.
Advanced tomfoolery: testmod runs methods of a local instance of
class doctest.Tester, then merges the results into (or creates)
global Tester instance doctest.master. Methods of doctest.master
can be called directly too, if you want to do something unusual.
Passing report=0 to testmod is especially useful then, to delay
displaying a summary. Invoke doctest.master.summarize(verbose)
when you're done fiddling.
"""
if package and not module_relative:
raise ValueError("Package may only be specified for module-"
"relative paths.")
# Relativize the path
if not PY3:
text, filename = pdoctest._load_testfile(
filename, package, module_relative)
if encoding is not None:
text = text.decode(encoding)
else:
text, filename = pdoctest._load_testfile(
filename, package, module_relative, encoding)
# If no name was given, then use the file's name.
if name is None:
name = os.path.basename(filename)
# Assemble the globals.
if globs is None:
globs = {}
else:
globs = globs.copy()
if extraglobs is not None:
globs.update(extraglobs)
if '__name__' not in globs:
globs['__name__'] = '__main__'
if raise_on_error:
runner = pdoctest.DebugRunner(verbose=verbose, optionflags=optionflags)
else:
runner = SymPyDocTestRunner(verbose=verbose, optionflags=optionflags)
runner._checker = SymPyOutputChecker()
# Read the file, convert it to a test, and run it.
test = parser.get_doctest(text, globs, name, filename, 0)
runner.run(test, compileflags=future_flags)
if report:
runner.summarize()
if pdoctest.master is None:
pdoctest.master = runner
else:
pdoctest.master.merge(runner)
return SymPyTestResults(runner.failures, runner.tries)
class SymPyTests(object):
def __init__(self, reporter, kw="", post_mortem=False,
seed=None, fast_threshold=None, slow_threshold=None):
self._post_mortem = post_mortem
self._kw = kw
self._count = 0
self._root_dir = sympy_dir
self._reporter = reporter
self._reporter.root_dir(self._root_dir)
self._testfiles = []
self._seed = seed if seed is not None else random.random()
# Defaults in seconds, from human / UX design limits
# http://www.nngroup.com/articles/response-times-3-important-limits/
#
# These defaults are *NOT* set in stone as we are measuring different
# things, so others feel free to come up with a better yardstick :)
if fast_threshold:
self._fast_threshold = float(fast_threshold)
else:
self._fast_threshold = 0.1
if slow_threshold:
self._slow_threshold = float(slow_threshold)
else:
self._slow_threshold = 10
def test(self, sort=False, timeout=False, slow=False, enhance_asserts=False):
"""
Runs the tests returning True if all tests pass, otherwise False.
If sort=False run tests in random order.
"""
if sort:
self._testfiles.sort()
elif slow:
pass
else:
random.seed(self._seed)
random.shuffle(self._testfiles)
self._reporter.start(self._seed)
for f in self._testfiles:
try:
self.test_file(f, sort, timeout, slow, enhance_asserts)
except KeyboardInterrupt:
print(" interrupted by user")
self._reporter.finish()
raise
return self._reporter.finish()
def _enhance_asserts(self, source):
from ast import (NodeTransformer, Compare, Name, Store, Load, Tuple,
Assign, BinOp, Str, Mod, Assert, parse, fix_missing_locations)
ops = {"Eq": '==', "NotEq": '!=', "Lt": '<', "LtE": '<=',
"Gt": '>', "GtE": '>=', "Is": 'is', "IsNot": 'is not',
"In": 'in', "NotIn": 'not in'}
class Transform(NodeTransformer):
def visit_Assert(self, stmt):
if isinstance(stmt.test, Compare):
compare = stmt.test
values = [compare.left] + compare.comparators
names = [ "_%s" % i for i, _ in enumerate(values) ]
names_store = [ Name(n, Store()) for n in names ]
names_load = [ Name(n, Load()) for n in names ]
target = Tuple(names_store, Store())
value = Tuple(values, Load())
assign = Assign([target], value)
new_compare = Compare(names_load[0], compare.ops, names_load[1:])
msg_format = "\n%s " + "\n%s ".join([ ops[op.__class__.__name__] for op in compare.ops ]) + "\n%s"
msg = BinOp(Str(msg_format), Mod(), Tuple(names_load, Load()))
test = Assert(new_compare, msg, lineno=stmt.lineno, col_offset=stmt.col_offset)
return [assign, test]
else:
return stmt
tree = parse(source)
new_tree = Transform().visit(tree)
return fix_missing_locations(new_tree)
def test_file(self, filename, sort=True, timeout=False, slow=False, enhance_asserts=False):
reporter = self._reporter
funcs = []
try:
gl = {'__file__': filename}
try:
if PY3:
open_file = lambda: open(filename, encoding="utf8")
else:
open_file = lambda: open(filename)
with open_file() as f:
source = f.read()
if self._kw:
for l in source.splitlines():
if l.lstrip().startswith('def '):
if any(l.find(k) != -1 for k in self._kw):
break
else:
return
if enhance_asserts:
try:
source = self._enhance_asserts(source)
except ImportError:
pass
code = compile(source, filename, "exec")
exec_(code, gl)
except (SystemExit, KeyboardInterrupt):
raise
except ImportError:
reporter.import_error(filename, sys.exc_info())
return
except Exception:
reporter.test_exception(sys.exc_info())
clear_cache()
self._count += 1
random.seed(self._seed)
disabled = gl.get("disabled", False)
if not disabled:
# we need to filter only those functions that begin with 'test_'
# We have to be careful about decorated functions. As long as
# the decorator uses functools.wraps, we can detect it.
funcs = []
for f in gl:
if (f.startswith("test_") and (inspect.isfunction(gl[f])
or inspect.ismethod(gl[f]))):
func = gl[f]
# Handle multiple decorators
while hasattr(func, '__wrapped__'):
func = func.__wrapped__
if inspect.getsourcefile(func) == filename:
funcs.append(gl[f])
if slow:
funcs = [f for f in funcs if getattr(f, '_slow', False)]
# Sorting of XFAILed functions isn't fixed yet :-(
funcs.sort(key=lambda x: inspect.getsourcelines(x)[1])
i = 0
while i < len(funcs):
if inspect.isgeneratorfunction(funcs[i]):
# some tests can be generators, that return the actual
# test functions. We unpack it below:
f = funcs.pop(i)
for fg in f():
func = fg[0]
args = fg[1:]
fgw = lambda: func(*args)
funcs.insert(i, fgw)
i += 1
else:
i += 1
# drop functions that are not selected with the keyword expression:
funcs = [x for x in funcs if self.matches(x)]
if not funcs:
return
except Exception:
reporter.entering_filename(filename, len(funcs))
raise
reporter.entering_filename(filename, len(funcs))
if not sort:
random.shuffle(funcs)
for f in funcs:
start = time.time()
reporter.entering_test(f)
try:
if getattr(f, '_slow', False) and not slow:
raise Skipped("Slow")
if timeout:
self._timeout(f, timeout)
else:
random.seed(self._seed)
f()
except KeyboardInterrupt:
if getattr(f, '_slow', False):
reporter.test_skip("KeyboardInterrupt")
else:
raise
except Exception:
if timeout:
signal.alarm(0) # Disable the alarm. It could not be handled before.
t, v, tr = sys.exc_info()
if t is AssertionError:
reporter.test_fail((t, v, tr))
if self._post_mortem:
pdb.post_mortem(tr)
elif t.__name__ == "Skipped":
reporter.test_skip(v)
elif t.__name__ == "XFail":
reporter.test_xfail()
elif t.__name__ == "XPass":
reporter.test_xpass(v)
else:
reporter.test_exception((t, v, tr))
if self._post_mortem:
pdb.post_mortem(tr)
else:
reporter.test_pass()
taken = time.time() - start
if taken > self._slow_threshold:
reporter.slow_test_functions.append((f.__name__, taken))
if getattr(f, '_slow', False) and slow:
if taken < self._fast_threshold:
reporter.fast_test_functions.append((f.__name__, taken))
reporter.leaving_filename()
def _timeout(self, function, timeout):
def callback(x, y):
signal.alarm(0)
raise Skipped("Timeout")
signal.signal(signal.SIGALRM, callback)
signal.alarm(timeout) # Set an alarm with a given timeout
function()
signal.alarm(0) # Disable the alarm
def matches(self, x):
"""
Does the keyword expression self._kw match "x"? Returns True/False.
Always returns True if self._kw is "".
"""
if not self._kw:
return True
for kw in self._kw:
if x.__name__.find(kw) != -1:
return True
return False
def get_test_files(self, dir, pat='test_*.py'):
"""
Returns the list of test_*.py (default) files at or below directory
``dir`` relative to the sympy home directory.
"""
dir = os.path.join(self._root_dir, convert_to_native_paths([dir])[0])
g = []
for path, folders, files in os.walk(dir):
g.extend([os.path.join(path, f) for f in files if fnmatch(f, pat)])
return sorted([sys_normcase(gi) for gi in g])
class SymPyDocTests(object):
def __init__(self, reporter, normal):
self._count = 0
self._root_dir = sympy_dir
self._reporter = reporter
self._reporter.root_dir(self._root_dir)
self._normal = normal
self._testfiles = []
def test(self):
"""
Runs the tests and returns True if all tests pass, otherwise False.
"""
self._reporter.start()
for f in self._testfiles:
try:
self.test_file(f)
except KeyboardInterrupt:
print(" interrupted by user")
self._reporter.finish()
raise
return self._reporter.finish()
def test_file(self, filename):
clear_cache()
from sympy.core.compatibility import StringIO
rel_name = filename[len(self._root_dir) + 1:]
dirname, file = os.path.split(filename)
module = rel_name.replace(os.sep, '.')[:-3]
if rel_name.startswith("examples"):
# Examples files do not have __init__.py files,
# So we have to temporarily extend sys.path to import them
sys.path.insert(0, dirname)
module = file[:-3] # remove ".py"
setup_pprint()
try:
module = pdoctest._normalize_module(module)
tests = SymPyDocTestFinder().find(module)
except (SystemExit, KeyboardInterrupt):
raise
except ImportError:
self._reporter.import_error(filename, sys.exc_info())
return
finally:
if rel_name.startswith("examples"):
del sys.path[0]
tests = [test for test in tests if len(test.examples) > 0]
# By default tests are sorted by alphabetical order by function name.
# We sort by line number so one can edit the file sequentially from
# bottom to top. However, if there are decorated functions, their line
# numbers will be too large and for now one must just search for these
# by text and function name.
tests.sort(key=lambda x: -x.lineno)
if not tests:
return
self._reporter.entering_filename(filename, len(tests))
for test in tests:
assert len(test.examples) != 0
# check if there are external dependencies which need to be met
if '_doctest_depends_on' in test.globs:
has_dependencies = self._process_dependencies(test.globs['_doctest_depends_on'])
if has_dependencies is not True:
# has_dependencies is either True or a message
self._reporter.test_skip(v="\n" + has_dependencies)
continue
if self._reporter._verbose:
self._reporter.write("\n{} ".format(test.name))
runner = SymPyDocTestRunner(optionflags=pdoctest.ELLIPSIS |
pdoctest.NORMALIZE_WHITESPACE |
pdoctest.IGNORE_EXCEPTION_DETAIL)
runner._checker = SymPyOutputChecker()
old = sys.stdout
new = StringIO()
sys.stdout = new
# If the testing is normal, the doctests get importing magic to
# provide the global namespace. If not normal (the default) then
# then must run on their own; all imports must be explicit within
# a function's docstring. Once imported that import will be
# available to the rest of the tests in a given function's
# docstring (unless clear_globs=True below).
if not self._normal:
test.globs = {}
# if this is uncommented then all the test would get is what
# comes by default with a "from sympy import *"
#exec('from sympy import *') in test.globs
test.globs['print_function'] = print_function
try:
f, t = runner.run(test, compileflags=future_flags,
out=new.write, clear_globs=False)
except KeyboardInterrupt:
raise
finally:
sys.stdout = old
if f > 0:
self._reporter.doctest_fail(test.name, new.getvalue())
else:
self._reporter.test_pass()
self._reporter.leaving_filename()
def get_test_files(self, dir, pat='*.py', init_only=True):
r"""
Returns the list of \*.py files (default) from which docstrings
will be tested which are at or below directory ``dir``. By default,
only those that have an __init__.py in their parent directory
and do not start with ``test_`` will be included.
"""
def importable(x):
"""
Checks if given pathname x is an importable module by checking for
__init__.py file.
Returns True/False.
Currently we only test if the __init__.py file exists in the
directory with the file "x" (in theory we should also test all the
parent dirs).
"""
init_py = os.path.join(os.path.dirname(x), "__init__.py")
return os.path.exists(init_py)
dir = os.path.join(self._root_dir, convert_to_native_paths([dir])[0])
g = []
for path, folders, files in os.walk(dir):
g.extend([os.path.join(path, f) for f in files
if not f.startswith('test_') and fnmatch(f, pat)])
if init_only:
# skip files that are not importable (i.e. missing __init__.py)
g = [x for x in g if importable(x)]
return [sys_normcase(gi) for gi in g]
def _process_dependencies(self, deps):
"""
Returns ``False`` if some dependencies are not met and the test should be
skipped otherwise returns ``True``.
"""
executables = deps.get('exe', None)
moduledeps = deps.get('modules', None)
viewers = deps.get('disable_viewers', None)
pyglet = deps.get('pyglet', None)
# print deps
if executables is not None:
for ex in executables:
found = find_executable(ex)
if found is None:
return "Could not find %s" % ex
if moduledeps is not None:
for extmod in moduledeps:
if extmod == 'matplotlib':
matplotlib = import_module(
'matplotlib',
__import__kwargs={'fromlist':
['pyplot', 'cm', 'collections']},
min_module_version='1.0.0', catch=(RuntimeError,))
if matplotlib is not None:
pass
else:
return "Could not import matplotlib"
else:
# TODO min version support
mod = import_module(extmod)
if mod is not None:
version = "unknown"
if hasattr(mod, '__version__'):
version = mod.__version__
else:
return "Could not import %s" % mod
if viewers is not None:
import tempfile
tempdir = tempfile.mkdtemp()
os.environ['PATH'] = '%s:%s' % (tempdir, os.environ['PATH'])
if PY3:
vw = '#!/usr/bin/env python3\n' \
'import sys\n' \
'if len(sys.argv) <= 1:\n' \
' exit("wrong number of args")\n'
else:
vw = '#!/usr/bin/env python\n' \
'import sys\n' \
'if len(sys.argv) <= 1:\n' \
' exit("wrong number of args")\n'
for viewer in viewers:
with open(os.path.join(tempdir, viewer), 'w') as fh:
fh.write(vw)
# make the file executable
os.chmod(os.path.join(tempdir, viewer),
stat.S_IREAD | stat.S_IWRITE | stat.S_IXUSR)
if pyglet:
# monkey-patch pyglet s.t. it does not open a window during
# doctesting
import pyglet
class DummyWindow(object):
def __init__(self, *args, **kwargs):
self.has_exit=True
self.width = 600
self.height = 400
def set_vsync(self, x):
pass
def switch_to(self):
pass
def push_handlers(self, x):
pass
def close(self):
pass
pyglet.window.Window = DummyWindow
return True
class SymPyDocTestFinder(DocTestFinder):
"""
A class used to extract the DocTests that are relevant to a given
object, from its docstring and the docstrings of its contained
objects. Doctests can currently be extracted from the following
object types: modules, functions, classes, methods, staticmethods,
classmethods, and properties.
Modified from doctest's version by looking harder for code in the
case that it looks like the the code comes from a different module.
In the case of decorated functions (e.g. @vectorize) they appear
to come from a different module (e.g. multidemensional) even though
their code is not there.
"""
def _find(self, tests, obj, name, module, source_lines, globs, seen):
"""
Find tests for the given object and any contained objects, and
add them to ``tests``.
"""
if self._verbose:
print('Finding tests in %s' % name)
# If we've already processed this object, then ignore it.
if id(obj) in seen:
return
seen[id(obj)] = 1
# Make sure we don't run doctests for classes outside of sympy, such
# as in numpy or scipy.
if inspect.isclass(obj):
if obj.__module__.split('.')[0] != 'sympy':
return
# Find a test for this object, and add it to the list of tests.
test = self._get_test(obj, name, module, globs, source_lines)
if test is not None:
tests.append(test)
if not self._recurse:
return
# Look for tests in a module's contained objects.
if inspect.ismodule(obj):
for rawname, val in obj.__dict__.items():
# Recurse to functions & classes.
if inspect.isfunction(val) or inspect.isclass(val):
# Make sure we don't run doctests functions or classes
# from different modules
if val.__module__ != module.__name__:
continue
assert self._from_module(module, val), \
"%s is not in module %s (rawname %s)" % (val, module, rawname)
try:
valname = '%s.%s' % (name, rawname)
self._find(tests, val, valname, module,
source_lines, globs, seen)
except KeyboardInterrupt:
raise
# Look for tests in a module's __test__ dictionary.
for valname, val in getattr(obj, '__test__', {}).items():
if not isinstance(valname, string_types):
raise ValueError("SymPyDocTestFinder.find: __test__ keys "
"must be strings: %r" %
(type(valname),))
if not (inspect.isfunction(val) or inspect.isclass(val) or
inspect.ismethod(val) or inspect.ismodule(val) or
isinstance(val, string_types)):
raise ValueError("SymPyDocTestFinder.find: __test__ values "
"must be strings, functions, methods, "
"classes, or modules: %r" %
(type(val),))
valname = '%s.__test__.%s' % (name, valname)
self._find(tests, val, valname, module, source_lines,
globs, seen)
# Look for tests in a class's contained objects.
if inspect.isclass(obj):
for valname, val in obj.__dict__.items():
# Special handling for staticmethod/classmethod.
if isinstance(val, staticmethod):
val = getattr(obj, valname)
if isinstance(val, classmethod):
val = getattr(obj, valname).__func__
# Recurse to methods, properties, and nested classes.
if (inspect.isfunction(val) or
inspect.isclass(val) or
isinstance(val, property)):
# Make sure we don't run doctests functions or classes
# from different modules
if isinstance(val, property):
if hasattr(val.fget, '__module__'):
if val.fget.__module__ != module.__name__:
continue
else:
if val.__module__ != module.__name__:
continue
assert self._from_module(module, val), \
"%s is not in module %s (valname %s)" % (
val, module, valname)
valname = '%s.%s' % (name, valname)
self._find(tests, val, valname, module, source_lines,
globs, seen)
def _get_test(self, obj, name, module, globs, source_lines):
"""
Return a DocTest for the given object, if it defines a docstring;
otherwise, return None.
"""
lineno = None
# Extract the object's docstring. If it doesn't have one,
# then return None (no test for this object).
if isinstance(obj, string_types):
# obj is a string in the case for objects in the polys package.
# Note that source_lines is a binary string (compiled polys
# modules), which can't be handled by _find_lineno so determine
# the line number here.
docstring = obj
matches = re.findall(r"line \d+", name)
assert len(matches) == 1, \
"string '%s' does not contain lineno " % name
# NOTE: this is not the exact linenumber but its better than no
# lineno ;)
lineno = int(matches[0][5:])
else:
try:
if obj.__doc__ is None:
docstring = ''
else:
docstring = obj.__doc__
if not isinstance(docstring, string_types):
docstring = str(docstring)
except (TypeError, AttributeError):
docstring = ''
# Don't bother if the docstring is empty.
if self._exclude_empty and not docstring:
return None
# check that properties have a docstring because _find_lineno
# assumes it
if isinstance(obj, property):
if obj.fget.__doc__ is None:
return None
# Find the docstring's location in the file.
if lineno is None:
# handling of properties is not implemented in _find_lineno so do
# it here
if hasattr(obj, 'func_closure') and obj.func_closure is not None:
tobj = obj.func_closure[0].cell_contents
elif isinstance(obj, property):
tobj = obj.fget
else:
tobj = obj
lineno = self._find_lineno(tobj, source_lines)
if lineno is None:
return None
# Return a DocTest for this object.
if module is None:
filename = None
else:
filename = getattr(module, '__file__', module.__name__)
if filename[-4:] in (".pyc", ".pyo"):
filename = filename[:-1]
if hasattr(obj, '_doctest_depends_on'):
globs['_doctest_depends_on'] = obj._doctest_depends_on
else:
globs['_doctest_depends_on'] = {}
return self._parser.get_doctest(docstring, globs, name,
filename, lineno)
class SymPyDocTestRunner(DocTestRunner):
"""
A class used to run DocTest test cases, and accumulate statistics.
The ``run`` method is used to process a single DocTest case. It
returns a tuple ``(f, t)``, where ``t`` is the number of test cases
tried, and ``f`` is the number of test cases that failed.
Modified from the doctest version to not reset the sys.displayhook (see
issue 5140).
See the docstring of the original DocTestRunner for more information.
"""
def run(self, test, compileflags=None, out=None, clear_globs=True):
"""
Run the examples in ``test``, and display the results using the
writer function ``out``.
The examples are run in the namespace ``test.globs``. If
``clear_globs`` is true (the default), then this namespace will
be cleared after the test runs, to help with garbage
collection. If you would like to examine the namespace after
the test completes, then use ``clear_globs=False``.
``compileflags`` gives the set of flags that should be used by
the Python compiler when running the examples. If not
specified, then it will default to the set of future-import
flags that apply to ``globs``.
The output of each example is checked using
``SymPyDocTestRunner.check_output``, and the results are
formatted by the ``SymPyDocTestRunner.report_*`` methods.
"""
self.test = test
if compileflags is None:
compileflags = pdoctest._extract_future_flags(test.globs)
save_stdout = sys.stdout
if out is None:
out = save_stdout.write
sys.stdout = self._fakeout
# Patch pdb.set_trace to restore sys.stdout during interactive
# debugging (so it's not still redirected to self._fakeout).
# Note that the interactive output will go to *our*
# save_stdout, even if that's not the real sys.stdout; this
# allows us to write test cases for the set_trace behavior.
save_set_trace = pdb.set_trace
self.debugger = pdoctest._OutputRedirectingPdb(save_stdout)
self.debugger.reset()
pdb.set_trace = self.debugger.set_trace
# Patch linecache.getlines, so we can see the example's source
# when we're inside the debugger.
self.save_linecache_getlines = pdoctest.linecache.getlines
linecache.getlines = self.__patched_linecache_getlines
try:
test.globs['print_function'] = print_function
return self.__run(test, compileflags, out)
finally:
sys.stdout = save_stdout
pdb.set_trace = save_set_trace
linecache.getlines = self.save_linecache_getlines
if clear_globs:
test.globs.clear()
# We have to override the name mangled methods.
SymPyDocTestRunner._SymPyDocTestRunner__patched_linecache_getlines = \
DocTestRunner._DocTestRunner__patched_linecache_getlines
SymPyDocTestRunner._SymPyDocTestRunner__run = DocTestRunner._DocTestRunner__run
SymPyDocTestRunner._SymPyDocTestRunner__record_outcome = \
DocTestRunner._DocTestRunner__record_outcome
class SymPyOutputChecker(pdoctest.OutputChecker):
"""
Compared to the OutputChecker from the stdlib our OutputChecker class
supports numerical comparison of floats occuring in the output of the
doctest examples
"""
def __init__(self):
# NOTE OutputChecker is an old-style class with no __init__ method,
# so we can't call the base class version of __init__ here
got_floats = r'(\d+\.\d*|\.\d+)'
# floats in the 'want' string may contain ellipses
want_floats = got_floats + r'(\.{3})?'
front_sep = r'\s|\+|\-|\*|,'
back_sep = front_sep + r'|j|e'
fbeg = r'^%s(?=%s|$)' % (got_floats, back_sep)
fmidend = r'(?<=%s)%s(?=%s|$)' % (front_sep, got_floats, back_sep)
self.num_got_rgx = re.compile(r'(%s|%s)' %(fbeg, fmidend))
fbeg = r'^%s(?=%s|$)' % (want_floats, back_sep)
fmidend = r'(?<=%s)%s(?=%s|$)' % (front_sep, want_floats, back_sep)
self.num_want_rgx = re.compile(r'(%s|%s)' %(fbeg, fmidend))
def check_output(self, want, got, optionflags):
"""
Return True iff the actual output from an example (`got`)
matches the expected output (`want`). These strings are
always considered to match if they are identical; but
depending on what option flags the test runner is using,
several non-exact match types are also possible. See the
documentation for `TestRunner` for more information about
option flags.
"""
# Handle the common case first, for efficiency:
# if they're string-identical, always return true.
if got == want:
return True
# TODO parse integers as well ?
# Parse floats and compare them. If some of the parsed floats contain
# ellipses, skip the comparison.
matches = self.num_got_rgx.finditer(got)
numbers_got = [match.group(1) for match in matches] # list of strs
matches = self.num_want_rgx.finditer(want)
numbers_want = [match.group(1) for match in matches] # list of strs
if len(numbers_got) != len(numbers_want):
return False
if len(numbers_got) > 0:
nw_ = []
for ng, nw in zip(numbers_got, numbers_want):
if '...' in nw:
nw_.append(ng)
continue
else:
nw_.append(nw)
if abs(float(ng)-float(nw)) > 1e-5:
return False
got = self.num_got_rgx.sub(r'%s', got)
got = got % tuple(nw_)
# <BLANKLINE> can be used as a special sequence to signify a
# blank line, unless the DONT_ACCEPT_BLANKLINE flag is used.
if not (optionflags & pdoctest.DONT_ACCEPT_BLANKLINE):
# Replace <BLANKLINE> in want with a blank line.
want = re.sub(r'(?m)^%s\s*?$' % re.escape(pdoctest.BLANKLINE_MARKER),
'', want)
# If a line in got contains only spaces, then remove the
# spaces.
got = re.sub(r'(?m)^\s*?$', '', got)
if got == want:
return True
# This flag causes doctest to ignore any differences in the
# contents of whitespace strings. Note that this can be used
# in conjunction with the ELLIPSIS flag.
if optionflags & pdoctest.NORMALIZE_WHITESPACE:
got = ' '.join(got.split())
want = ' '.join(want.split())
if got == want:
return True
# The ELLIPSIS flag says to let the sequence "..." in `want`
# match any substring in `got`.
if optionflags & pdoctest.ELLIPSIS:
if pdoctest._ellipsis_match(want, got):
return True
# We didn't find any match; return false.
return False
class Reporter(object):
"""
Parent class for all reporters.
"""
pass
class PyTestReporter(Reporter):
"""
Py.test like reporter. Should produce output identical to py.test.
"""
def __init__(self, verbose=False, tb="short", colors=True,
force_colors=False, split=None):
self._verbose = verbose
self._tb_style = tb
self._colors = colors
self._force_colors = force_colors
self._xfailed = 0
self._xpassed = []
self._failed = []
self._failed_doctest = []
self._passed = 0
self._skipped = 0
self._exceptions = []
self._terminal_width = None
self._default_width = 80
self._split = split
# TODO: Should these be protected?
self.slow_test_functions = []
self.fast_test_functions = []
# this tracks the x-position of the cursor (useful for positioning
# things on the screen), without the need for any readline library:
self._write_pos = 0
self._line_wrap = False
def root_dir(self, dir):
self._root_dir = dir
@property
def terminal_width(self):
if self._terminal_width is not None:
return self._terminal_width
def findout_terminal_width():
if sys.platform == "win32":
# Windows support is based on:
#
# http://code.activestate.com/recipes/
# 440694-determine-size-of-console-window-on-windows/
from ctypes import windll, create_string_buffer
h = windll.kernel32.GetStdHandle(-12)
csbi = create_string_buffer(22)
res = windll.kernel32.GetConsoleScreenBufferInfo(h, csbi)
if res:
import struct
(_, _, _, _, _, left, _, right, _, _, _) = \
struct.unpack("hhhhHhhhhhh", csbi.raw)
return right - left
else:
return self._default_width
if hasattr(sys.stdout, 'isatty') and not sys.stdout.isatty():
return self._default_width # leave PIPEs alone
try:
process = subprocess.Popen(['stty', '-a'],
stdout=subprocess.PIPE,
stderr=subprocess.PIPE)
stdout = process.stdout.read()
if PY3:
stdout = stdout.decode("utf-8")
except (OSError, IOError):
pass
else:
# We support the following output formats from stty:
#
# 1) Linux -> columns 80
# 2) OS X -> 80 columns
# 3) Solaris -> columns = 80
re_linux = r"columns\s+(?P<columns>\d+);"
re_osx = r"(?P<columns>\d+)\s*columns;"
re_solaris = r"columns\s+=\s+(?P<columns>\d+);"
for regex in (re_linux, re_osx, re_solaris):
match = re.search(regex, stdout)
if match is not None:
columns = match.group('columns')
try:
width = int(columns)
except ValueError:
pass
if width != 0:
return width
return self._default_width
width = findout_terminal_width()
self._terminal_width = width
return width
def write(self, text, color="", align="left", width=None,
force_colors=False):
"""
Prints a text on the screen.
It uses sys.stdout.write(), so no readline library is necessary.
Parameters
==========
color : choose from the colors below, "" means default color
align : "left"/"right", "left" is a normal print, "right" is aligned on
the right-hand side of the screen, filled with spaces if
necessary
width : the screen width
"""
color_templates = (
("Black", "0;30"),
("Red", "0;31"),
("Green", "0;32"),
("Brown", "0;33"),
("Blue", "0;34"),
("Purple", "0;35"),
("Cyan", "0;36"),
("LightGray", "0;37"),
("DarkGray", "1;30"),
("LightRed", "1;31"),
("LightGreen", "1;32"),
("Yellow", "1;33"),
("LightBlue", "1;34"),
("LightPurple", "1;35"),
("LightCyan", "1;36"),
("White", "1;37"),
)
colors = {}
for name, value in color_templates:
colors[name] = value
c_normal = '\033[0m'
c_color = '\033[%sm'
if width is None:
width = self.terminal_width
if align == "right":
if self._write_pos + len(text) > width:
# we don't fit on the current line, create a new line
self.write("\n")
self.write(" "*(width - self._write_pos - len(text)))
if not self._force_colors and hasattr(sys.stdout, 'isatty') and not \
sys.stdout.isatty():
# the stdout is not a terminal, this for example happens if the
# output is piped to less, e.g. "bin/test | less". In this case,
# the terminal control sequences would be printed verbatim, so
# don't use any colors.
color = ""
elif sys.platform == "win32":
# Windows consoles don't support ANSI escape sequences
color = ""
elif not self._colors:
color = ""
if self._line_wrap:
if text[0] != "\n":
sys.stdout.write("\n")
# Avoid UnicodeEncodeError when printing out test failures
if PY3 and IS_WINDOWS:
text = text.encode('raw_unicode_escape').decode('utf8', 'ignore')
elif PY3 and not sys.stdout.encoding.lower().startswith('utf'):
text = text.encode(sys.stdout.encoding, 'backslashreplace'
).decode(sys.stdout.encoding)
if color == "":
sys.stdout.write(text)
else:
sys.stdout.write("%s%s%s" %
(c_color % colors[color], text, c_normal))
sys.stdout.flush()
l = text.rfind("\n")
if l == -1:
self._write_pos += len(text)
else:
self._write_pos = len(text) - l - 1
self._line_wrap = self._write_pos >= width
self._write_pos %= width
def write_center(self, text, delim="="):
width = self.terminal_width
if text != "":
text = " %s " % text
idx = (width - len(text)) // 2
t = delim*idx + text + delim*(width - idx - len(text))
self.write(t + "\n")
def write_exception(self, e, val, tb):
t = traceback.extract_tb(tb)
# remove the first item, as that is always runtests.py
t = t[1:]
t = traceback.format_list(t)
self.write("".join(t))
t = traceback.format_exception_only(e, val)
self.write("".join(t))
def start(self, seed=None, msg="test process starts"):
self.write_center(msg)
executable = sys.executable
v = tuple(sys.version_info)
python_version = "%s.%s.%s-%s-%s" % v
implementation = platform.python_implementation()
if implementation == 'PyPy':
implementation += " %s.%s.%s-%s-%s" % sys.pypy_version_info
self.write("executable: %s (%s) [%s]\n" %
(executable, python_version, implementation))
from .misc import ARCH
self.write("architecture: %s\n" % ARCH)
from sympy.core.cache import USE_CACHE
self.write("cache: %s\n" % USE_CACHE)
from sympy.core.compatibility import GROUND_TYPES, HAS_GMPY
version = ''
if GROUND_TYPES =='gmpy':
if HAS_GMPY == 1:
import gmpy
elif HAS_GMPY == 2:
import gmpy2 as gmpy
version = gmpy.version()
self.write("ground types: %s %s\n" % (GROUND_TYPES, version))
if seed is not None:
self.write("random seed: %d\n" % seed)
from .misc import HASH_RANDOMIZATION
self.write("hash randomization: ")
hash_seed = os.getenv("PYTHONHASHSEED") or '0'
if HASH_RANDOMIZATION and (hash_seed == "random" or int(hash_seed)):
self.write("on (PYTHONHASHSEED=%s)\n" % hash_seed)
else:
self.write("off\n")
if self._split:
self.write("split: %s\n" % self._split)
self.write('\n')
self._t_start = clock()
def finish(self):
self._t_end = clock()
self.write("\n")
global text, linelen
text = "tests finished: %d passed, " % self._passed
linelen = len(text)
def add_text(mytext):
global text, linelen
"""Break new text if too long."""
if linelen + len(mytext) > self.terminal_width:
text += '\n'
linelen = 0
text += mytext
linelen += len(mytext)
if len(self._failed) > 0:
add_text("%d failed, " % len(self._failed))
if len(self._failed_doctest) > 0:
add_text("%d failed, " % len(self._failed_doctest))
if self._skipped > 0:
add_text("%d skipped, " % self._skipped)
if self._xfailed > 0:
add_text("%d expected to fail, " % self._xfailed)
if len(self._xpassed) > 0:
add_text("%d expected to fail but passed, " % len(self._xpassed))
if len(self._exceptions) > 0:
add_text("%d exceptions, " % len(self._exceptions))
add_text("in %.2f seconds" % (self._t_end - self._t_start))
if self.slow_test_functions:
self.write_center('slowest tests', '_')
sorted_slow = sorted(self.slow_test_functions, key=lambda r: r[1])
for slow_func_name, taken in sorted_slow:
print('%s - Took %.3f seconds' % (slow_func_name, taken))
if self.fast_test_functions:
self.write_center('unexpectedly fast tests', '_')
sorted_fast = sorted(self.fast_test_functions,
key=lambda r: r[1])
for fast_func_name, taken in sorted_fast:
print('%s - Took %.3f seconds' % (fast_func_name, taken))
if len(self._xpassed) > 0:
self.write_center("xpassed tests", "_")
for e in self._xpassed:
self.write("%s: %s\n" % (e[0], e[1]))
self.write("\n")
if self._tb_style != "no" and len(self._exceptions) > 0:
for e in self._exceptions:
filename, f, (t, val, tb) = e
self.write_center("", "_")
if f is None:
s = "%s" % filename
else:
s = "%s:%s" % (filename, f.__name__)
self.write_center(s, "_")
self.write_exception(t, val, tb)
self.write("\n")
if self._tb_style != "no" and len(self._failed) > 0:
for e in self._failed:
filename, f, (t, val, tb) = e
self.write_center("", "_")
self.write_center("%s:%s" % (filename, f.__name__), "_")
self.write_exception(t, val, tb)
self.write("\n")
if self._tb_style != "no" and len(self._failed_doctest) > 0:
for e in self._failed_doctest:
filename, msg = e
self.write_center("", "_")
self.write_center("%s" % filename, "_")
self.write(msg)
self.write("\n")
self.write_center(text)
ok = len(self._failed) == 0 and len(self._exceptions) == 0 and \
len(self._failed_doctest) == 0
if not ok:
self.write("DO *NOT* COMMIT!\n")
return ok
def entering_filename(self, filename, n):
rel_name = filename[len(self._root_dir) + 1:]
self._active_file = rel_name
self._active_file_error = False
self.write(rel_name)
self.write("[%d] " % n)
def leaving_filename(self):
self.write(" ")
if self._active_file_error:
self.write("[FAIL]", "Red", align="right")
else:
self.write("[OK]", "Green", align="right")
self.write("\n")
if self._verbose:
self.write("\n")
def entering_test(self, f):
self._active_f = f
if self._verbose:
self.write("\n" + f.__name__ + " ")
def test_xfail(self):
self._xfailed += 1
self.write("f", "Green")
def test_xpass(self, v):
message = str(v)
self._xpassed.append((self._active_file, message))
self.write("X", "Green")
def test_fail(self, exc_info):
self._failed.append((self._active_file, self._active_f, exc_info))
self.write("F", "Red")
self._active_file_error = True
def doctest_fail(self, name, error_msg):
# the first line contains "******", remove it:
error_msg = "\n".join(error_msg.split("\n")[1:])
self._failed_doctest.append((name, error_msg))
self.write("F", "Red")
self._active_file_error = True
def test_pass(self, char="."):
self._passed += 1
if self._verbose:
self.write("ok", "Green")
else:
self.write(char, "Green")
def test_skip(self, v=None):
char = "s"
self._skipped += 1
if v is not None:
message = str(v)
if message == "KeyboardInterrupt":
char = "K"
elif message == "Timeout":
char = "T"
elif message == "Slow":
char = "w"
if self._verbose:
if v is not None:
self.write(message + ' ', "Blue")
else:
self.write(" - ", "Blue")
self.write(char, "Blue")
def test_exception(self, exc_info):
self._exceptions.append((self._active_file, self._active_f, exc_info))
self.write("E", "Red")
self._active_file_error = True
def import_error(self, filename, exc_info):
self._exceptions.append((filename, None, exc_info))
rel_name = filename[len(self._root_dir) + 1:]
self.write(rel_name)
self.write("[?] Failed to import", "Red")
self.write(" ")
self.write("[FAIL]", "Red", align="right")
self.write("\n")
sympy_dir = get_sympy_dir()
| 85,291 | 36.148084 | 261 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/tests/test_codegen_octave.py
|
from sympy.core import (S, symbols, Eq, pi, Catalan, EulerGamma, Lambda,
Dummy, Function)
from sympy.core.compatibility import StringIO
from sympy import erf, Integral, Piecewise
from sympy import Equality
from sympy.matrices import Matrix, MatrixSymbol
from sympy.utilities.codegen import OctaveCodeGen, codegen, make_routine
from sympy.utilities.pytest import raises
from sympy.utilities.lambdify import implemented_function
from sympy.utilities.pytest import XFAIL
import sympy
x, y, z = symbols('x,y,z')
def test_empty_m_code():
code_gen = OctaveCodeGen()
output = StringIO()
code_gen.dump_m([], output, "file", header=False, empty=False)
source = output.getvalue()
assert source == ""
def test_m_simple_code():
name_expr = ("test", (x + y)*z)
result, = codegen(name_expr, "Octave", header=False, empty=False)
assert result[0] == "test.m"
source = result[1]
expected = (
"function out1 = test(x, y, z)\n"
" out1 = z.*(x + y);\n"
"end\n"
)
assert source == expected
def test_m_simple_code_with_header():
name_expr = ("test", (x + y)*z)
result, = codegen(name_expr, "Octave", header=True, empty=False)
assert result[0] == "test.m"
source = result[1]
expected = (
"function out1 = test(x, y, z)\n"
" %TEST Autogenerated by sympy\n"
" % Code generated with sympy " + sympy.__version__ + "\n"
" %\n"
" % See http://www.sympy.org/ for more information.\n"
" %\n"
" % This file is part of 'project'\n"
" out1 = z.*(x + y);\n"
"end\n"
)
assert source == expected
def test_m_simple_code_nameout():
expr = Equality(z, (x + y))
name_expr = ("test", expr)
result, = codegen(name_expr, "Octave", header=False, empty=False)
source = result[1]
expected = (
"function z = test(x, y)\n"
" z = x + y;\n"
"end\n"
)
assert source == expected
def test_m_numbersymbol():
name_expr = ("test", pi**Catalan)
result, = codegen(name_expr, "Octave", header=False, empty=False)
source = result[1]
expected = (
"function out1 = test()\n"
" out1 = pi^0.915965594177219;\n"
"end\n"
)
assert source == expected
@XFAIL
def test_m_numbersymbol_no_inline():
# FIXME: how to pass inline=False to the OctaveCodePrinter?
name_expr = ("test", [pi**Catalan, EulerGamma])
result, = codegen(name_expr, "Octave", header=False,
empty=False, inline=False)
source = result[1]
expected = (
"function [out1, out2] = test()\n"
" Catalan = 0.915965594177219; % constant\n"
" EulerGamma = 0.5772156649015329; % constant\n"
" out1 = pi^Catalan;\n"
" out2 = EulerGamma;\n"
"end\n"
)
assert source == expected
def test_m_code_argument_order():
expr = x + y
routine = make_routine("test", expr, argument_sequence=[z, x, y], language="octave")
code_gen = OctaveCodeGen()
output = StringIO()
code_gen.dump_m([routine], output, "test", header=False, empty=False)
source = output.getvalue()
expected = (
"function out1 = test(z, x, y)\n"
" out1 = x + y;\n"
"end\n"
)
assert source == expected
def test_multiple_results_m():
# Here the output order is the input order
expr1 = (x + y)*z
expr2 = (x - y)*z
name_expr = ("test", [expr1, expr2])
result, = codegen(name_expr, "Octave", header=False, empty=False)
source = result[1]
expected = (
"function [out1, out2] = test(x, y, z)\n"
" out1 = z.*(x + y);\n"
" out2 = z.*(x - y);\n"
"end\n"
)
assert source == expected
def test_results_named_unordered():
# Here output order is based on name_expr
A, B, C = symbols('A,B,C')
expr1 = Equality(C, (x + y)*z)
expr2 = Equality(A, (x - y)*z)
expr3 = Equality(B, 2*x)
name_expr = ("test", [expr1, expr2, expr3])
result, = codegen(name_expr, "Octave", header=False, empty=False)
source = result[1]
expected = (
"function [C, A, B] = test(x, y, z)\n"
" C = z.*(x + y);\n"
" A = z.*(x - y);\n"
" B = 2*x;\n"
"end\n"
)
assert source == expected
def test_results_named_ordered():
A, B, C = symbols('A,B,C')
expr1 = Equality(C, (x + y)*z)
expr2 = Equality(A, (x - y)*z)
expr3 = Equality(B, 2*x)
name_expr = ("test", [expr1, expr2, expr3])
result = codegen(name_expr, "Octave", header=False, empty=False,
argument_sequence=(x, z, y))
assert result[0][0] == "test.m"
source = result[0][1]
expected = (
"function [C, A, B] = test(x, z, y)\n"
" C = z.*(x + y);\n"
" A = z.*(x - y);\n"
" B = 2*x;\n"
"end\n"
)
assert source == expected
def test_complicated_m_codegen():
from sympy import sin, cos, tan
name_expr = ("testlong",
[ ((sin(x) + cos(y) + tan(z))**3).expand(),
cos(cos(cos(cos(cos(cos(cos(cos(x + y + z))))))))
])
result = codegen(name_expr, "Octave", header=False, empty=False)
assert result[0][0] == "testlong.m"
source = result[0][1]
expected = (
"function [out1, out2] = testlong(x, y, z)\n"
" out1 = sin(x).^3 + 3*sin(x).^2.*cos(y) + 3*sin(x).^2.*tan(z)"
" + 3*sin(x).*cos(y).^2 + 6*sin(x).*cos(y).*tan(z) + 3*sin(x).*tan(z).^2"
" + cos(y).^3 + 3*cos(y).^2.*tan(z) + 3*cos(y).*tan(z).^2 + tan(z).^3;\n"
" out2 = cos(cos(cos(cos(cos(cos(cos(cos(x + y + z))))))));\n"
"end\n"
)
assert source == expected
def test_m_output_arg_mixed_unordered():
# named outputs are alphabetical, unnamed output appear in the given order
from sympy import sin, cos, tan
a = symbols("a")
name_expr = ("foo", [cos(2*x), Equality(y, sin(x)), cos(x), Equality(a, sin(2*x))])
result, = codegen(name_expr, "Octave", header=False, empty=False)
assert result[0] == "foo.m"
source = result[1];
expected = (
'function [out1, y, out3, a] = foo(x)\n'
' out1 = cos(2*x);\n'
' y = sin(x);\n'
' out3 = cos(x);\n'
' a = sin(2*x);\n'
'end\n'
)
assert source == expected
def test_m_piecewise_():
pw = Piecewise((0, x < -1), (x**2, x <= 1), (-x+2, x > 1), (1, True))
name_expr = ("pwtest", pw)
result, = codegen(name_expr, "Octave", header=False, empty=False)
source = result[1]
expected = (
"function out1 = pwtest(x)\n"
" out1 = ((x < -1).*(0) + (~(x < -1)).*( ...\n"
" (x <= 1).*(x.^2) + (~(x <= 1)).*( ...\n"
" (x > 1).*(-x + 2) + (~(x > 1)).*(1))));\n"
"end\n"
)
assert source == expected
@XFAIL
def test_m_piecewise_no_inline():
# FIXME: how to pass inline=False to the OctaveCodePrinter?
pw = Piecewise((0, x < -1), (x**2, x <= 1), (-x+2, x > 1), (1, True))
name_expr = ("pwtest", pw)
result, = codegen(name_expr, "Octave", header=False, empty=False,
inline=False)
source = result[1]
expected = (
"function out1 = pwtest(x)\n"
" if (x < -1)\n"
" out1 = 0;\n"
" elseif (x <= 1)\n"
" out1 = x.^2;\n"
" elseif (x > 1)\n"
" out1 = -x + 2;\n"
" else\n"
" out1 = 1;\n"
" end\n"
"end\n"
)
assert source == expected
def test_m_multifcns_per_file():
name_expr = [ ("foo", [2*x, 3*y]), ("bar", [y**2, 4*y]) ]
result = codegen(name_expr, "Octave", header=False, empty=False)
assert result[0][0] == "foo.m"
source = result[0][1];
expected = (
"function [out1, out2] = foo(x, y)\n"
" out1 = 2*x;\n"
" out2 = 3*y;\n"
"end\n"
"function [out1, out2] = bar(y)\n"
" out1 = y.^2;\n"
" out2 = 4*y;\n"
"end\n"
)
assert source == expected
def test_m_multifcns_per_file_w_header():
name_expr = [ ("foo", [2*x, 3*y]), ("bar", [y**2, 4*y]) ]
result = codegen(name_expr, "Octave", header=True, empty=False)
assert result[0][0] == "foo.m"
source = result[0][1];
expected = (
"function [out1, out2] = foo(x, y)\n"
" %FOO Autogenerated by sympy\n"
" % Code generated with sympy " + sympy.__version__ + "\n"
" %\n"
" % See http://www.sympy.org/ for more information.\n"
" %\n"
" % This file is part of 'project'\n"
" out1 = 2*x;\n"
" out2 = 3*y;\n"
"end\n"
"function [out1, out2] = bar(y)\n"
" out1 = y.^2;\n"
" out2 = 4*y;\n"
"end\n"
)
assert source == expected
def test_m_filename_match_first_fcn():
name_expr = [ ("foo", [2*x, 3*y]), ("bar", [y**2, 4*y]) ]
raises(ValueError, lambda: codegen(name_expr,
"Octave", prefix="bar", header=False, empty=False))
def test_m_matrix_named():
e2 = Matrix([[x, 2*y, pi*z]])
name_expr = ("test", Equality(MatrixSymbol('myout1', 1, 3), e2))
result = codegen(name_expr, "Octave", header=False, empty=False)
assert result[0][0] == "test.m"
source = result[0][1]
expected = (
"function myout1 = test(x, y, z)\n"
" myout1 = [x 2*y pi*z];\n"
"end\n"
)
assert source == expected
def test_m_matrix_named_matsym():
myout1 = MatrixSymbol('myout1', 1, 3)
e2 = Matrix([[x, 2*y, pi*z]])
name_expr = ("test", Equality(myout1, e2, evaluate=False))
result, = codegen(name_expr, "Octave", header=False, empty=False)
source = result[1]
expected = (
"function myout1 = test(x, y, z)\n"
" myout1 = [x 2*y pi*z];\n"
"end\n"
)
assert source == expected
def test_m_matrix_output_autoname():
expr = Matrix([[x, x+y, 3]])
name_expr = ("test", expr)
result, = codegen(name_expr, "Octave", header=False, empty=False)
source = result[1]
expected = (
"function out1 = test(x, y)\n"
" out1 = [x x + y 3];\n"
"end\n"
)
assert source == expected
def test_m_matrix_output_autoname_2():
e1 = (x + y)
e2 = Matrix([[2*x, 2*y, 2*z]])
e3 = Matrix([[x], [y], [z]])
e4 = Matrix([[x, y], [z, 16]])
name_expr = ("test", (e1, e2, e3, e4))
result, = codegen(name_expr, "Octave", header=False, empty=False)
source = result[1]
expected = (
"function [out1, out2, out3, out4] = test(x, y, z)\n"
" out1 = x + y;\n"
" out2 = [2*x 2*y 2*z];\n"
" out3 = [x; y; z];\n"
" out4 = [x y; z 16];\n"
"end\n"
)
assert source == expected
def test_m_results_matrix_named_ordered():
B, C = symbols('B,C')
A = MatrixSymbol('A', 1, 3)
expr1 = Equality(C, (x + y)*z)
expr2 = Equality(A, Matrix([[1, 2, x]]))
expr3 = Equality(B, 2*x)
name_expr = ("test", [expr1, expr2, expr3])
result, = codegen(name_expr, "Octave", header=False, empty=False,
argument_sequence=(x, z, y))
source = result[1]
expected = (
"function [C, A, B] = test(x, z, y)\n"
" C = z.*(x + y);\n"
" A = [1 2 x];\n"
" B = 2*x;\n"
"end\n"
)
assert source == expected
def test_m_matrixsymbol_slice():
A = MatrixSymbol('A', 2, 3)
B = MatrixSymbol('B', 1, 3)
C = MatrixSymbol('C', 1, 3)
D = MatrixSymbol('D', 2, 1)
name_expr = ("test", [Equality(B, A[0, :]),
Equality(C, A[1, :]),
Equality(D, A[:, 2])])
result, = codegen(name_expr, "Octave", header=False, empty=False)
source = result[1]
expected = (
"function [B, C, D] = test(A)\n"
" B = A(1, :);\n"
" C = A(2, :);\n"
" D = A(:, 3);\n"
"end\n"
)
assert source == expected
def test_m_matrixsymbol_slice2():
A = MatrixSymbol('A', 3, 4)
B = MatrixSymbol('B', 2, 2)
C = MatrixSymbol('C', 2, 2)
name_expr = ("test", [Equality(B, A[0:2, 0:2]),
Equality(C, A[0:2, 1:3])])
result, = codegen(name_expr, "Octave", header=False, empty=False)
source = result[1]
expected = (
"function [B, C] = test(A)\n"
" B = A(1:2, 1:2);\n"
" C = A(1:2, 2:3);\n"
"end\n"
)
assert source == expected
def test_m_matrixsymbol_slice3():
A = MatrixSymbol('A', 8, 7)
B = MatrixSymbol('B', 2, 2)
C = MatrixSymbol('C', 4, 2)
name_expr = ("test", [Equality(B, A[6:, 1::3]),
Equality(C, A[::2, ::3])])
result, = codegen(name_expr, "Octave", header=False, empty=False)
source = result[1]
expected = (
"function [B, C] = test(A)\n"
" B = A(7:end, 2:3:end);\n"
" C = A(1:2:end, 1:3:end);\n"
"end\n"
)
assert source == expected
def test_m_matrixsymbol_slice_autoname():
A = MatrixSymbol('A', 2, 3)
B = MatrixSymbol('B', 1, 3)
name_expr = ("test", [Equality(B, A[0,:]), A[1,:], A[:,0], A[:,1]])
result, = codegen(name_expr, "Octave", header=False, empty=False)
source = result[1]
expected = (
"function [B, out2, out3, out4] = test(A)\n"
" B = A(1, :);\n"
" out2 = A(2, :);\n"
" out3 = A(:, 1);\n"
" out4 = A(:, 2);\n"
"end\n"
)
assert source == expected
def test_m_loops():
# Note: an Octave programmer would probably vectorize this across one or
# more dimensions. Also, size(A) would be used rather than passing in m
# and n. Perhaps users would expect us to vectorize automatically here?
# Or is it possible to represent such things using IndexedBase?
from sympy.tensor import IndexedBase, Idx
from sympy import symbols
n, m = symbols('n m', integer=True)
A = IndexedBase('A')
x = IndexedBase('x')
y = IndexedBase('y')
i = Idx('i', m)
j = Idx('j', n)
result, = codegen(('mat_vec_mult', Eq(y[i], A[i, j]*x[j])), "Octave",
header=False, empty=False)
source = result[1]
expected = (
'function y = mat_vec_mult(A, m, n, x)\n'
' for i = 1:m\n'
' y(i) = 0;\n'
' end\n'
' for i = 1:m\n'
' for j = 1:n\n'
' y(i) = %(rhs)s + y(i);\n'
' end\n'
' end\n'
'end\n'
)
assert (source == expected % {'rhs': 'A(%s, %s).*x(j)' % (i, j)} or
source == expected % {'rhs': 'x(j).*A(%s, %s)' % (i, j)})
def test_m_tensor_loops_multiple_contractions():
# see comments in previous test about vectorizing
from sympy.tensor import IndexedBase, Idx
from sympy import symbols
n, m, o, p = symbols('n m o p', integer=True)
A = IndexedBase('A')
B = IndexedBase('B')
y = IndexedBase('y')
i = Idx('i', m)
j = Idx('j', n)
k = Idx('k', o)
l = Idx('l', p)
result, = codegen(('tensorthing', Eq(y[i], B[j, k, l]*A[i, j, k, l])),
"Octave", header=False, empty=False)
source = result[1]
expected = (
'function y = tensorthing(A, B, m, n, o, p)\n'
' for i = 1:m\n'
' y(i) = 0;\n'
' end\n'
' for i = 1:m\n'
' for j = 1:n\n'
' for k = 1:o\n'
' for l = 1:p\n'
' y(i) = A(i, j, k, l).*B(j, k, l) + y(i);\n'
' end\n'
' end\n'
' end\n'
' end\n'
'end\n'
)
assert source == expected
def test_m_InOutArgument():
expr = Equality(x, x**2)
name_expr = ("mysqr", expr)
result, = codegen(name_expr, "Octave", header=False, empty=False)
source = result[1]
expected = (
"function x = mysqr(x)\n"
" x = x.^2;\n"
"end\n"
)
assert source == expected
def test_m_InOutArgument_order():
# can specify the order as (x, y)
expr = Equality(x, x**2 + y)
name_expr = ("test", expr)
result, = codegen(name_expr, "Octave", header=False,
empty=False, argument_sequence=(x,y))
source = result[1]
expected = (
"function x = test(x, y)\n"
" x = x.^2 + y;\n"
"end\n"
)
assert source == expected
# make sure it gives (x, y) not (y, x)
expr = Equality(x, x**2 + y)
name_expr = ("test", expr)
result, = codegen(name_expr, "Octave", header=False, empty=False)
source = result[1]
expected = (
"function x = test(x, y)\n"
" x = x.^2 + y;\n"
"end\n"
)
assert source == expected
def test_m_not_supported():
f = Function('f')
name_expr = ("test", [f(x).diff(x), S.ComplexInfinity])
result, = codegen(name_expr, "Octave", header=False, empty=False)
source = result[1]
expected = (
"function [out1, out2] = test(x)\n"
" % unsupported: Derivative(f(x), x)\n"
" % unsupported: zoo\n"
" out1 = Derivative(f(x), x);\n"
" out2 = zoo;\n"
"end\n"
)
assert source == expected
def test_global_vars_octave():
x, y, z, t = symbols("x y z t")
result = codegen(('f', x*y), "Octave", header=False, empty=False,
global_vars=(y,))
source = result[0][1]
expected = (
"function out1 = f(x)\n"
" global y\n"
" out1 = x.*y;\n"
"end\n"
)
assert source == expected
result = codegen(('f', x*y+z), "Octave", header=False, empty=False,
argument_sequence=(x, y), global_vars=(z, t))
source = result[0][1]
expected = (
"function out1 = f(x, y)\n"
" global t z\n"
" out1 = x.*y + z;\n"
"end\n"
)
assert source == expected
| 17,812 | 29.14044 | 88 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/tests/test_iterables.py
|
from __future__ import print_function
from textwrap import dedent
from sympy import (
symbols, Integral, Tuple, Dummy, Basic, default_sort_key, Matrix,
factorial, true)
from sympy.combinatorics import RGS_enum, RGS_unrank, Permutation
from sympy.core.compatibility import range
from sympy.utilities.iterables import (
_partition, _set_partitions, binary_partitions, bracelets, capture,
cartes, common_prefix, common_suffix, dict_merge, filter_symbols,
flatten, generate_bell, generate_derangements, generate_involutions,
generate_oriented_forest, group, has_dups, kbins, minlex, multiset,
multiset_combinations, multiset_partitions,
multiset_permutations, necklaces, numbered_symbols, ordered, partitions,
permutations, postfixes, postorder_traversal, prefixes, reshape,
rotate_left, rotate_right, runs, sift, subsets, take, topological_sort,
unflatten, uniq, variations, ordered_partitions)
from sympy.utilities.enumerative import (
factoring_visitor, multiset_partitions_taocp )
from sympy.core.singleton import S
from sympy.functions.elementary.piecewise import Piecewise, ExprCondPair
from sympy.utilities.pytest import raises
w, x, y, z = symbols('w,x,y,z')
def test_postorder_traversal():
expr = z + w*(x + y)
expected = [z, w, x, y, x + y, w*(x + y), w*(x + y) + z]
assert list(postorder_traversal(expr, keys=default_sort_key)) == expected
assert list(postorder_traversal(expr, keys=True)) == expected
expr = Piecewise((x, x < 1), (x**2, True))
expected = [
x, 1, x, x < 1, ExprCondPair(x, x < 1),
2, x, x**2, true,
ExprCondPair(x**2, True), Piecewise((x, x < 1), (x**2, True))
]
assert list(postorder_traversal(expr, keys=default_sort_key)) == expected
assert list(postorder_traversal(
[expr], keys=default_sort_key)) == expected + [[expr]]
assert list(postorder_traversal(Integral(x**2, (x, 0, 1)),
keys=default_sort_key)) == [
2, x, x**2, 0, 1, x, Tuple(x, 0, 1),
Integral(x**2, Tuple(x, 0, 1))
]
assert list(postorder_traversal(('abc', ('d', 'ef')))) == [
'abc', 'd', 'ef', ('d', 'ef'), ('abc', ('d', 'ef'))]
def test_flatten():
assert flatten((1, (1,))) == [1, 1]
assert flatten((x, (x,))) == [x, x]
ls = [[(-2, -1), (1, 2)], [(0, 0)]]
assert flatten(ls, levels=0) == ls
assert flatten(ls, levels=1) == [(-2, -1), (1, 2), (0, 0)]
assert flatten(ls, levels=2) == [-2, -1, 1, 2, 0, 0]
assert flatten(ls, levels=3) == [-2, -1, 1, 2, 0, 0]
raises(ValueError, lambda: flatten(ls, levels=-1))
class MyOp(Basic):
pass
assert flatten([MyOp(x, y), z]) == [MyOp(x, y), z]
assert flatten([MyOp(x, y), z], cls=MyOp) == [x, y, z]
assert flatten({1, 11, 2}) == list({1, 11, 2})
def test_group():
assert group([]) == []
assert group([], multiple=False) == []
assert group([1]) == [[1]]
assert group([1], multiple=False) == [(1, 1)]
assert group([1, 1]) == [[1, 1]]
assert group([1, 1], multiple=False) == [(1, 2)]
assert group([1, 1, 1]) == [[1, 1, 1]]
assert group([1, 1, 1], multiple=False) == [(1, 3)]
assert group([1, 2, 1]) == [[1], [2], [1]]
assert group([1, 2, 1], multiple=False) == [(1, 1), (2, 1), (1, 1)]
assert group([1, 1, 2, 2, 2, 1, 3, 3]) == [[1, 1], [2, 2, 2], [1], [3, 3]]
assert group([1, 1, 2, 2, 2, 1, 3, 3], multiple=False) == [(1, 2),
(2, 3), (1, 1), (3, 2)]
def test_subsets():
# combinations
assert list(subsets([1, 2, 3], 0)) == [()]
assert list(subsets([1, 2, 3], 1)) == [(1,), (2,), (3,)]
assert list(subsets([1, 2, 3], 2)) == [(1, 2), (1, 3), (2, 3)]
assert list(subsets([1, 2, 3], 3)) == [(1, 2, 3)]
l = list(range(4))
assert list(subsets(l, 0, repetition=True)) == [()]
assert list(subsets(l, 1, repetition=True)) == [(0,), (1,), (2,), (3,)]
assert list(subsets(l, 2, repetition=True)) == [(0, 0), (0, 1), (0, 2),
(0, 3), (1, 1), (1, 2),
(1, 3), (2, 2), (2, 3),
(3, 3)]
assert list(subsets(l, 3, repetition=True)) == [(0, 0, 0), (0, 0, 1),
(0, 0, 2), (0, 0, 3),
(0, 1, 1), (0, 1, 2),
(0, 1, 3), (0, 2, 2),
(0, 2, 3), (0, 3, 3),
(1, 1, 1), (1, 1, 2),
(1, 1, 3), (1, 2, 2),
(1, 2, 3), (1, 3, 3),
(2, 2, 2), (2, 2, 3),
(2, 3, 3), (3, 3, 3)]
assert len(list(subsets(l, 4, repetition=True))) == 35
assert list(subsets(l[:2], 3, repetition=False)) == []
assert list(subsets(l[:2], 3, repetition=True)) == [(0, 0, 0),
(0, 0, 1),
(0, 1, 1),
(1, 1, 1)]
assert list(subsets([1, 2], repetition=True)) == \
[(), (1,), (2,), (1, 1), (1, 2), (2, 2)]
assert list(subsets([1, 2], repetition=False)) == \
[(), (1,), (2,), (1, 2)]
assert list(subsets([1, 2, 3], 2)) == \
[(1, 2), (1, 3), (2, 3)]
assert list(subsets([1, 2, 3], 2, repetition=True)) == \
[(1, 1), (1, 2), (1, 3), (2, 2), (2, 3), (3, 3)]
def test_variations():
# permutations
l = list(range(4))
assert list(variations(l, 0, repetition=False)) == [()]
assert list(variations(l, 1, repetition=False)) == [(0,), (1,), (2,), (3,)]
assert list(variations(l, 2, repetition=False)) == [(0, 1), (0, 2), (0, 3), (1, 0), (1, 2), (1, 3), (2, 0), (2, 1), (2, 3), (3, 0), (3, 1), (3, 2)]
assert list(variations(l, 3, repetition=False)) == [(0, 1, 2), (0, 1, 3), (0, 2, 1), (0, 2, 3), (0, 3, 1), (0, 3, 2), (1, 0, 2), (1, 0, 3), (1, 2, 0), (1, 2, 3), (1, 3, 0), (1, 3, 2), (2, 0, 1), (2, 0, 3), (2, 1, 0), (2, 1, 3), (2, 3, 0), (2, 3, 1), (3, 0, 1), (3, 0, 2), (3, 1, 0), (3, 1, 2), (3, 2, 0), (3, 2, 1)]
assert list(variations(l, 0, repetition=True)) == [()]
assert list(variations(l, 1, repetition=True)) == [(0,), (1,), (2,), (3,)]
assert list(variations(l, 2, repetition=True)) == [(0, 0), (0, 1), (0, 2),
(0, 3), (1, 0), (1, 1),
(1, 2), (1, 3), (2, 0),
(2, 1), (2, 2), (2, 3),
(3, 0), (3, 1), (3, 2),
(3, 3)]
assert len(list(variations(l, 3, repetition=True))) == 64
assert len(list(variations(l, 4, repetition=True))) == 256
assert list(variations(l[:2], 3, repetition=False)) == []
assert list(variations(l[:2], 3, repetition=True)) == [
(0, 0, 0), (0, 0, 1), (0, 1, 0), (0, 1, 1),
(1, 0, 0), (1, 0, 1), (1, 1, 0), (1, 1, 1)
]
def test_cartes():
assert list(cartes([1, 2], [3, 4, 5])) == \
[(1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5)]
assert list(cartes()) == [()]
assert list(cartes('a')) == [('a',)]
assert list(cartes('a', repeat=2)) == [('a', 'a')]
assert list(cartes(list(range(2)))) == [(0,), (1,)]
def test_filter_symbols():
s = numbered_symbols()
filtered = filter_symbols(s, symbols("x0 x2 x3"))
assert take(filtered, 3) == list(symbols("x1 x4 x5"))
def test_numbered_symbols():
s = numbered_symbols(cls=Dummy)
assert isinstance(next(s), Dummy)
assert next(numbered_symbols('C', start=1, exclude=[symbols('C1')])) == \
symbols('C2')
def test_sift():
assert sift(list(range(5)), lambda _: _ % 2) == {1: [1, 3], 0: [0, 2, 4]}
assert sift([x, y], lambda _: _.has(x)) == {False: [y], True: [x]}
assert sift([S.One], lambda _: _.has(x)) == {False: [1]}
def test_take():
X = numbered_symbols()
assert take(X, 5) == list(symbols('x0:5'))
assert take(X, 5) == list(symbols('x5:10'))
assert take([1, 2, 3, 4, 5], 5) == [1, 2, 3, 4, 5]
def test_dict_merge():
assert dict_merge({}, {1: x, y: z}) == {1: x, y: z}
assert dict_merge({1: x, y: z}, {}) == {1: x, y: z}
assert dict_merge({2: z}, {1: x, y: z}) == {1: x, 2: z, y: z}
assert dict_merge({1: x, y: z}, {2: z}) == {1: x, 2: z, y: z}
assert dict_merge({1: y, 2: z}, {1: x, y: z}) == {1: x, 2: z, y: z}
assert dict_merge({1: x, y: z}, {1: y, 2: z}) == {1: y, 2: z, y: z}
def test_prefixes():
assert list(prefixes([])) == []
assert list(prefixes([1])) == [[1]]
assert list(prefixes([1, 2])) == [[1], [1, 2]]
assert list(prefixes([1, 2, 3, 4, 5])) == \
[[1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 3, 4, 5]]
def test_postfixes():
assert list(postfixes([])) == []
assert list(postfixes([1])) == [[1]]
assert list(postfixes([1, 2])) == [[2], [1, 2]]
assert list(postfixes([1, 2, 3, 4, 5])) == \
[[5], [4, 5], [3, 4, 5], [2, 3, 4, 5], [1, 2, 3, 4, 5]]
def test_topological_sort():
V = [2, 3, 5, 7, 8, 9, 10, 11]
E = [(7, 11), (7, 8), (5, 11),
(3, 8), (3, 10), (11, 2),
(11, 9), (11, 10), (8, 9)]
assert topological_sort((V, E)) == [3, 5, 7, 8, 11, 2, 9, 10]
assert topological_sort((V, E), key=lambda v: -v) == \
[7, 5, 11, 3, 10, 8, 9, 2]
raises(ValueError, lambda: topological_sort((V, E + [(10, 7)])))
def test_rotate():
A = [0, 1, 2, 3, 4]
assert rotate_left(A, 2) == [2, 3, 4, 0, 1]
assert rotate_right(A, 1) == [4, 0, 1, 2, 3]
A = []
B = rotate_right(A, 1)
assert B == []
B.append(1)
assert A == []
B = rotate_left(A, 1)
assert B == []
B.append(1)
assert A == []
def test_multiset_partitions():
A = [0, 1, 2, 3, 4]
assert list(multiset_partitions(A, 5)) == [[[0], [1], [2], [3], [4]]]
assert len(list(multiset_partitions(A, 4))) == 10
assert len(list(multiset_partitions(A, 3))) == 25
assert list(multiset_partitions([1, 1, 1, 2, 2], 2)) == [
[[1, 1, 1, 2], [2]], [[1, 1, 1], [2, 2]], [[1, 1, 2, 2], [1]],
[[1, 1, 2], [1, 2]], [[1, 1], [1, 2, 2]]]
assert list(multiset_partitions([1, 1, 2, 2], 2)) == [
[[1, 1, 2], [2]], [[1, 1], [2, 2]], [[1, 2, 2], [1]],
[[1, 2], [1, 2]]]
assert list(multiset_partitions([1, 2, 3, 4], 2)) == [
[[1, 2, 3], [4]], [[1, 2, 4], [3]], [[1, 2], [3, 4]],
[[1, 3, 4], [2]], [[1, 3], [2, 4]], [[1, 4], [2, 3]],
[[1], [2, 3, 4]]]
assert list(multiset_partitions([1, 2, 2], 2)) == [
[[1, 2], [2]], [[1], [2, 2]]]
assert list(multiset_partitions(3)) == [
[[0, 1, 2]], [[0, 1], [2]], [[0, 2], [1]], [[0], [1, 2]],
[[0], [1], [2]]]
assert list(multiset_partitions(3, 2)) == [
[[0, 1], [2]], [[0, 2], [1]], [[0], [1, 2]]]
assert list(multiset_partitions([1] * 3, 2)) == [[[1], [1, 1]]]
assert list(multiset_partitions([1] * 3)) == [
[[1, 1, 1]], [[1], [1, 1]], [[1], [1], [1]]]
a = [3, 2, 1]
assert list(multiset_partitions(a)) == \
list(multiset_partitions(sorted(a)))
assert list(multiset_partitions(a, 5)) == []
assert list(multiset_partitions(a, 1)) == [[[1, 2, 3]]]
assert list(multiset_partitions(a + [4], 5)) == []
assert list(multiset_partitions(a + [4], 1)) == [[[1, 2, 3, 4]]]
assert list(multiset_partitions(2, 5)) == []
assert list(multiset_partitions(2, 1)) == [[[0, 1]]]
assert list(multiset_partitions('a')) == [[['a']]]
assert list(multiset_partitions('a', 2)) == []
assert list(multiset_partitions('ab')) == [[['a', 'b']], [['a'], ['b']]]
assert list(multiset_partitions('ab', 1)) == [[['a', 'b']]]
assert list(multiset_partitions('aaa', 1)) == [['aaa']]
assert list(multiset_partitions([1, 1], 1)) == [[[1, 1]]]
ans = [('mpsyy',), ('mpsy', 'y'), ('mps', 'yy'), ('mps', 'y', 'y'),
('mpyy', 's'), ('mpy', 'sy'), ('mpy', 's', 'y'), ('mp', 'syy'),
('mp', 'sy', 'y'), ('mp', 's', 'yy'), ('mp', 's', 'y', 'y'),
('msyy', 'p'), ('msy', 'py'), ('msy', 'p', 'y'), ('ms', 'pyy'),
('ms', 'py', 'y'), ('ms', 'p', 'yy'), ('ms', 'p', 'y', 'y'),
('myy', 'ps'), ('myy', 'p', 's'), ('my', 'psy'), ('my', 'ps', 'y'),
('my', 'py', 's'), ('my', 'p', 'sy'), ('my', 'p', 's', 'y'),
('m', 'psyy'), ('m', 'psy', 'y'), ('m', 'ps', 'yy'),
('m', 'ps', 'y', 'y'), ('m', 'pyy', 's'), ('m', 'py', 'sy'),
('m', 'py', 's', 'y'), ('m', 'p', 'syy'),
('m', 'p', 'sy', 'y'), ('m', 'p', 's', 'yy'),
('m', 'p', 's', 'y', 'y')]
assert list(tuple("".join(part) for part in p)
for p in multiset_partitions('sympy')) == ans
factorings = [[24], [8, 3], [12, 2], [4, 6], [4, 2, 3],
[6, 2, 2], [2, 2, 2, 3]]
assert list(factoring_visitor(p, [2,3]) for
p in multiset_partitions_taocp([3, 1])) == factorings
def test_multiset_combinations():
ans = ['iii', 'iim', 'iip', 'iis', 'imp', 'ims', 'ipp', 'ips',
'iss', 'mpp', 'mps', 'mss', 'pps', 'pss', 'sss']
assert [''.join(i) for i in
list(multiset_combinations('mississippi', 3))] == ans
M = multiset('mississippi')
assert [''.join(i) for i in
list(multiset_combinations(M, 3))] == ans
assert [''.join(i) for i in multiset_combinations(M, 30)] == []
assert list(multiset_combinations([[1], [2, 3]], 2)) == [[[1], [2, 3]]]
assert len(list(multiset_combinations('a', 3))) == 0
assert len(list(multiset_combinations('a', 0))) == 1
assert list(multiset_combinations('abc', 1)) == [['a'], ['b'], ['c']]
def test_multiset_permutations():
ans = ['abby', 'abyb', 'aybb', 'baby', 'bayb', 'bbay', 'bbya', 'byab',
'byba', 'yabb', 'ybab', 'ybba']
assert [''.join(i) for i in multiset_permutations('baby')] == ans
assert [''.join(i) for i in multiset_permutations(multiset('baby'))] == ans
assert list(multiset_permutations([0, 0, 0], 2)) == [[0, 0]]
assert list(multiset_permutations([0, 2, 1], 2)) == [
[0, 1], [0, 2], [1, 0], [1, 2], [2, 0], [2, 1]]
assert len(list(multiset_permutations('a', 0))) == 1
assert len(list(multiset_permutations('a', 3))) == 0
def test():
for i in range(1, 7):
print(i)
for p in multiset_permutations([0, 0, 1, 0, 1], i):
print(p)
assert capture(lambda: test()) == dedent('''\
1
[0]
[1]
2
[0, 0]
[0, 1]
[1, 0]
[1, 1]
3
[0, 0, 0]
[0, 0, 1]
[0, 1, 0]
[0, 1, 1]
[1, 0, 0]
[1, 0, 1]
[1, 1, 0]
4
[0, 0, 0, 1]
[0, 0, 1, 0]
[0, 0, 1, 1]
[0, 1, 0, 0]
[0, 1, 0, 1]
[0, 1, 1, 0]
[1, 0, 0, 0]
[1, 0, 0, 1]
[1, 0, 1, 0]
[1, 1, 0, 0]
5
[0, 0, 0, 1, 1]
[0, 0, 1, 0, 1]
[0, 0, 1, 1, 0]
[0, 1, 0, 0, 1]
[0, 1, 0, 1, 0]
[0, 1, 1, 0, 0]
[1, 0, 0, 0, 1]
[1, 0, 0, 1, 0]
[1, 0, 1, 0, 0]
[1, 1, 0, 0, 0]
6\n''')
def test_partitions():
ans = [[{}], [(0, {})]]
for i in range(2):
assert list(partitions(0, size=i)) == ans[i]
assert list(partitions(1, 0, size=i)) == ans[i]
assert list(partitions(6, 2, 2, size=i)) == ans[i]
assert list(partitions(6, 2, None, size=i)) != ans[i]
assert list(partitions(6, None, 2, size=i)) != ans[i]
assert list(partitions(6, 2, 0, size=i)) == ans[i]
assert [p.copy() for p in partitions(6, k=2)] == [
{2: 3}, {1: 2, 2: 2}, {1: 4, 2: 1}, {1: 6}]
assert [p.copy() for p in partitions(6, k=3)] == [
{3: 2}, {1: 1, 2: 1, 3: 1}, {1: 3, 3: 1}, {2: 3}, {1: 2, 2: 2},
{1: 4, 2: 1}, {1: 6}]
assert [p.copy() for p in partitions(8, k=4, m=3)] == [
{4: 2}, {1: 1, 3: 1, 4: 1}, {2: 2, 4: 1}, {2: 1, 3: 2}] == [
i.copy() for i in partitions(8, k=4, m=3) if all(k <= 4 for k in i)
and sum(i.values()) <=3]
assert [p.copy() for p in partitions(S(3), m=2)] == [
{3: 1}, {1: 1, 2: 1}]
assert [i.copy() for i in partitions(4, k=3)] == [
{1: 1, 3: 1}, {2: 2}, {1: 2, 2: 1}, {1: 4}] == [
i.copy() for i in partitions(4) if all(k <= 3 for k in i)]
# Consistency check on output of _partitions and RGS_unrank.
# This provides a sanity test on both routines. Also verifies that
# the total number of partitions is the same in each case.
# (from pkrathmann2)
for n in range(2, 6):
i = 0
for m, q in _set_partitions(n):
assert q == RGS_unrank(i, n)
i += 1
assert i == RGS_enum(n)
def test_binary_partitions():
assert [i[:] for i in binary_partitions(10)] == [[8, 2], [8, 1, 1],
[4, 4, 2], [4, 4, 1, 1], [4, 2, 2, 2], [4, 2, 2, 1, 1],
[4, 2, 1, 1, 1, 1], [4, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2],
[2, 2, 2, 2, 1, 1], [2, 2, 2, 1, 1, 1, 1], [2, 2, 1, 1, 1, 1, 1, 1],
[2, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]
assert len([j[:] for j in binary_partitions(16)]) == 36
def test_bell_perm():
assert [len(set(generate_bell(i))) for i in range(1, 7)] == [
factorial(i) for i in range(1, 7)]
assert list(generate_bell(3)) == [
(0, 1, 2), (0, 2, 1), (2, 0, 1), (2, 1, 0), (1, 2, 0), (1, 0, 2)]
# generate_bell and trotterjohnson are advertised to return the same
# permutations; this is not technically necessary so this test could
# be removed
for n in range(1, 5):
p = Permutation(range(n))
b = generate_bell(n)
for bi in b:
assert bi == tuple(p.array_form)
p = p.next_trotterjohnson()
raises(ValueError, lambda: list(generate_bell(0))) # XXX is this consistent with other permutation algorithms?
def test_involutions():
lengths = [1, 2, 4, 10, 26, 76]
for n, N in enumerate(lengths):
i = list(generate_involutions(n + 1))
assert len(i) == N
assert len({Permutation(j)**2 for j in i}) == 1
def test_derangements():
assert len(list(generate_derangements(list(range(6))))) == 265
assert ''.join(''.join(i) for i in generate_derangements('abcde')) == (
'badecbaecdbcaedbcdeabceadbdaecbdeacbdecabeacdbedacbedcacabedcadebcaebd'
'cdaebcdbeacdeabcdebaceabdcebadcedabcedbadabecdaebcdaecbdcaebdcbeadceab'
'dcebadeabcdeacbdebacdebcaeabcdeadbceadcbecabdecbadecdabecdbaedabcedacb'
'edbacedbca')
assert list(generate_derangements([0, 1, 2, 3])) == [
[1, 0, 3, 2], [1, 2, 3, 0], [1, 3, 0, 2], [2, 0, 3, 1],
[2, 3, 0, 1], [2, 3, 1, 0], [3, 0, 1, 2], [3, 2, 0, 1], [3, 2, 1, 0]]
assert list(generate_derangements([0, 1, 2, 2])) == [
[2, 2, 0, 1], [2, 2, 1, 0]]
def test_necklaces():
def count(n, k, f):
return len(list(necklaces(n, k, f)))
m = []
for i in range(1, 8):
m.append((
i, count(i, 2, 0), count(i, 2, 1), count(i, 3, 1)))
assert Matrix(m) == Matrix([
[1, 2, 2, 3],
[2, 3, 3, 6],
[3, 4, 4, 10],
[4, 6, 6, 21],
[5, 8, 8, 39],
[6, 14, 13, 92],
[7, 20, 18, 198]])
def test_bracelets():
bc = [i for i in bracelets(2, 4)]
assert Matrix(bc) == Matrix([
[0, 0],
[0, 1],
[0, 2],
[0, 3],
[1, 1],
[1, 2],
[1, 3],
[2, 2],
[2, 3],
[3, 3]
])
bc = [i for i in bracelets(4, 2)]
assert Matrix(bc) == Matrix([
[0, 0, 0, 0],
[0, 0, 0, 1],
[0, 0, 1, 1],
[0, 1, 0, 1],
[0, 1, 1, 1],
[1, 1, 1, 1]
])
def test_generate_oriented_forest():
assert list(generate_oriented_forest(5)) == [[0, 1, 2, 3, 4],
[0, 1, 2, 3, 3], [0, 1, 2, 3, 2], [0, 1, 2, 3, 1], [0, 1, 2, 3, 0],
[0, 1, 2, 2, 2], [0, 1, 2, 2, 1], [0, 1, 2, 2, 0], [0, 1, 2, 1, 2],
[0, 1, 2, 1, 1], [0, 1, 2, 1, 0], [0, 1, 2, 0, 1], [0, 1, 2, 0, 0],
[0, 1, 1, 1, 1], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [0, 1, 1, 0, 0],
[0, 1, 0, 1, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 0]]
assert len(list(generate_oriented_forest(10))) == 1842
def test_unflatten():
r = list(range(10))
assert unflatten(r) == list(zip(r[::2], r[1::2]))
assert unflatten(r, 5) == [tuple(r[:5]), tuple(r[5:])]
raises(ValueError, lambda: unflatten(list(range(10)), 3))
raises(ValueError, lambda: unflatten(list(range(10)), -2))
def test_common_prefix_suffix():
assert common_prefix([], [1]) == []
assert common_prefix(list(range(3))) == [0, 1, 2]
assert common_prefix(list(range(3)), list(range(4))) == [0, 1, 2]
assert common_prefix([1, 2, 3], [1, 2, 5]) == [1, 2]
assert common_prefix([1, 2, 3], [1, 3, 5]) == [1]
assert common_suffix([], [1]) == []
assert common_suffix(list(range(3))) == [0, 1, 2]
assert common_suffix(list(range(3)), list(range(3))) == [0, 1, 2]
assert common_suffix(list(range(3)), list(range(4))) == []
assert common_suffix([1, 2, 3], [9, 2, 3]) == [2, 3]
assert common_suffix([1, 2, 3], [9, 7, 3]) == [3]
def test_minlex():
assert minlex([1, 2, 0]) == (0, 1, 2)
assert minlex((1, 2, 0)) == (0, 1, 2)
assert minlex((1, 0, 2)) == (0, 2, 1)
assert minlex((1, 0, 2), directed=False) == (0, 1, 2)
assert minlex('aba') == 'aab'
def test_ordered():
assert list(ordered((x, y), hash, default=False)) in [[x, y], [y, x]]
assert list(ordered((x, y), hash, default=False)) == \
list(ordered((y, x), hash, default=False))
assert list(ordered((x, y))) == [x, y]
seq, keys = [[[1, 2, 1], [0, 3, 1], [1, 1, 3], [2], [1]],
(lambda x: len(x), lambda x: sum(x))]
assert list(ordered(seq, keys, default=False, warn=False)) == \
[[1], [2], [1, 2, 1], [0, 3, 1], [1, 1, 3]]
raises(ValueError, lambda:
list(ordered(seq, keys, default=False, warn=True)))
def test_runs():
assert runs([]) == []
assert runs([1]) == [[1]]
assert runs([1, 1]) == [[1], [1]]
assert runs([1, 1, 2]) == [[1], [1, 2]]
assert runs([1, 2, 1]) == [[1, 2], [1]]
assert runs([2, 1, 1]) == [[2], [1], [1]]
from operator import lt
assert runs([2, 1, 1], lt) == [[2, 1], [1]]
def test_reshape():
seq = list(range(1, 9))
assert reshape(seq, [4]) == \
[[1, 2, 3, 4], [5, 6, 7, 8]]
assert reshape(seq, (4,)) == \
[(1, 2, 3, 4), (5, 6, 7, 8)]
assert reshape(seq, (2, 2)) == \
[(1, 2, 3, 4), (5, 6, 7, 8)]
assert reshape(seq, (2, [2])) == \
[(1, 2, [3, 4]), (5, 6, [7, 8])]
assert reshape(seq, ((2,), [2])) == \
[((1, 2), [3, 4]), ((5, 6), [7, 8])]
assert reshape(seq, (1, [2], 1)) == \
[(1, [2, 3], 4), (5, [6, 7], 8)]
assert reshape(tuple(seq), ([[1], 1, (2,)],)) == \
(([[1], 2, (3, 4)],), ([[5], 6, (7, 8)],))
assert reshape(tuple(seq), ([1], 1, (2,))) == \
(([1], 2, (3, 4)), ([5], 6, (7, 8)))
assert reshape(list(range(12)), [2, [3], {2}, (1, (3,), 1)]) == \
[[0, 1, [2, 3, 4], {5, 6}, (7, (8, 9, 10), 11)]]
def test_uniq():
assert list(uniq(p.copy() for p in partitions(4))) == \
[{4: 1}, {1: 1, 3: 1}, {2: 2}, {1: 2, 2: 1}, {1: 4}]
assert list(uniq(x % 2 for x in range(5))) == [0, 1]
assert list(uniq('a')) == ['a']
assert list(uniq('ababc')) == list('abc')
assert list(uniq([[1], [2, 1], [1]])) == [[1], [2, 1]]
assert list(uniq(permutations(i for i in [[1], 2, 2]))) == \
[([1], 2, 2), (2, [1], 2), (2, 2, [1])]
assert list(uniq([2, 3, 2, 4, [2], [1], [2], [3], [1]])) == \
[2, 3, 4, [2], [1], [3]]
def test_kbins():
assert len(list(kbins('1123', 2, ordered=1))) == 24
assert len(list(kbins('1123', 2, ordered=11))) == 36
assert len(list(kbins('1123', 2, ordered=10))) == 10
assert len(list(kbins('1123', 2, ordered=0))) == 5
assert len(list(kbins('1123', 2, ordered=None))) == 3
def test():
for ordered in [None, 0, 1, 10, 11]:
print('ordered =', ordered)
for p in kbins([0, 0, 1], 2, ordered=ordered):
print(' ', p)
assert capture(lambda : test()) == dedent('''\
ordered = None
[[0], [0, 1]]
[[0, 0], [1]]
ordered = 0
[[0, 0], [1]]
[[0, 1], [0]]
ordered = 1
[[0], [0, 1]]
[[0], [1, 0]]
[[1], [0, 0]]
ordered = 10
[[0, 0], [1]]
[[1], [0, 0]]
[[0, 1], [0]]
[[0], [0, 1]]
ordered = 11
[[0], [0, 1]]
[[0, 0], [1]]
[[0], [1, 0]]
[[0, 1], [0]]
[[1], [0, 0]]
[[1, 0], [0]]\n''')
def test():
for ordered in [None, 0, 1, 10, 11]:
print('ordered =', ordered)
for p in kbins(list(range(3)), 2, ordered=ordered):
print(' ', p)
assert capture(lambda : test()) == dedent('''\
ordered = None
[[0], [1, 2]]
[[0, 1], [2]]
ordered = 0
[[0, 1], [2]]
[[0, 2], [1]]
[[0], [1, 2]]
ordered = 1
[[0], [1, 2]]
[[0], [2, 1]]
[[1], [0, 2]]
[[1], [2, 0]]
[[2], [0, 1]]
[[2], [1, 0]]
ordered = 10
[[0, 1], [2]]
[[2], [0, 1]]
[[0, 2], [1]]
[[1], [0, 2]]
[[0], [1, 2]]
[[1, 2], [0]]
ordered = 11
[[0], [1, 2]]
[[0, 1], [2]]
[[0], [2, 1]]
[[0, 2], [1]]
[[1], [0, 2]]
[[1, 0], [2]]
[[1], [2, 0]]
[[1, 2], [0]]
[[2], [0, 1]]
[[2, 0], [1]]
[[2], [1, 0]]
[[2, 1], [0]]\n''')
def test_has_dups():
assert has_dups(set()) is False
assert has_dups(list(range(3))) is False
assert has_dups([1, 2, 1]) is True
def test__partition():
assert _partition('abcde', [1, 0, 1, 2, 0]) == [
['b', 'e'], ['a', 'c'], ['d']]
assert _partition('abcde', [1, 0, 1, 2, 0], 3) == [
['b', 'e'], ['a', 'c'], ['d']]
output = (3, [1, 0, 1, 2, 0])
assert _partition('abcde', *output) == [['b', 'e'], ['a', 'c'], ['d']]
def test_ordered_partitions():
from sympy.functions.combinatorial.numbers import nT
f = ordered_partitions
assert list(f(0, 1)) == [[]]
assert list(f(1, 0)) == [[]]
for i in range(1, 7):
for j in [None] + list(range(1, i)):
assert (
sum(1 for p in f(i, j, 1)) ==
sum(1 for p in f(i, j, 0)) ==
nT(i, j))
| 27,302 | 36.452675 | 319 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/tests/test_code_quality.py
|
from os import walk, sep, pardir
from os.path import split, join, abspath, exists, isfile
from glob import glob
import re
import random
import ast
from sympy.core.compatibility import PY3
# System path separator (usually slash or backslash) to be
# used with excluded files, e.g.
# exclude = set([
# "%(sep)smpmath%(sep)s" % sepd,
# ])
sepd = {"sep": sep}
# path and sympy_path
SYMPY_PATH = abspath(join(split(__file__)[0], pardir, pardir)) # go to sympy/
assert exists(SYMPY_PATH)
TOP_PATH = abspath(join(SYMPY_PATH, pardir))
BIN_PATH = join(TOP_PATH, "bin")
EXAMPLES_PATH = join(TOP_PATH, "examples")
# Error messages
message_space = "File contains trailing whitespace: %s, line %s."
message_implicit = "File contains an implicit import: %s, line %s."
message_tabs = "File contains tabs instead of spaces: %s, line %s."
message_carriage = "File contains carriage returns at end of line: %s, line %s"
message_str_raise = "File contains string exception: %s, line %s"
message_gen_raise = "File contains generic exception: %s, line %s"
message_old_raise = "File contains old-style raise statement: %s, line %s, \"%s\""
message_eof = "File does not end with a newline: %s, line %s"
message_multi_eof = "File ends with more than 1 newline: %s, line %s"
message_test_suite_def = "Function should start with 'test_' or '_': %s, line %s"
message_duplicate_test = "This is a duplicate test function: %s, line %s"
message_self_assignments = "File contains assignments to self/cls: %s, line %s."
implicit_test_re = re.compile(r'^\s*(>>> )?(\.\.\. )?from .* import .*\*')
str_raise_re = re.compile(
r'^\s*(>>> )?(\.\.\. )?raise(\s+(\'|\")|\s*(\(\s*)+(\'|\"))')
gen_raise_re = re.compile(
r'^\s*(>>> )?(\.\.\. )?raise(\s+Exception|\s*(\(\s*)+Exception)')
old_raise_re = re.compile(r'^\s*(>>> )?(\.\.\. )?raise((\s*\(\s*)|\s+)\w+\s*,')
test_suite_def_re = re.compile(r'^def\s+(?!(_|test))[^(]*\(\s*\)\s*:$')
test_ok_def_re = re.compile(r'^def\s+test_.*:$')
test_file_re = re.compile(r'.*[/\\]test_.*\.py$')
def tab_in_leading(s):
"""Returns True if there are tabs in the leading whitespace of a line,
including the whitespace of docstring code samples."""
n = len(s) - len(s.lstrip())
if not s[n:n + 3] in ['...', '>>>']:
check = s[:n]
else:
smore = s[n + 3:]
check = s[:n] + smore[:len(smore) - len(smore.lstrip())]
return not (check.expandtabs() == check)
def find_self_assignments(s):
"""Returns a list of "bad" assignments: if there are instances
of assigning to the first argument of the class method (except
for staticmethod's).
"""
t = [n for n in ast.parse(s).body if isinstance(n, ast.ClassDef)]
bad = []
for c in t:
for n in c.body:
if not isinstance(n, ast.FunctionDef):
continue
if any(d.id == 'staticmethod'
for d in n.decorator_list if isinstance(d, ast.Name)):
continue
if n.name == '__new__':
continue
if not n.args.args:
continue
if PY3:
first_arg = n.args.args[0].arg
else:
first_arg = n.args.args[0].id
for m in ast.walk(n):
if isinstance(m, ast.Assign):
for a in m.targets:
if isinstance(a, ast.Name) and a.id == first_arg:
bad.append(m)
elif (isinstance(a, ast.Tuple) and
any(q.id == first_arg for q in a.elts
if isinstance(q, ast.Name))):
bad.append(m)
return bad
def check_directory_tree(base_path, file_check, exclusions=set(), pattern="*.py"):
"""
Checks all files in the directory tree (with base_path as starting point)
with the file_check function provided, skipping files that contain
any of the strings in the set provided by exclusions.
"""
if not base_path:
return
for root, dirs, files in walk(base_path):
check_files(glob(join(root, pattern)), file_check, exclusions)
def check_files(files, file_check, exclusions=set(), pattern=None):
"""
Checks all files with the file_check function provided, skipping files
that contain any of the strings in the set provided by exclusions.
"""
if not files:
return
for fname in files:
if not exists(fname) or not isfile(fname):
continue
if any(ex in fname for ex in exclusions):
continue
if pattern is None or re.match(pattern, fname):
file_check(fname)
def test_files():
"""
This test tests all files in sympy and checks that:
o no lines contains a trailing whitespace
o no lines end with \r\n
o no line uses tabs instead of spaces
o that the file ends with a single newline
o there are no general or string exceptions
o there are no old style raise statements
o name of arg-less test suite functions start with _ or test_
o no duplicate function names that start with test_
o no assignments to self variable in class methods
"""
def test(fname):
if PY3:
with open(fname, "rt", encoding="utf8") as test_file:
test_this_file(fname, test_file)
else:
with open(fname, "rt") as test_file:
test_this_file(fname, test_file)
with open(fname, "rt") as test_file:
source = test_file.read()
result = find_self_assignments(source)
if result:
assert False, message_self_assignments % (fname,
result[0].lineno)
def test_this_file(fname, test_file):
line = None # to flag the case where there were no lines in file
tests = 0
test_set = set()
for idx, line in enumerate(test_file):
if test_file_re.match(fname):
if test_suite_def_re.match(line):
assert False, message_test_suite_def % (fname, idx + 1)
if test_ok_def_re.match(line):
tests += 1
test_set.add(line[3:].split('(')[0].strip())
if len(test_set) != tests:
assert False, message_duplicate_test % (fname, idx + 1)
if line.endswith(" \n") or line.endswith("\t\n"):
assert False, message_space % (fname, idx + 1)
if line.endswith("\r\n"):
assert False, message_carriage % (fname, idx + 1)
if tab_in_leading(line):
assert False, message_tabs % (fname, idx + 1)
if str_raise_re.search(line):
assert False, message_str_raise % (fname, idx + 1)
if gen_raise_re.search(line):
assert False, message_gen_raise % (fname, idx + 1)
if (implicit_test_re.search(line) and
not filter(lambda ex: ex in fname, import_exclude)):
assert False, message_implicit % (fname, idx + 1)
result = old_raise_re.search(line)
if result is not None:
assert False, message_old_raise % (
fname, idx + 1, result.group(2))
if line is not None:
if line == '\n' and idx > 0:
assert False, message_multi_eof % (fname, idx + 1)
elif not line.endswith('\n'):
# eof newline check
assert False, message_eof % (fname, idx + 1)
# Files to test at top level
top_level_files = [join(TOP_PATH, file) for file in [
"build.py",
"setup.py",
"setupegg.py",
]]
# Files to exclude from all tests
exclude = set()
# Files to exclude from the implicit import test
import_exclude = set([
# glob imports are allowed in top-level __init__.py:
"%(sep)ssympy%(sep)s__init__.py" % sepd,
# these __init__.py should be fixed:
# XXX: not really, they use useful import pattern (DRY)
"%(sep)svector%(sep)s__init__.py" % sepd,
"%(sep)smechanics%(sep)s__init__.py" % sepd,
"%(sep)squantum%(sep)s__init__.py" % sepd,
"%(sep)spolys%(sep)s__init__.py" % sepd,
"%(sep)spolys%(sep)sdomains%(sep)s__init__.py" % sepd,
# interactive sympy executes ``from sympy import *``:
"%(sep)sinteractive%(sep)ssession.py" % sepd,
# isympy executes ``from sympy import *``:
"%(sep)sbin%(sep)sisympy" % sepd,
# these two are import timing tests:
"%(sep)sbin%(sep)ssympy_time.py" % sepd,
"%(sep)sbin%(sep)ssympy_time_cache.py" % sepd,
# Taken from Python stdlib:
"%(sep)sparsing%(sep)ssympy_tokenize.py" % sepd,
# this one should be fixed:
"%(sep)splotting%(sep)spygletplot%(sep)s" % sepd,
])
check_files(top_level_files, test)
check_directory_tree(BIN_PATH, test, set(["~", ".pyc", ".sh"]), "*")
check_directory_tree(SYMPY_PATH, test, exclude)
check_directory_tree(EXAMPLES_PATH, test, exclude)
def _with_space(c):
# return c with a random amount of leading space
return random.randint(0, 10)*' ' + c
def test_raise_statement_regular_expression():
candidates_ok = [
"some text # raise Exception, 'text'",
"raise ValueError('text') # raise Exception, 'text'",
"raise ValueError('text')",
"raise ValueError",
"raise ValueError('text')",
"raise ValueError('text') #,",
# Talking about an exception in a docstring
''''"""This function will raise ValueError, except when it doesn't"""''',
"raise (ValueError('text')",
]
str_candidates_fail = [
"raise 'exception'",
"raise 'Exception'",
'raise "exception"',
'raise "Exception"',
"raise 'ValueError'",
]
gen_candidates_fail = [
"raise Exception('text') # raise Exception, 'text'",
"raise Exception('text')",
"raise Exception",
"raise Exception('text')",
"raise Exception('text') #,",
"raise Exception, 'text'",
"raise Exception, 'text' # raise Exception('text')",
"raise Exception, 'text' # raise Exception, 'text'",
">>> raise Exception, 'text'",
">>> raise Exception, 'text' # raise Exception('text')",
">>> raise Exception, 'text' # raise Exception, 'text'",
]
old_candidates_fail = [
"raise Exception, 'text'",
"raise Exception, 'text' # raise Exception('text')",
"raise Exception, 'text' # raise Exception, 'text'",
">>> raise Exception, 'text'",
">>> raise Exception, 'text' # raise Exception('text')",
">>> raise Exception, 'text' # raise Exception, 'text'",
"raise ValueError, 'text'",
"raise ValueError, 'text' # raise Exception('text')",
"raise ValueError, 'text' # raise Exception, 'text'",
">>> raise ValueError, 'text'",
">>> raise ValueError, 'text' # raise Exception('text')",
">>> raise ValueError, 'text' # raise Exception, 'text'",
"raise(ValueError,",
"raise (ValueError,",
"raise( ValueError,",
"raise ( ValueError,",
"raise(ValueError ,",
"raise (ValueError ,",
"raise( ValueError ,",
"raise ( ValueError ,",
]
for c in candidates_ok:
assert str_raise_re.search(_with_space(c)) is None, c
assert gen_raise_re.search(_with_space(c)) is None, c
assert old_raise_re.search(_with_space(c)) is None, c
for c in str_candidates_fail:
assert str_raise_re.search(_with_space(c)) is not None, c
for c in gen_candidates_fail:
assert gen_raise_re.search(_with_space(c)) is not None, c
for c in old_candidates_fail:
assert old_raise_re.search(_with_space(c)) is not None, c
def test_implicit_imports_regular_expression():
candidates_ok = [
"from sympy import something",
">>> from sympy import something",
"from sympy.somewhere import something",
">>> from sympy.somewhere import something",
"import sympy",
">>> import sympy",
"import sympy.something.something",
"... import sympy",
"... import sympy.something.something",
"... from sympy import something",
"... from sympy.somewhere import something",
">> from sympy import *", # To allow 'fake' docstrings
"# from sympy import *",
"some text # from sympy import *",
]
candidates_fail = [
"from sympy import *",
">>> from sympy import *",
"from sympy.somewhere import *",
">>> from sympy.somewhere import *",
"... from sympy import *",
"... from sympy.somewhere import *",
]
for c in candidates_ok:
assert implicit_test_re.search(_with_space(c)) is None, c
for c in candidates_fail:
assert implicit_test_re.search(_with_space(c)) is not None, c
def test_test_suite_defs():
candidates_ok = [
" def foo():\n",
"def foo(arg):\n",
"def _foo():\n",
"def test_foo():\n",
]
candidates_fail = [
"def foo():\n",
"def foo() :\n",
"def foo( ):\n",
"def foo():\n",
]
for c in candidates_ok:
assert test_suite_def_re.search(c) is None, c
for c in candidates_fail:
assert test_suite_def_re.search(c) is not None, c
def test_test_duplicate_defs():
candidates_ok = [
"def foo():\ndef foo():\n",
"def test():\ndef test_():\n",
"def test_():\ndef test__():\n",
]
candidates_fail = [
"def test_():\ndef test_ ():\n",
"def test_1():\ndef test_1():\n",
]
ok = (None, 'check')
def check(file):
tests = 0
test_set = set()
for idx, line in enumerate(file.splitlines()):
if test_ok_def_re.match(line):
tests += 1
test_set.add(line[3:].split('(')[0].strip())
if len(test_set) != tests:
return False, message_duplicate_test % ('check', idx + 1)
return None, 'check'
for c in candidates_ok:
assert check(c) == ok
for c in candidates_fail:
assert check(c) != ok
def test_find_self_assignments():
candidates_ok = [
"class A(object):\n def foo(self, arg): arg = self\n",
"class A(object):\n def foo(self, arg): self.prop = arg\n",
"class A(object):\n def foo(self, arg): obj, obj2 = arg, self\n",
"class A(object):\n @classmethod\n def bar(cls, arg): arg = cls\n",
"class A(object):\n def foo(var, arg): arg = var\n",
]
candidates_fail = [
"class A(object):\n def foo(self, arg): self = arg\n",
"class A(object):\n def foo(self, arg): obj, self = arg, arg\n",
"class A(object):\n def foo(self, arg):\n if arg: self = arg",
"class A(object):\n @classmethod\n def foo(cls, arg): cls = arg\n",
"class A(object):\n def foo(var, arg): var = arg\n",
]
for c in candidates_ok:
assert find_self_assignments(c) == []
for c in candidates_fail:
assert find_self_assignments(c) != []
| 15,426 | 37.471322 | 82 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/tests/test_pickling.py
|
import sys
import inspect
import copy
import pickle
import warnings
from sympy.physics.units import meter
from sympy.utilities.pytest import XFAIL
from sympy.core.basic import Atom, Basic
from sympy.core.core import BasicMeta
from sympy.core.singleton import SingletonRegistry
from sympy.core.symbol import Dummy, Symbol, Wild
from sympy.core.numbers import (E, I, pi, oo, zoo, nan, Integer,
Rational, Float)
from sympy.core.relational import (Equality, GreaterThan, LessThan, Relational,
StrictGreaterThan, StrictLessThan, Unequality)
from sympy.core.add import Add
from sympy.core.mul import Mul
from sympy.core.power import Pow
from sympy.core.function import Derivative, Function, FunctionClass, Lambda, \
WildFunction
from sympy.sets.sets import Interval
from sympy.core.multidimensional import vectorize
from sympy.core.compatibility import HAS_GMPY
from sympy.utilities.exceptions import SymPyDeprecationWarning
from sympy import symbols, S
from sympy.external import import_module
cloudpickle = import_module('cloudpickle')
excluded_attrs = set(['_assumptions', '_mhash'])
def check(a, exclude=[], check_attr=True):
""" Check that pickling and copying round-trips.
"""
protocols = [0, 1, 2, copy.copy, copy.deepcopy]
# Python 2.x doesn't support the third pickling protocol
if sys.version_info >= (3,):
protocols.extend([3])
if sys.version_info >= (3, 4):
protocols.extend([4])
if cloudpickle:
protocols.extend([cloudpickle])
for protocol in protocols:
if protocol in exclude:
continue
if callable(protocol):
if isinstance(a, BasicMeta):
# Classes can't be copied, but that's okay.
continue
b = protocol(a)
elif inspect.ismodule(protocol):
b = protocol.loads(protocol.dumps(a))
else:
b = pickle.loads(pickle.dumps(a, protocol))
d1 = dir(a)
d2 = dir(b)
assert set(d1) == set(d2)
if not check_attr:
continue
def c(a, b, d):
for i in d:
if not hasattr(a, i) or i in excluded_attrs:
continue
attr = getattr(a, i)
if not hasattr(attr, "__call__"):
assert hasattr(b, i), i
assert getattr(b, i) == attr, "%s != %s" % (getattr(b, i), attr)
c(a, b, d1)
c(b, a, d2)
#================== core =========================
def test_core_basic():
for c in (Atom, Atom(),
Basic, Basic(),
# XXX: dynamically created types are not picklable
# BasicMeta, BasicMeta("test", (), {}),
SingletonRegistry, S):
check(c)
def test_core_symbol():
# make the Symbol a unique name that doesn't class with any other
# testing variable in this file since after this test the symbol
# having the same name will be cached as noncommutative
for c in (Dummy, Dummy("x", commutative=False), Symbol,
Symbol("_issue_3130", commutative=False), Wild, Wild("x")):
check(c)
def test_core_numbers():
for c in (Integer(2), Rational(2, 3), Float("1.2")):
check(c)
def test_core_relational():
x = Symbol("x")
y = Symbol("y")
for c in (Equality, Equality(x, y), GreaterThan, GreaterThan(x, y),
LessThan, LessThan(x, y), Relational, Relational(x, y),
StrictGreaterThan, StrictGreaterThan(x, y), StrictLessThan,
StrictLessThan(x, y), Unequality, Unequality(x, y)):
check(c)
def test_core_add():
x = Symbol("x")
for c in (Add, Add(x, 4)):
check(c)
def test_core_mul():
x = Symbol("x")
for c in (Mul, Mul(x, 4)):
check(c)
def test_core_power():
x = Symbol("x")
for c in (Pow, Pow(x, 4)):
check(c)
def test_core_function():
x = Symbol("x")
for f in (Derivative, Derivative(x), Function, FunctionClass, Lambda,
WildFunction):
check(f)
def test_core_undefinedfunctions():
f = Function("f")
# Full XFAILed test below
exclude = list(range(5))
if sys.version_info < (3,):
# https://github.com/cloudpipe/cloudpickle/issues/65
exclude.append(cloudpickle)
check(f, exclude=exclude)
@XFAIL
def test_core_undefinedfunctions_fail():
# This fails because f is assumed to be a class at sympy.basic.function.f
f = Function("f")
check(f)
def test_core_interval():
for c in (Interval, Interval(0, 2)):
check(c)
def test_core_multidimensional():
for c in (vectorize, vectorize(0)):
check(c)
def test_Singletons():
protocols = [0, 1, 2]
if sys.version_info >= (3,):
protocols.extend([3])
if sys.version_info >= (3, 4):
protocols.extend([4])
copiers = [copy.copy, copy.deepcopy]
copiers += [lambda x: pickle.loads(pickle.dumps(x, proto))
for proto in protocols]
if cloudpickle:
copiers += [lambda x: cloudpickle.loads(cloudpickle.dumps(x))]
for obj in (Integer(-1), Integer(0), Integer(1), Rational(1, 2), pi, E, I,
oo, -oo, zoo, nan, S.GoldenRatio, S.EulerGamma, S.Catalan,
S.EmptySet, S.IdentityFunction):
for func in copiers:
assert func(obj) is obj
#================== functions ===================
from sympy.functions import (Piecewise, lowergamma, acosh,
chebyshevu, chebyshevt, ln, chebyshevt_root, binomial, legendre,
Heaviside, factorial, bernoulli, coth, tanh, assoc_legendre, sign,
arg, asin, DiracDelta, re, rf, Abs, uppergamma, binomial, sinh, Ynm,
cos, cot, acos, acot, gamma, bell, hermite, harmonic,
LambertW, zeta, log, factorial, asinh, acoth, Znm,
cosh, dirichlet_eta, Eijk, loggamma, erf, ceiling, im, fibonacci,
conjugate, tan, chebyshevu_root, floor, atanh, sqrt,
RisingFactorial, sin, atan, ff, FallingFactorial, lucas, atan2,
polygamma, exp)
def test_functions():
one_var = (acosh, ln, Heaviside, factorial, bernoulli, coth, tanh,
sign, arg, asin, DiracDelta, re, Abs, sinh, cos, cot, acos, acot,
gamma, bell, harmonic, LambertW, zeta, log, factorial, asinh,
acoth, cosh, dirichlet_eta, loggamma, erf, ceiling, im, fibonacci,
conjugate, tan, floor, atanh, sin, atan, lucas, exp)
two_var = (rf, ff, lowergamma, chebyshevu, chebyshevt, binomial,
atan2, polygamma, hermite, legendre, uppergamma)
x, y, z = symbols("x,y,z")
others = (chebyshevt_root, chebyshevu_root, Eijk(x, y, z),
Piecewise( (0, x < -1), (x**2, x <= 1), (x**3, True)),
assoc_legendre)
for cls in one_var:
check(cls)
c = cls(x)
check(c)
for cls in two_var:
check(cls)
c = cls(x, y)
check(c)
for cls in others:
check(cls)
#================== geometry ====================
from sympy.geometry.entity import GeometryEntity
from sympy.geometry.point import Point
from sympy.geometry.ellipse import Circle, Ellipse
from sympy.geometry.line import Line, LinearEntity, Ray, Segment
from sympy.geometry.polygon import Polygon, RegularPolygon, Triangle
def test_geometry():
p1 = Point(1, 2)
p2 = Point(2, 3)
p3 = Point(0, 0)
p4 = Point(0, 1)
for c in (
GeometryEntity, GeometryEntity(), Point, p1, Circle, Circle(p1, 2),
Ellipse, Ellipse(p1, 3, 4), Line, Line(p1, p2), LinearEntity,
LinearEntity(p1, p2), Ray, Ray(p1, p2), Segment, Segment(p1, p2),
Polygon, Polygon(p1, p2, p3, p4), RegularPolygon,
RegularPolygon(p1, 4, 5), Triangle, Triangle(p1, p2, p3)):
check(c, check_attr=False)
#================== integrals ====================
from sympy.integrals.integrals import Integral
def test_integrals():
x = Symbol("x")
for c in (Integral, Integral(x)):
check(c)
#==================== logic =====================
from sympy.core.logic import Logic
def test_logic():
for c in (Logic, Logic(1)):
check(c)
#================== matrices ====================
from sympy.matrices import Matrix, SparseMatrix
def test_matrices():
for c in (Matrix, Matrix([1, 2, 3]), SparseMatrix, SparseMatrix([[1, 2], [3, 4]])):
check(c)
#================== ntheory =====================
from sympy.ntheory.generate import Sieve
def test_ntheory():
for c in (Sieve, Sieve()):
check(c)
#================== physics =====================
from sympy.physics.paulialgebra import Pauli
from sympy.physics.units import Unit
def test_physics():
for c in (Unit, meter, Pauli, Pauli(1)):
check(c)
#================== plotting ====================
# XXX: These tests are not complete, so XFAIL them
@XFAIL
def test_plotting():
from sympy.plotting.color_scheme import ColorGradient, ColorScheme
from sympy.plotting.managed_window import ManagedWindow
from sympy.plotting.plot import Plot, ScreenShot
from sympy.plotting.plot_axes import PlotAxes, PlotAxesBase, PlotAxesFrame, PlotAxesOrdinate
from sympy.plotting.plot_camera import PlotCamera
from sympy.plotting.plot_controller import PlotController
from sympy.plotting.plot_curve import PlotCurve
from sympy.plotting.plot_interval import PlotInterval
from sympy.plotting.plot_mode import PlotMode
from sympy.plotting.plot_modes import Cartesian2D, Cartesian3D, Cylindrical, \
ParametricCurve2D, ParametricCurve3D, ParametricSurface, Polar, Spherical
from sympy.plotting.plot_object import PlotObject
from sympy.plotting.plot_surface import PlotSurface
from sympy.plotting.plot_window import PlotWindow
for c in (
ColorGradient, ColorGradient(0.2, 0.4), ColorScheme, ManagedWindow,
ManagedWindow, Plot, ScreenShot, PlotAxes, PlotAxesBase,
PlotAxesFrame, PlotAxesOrdinate, PlotCamera, PlotController,
PlotCurve, PlotInterval, PlotMode, Cartesian2D, Cartesian3D,
Cylindrical, ParametricCurve2D, ParametricCurve3D,
ParametricSurface, Polar, Spherical, PlotObject, PlotSurface,
PlotWindow):
check(c)
@XFAIL
def test_plotting2():
from sympy.plotting.color_scheme import ColorGradient, ColorScheme
from sympy.plotting.managed_window import ManagedWindow
from sympy.plotting.plot import Plot, ScreenShot
from sympy.plotting.plot_axes import PlotAxes, PlotAxesBase, PlotAxesFrame, PlotAxesOrdinate
from sympy.plotting.plot_camera import PlotCamera
from sympy.plotting.plot_controller import PlotController
from sympy.plotting.plot_curve import PlotCurve
from sympy.plotting.plot_interval import PlotInterval
from sympy.plotting.plot_mode import PlotMode
from sympy.plotting.plot_modes import Cartesian2D, Cartesian3D, Cylindrical, \
ParametricCurve2D, ParametricCurve3D, ParametricSurface, Polar, Spherical
from sympy.plotting.plot_object import PlotObject
from sympy.plotting.plot_surface import PlotSurface
from sympy.plotting.plot_window import PlotWindow
check(ColorScheme("rainbow"))
check(Plot(1, visible=False))
check(PlotAxes())
#================== polys =======================
from sympy import Poly, ZZ, QQ, lex
def test_pickling_polys_polytools():
from sympy.polys.polytools import Poly, PurePoly, GroebnerBasis
x = Symbol('x')
for c in (Poly, Poly(x, x)):
check(c)
for c in (PurePoly, PurePoly(x)):
check(c)
# TODO: fix pickling of Options class (see GroebnerBasis._options)
# for c in (GroebnerBasis, GroebnerBasis([x**2 - 1], x, order=lex)):
# check(c)
def test_pickling_polys_polyclasses():
from sympy.polys.polyclasses import DMP, DMF, ANP
for c in (DMP, DMP([[ZZ(1)], [ZZ(2)], [ZZ(3)]], ZZ)):
check(c)
for c in (DMF, DMF(([ZZ(1), ZZ(2)], [ZZ(1), ZZ(3)]), ZZ)):
check(c)
for c in (ANP, ANP([QQ(1), QQ(2)], [QQ(1), QQ(2), QQ(3)], QQ)):
check(c)
@XFAIL
def test_pickling_polys_rings():
# NOTE: can't use protocols < 2 because we have to execute __new__ to
# make sure caching of rings works properly.
from sympy.polys.rings import PolyRing
ring = PolyRing("x,y,z", ZZ, lex)
for c in (PolyRing, ring):
check(c, exclude=[0, 1])
for c in (ring.dtype, ring.one):
check(c, exclude=[0, 1], check_attr=False) # TODO: Py3k
def test_pickling_polys_fields():
# NOTE: can't use protocols < 2 because we have to execute __new__ to
# make sure caching of fields works properly.
from sympy.polys.fields import FracField
field = FracField("x,y,z", ZZ, lex)
# TODO: AssertionError: assert id(obj) not in self.memo
# for c in (FracField, field):
# check(c, exclude=[0, 1])
# TODO: AssertionError: assert id(obj) not in self.memo
# for c in (field.dtype, field.one):
# check(c, exclude=[0, 1])
def test_pickling_polys_elements():
from sympy.polys.domains.pythonrational import PythonRational
from sympy.polys.domains.pythonfinitefield import PythonFiniteField
from sympy.polys.domains.mpelements import MPContext
for c in (PythonRational, PythonRational(1, 7)):
check(c)
gf = PythonFiniteField(17)
# TODO: fix pickling of ModularInteger
# for c in (gf.dtype, gf(5)):
# check(c)
mp = MPContext()
# TODO: fix pickling of RealElement
# for c in (mp.mpf, mp.mpf(1.0)):
# check(c)
# TODO: fix pickling of ComplexElement
# for c in (mp.mpc, mp.mpc(1.0, -1.5)):
# check(c)
def test_pickling_polys_domains():
from sympy.polys.domains.pythonfinitefield import PythonFiniteField
from sympy.polys.domains.pythonintegerring import PythonIntegerRing
from sympy.polys.domains.pythonrationalfield import PythonRationalField
# TODO: fix pickling of ModularInteger
# for c in (PythonFiniteField, PythonFiniteField(17)):
# check(c)
for c in (PythonIntegerRing, PythonIntegerRing()):
check(c, check_attr=False)
for c in (PythonRationalField, PythonRationalField()):
check(c, check_attr=False)
if HAS_GMPY:
from sympy.polys.domains.gmpyfinitefield import GMPYFiniteField
from sympy.polys.domains.gmpyintegerring import GMPYIntegerRing
from sympy.polys.domains.gmpyrationalfield import GMPYRationalField
# TODO: fix pickling of ModularInteger
# for c in (GMPYFiniteField, GMPYFiniteField(17)):
# check(c)
for c in (GMPYIntegerRing, GMPYIntegerRing()):
check(c, check_attr=False)
for c in (GMPYRationalField, GMPYRationalField()):
check(c, check_attr=False)
from sympy.polys.domains.realfield import RealField
from sympy.polys.domains.complexfield import ComplexField
from sympy.polys.domains.algebraicfield import AlgebraicField
from sympy.polys.domains.polynomialring import PolynomialRing
from sympy.polys.domains.fractionfield import FractionField
from sympy.polys.domains.expressiondomain import ExpressionDomain
# TODO: fix pickling of RealElement
# for c in (RealField, RealField(100)):
# check(c)
# TODO: fix pickling of ComplexElement
# for c in (ComplexField, ComplexField(100)):
# check(c)
for c in (AlgebraicField, AlgebraicField(QQ, sqrt(3))):
check(c, check_attr=False)
# TODO: AssertionError
# for c in (PolynomialRing, PolynomialRing(ZZ, "x,y,z")):
# check(c)
# TODO: AttributeError: 'PolyElement' object has no attribute 'ring'
# for c in (FractionField, FractionField(ZZ, "x,y,z")):
# check(c)
for c in (ExpressionDomain, ExpressionDomain()):
check(c, check_attr=False)
def test_pickling_polys_numberfields():
from sympy.polys.numberfields import AlgebraicNumber
for c in (AlgebraicNumber, AlgebraicNumber(sqrt(3))):
check(c, check_attr=False)
def test_pickling_polys_orderings():
from sympy.polys.orderings import (LexOrder, GradedLexOrder,
ReversedGradedLexOrder, ProductOrder, InverseOrder)
for c in (LexOrder, LexOrder()):
check(c)
for c in (GradedLexOrder, GradedLexOrder()):
check(c)
for c in (ReversedGradedLexOrder, ReversedGradedLexOrder()):
check(c)
# TODO: Argh, Python is so naive. No lambdas nor inner function support in
# pickling module. Maybe someone could figure out what to do with this.
#
# for c in (ProductOrder, ProductOrder((LexOrder(), lambda m: m[:2]),
# (GradedLexOrder(), lambda m: m[2:]))):
# check(c)
for c in (InverseOrder, InverseOrder(LexOrder())):
check(c)
def test_pickling_polys_monomials():
from sympy.polys.monomials import MonomialOps, Monomial
x, y, z = symbols("x,y,z")
for c in (MonomialOps, MonomialOps(3)):
check(c)
for c in (Monomial, Monomial((1, 2, 3), (x, y, z))):
check(c)
def test_pickling_polys_errors():
from sympy.polys.polyerrors import (ExactQuotientFailed, OperationNotSupported,
HeuristicGCDFailed, HomomorphismFailed, IsomorphismFailed, ExtraneousFactors,
EvaluationFailed, RefinementFailed, CoercionFailed, NotInvertible, NotReversible,
NotAlgebraic, DomainError, PolynomialError, UnificationFailed, GeneratorsError,
GeneratorsNeeded, ComputationFailed, UnivariatePolynomialError,
MultivariatePolynomialError, PolificationFailed, OptionError, FlagError)
x = Symbol('x')
# TODO: TypeError: __init__() takes at least 3 arguments (1 given)
# for c in (ExactQuotientFailed, ExactQuotientFailed(x, 3*x, ZZ)):
# check(c)
# TODO: TypeError: can't pickle instancemethod objects
# for c in (OperationNotSupported, OperationNotSupported(Poly(x), Poly.gcd)):
# check(c)
for c in (HeuristicGCDFailed, HeuristicGCDFailed()):
check(c)
for c in (HomomorphismFailed, HomomorphismFailed()):
check(c)
for c in (IsomorphismFailed, IsomorphismFailed()):
check(c)
for c in (ExtraneousFactors, ExtraneousFactors()):
check(c)
for c in (EvaluationFailed, EvaluationFailed()):
check(c)
for c in (RefinementFailed, RefinementFailed()):
check(c)
for c in (CoercionFailed, CoercionFailed()):
check(c)
for c in (NotInvertible, NotInvertible()):
check(c)
for c in (NotReversible, NotReversible()):
check(c)
for c in (NotAlgebraic, NotAlgebraic()):
check(c)
for c in (DomainError, DomainError()):
check(c)
for c in (PolynomialError, PolynomialError()):
check(c)
for c in (UnificationFailed, UnificationFailed()):
check(c)
for c in (GeneratorsError, GeneratorsError()):
check(c)
for c in (GeneratorsNeeded, GeneratorsNeeded()):
check(c)
# TODO: PicklingError: Can't pickle <function <lambda> at 0x38578c0>: it's not found as __main__.<lambda>
# for c in (ComputationFailed, ComputationFailed(lambda t: t, 3, None)):
# check(c)
for c in (UnivariatePolynomialError, UnivariatePolynomialError()):
check(c)
for c in (MultivariatePolynomialError, MultivariatePolynomialError()):
check(c)
# TODO: TypeError: __init__() takes at least 3 arguments (1 given)
# for c in (PolificationFailed, PolificationFailed({}, x, x, False)):
# check(c)
for c in (OptionError, OptionError()):
check(c)
for c in (FlagError, FlagError()):
check(c)
def test_pickling_polys_options():
from sympy.polys.polyoptions import Options
# TODO: fix pickling of `symbols' flag
# for c in (Options, Options((), dict(domain='ZZ', polys=False))):
# check(c)
# TODO: def test_pickling_polys_rootisolation():
# RealInterval
# ComplexInterval
def test_pickling_polys_rootoftools():
from sympy.polys.rootoftools import CRootOf, RootSum
x = Symbol('x')
f = x**3 + x + 3
for c in (CRootOf, CRootOf(f, 0)):
check(c)
for c in (RootSum, RootSum(f, exp)):
check(c)
#================== printing ====================
from sympy.printing.latex import LatexPrinter
from sympy.printing.mathml import MathMLPrinter
from sympy.printing.pretty.pretty import PrettyPrinter
from sympy.printing.pretty.stringpict import prettyForm, stringPict
from sympy.printing.printer import Printer
from sympy.printing.python import PythonPrinter
def test_printing():
for c in (LatexPrinter, LatexPrinter(), MathMLPrinter,
PrettyPrinter, prettyForm, stringPict, stringPict("a"),
Printer, Printer(), PythonPrinter, PythonPrinter()):
check(c)
@XFAIL
def test_printing1():
check(MathMLPrinter())
@XFAIL
def test_printing2():
check(PrettyPrinter())
#================== series ======================
from sympy.series.limits import Limit
from sympy.series.order import Order
def test_series():
e = Symbol("e")
x = Symbol("x")
for c in (Limit, Limit(e, x, 1), Order, Order(e)):
check(c)
#================== concrete ==================
from sympy.concrete.products import Product
from sympy.concrete.summations import Sum
def test_concrete():
x = Symbol("x")
for c in (Product, Product(x, (x, 2, 4)), Sum, Sum(x, (x, 2, 4))):
check(c)
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cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/tests/test_timeutils.py
|
"""Tests for simple tools for timing functions' execution. """
import sys
from sympy.utilities.timeutils import timed
def test_timed():
result = timed(lambda: 1 + 1, limit=100000)
assert result[0] == 100000 and result[3] == "ns"
result = timed("1 + 1", limit=100000)
assert result[0] == 100000 and result[3] == "ns"
| 336 | 24.923077 | 62 |
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cba-pipeline-public
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cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/tests/test_misc.py
|
from sympy.core.compatibility import unichr
from sympy.utilities.misc import translate, replace
def test_translate():
abc = 'abc'
translate(abc, None, 'a') == 'bc'
translate(abc, None, '') == 'abc'
translate(abc, {'a': 'x'}, 'c') == 'xb'
assert translate(abc, {'a': 'bc'}, 'c') == 'bcb'
assert translate(abc, {'ab': 'x'}, 'c') == 'x'
assert translate(abc, {'ab': ''}, 'c') == ''
assert translate(abc, {'bc': 'x'}, 'c') == 'ab'
assert translate(abc, {'abc': 'x', 'a': 'y'}) == 'x'
u = unichr(4096)
assert translate(abc, 'a', 'x', u) == 'xbc'
assert (u in translate(abc, 'a', u, u)) is True
def test_replace():
assert replace('abc', ('a', 'b')) == 'bbc'
assert replace('abc', {'a': 'Aa'}) == 'Aabc'
assert replace('abc', ('a', 'b'), ('c', 'C')) == 'bbC'
| 815 | 34.478261 | 58 |
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cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/tests/test_pytest.py
|
from sympy.utilities.pytest import raises, USE_PYTEST
if USE_PYTEST:
import py.test
pytestmark = py.test.mark.skipif(USE_PYTEST,
reason=("using py.test"))
# Test callables
def test_expected_exception_is_silent_callable():
def f():
raise ValueError()
raises(ValueError, f)
def test_lack_of_exception_triggers_AssertionError_callable():
try:
raises(Exception, lambda: 1 + 1)
assert False
except AssertionError as e:
assert str(e) == "DID NOT RAISE"
def test_unexpected_exception_is_passed_through_callable():
def f():
raise ValueError("some error message")
try:
raises(TypeError, f)
assert False
except ValueError as e:
assert str(e) == "some error message"
# Test with statement
def test_expected_exception_is_silent_with():
with raises(ValueError):
raise ValueError()
def test_lack_of_exception_triggers_AssertionError_with():
try:
with raises(Exception):
1 + 1
assert False
except AssertionError as e:
assert str(e) == "DID NOT RAISE"
def test_unexpected_exception_is_passed_through_with():
try:
with raises(TypeError):
raise ValueError("some error message")
assert False
except ValueError as e:
assert str(e) == "some error message"
# Now we can use raises() instead of try/catch
# to test that a specific exception class is raised
def test_second_argument_should_be_callable_or_string():
raises(TypeError, lambda: raises("irrelevant", 42))
| 1,601 | 24.03125 | 62 |
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cba-pipeline-public
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cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/tests/test_enumerative.py
|
from sympy.core.compatibility import range, zip_longest
from sympy.utilities.enumerative import (
list_visitor,
MultisetPartitionTraverser,
multiset_partitions_taocp
)
from sympy.utilities.iterables import _set_partitions
from sympy.utilities.pytest import slow
# first some functions only useful as test scaffolding - these provide
# straightforward, but slow reference implementations against which to
# compare the real versions, and also a comparision to verify that
# different versions are giving identical results.
def part_range_filter(partition_iterator, lb, ub):
"""
Filters (on the number of parts) a multiset partition enumeration
Arguments
=========
lb, and ub are a range (in the python slice sense) on the lpart
variable returned from a multiset partition enumeration. Recall
that lpart is 0-based (it points to the topmost part on the part
stack), so if you want to return parts of sizes 2,3,4,5 you would
use lb=1 and ub=5.
"""
for state in partition_iterator:
f, lpart, pstack = state
if lpart >= lb and lpart < ub:
yield state
def multiset_partitions_baseline(multiplicities, components):
"""Enumerates partitions of a multiset
Parameters
==========
multiplicities
list of integer multiplicities of the components of the multiset.
components
the components (elements) themselves
Returns
=======
Set of partitions. Each partition is tuple of parts, and each
part is a tuple of components (with repeats to indicate
multiplicity)
Notes
=====
Multiset partitions can be created as equivalence classes of set
partitions, and this function does just that. This approach is
slow and memory intensive compared to the more advanced algorithms
available, but the code is simple and easy to understand. Hence
this routine is strictly for testing -- to provide a
straightforward baseline against which to regress the production
versions. (This code is a simplified version of an earlier
production implementation.)
"""
canon = [] # list of components with repeats
for ct, elem in zip(multiplicities, components):
canon.extend([elem]*ct)
# accumulate the multiset partitions in a set to eliminate dups
cache = set()
n = len(canon)
for nc, q in _set_partitions(n):
rv = [[] for i in range(nc)]
for i in range(n):
rv[q[i]].append(canon[i])
canonical = tuple(
sorted([tuple(p) for p in rv]))
cache.add(canonical)
return cache
def compare_multiset_w_baseline(multiplicities):
"""
Enumerates the partitions of multiset with AOCP algorithm and
baseline implementation, and compare the results.
"""
letters = "abcdefghijklmnopqrstuvwxyz"
bl_partitions = multiset_partitions_baseline(multiplicities, letters)
# The partitions returned by the different algorithms may have
# their parts in different orders. Also, they generate partitions
# in different orders. Hence the sorting, and set comparison.
aocp_partitions = set()
for state in multiset_partitions_taocp(multiplicities):
p1 = tuple(sorted(
[tuple(p) for p in list_visitor(state, letters)]))
aocp_partitions.add(p1)
assert bl_partitions == aocp_partitions
def compare_multiset_states(s1, s2):
"""compare for equality two instances of multiset partition states
This is useful for comparing different versions of the algorithm
to verify correctness."""
# Comparison is physical, the only use of semantics is to ignore
# trash off the top of the stack.
f1, lpart1, pstack1 = s1
f2, lpart2, pstack2 = s2
if (lpart1 == lpart2) and (f1[0:lpart1+1] == f2[0:lpart2+1]):
if pstack1[0:f1[lpart1+1]] == pstack2[0:f2[lpart2+1]]:
return True
return False
def test_multiset_partitions_taocp():
"""Compares the output of multiset_partitions_taocp with a baseline
(set partition based) implementation."""
# Test cases should not be too large, since the baseline
# implementation is fairly slow.
multiplicities = [2,2]
compare_multiset_w_baseline(multiplicities)
multiplicities = [4,3,1]
compare_multiset_w_baseline(multiplicities)
def test_multiset_partitions_versions():
"""Compares Knuth-based versions of multiset_partitions"""
multiplicities = [5,2,2,1]
m = MultisetPartitionTraverser()
for s1, s2 in zip_longest(m.enum_all(multiplicities),
multiset_partitions_taocp(multiplicities)):
assert compare_multiset_states(s1, s2)
def subrange_exercise(mult, lb, ub):
"""Compare filter-based and more optimized subrange implementations
Helper for tests, called with both small and larger multisets.
"""
m = MultisetPartitionTraverser()
assert m.count_partitions(mult) == \
m.count_partitions_slow(mult)
# Note - multiple traversals from the same
# MultisetPartitionTraverser object cannot execute at the same
# time, hence make several instances here.
ma = MultisetPartitionTraverser()
mc = MultisetPartitionTraverser()
md = MultisetPartitionTraverser()
# Several paths to compute just the size two partitions
a_it = ma.enum_range(mult, lb, ub)
b_it = part_range_filter(multiset_partitions_taocp(mult), lb, ub)
c_it = part_range_filter(mc.enum_small(mult, ub), lb, sum(mult))
d_it = part_range_filter(md.enum_large(mult, lb), 0, ub)
for sa, sb, sc, sd in zip_longest(a_it, b_it, c_it, d_it):
assert compare_multiset_states(sa, sb)
assert compare_multiset_states(sa, sc)
assert compare_multiset_states(sa, sd)
def test_subrange():
# Quick, but doesn't hit some of the corner cases
mult = [4,4,2,1] # mississippi
lb = 1
ub = 2
subrange_exercise(mult, lb, ub)
@slow
def test_subrange_large():
# takes a second or so, depending on cpu, Python version, etc.
mult = [6,3,2,1]
lb = 4
ub = 7
subrange_exercise(mult, lb, ub)
| 6,156 | 33.396648 | 74 |
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cba-pipeline-public
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cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/tests/test_module_imports.py
|
"""
Checks that SymPy does not contain indirect imports.
An indirect import is importing a symbol from a module that itself imported the
symbol from elsewhere. Such a constellation makes it harder to diagnose
inter-module dependencies and import order problems, and is therefore strongly
discouraged.
(Indirect imports from end-user code is fine and in fact a best practice.)
Implementation note: Forcing Python into actually unloading already-imported
submodules is a tricky and partly undocumented process. To avoid these issues,
the actual diagnostic code is in bin/diagnose_imports, which is run as a
separate, pristine Python process.
"""
from __future__ import print_function
import subprocess
import sys
from os.path import abspath, dirname, join, normpath
import inspect
from sympy.utilities.pytest import XFAIL
@XFAIL
def test_module_imports_are_direct():
my_filename = abspath(inspect.getfile(inspect.currentframe()))
my_dirname = dirname(my_filename)
diagnose_imports_filename = join(my_dirname, 'diagnose_imports.py')
diagnose_imports_filename = normpath(diagnose_imports_filename)
process = subprocess.Popen(
[
sys.executable,
normpath(diagnose_imports_filename),
'--problems',
'--by-importer'
],
stdout=subprocess.PIPE,
stderr=subprocess.STDOUT,
bufsize=-1)
output, _ = process.communicate()
assert output == '', "There are import problems:\n" + output.decode()
| 1,500 | 32.355556 | 79 |
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cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/tests/test_codegen_rust.py
|
from sympy.core import (S, symbols, Eq, pi, Catalan, EulerGamma, Lambda,
Dummy, Function)
from sympy.core.compatibility import StringIO
from sympy import erf, Integral, Piecewise
from sympy import Equality
from sympy.matrices import Matrix, MatrixSymbol
from sympy.printing.codeprinter import Assignment
from sympy.utilities.codegen import RustCodeGen, codegen, make_routine
from sympy.utilities.pytest import raises
from sympy.utilities.lambdify import implemented_function
from sympy.utilities.pytest import XFAIL
import sympy
x, y, z = symbols('x,y,z')
def test_empty_rust_code():
code_gen = RustCodeGen()
output = StringIO()
code_gen.dump_rs([], output, "file", header=False, empty=False)
source = output.getvalue()
assert source == ""
def test_simple_rust_code():
name_expr = ("test", (x + y)*z)
result, = codegen(name_expr, "Rust", header=False, empty=False)
assert result[0] == "test.rs"
source = result[1]
expected = (
"fn test(x: f64, y: f64, z: f64) -> f64 {\n"
" let out1 = z*(x + y);\n"
" out1\n"
"}\n"
)
assert source == expected
def test_simple_code_with_header():
name_expr = ("test", (x + y)*z)
result, = codegen(name_expr, "Rust", header=True, empty=False)
assert result[0] == "test.rs"
source = result[1]
version_str = "Code generated with sympy %s" % sympy.__version__
version_line = version_str.center(76).rstrip()
expected = (
"/*\n"
" *%(version_line)s\n"
" *\n"
" * See http://www.sympy.org/ for more information.\n"
" *\n"
" * This file is part of 'project'\n"
" */\n"
"fn test(x: f64, y: f64, z: f64) -> f64 {\n"
" let out1 = z*(x + y);\n"
" out1\n"
"}\n"
) % {'version_line': version_line}
assert source == expected
def test_simple_code_nameout():
expr = Equality(z, (x + y))
name_expr = ("test", expr)
result, = codegen(name_expr, "Rust", header=False, empty=False)
source = result[1]
expected = (
"fn test(x: f64, y: f64) -> f64 {\n"
" let z = x + y;\n"
" z\n"
"}\n"
)
assert source == expected
def test_numbersymbol():
name_expr = ("test", pi**Catalan)
result, = codegen(name_expr, "Rust", header=False, empty=False)
source = result[1]
expected = (
"fn test() -> f64 {\n"
" const Catalan: f64 = 0.915965594177219;\n"
" let out1 = PI.powf(Catalan);\n"
" out1\n"
"}\n"
)
assert source == expected
@XFAIL
def test_numbersymbol_inline():
# FIXME: how to pass inline to the RustCodePrinter?
name_expr = ("test", [pi**Catalan, EulerGamma])
result, = codegen(name_expr, "Rust", header=False,
empty=False, inline=True)
source = result[1]
expected = (
"fn test() -> (f64, f64) {\n"
" const Catalan: f64 = 0.915965594177219;\n"
" const EulerGamma: f64 = 0.5772156649015329;\n"
" let out1 = PI.powf(Catalan);\n"
" let out2 = EulerGamma);\n"
" (out1, out2)\n"
"}\n"
)
assert source == expected
def test_argument_order():
expr = x + y
routine = make_routine("test", expr, argument_sequence=[z, x, y], language="rust")
code_gen = RustCodeGen()
output = StringIO()
code_gen.dump_rs([routine], output, "test", header=False, empty=False)
source = output.getvalue()
expected = (
"fn test(z: f64, x: f64, y: f64) -> f64 {\n"
" let out1 = x + y;\n"
" out1\n"
"}\n"
)
assert source == expected
def test_multiple_results_rust():
# Here the output order is the input order
expr1 = (x + y)*z
expr2 = (x - y)*z
name_expr = ("test", [expr1, expr2])
result, = codegen(name_expr, "Rust", header=False, empty=False)
source = result[1]
expected = (
"fn test(x: f64, y: f64, z: f64) -> (f64, f64) {\n"
" let out1 = z*(x + y);\n"
" let out2 = z*(x - y);\n"
" (out1, out2)\n"
"}\n"
)
assert source == expected
def test_results_named_unordered():
# Here output order is based on name_expr
A, B, C = symbols('A,B,C')
expr1 = Equality(C, (x + y)*z)
expr2 = Equality(A, (x - y)*z)
expr3 = Equality(B, 2*x)
name_expr = ("test", [expr1, expr2, expr3])
result, = codegen(name_expr, "Rust", header=False, empty=False)
source = result[1]
expected = (
"fn test(x: f64, y: f64, z: f64) -> (f64, f64, f64) {\n"
" let C = z*(x + y);\n"
" let A = z*(x - y);\n"
" let B = 2*x;\n"
" (C, A, B)\n"
"}\n"
)
assert source == expected
def test_results_named_ordered():
A, B, C = symbols('A,B,C')
expr1 = Equality(C, (x + y)*z)
expr2 = Equality(A, (x - y)*z)
expr3 = Equality(B, 2*x)
name_expr = ("test", [expr1, expr2, expr3])
result = codegen(name_expr, "Rust", header=False, empty=False,
argument_sequence=(x, z, y))
assert result[0][0] == "test.rs"
source = result[0][1]
expected = (
"fn test(x: f64, z: f64, y: f64) -> (f64, f64, f64) {\n"
" let C = z*(x + y);\n"
" let A = z*(x - y);\n"
" let B = 2*x;\n"
" (C, A, B)\n"
"}\n"
)
assert source == expected
def test_complicated_rs_codegen():
from sympy import sin, cos, tan
name_expr = ("testlong",
[ ((sin(x) + cos(y) + tan(z))**3).expand(),
cos(cos(cos(cos(cos(cos(cos(cos(x + y + z))))))))
])
result = codegen(name_expr, "Rust", header=False, empty=False)
assert result[0][0] == "testlong.rs"
source = result[0][1]
expected = (
"fn testlong(x: f64, y: f64, z: f64) -> (f64, f64) {\n"
" let out1 = x.sin().powi(3) + 3*x.sin().powi(2)*y.cos()"
" + 3*x.sin().powi(2)*z.tan() + 3*x.sin()*y.cos().powi(2)"
" + 6*x.sin()*y.cos()*z.tan() + 3*x.sin()*z.tan().powi(2)"
" + y.cos().powi(3) + 3*y.cos().powi(2)*z.tan()"
" + 3*y.cos()*z.tan().powi(2) + z.tan().powi(3);\n"
" let out2 = (x + y + z).cos().cos().cos().cos()"
".cos().cos().cos().cos();\n"
" (out1, out2)\n"
"}\n"
)
assert source == expected
def test_output_arg_mixed_unordered():
# named outputs are alphabetical, unnamed output appear in the given order
from sympy import sin, cos, tan
a = symbols("a")
name_expr = ("foo", [cos(2*x), Equality(y, sin(x)), cos(x), Equality(a, sin(2*x))])
result, = codegen(name_expr, "Rust", header=False, empty=False)
assert result[0] == "foo.rs"
source = result[1];
expected = (
"fn foo(x: f64) -> (f64, f64, f64, f64) {\n"
" let out1 = (2*x).cos();\n"
" let y = x.sin();\n"
" let out3 = x.cos();\n"
" let a = (2*x).sin();\n"
" (out1, y, out3, a)\n"
"}\n"
)
assert source == expected
def test_piecewise_():
pw = Piecewise((0, x < -1), (x**2, x <= 1), (-x+2, x > 1), (1, True))
name_expr = ("pwtest", pw)
result, = codegen(name_expr, "Rust", header=False, empty=False)
source = result[1]
expected = (
"fn pwtest(x: f64) -> f64 {\n"
" let out1 = if (x < -1) {\n"
" 0\n"
" } else if (x <= 1) {\n"
" x.powi(2)\n"
" } else if (x > 1) {\n"
" -x + 2\n"
" } else {\n"
" 1\n"
" };\n"
" out1\n"
"}\n"
)
assert source == expected
@XFAIL
def test_piecewise_inline():
# FIXME: how to pass inline to the RustCodePrinter?
pw = Piecewise((0, x < -1), (x**2, x <= 1), (-x+2, x > 1), (1, True))
name_expr = ("pwtest", pw)
result, = codegen(name_expr, "Rust", header=False, empty=False,
inline=True)
source = result[1]
expected = (
"fn pwtest(x: f64) -> f64 {\n"
" let out1 = if (x < -1) { 0 } else if (x <= 1) { x.powi(2) }"
" else if (x > 1) { -x + 2 } else { 1 };\n"
" out1\n"
"}\n"
)
assert source == expected
def test_multifcns_per_file():
name_expr = [ ("foo", [2*x, 3*y]), ("bar", [y**2, 4*y]) ]
result = codegen(name_expr, "Rust", header=False, empty=False)
assert result[0][0] == "foo.rs"
source = result[0][1];
expected = (
"fn foo(x: f64, y: f64) -> (f64, f64) {\n"
" let out1 = 2*x;\n"
" let out2 = 3*y;\n"
" (out1, out2)\n"
"}\n"
"fn bar(y: f64) -> (f64, f64) {\n"
" let out1 = y.powi(2);\n"
" let out2 = 4*y;\n"
" (out1, out2)\n"
"}\n"
)
assert source == expected
def test_multifcns_per_file_w_header():
name_expr = [ ("foo", [2*x, 3*y]), ("bar", [y**2, 4*y]) ]
result = codegen(name_expr, "Rust", header=True, empty=False)
assert result[0][0] == "foo.rs"
source = result[0][1];
version_str = "Code generated with sympy %s" % sympy.__version__
version_line = version_str.center(76).rstrip()
expected = (
"/*\n"
" *%(version_line)s\n"
" *\n"
" * See http://www.sympy.org/ for more information.\n"
" *\n"
" * This file is part of 'project'\n"
" */\n"
"fn foo(x: f64, y: f64) -> (f64, f64) {\n"
" let out1 = 2*x;\n"
" let out2 = 3*y;\n"
" (out1, out2)\n"
"}\n"
"fn bar(y: f64) -> (f64, f64) {\n"
" let out1 = y.powi(2);\n"
" let out2 = 4*y;\n"
" (out1, out2)\n"
"}\n"
) % {'version_line': version_line}
assert source == expected
def test_filename_match_prefix():
name_expr = [ ("foo", [2*x, 3*y]), ("bar", [y**2, 4*y]) ]
result, = codegen(name_expr, "Rust", prefix="baz", header=False,
empty=False)
assert result[0] == "baz.rs"
def test_InOutArgument():
expr = Equality(x, x**2)
name_expr = ("mysqr", expr)
result, = codegen(name_expr, "Rust", header=False, empty=False)
source = result[1]
expected = (
"fn mysqr(x: f64) -> f64 {\n"
" let x = x.powi(2);\n"
" x\n"
"}\n"
)
assert source == expected
def test_InOutArgument_order():
# can specify the order as (x, y)
expr = Equality(x, x**2 + y)
name_expr = ("test", expr)
result, = codegen(name_expr, "Rust", header=False,
empty=False, argument_sequence=(x,y))
source = result[1]
expected = (
"fn test(x: f64, y: f64) -> f64 {\n"
" let x = x.powi(2) + y;\n"
" x\n"
"}\n"
)
assert source == expected
# make sure it gives (x, y) not (y, x)
expr = Equality(x, x**2 + y)
name_expr = ("test", expr)
result, = codegen(name_expr, "Rust", header=False, empty=False)
source = result[1]
expected = (
"fn test(x: f64, y: f64) -> f64 {\n"
" let x = x.powi(2) + y;\n"
" x\n"
"}\n"
)
assert source == expected
def test_not_supported():
f = Function('f')
name_expr = ("test", [f(x).diff(x), S.ComplexInfinity])
result, = codegen(name_expr, "Rust", header=False, empty=False)
source = result[1]
expected = (
"fn test(x: f64) -> (f64, f64) {\n"
" // unsupported: Derivative(f(x), x)\n"
" // unsupported: zoo\n"
" let out1 = Derivative(f(x), x);\n"
" let out2 = zoo;\n"
" (out1, out2)\n"
"}\n"
)
assert source == expected
def test_global_vars_rust():
x, y, z, t = symbols("x y z t")
result = codegen(('f', x*y), "Rust", header=False, empty=False,
global_vars=(y,))
source = result[0][1]
expected = (
"fn f(x: f64) -> f64 {\n"
" let out1 = x*y;\n"
" out1\n"
"}\n"
)
assert source == expected
result = codegen(('f', x*y+z), "Rust", header=False, empty=False,
argument_sequence=(x, y), global_vars=(z, t))
source = result[0][1]
expected = (
"fn f(x: f64, y: f64) -> f64 {\n"
" let out1 = x*y + z;\n"
" out1\n"
"}\n"
)
assert source == expected
| 12,455 | 29.679803 | 87 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/tests/diagnose_imports.py
|
#!/usr/bin/env python
"""
Import diagnostics. Run bin/diagnose_imports.py --help for details.
"""
from __future__ import print_function
if __name__ == "__main__":
import sys
import inspect
from sympy.core.compatibility import builtins
import optparse
from os.path import abspath, dirname, join, normpath
this_file = abspath(__file__)
sympy_dir = join(dirname(this_file), '..', '..', '..')
sympy_dir = normpath(sympy_dir)
sys.path.insert(0, sympy_dir)
option_parser = optparse.OptionParser(
usage=
"Usage: %prog option [options]\n"
"\n"
"Import analysis for imports between SymPy modules.")
option_group = optparse.OptionGroup(
option_parser,
'Analysis options',
'Options that define what to do. Exactly one of these must be given.')
option_group.add_option(
'--problems',
help=
'Print all import problems, that is: '
'If an import pulls in a package instead of a module '
'(e.g. sympy.core instead of sympy.core.add); ' # see ##PACKAGE##
'if it imports a symbol that is already present; ' # see ##DUPLICATE##
'if it imports a symbol '
'from somewhere other than the defining module.', # see ##ORIGIN##
action='count')
option_group.add_option(
'--origins',
help=
'For each imported symbol in each module, '
'print the module that defined it. '
'(This is useful for import refactoring.)',
action='count')
option_parser.add_option_group(option_group)
option_group = optparse.OptionGroup(
option_parser,
'Sort options',
'These options define the sort order for output lines. '
'At most one of these options is allowed. '
'Unsorted output will reflect the order in which imports happened.')
option_group.add_option(
'--by-importer',
help='Sort output lines by name of importing module.',
action='count')
option_group.add_option(
'--by-origin',
help='Sort output lines by name of imported module.',
action='count')
option_parser.add_option_group(option_group)
(options, args) = option_parser.parse_args()
if args:
option_parser.error(
'Unexpected arguments %s (try %s --help)' % (args, sys.argv[0]))
if options.problems > 1:
option_parser.error('--problems must not be given more than once.')
if options.origins > 1:
option_parser.error('--origins must not be given more than once.')
if options.by_importer > 1:
option_parser.error('--by-importer must not be given more than once.')
if options.by_origin > 1:
option_parser.error('--by-origin must not be given more than once.')
options.problems = options.problems == 1
options.origins = options.origins == 1
options.by_importer = options.by_importer == 1
options.by_origin = options.by_origin == 1
if not options.problems and not options.origins:
option_parser.error(
'At least one of --problems and --origins is required')
if options.problems and options.origins:
option_parser.error(
'At most one of --problems and --origins is allowed')
if options.by_importer and options.by_origin:
option_parser.error(
'At most one of --by-importer and --by-origin is allowed')
options.by_process = not options.by_importer and not options.by_origin
builtin_import = builtins.__import__
class Definition(object):
"""Information about a symbol's definition."""
def __init__(self, name, value, definer):
self.name = name
self.value = value
self.definer = definer
def __hash__(self):
return hash(self.name)
def __eq__(self, other):
return self.name == other.name and self.value == other.value
def __ne__(self, other):
return not (self == other)
def __repr__(self):
return 'Definition(%s, ..., %s)' % (
repr(self.name), repr(self.definer))
symbol_definers = {} # Maps each function/variable to name of module to define it
def in_module(a, b):
"""Is a the same module as or a submodule of b?"""
return a == b or a != None and b != None and a.startswith(b + '.')
def relevant(module):
"""Is module relevant for import checking?
Only imports between relevant modules will be checked."""
return in_module(module, 'sympy')
sorted_messages = []
def msg(msg, *args):
global options, sorted_messages
if options.by_process:
print(msg % args)
else:
sorted_messages.append(msg % args)
def tracking_import(module, globals=globals(), locals=[], fromlist=None, level=-1):
"""__import__ wrapper - does not change imports at all, but tracks them.
Default order is implemented by doing output directly.
All other orders are implemented by collecting output information into
a sorted list that will be emitted after all imports are processed.
Indirect imports can only occur after the requested symbol has been
imported directly (because the indirect import would not have a module
to pick the symbol up from).
So this code detects indirect imports by checking whether the symbol in
question was already imported.
Keeps the semantics of __import__ unchanged."""
global options, symbol_definers
caller_frame = inspect.getframeinfo(sys._getframe(1))
importer_filename = caller_frame.filename
importer_module = globals['__name__']
if importer_filename == caller_frame.filename:
importer_reference = '%s line %s' % (
importer_filename, str(caller_frame.lineno))
else:
importer_reference = importer_filename
result = builtin_import(module, globals, locals, fromlist, level)
importee_module = result.__name__
# We're only interested if importer and importee are in SymPy
if relevant(importer_module) and relevant(importee_module):
for symbol in result.__dict__.iterkeys():
definition = Definition(
symbol, result.__dict__[symbol], importer_module)
if not definition in symbol_definers:
symbol_definers[definition] = importee_module
if hasattr(result, '__path__'):
##PACKAGE##
# The existence of __path__ is documented in the tutorial on modules.
# Python 3.3 documents this in http://docs.python.org/3.3/reference/import.html
if options.by_origin:
msg('Error: %s (a package) is imported by %s',
module, importer_reference)
else:
msg('Error: %s contains package import %s',
importer_reference, module)
if fromlist != None:
symbol_list = fromlist
if '*' in symbol_list:
if (importer_filename.endswith('__init__.py')
or importer_filename.endswith('__init__.pyc')
or importer_filename.endswith('__init__.pyo')):
# We do not check starred imports inside __init__
# That's the normal "please copy over its imports to my namespace"
symbol_list = []
else:
symbol_list = result.__dict__.iterkeys()
for symbol in symbol_list:
if not symbol in result.__dict__:
if options.by_origin:
msg('Error: %s.%s is not defined (yet), but %s tries to import it',
importee_module, symbol, importer_reference)
else:
msg('Error: %s tries to import %s.%s, which did not define it (yet)',
importer_reference, importee_module, symbol)
else:
definition = Definition(
symbol, result.__dict__[symbol], importer_module)
symbol_definer = symbol_definers[definition]
if symbol_definer == importee_module:
##DUPLICATE##
if options.by_origin:
msg('Error: %s.%s is imported again into %s',
importee_module, symbol, importer_reference)
else:
msg('Error: %s imports %s.%s again',
importer_reference, importee_module, symbol)
else:
##ORIGIN##
if options.by_origin:
msg('Error: %s.%s is imported by %s, which should import %s.%s instead',
importee_module, symbol, importer_reference, symbol_definer, symbol)
else:
msg('Error: %s imports %s.%s but should import %s.%s instead',
importer_reference, importee_module, symbol, symbol_definer, symbol)
return result
builtins.__import__ = tracking_import
__import__('sympy')
sorted_messages.sort()
for message in sorted_messages:
print(message)
| 9,708 | 43.131818 | 106 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/tests/test_codegen_julia.py
|
from sympy.core import (S, symbols, Eq, pi, Catalan, EulerGamma, Lambda,
Dummy, Function)
from sympy.core.compatibility import StringIO
from sympy import erf, Integral, Piecewise
from sympy import Equality
from sympy.matrices import Matrix, MatrixSymbol
from sympy.printing.codeprinter import Assignment
from sympy.utilities.codegen import JuliaCodeGen, codegen, make_routine
from sympy.utilities.pytest import raises
from sympy.utilities.lambdify import implemented_function
from sympy.utilities.pytest import XFAIL
import sympy
x, y, z = symbols('x,y,z')
def test_empty_jl_code():
code_gen = JuliaCodeGen()
output = StringIO()
code_gen.dump_jl([], output, "file", header=False, empty=False)
source = output.getvalue()
assert source == ""
def test_jl_simple_code():
name_expr = ("test", (x + y)*z)
result, = codegen(name_expr, "Julia", header=False, empty=False)
assert result[0] == "test.jl"
source = result[1]
expected = (
"function test(x, y, z)\n"
" out1 = z.*(x + y)\n"
" return out1\n"
"end\n"
)
assert source == expected
def test_jl_simple_code_with_header():
name_expr = ("test", (x + y)*z)
result, = codegen(name_expr, "Julia", header=True, empty=False)
assert result[0] == "test.jl"
source = result[1]
expected = (
"# Code generated with sympy " + sympy.__version__ + "\n"
"#\n"
"# See http://www.sympy.org/ for more information.\n"
"#\n"
"# This file is part of 'project'\n"
"function test(x, y, z)\n"
" out1 = z.*(x + y)\n"
" return out1\n"
"end\n"
)
assert source == expected
def test_jl_simple_code_nameout():
expr = Equality(z, (x + y))
name_expr = ("test", expr)
result, = codegen(name_expr, "Julia", header=False, empty=False)
source = result[1]
expected = (
"function test(x, y)\n"
" z = x + y\n"
" return z\n"
"end\n"
)
assert source == expected
def test_jl_numbersymbol():
name_expr = ("test", pi**Catalan)
result, = codegen(name_expr, "Julia", header=False, empty=False)
source = result[1]
expected = (
"function test()\n"
" out1 = pi^catalan\n"
" return out1\n"
"end\n"
)
assert source == expected
@XFAIL
def test_jl_numbersymbol_no_inline():
# FIXME: how to pass inline=False to the JuliaCodePrinter?
name_expr = ("test", [pi**Catalan, EulerGamma])
result, = codegen(name_expr, "Julia", header=False,
empty=False, inline=False)
source = result[1]
expected = (
"function test()\n"
" Catalan = 0.915965594177219\n"
" EulerGamma = 0.5772156649015329\n"
" out1 = pi^Catalan\n"
" out2 = EulerGamma\n"
" return out1, out2\n"
"end\n"
)
assert source == expected
def test_jl_code_argument_order():
expr = x + y
routine = make_routine("test", expr, argument_sequence=[z, x, y], language="julia")
code_gen = JuliaCodeGen()
output = StringIO()
code_gen.dump_jl([routine], output, "test", header=False, empty=False)
source = output.getvalue()
expected = (
"function test(z, x, y)\n"
" out1 = x + y\n"
" return out1\n"
"end\n"
)
assert source == expected
def test_multiple_results_m():
# Here the output order is the input order
expr1 = (x + y)*z
expr2 = (x - y)*z
name_expr = ("test", [expr1, expr2])
result, = codegen(name_expr, "Julia", header=False, empty=False)
source = result[1]
expected = (
"function test(x, y, z)\n"
" out1 = z.*(x + y)\n"
" out2 = z.*(x - y)\n"
" return out1, out2\n"
"end\n"
)
assert source == expected
def test_results_named_unordered():
# Here output order is based on name_expr
A, B, C = symbols('A,B,C')
expr1 = Equality(C, (x + y)*z)
expr2 = Equality(A, (x - y)*z)
expr3 = Equality(B, 2*x)
name_expr = ("test", [expr1, expr2, expr3])
result, = codegen(name_expr, "Julia", header=False, empty=False)
source = result[1]
expected = (
"function test(x, y, z)\n"
" C = z.*(x + y)\n"
" A = z.*(x - y)\n"
" B = 2*x\n"
" return C, A, B\n"
"end\n"
)
assert source == expected
def test_results_named_ordered():
A, B, C = symbols('A,B,C')
expr1 = Equality(C, (x + y)*z)
expr2 = Equality(A, (x - y)*z)
expr3 = Equality(B, 2*x)
name_expr = ("test", [expr1, expr2, expr3])
result = codegen(name_expr, "Julia", header=False, empty=False,
argument_sequence=(x, z, y))
assert result[0][0] == "test.jl"
source = result[0][1]
expected = (
"function test(x, z, y)\n"
" C = z.*(x + y)\n"
" A = z.*(x - y)\n"
" B = 2*x\n"
" return C, A, B\n"
"end\n"
)
assert source == expected
def test_complicated_jl_codegen():
from sympy import sin, cos, tan
name_expr = ("testlong",
[ ((sin(x) + cos(y) + tan(z))**3).expand(),
cos(cos(cos(cos(cos(cos(cos(cos(x + y + z))))))))
])
result = codegen(name_expr, "Julia", header=False, empty=False)
assert result[0][0] == "testlong.jl"
source = result[0][1]
expected = (
"function testlong(x, y, z)\n"
" out1 = sin(x).^3 + 3*sin(x).^2.*cos(y) + 3*sin(x).^2.*tan(z)"
" + 3*sin(x).*cos(y).^2 + 6*sin(x).*cos(y).*tan(z) + 3*sin(x).*tan(z).^2"
" + cos(y).^3 + 3*cos(y).^2.*tan(z) + 3*cos(y).*tan(z).^2 + tan(z).^3\n"
" out2 = cos(cos(cos(cos(cos(cos(cos(cos(x + y + z))))))))\n"
" return out1, out2\n"
"end\n"
)
assert source == expected
def test_jl_output_arg_mixed_unordered():
# named outputs are alphabetical, unnamed output appear in the given order
from sympy import sin, cos, tan
a = symbols("a")
name_expr = ("foo", [cos(2*x), Equality(y, sin(x)), cos(x), Equality(a, sin(2*x))])
result, = codegen(name_expr, "Julia", header=False, empty=False)
assert result[0] == "foo.jl"
source = result[1];
expected = (
'function foo(x)\n'
' out1 = cos(2*x)\n'
' y = sin(x)\n'
' out3 = cos(x)\n'
' a = sin(2*x)\n'
' return out1, y, out3, a\n'
'end\n'
)
assert source == expected
def test_jl_piecewise_():
pw = Piecewise((0, x < -1), (x**2, x <= 1), (-x+2, x > 1), (1, True))
name_expr = ("pwtest", pw)
result, = codegen(name_expr, "Julia", header=False, empty=False)
source = result[1]
expected = (
"function pwtest(x)\n"
" out1 = ((x < -1) ? (0) :\n"
" (x <= 1) ? (x.^2) :\n"
" (x > 1) ? (-x + 2) : (1))\n"
" return out1\n"
"end\n"
)
assert source == expected
@XFAIL
def test_jl_piecewise_no_inline():
# FIXME: how to pass inline=False to the JuliaCodePrinter?
pw = Piecewise((0, x < -1), (x**2, x <= 1), (-x+2, x > 1), (1, True))
name_expr = ("pwtest", pw)
result, = codegen(name_expr, "Julia", header=False, empty=False,
inline=False)
source = result[1]
expected = (
"function pwtest(x)\n"
" if (x < -1)\n"
" out1 = 0\n"
" elseif (x <= 1)\n"
" out1 = x.^2\n"
" elseif (x > 1)\n"
" out1 = -x + 2\n"
" else\n"
" out1 = 1\n"
" end\n"
" return out1\n"
"end\n"
)
assert source == expected
def test_jl_multifcns_per_file():
name_expr = [ ("foo", [2*x, 3*y]), ("bar", [y**2, 4*y]) ]
result = codegen(name_expr, "Julia", header=False, empty=False)
assert result[0][0] == "foo.jl"
source = result[0][1];
expected = (
"function foo(x, y)\n"
" out1 = 2*x\n"
" out2 = 3*y\n"
" return out1, out2\n"
"end\n"
"function bar(y)\n"
" out1 = y.^2\n"
" out2 = 4*y\n"
" return out1, out2\n"
"end\n"
)
assert source == expected
def test_jl_multifcns_per_file_w_header():
name_expr = [ ("foo", [2*x, 3*y]), ("bar", [y**2, 4*y]) ]
result = codegen(name_expr, "Julia", header=True, empty=False)
assert result[0][0] == "foo.jl"
source = result[0][1];
expected = (
"# Code generated with sympy " + sympy.__version__ + "\n"
"#\n"
"# See http://www.sympy.org/ for more information.\n"
"#\n"
"# This file is part of 'project'\n"
"function foo(x, y)\n"
" out1 = 2*x\n"
" out2 = 3*y\n"
" return out1, out2\n"
"end\n"
"function bar(y)\n"
" out1 = y.^2\n"
" out2 = 4*y\n"
" return out1, out2\n"
"end\n"
)
assert source == expected
def test_jl_filename_match_prefix():
name_expr = [ ("foo", [2*x, 3*y]), ("bar", [y**2, 4*y]) ]
result, = codegen(name_expr, "Julia", prefix="baz", header=False,
empty=False)
assert result[0] == "baz.jl"
def test_jl_matrix_named():
e2 = Matrix([[x, 2*y, pi*z]])
name_expr = ("test", Equality(MatrixSymbol('myout1', 1, 3), e2))
result = codegen(name_expr, "Julia", header=False, empty=False)
assert result[0][0] == "test.jl"
source = result[0][1]
expected = (
"function test(x, y, z)\n"
" myout1 = [x 2*y pi*z]\n"
" return myout1\n"
"end\n"
)
assert source == expected
def test_jl_matrix_named_matsym():
myout1 = MatrixSymbol('myout1', 1, 3)
e2 = Matrix([[x, 2*y, pi*z]])
name_expr = ("test", Equality(myout1, e2, evaluate=False))
result, = codegen(name_expr, "Julia", header=False, empty=False)
source = result[1]
expected = (
"function test(x, y, z)\n"
" myout1 = [x 2*y pi*z]\n"
" return myout1\n"
"end\n"
)
assert source == expected
def test_jl_matrix_output_autoname():
expr = Matrix([[x, x+y, 3]])
name_expr = ("test", expr)
result, = codegen(name_expr, "Julia", header=False, empty=False)
source = result[1]
expected = (
"function test(x, y)\n"
" out1 = [x x + y 3]\n"
" return out1\n"
"end\n"
)
assert source == expected
def test_jl_matrix_output_autoname_2():
e1 = (x + y)
e2 = Matrix([[2*x, 2*y, 2*z]])
e3 = Matrix([[x], [y], [z]])
e4 = Matrix([[x, y], [z, 16]])
name_expr = ("test", (e1, e2, e3, e4))
result, = codegen(name_expr, "Julia", header=False, empty=False)
source = result[1]
expected = (
"function test(x, y, z)\n"
" out1 = x + y\n"
" out2 = [2*x 2*y 2*z]\n"
" out3 = [x, y, z]\n"
" out4 = [x y;\n"
" z 16]\n"
" return out1, out2, out3, out4\n"
"end\n"
)
assert source == expected
def test_jl_results_matrix_named_ordered():
B, C = symbols('B,C')
A = MatrixSymbol('A', 1, 3)
expr1 = Equality(C, (x + y)*z)
expr2 = Equality(A, Matrix([[1, 2, x]]))
expr3 = Equality(B, 2*x)
name_expr = ("test", [expr1, expr2, expr3])
result, = codegen(name_expr, "Julia", header=False, empty=False,
argument_sequence=(x, z, y))
source = result[1]
expected = (
"function test(x, z, y)\n"
" C = z.*(x + y)\n"
" A = [1 2 x]\n"
" B = 2*x\n"
" return C, A, B\n"
"end\n"
)
assert source == expected
def test_jl_matrixsymbol_slice():
A = MatrixSymbol('A', 2, 3)
B = MatrixSymbol('B', 1, 3)
C = MatrixSymbol('C', 1, 3)
D = MatrixSymbol('D', 2, 1)
name_expr = ("test", [Equality(B, A[0, :]),
Equality(C, A[1, :]),
Equality(D, A[:, 2])])
result, = codegen(name_expr, "Julia", header=False, empty=False)
source = result[1]
expected = (
"function test(A)\n"
" B = A[1,:]\n"
" C = A[2,:]\n"
" D = A[:,3]\n"
" return B, C, D\n"
"end\n"
)
assert source == expected
def test_jl_matrixsymbol_slice2():
A = MatrixSymbol('A', 3, 4)
B = MatrixSymbol('B', 2, 2)
C = MatrixSymbol('C', 2, 2)
name_expr = ("test", [Equality(B, A[0:2, 0:2]),
Equality(C, A[0:2, 1:3])])
result, = codegen(name_expr, "Julia", header=False, empty=False)
source = result[1]
expected = (
"function test(A)\n"
" B = A[1:2,1:2]\n"
" C = A[1:2,2:3]\n"
" return B, C\n"
"end\n"
)
assert source == expected
def test_jl_matrixsymbol_slice3():
A = MatrixSymbol('A', 8, 7)
B = MatrixSymbol('B', 2, 2)
C = MatrixSymbol('C', 4, 2)
name_expr = ("test", [Equality(B, A[6:, 1::3]),
Equality(C, A[::2, ::3])])
result, = codegen(name_expr, "Julia", header=False, empty=False)
source = result[1]
expected = (
"function test(A)\n"
" B = A[7:end,2:3:end]\n"
" C = A[1:2:end,1:3:end]\n"
" return B, C\n"
"end\n"
)
assert source == expected
def test_jl_matrixsymbol_slice_autoname():
A = MatrixSymbol('A', 2, 3)
B = MatrixSymbol('B', 1, 3)
name_expr = ("test", [Equality(B, A[0,:]), A[1,:], A[:,0], A[:,1]])
result, = codegen(name_expr, "Julia", header=False, empty=False)
source = result[1]
expected = (
"function test(A)\n"
" B = A[1,:]\n"
" out2 = A[2,:]\n"
" out3 = A[:,1]\n"
" out4 = A[:,2]\n"
" return B, out2, out3, out4\n"
"end\n"
)
assert source == expected
def test_jl_loops():
# Note: an Julia programmer would probably vectorize this across one or
# more dimensions. Also, size(A) would be used rather than passing in m
# and n. Perhaps users would expect us to vectorize automatically here?
# Or is it possible to represent such things using IndexedBase?
from sympy.tensor import IndexedBase, Idx
from sympy import symbols
n, m = symbols('n m', integer=True)
A = IndexedBase('A')
x = IndexedBase('x')
y = IndexedBase('y')
i = Idx('i', m)
j = Idx('j', n)
result, = codegen(('mat_vec_mult', Eq(y[i], A[i, j]*x[j])), "Julia",
header=False, empty=False)
source = result[1]
expected = (
'function mat_vec_mult(y, A, m, n, x)\n'
' for i = 1:m\n'
' y[i] = 0\n'
' end\n'
' for i = 1:m\n'
' for j = 1:n\n'
' y[i] = %(rhs)s + y[i]\n'
' end\n'
' end\n'
' return y\n'
'end\n'
)
assert (source == expected % {'rhs': 'A[%s,%s].*x[j]' % (i, j)} or
source == expected % {'rhs': 'x[j].*A[%s,%s]' % (i, j)})
def test_jl_tensor_loops_multiple_contractions():
# see comments in previous test about vectorizing
from sympy.tensor import IndexedBase, Idx
from sympy import symbols
n, m, o, p = symbols('n m o p', integer=True)
A = IndexedBase('A')
B = IndexedBase('B')
y = IndexedBase('y')
i = Idx('i', m)
j = Idx('j', n)
k = Idx('k', o)
l = Idx('l', p)
result, = codegen(('tensorthing', Eq(y[i], B[j, k, l]*A[i, j, k, l])),
"Julia", header=False, empty=False)
source = result[1]
expected = (
'function tensorthing(y, A, B, m, n, o, p)\n'
' for i = 1:m\n'
' y[i] = 0\n'
' end\n'
' for i = 1:m\n'
' for j = 1:n\n'
' for k = 1:o\n'
' for l = 1:p\n'
' y[i] = A[i,j,k,l].*B[j,k,l] + y[i]\n'
' end\n'
' end\n'
' end\n'
' end\n'
' return y\n'
'end\n'
)
assert source == expected
def test_jl_InOutArgument():
expr = Equality(x, x**2)
name_expr = ("mysqr", expr)
result, = codegen(name_expr, "Julia", header=False, empty=False)
source = result[1]
expected = (
"function mysqr(x)\n"
" x = x.^2\n"
" return x\n"
"end\n"
)
assert source == expected
def test_jl_InOutArgument_order():
# can specify the order as (x, y)
expr = Equality(x, x**2 + y)
name_expr = ("test", expr)
result, = codegen(name_expr, "Julia", header=False,
empty=False, argument_sequence=(x,y))
source = result[1]
expected = (
"function test(x, y)\n"
" x = x.^2 + y\n"
" return x\n"
"end\n"
)
assert source == expected
# make sure it gives (x, y) not (y, x)
expr = Equality(x, x**2 + y)
name_expr = ("test", expr)
result, = codegen(name_expr, "Julia", header=False, empty=False)
source = result[1]
expected = (
"function test(x, y)\n"
" x = x.^2 + y\n"
" return x\n"
"end\n"
)
assert source == expected
def test_jl_not_supported():
f = Function('f')
name_expr = ("test", [f(x).diff(x), S.ComplexInfinity])
result, = codegen(name_expr, "Julia", header=False, empty=False)
source = result[1]
expected = (
"function test(x)\n"
" # unsupported: Derivative(f(x), x)\n"
" # unsupported: zoo\n"
" out1 = Derivative(f(x), x)\n"
" out2 = zoo\n"
" return out1, out2\n"
"end\n"
)
assert source == expected
def test_global_vars_octave():
x, y, z, t = symbols("x y z t")
result = codegen(('f', x*y), "Julia", header=False, empty=False,
global_vars=(y,))
source = result[0][1]
expected = (
"function f(x)\n"
" out1 = x.*y\n"
" return out1\n"
"end\n"
)
assert source == expected
result = codegen(('f', x*y+z), "Julia", header=False, empty=False,
argument_sequence=(x, y), global_vars=(z, t))
source = result[0][1]
expected = (
"function f(x, y)\n"
" out1 = x.*y + z\n"
" return out1\n"
"end\n"
)
assert source == expected
| 18,487 | 28.628205 | 87 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/tests/test_codegen.py
|
import warnings
from sympy.core import symbols, Eq, pi, Catalan, Lambda, Dummy
from sympy.core.compatibility import StringIO
from sympy import erf, Integral
from sympy import Equality
from sympy.matrices import Matrix, MatrixSymbol
from sympy.utilities.codegen import (
codegen, make_routine, CCodeGen, C89CodeGen, C99CodeGen, InputArgument,
CodeGenError, FCodeGen, CodeGenArgumentListError, OutputArgument,
InOutArgument)
from sympy.utilities.exceptions import SymPyDeprecationWarning
from sympy.utilities.pytest import raises
from sympy.utilities.lambdify import implemented_function
#FIXME: Fails due to circular import in with core
# from sympy import codegen
def get_string(dump_fn, routines, prefix="file", header=False, empty=False):
"""Wrapper for dump_fn. dump_fn writes its results to a stream object and
this wrapper returns the contents of that stream as a string. This
auxiliary function is used by many tests below.
The header and the empty lines are not generated to facilitate the
testing of the output.
"""
output = StringIO()
dump_fn(routines, output, prefix, header, empty)
source = output.getvalue()
output.close()
return source
def test_Routine_argument_order():
a, x, y, z = symbols('a x y z')
expr = (x + y)*z
raises(CodeGenArgumentListError, lambda: make_routine("test", expr,
argument_sequence=[z, x]))
raises(CodeGenArgumentListError, lambda: make_routine("test", Eq(a,
expr), argument_sequence=[z, x, y]))
r = make_routine('test', Eq(a, expr), argument_sequence=[z, x, a, y])
assert [ arg.name for arg in r.arguments ] == [z, x, a, y]
assert [ type(arg) for arg in r.arguments ] == [
InputArgument, InputArgument, OutputArgument, InputArgument ]
r = make_routine('test', Eq(z, expr), argument_sequence=[z, x, y])
assert [ type(arg) for arg in r.arguments ] == [
InOutArgument, InputArgument, InputArgument ]
from sympy.tensor import IndexedBase, Idx
A, B = map(IndexedBase, ['A', 'B'])
m = symbols('m', integer=True)
i = Idx('i', m)
r = make_routine('test', Eq(A[i], B[i]), argument_sequence=[B, A, m])
assert [ arg.name for arg in r.arguments ] == [B.label, A.label, m]
expr = Integral(x*y*z, (x, 1, 2), (y, 1, 3))
r = make_routine('test', Eq(a, expr), argument_sequence=[z, x, a, y])
assert [ arg.name for arg in r.arguments ] == [z, x, a, y]
def test_empty_c_code():
code_gen = C89CodeGen()
with warnings.catch_warnings():
warnings.filterwarnings("ignore", category=SymPyDeprecationWarning)
source = get_string(code_gen.dump_c, [])
assert source == "#include \"file.h\"\n#include <math.h>\n"
def test_empty_c_code_with_comment():
code_gen = C89CodeGen()
source = get_string(code_gen.dump_c, [], header=True)
assert source[:82] == (
"/******************************************************************************\n *"
)
# " Code generated with sympy 0.7.2-git "
assert source[158:] == ( "*\n"
" * *\n"
" * See http://www.sympy.org/ for more information. *\n"
" * *\n"
" * This file is part of 'project' *\n"
" ******************************************************************************/\n"
"#include \"file.h\"\n"
"#include <math.h>\n"
)
def test_empty_c_header():
code_gen = C99CodeGen()
source = get_string(code_gen.dump_h, [])
assert source == "#ifndef PROJECT__FILE__H\n#define PROJECT__FILE__H\n#endif\n"
def test_simple_c_code():
x, y, z = symbols('x,y,z')
expr = (x + y)*z
routine = make_routine("test", expr)
code_gen = C89CodeGen()
source = get_string(code_gen.dump_c, [routine])
expected = (
"#include \"file.h\"\n"
"#include <math.h>\n"
"double test(double x, double y, double z) {\n"
" double test_result;\n"
" test_result = z*(x + y);\n"
" return test_result;\n"
"}\n"
)
assert source == expected
def test_c_code_reserved_words():
x, y, z = symbols('if, typedef, while')
expr = (x + y) * z
routine = make_routine("test", expr)
code_gen = C99CodeGen()
source = get_string(code_gen.dump_c, [routine])
expected = (
"#include \"file.h\"\n"
"#include <math.h>\n"
"double test(double if_, double typedef_, double while_) {\n"
" double test_result;\n"
" test_result = while_*(if_ + typedef_);\n"
" return test_result;\n"
"}\n"
)
assert source == expected
def test_numbersymbol_c_code():
routine = make_routine("test", pi**Catalan)
code_gen = C89CodeGen()
source = get_string(code_gen.dump_c, [routine])
expected = (
"#include \"file.h\"\n"
"#include <math.h>\n"
"double test() {\n"
" double test_result;\n"
" double const Catalan = 0.915965594177219;\n"
" test_result = pow(M_PI, Catalan);\n"
" return test_result;\n"
"}\n"
)
assert source == expected
def test_c_code_argument_order():
x, y, z = symbols('x,y,z')
expr = x + y
routine = make_routine("test", expr, argument_sequence=[z, x, y])
code_gen = C89CodeGen()
source = get_string(code_gen.dump_c, [routine])
expected = (
"#include \"file.h\"\n"
"#include <math.h>\n"
"double test(double z, double x, double y) {\n"
" double test_result;\n"
" test_result = x + y;\n"
" return test_result;\n"
"}\n"
)
assert source == expected
def test_simple_c_header():
x, y, z = symbols('x,y,z')
expr = (x + y)*z
routine = make_routine("test", expr)
code_gen = C89CodeGen()
source = get_string(code_gen.dump_h, [routine])
expected = (
"#ifndef PROJECT__FILE__H\n"
"#define PROJECT__FILE__H\n"
"double test(double x, double y, double z);\n"
"#endif\n"
)
assert source == expected
def test_simple_c_codegen():
x, y, z = symbols('x,y,z')
expr = (x + y)*z
expected = [
("file.c",
"#include \"file.h\"\n"
"#include <math.h>\n"
"double test(double x, double y, double z) {\n"
" double test_result;\n"
" test_result = z*(x + y);\n"
" return test_result;\n"
"}\n"),
("file.h",
"#ifndef PROJECT__FILE__H\n"
"#define PROJECT__FILE__H\n"
"double test(double x, double y, double z);\n"
"#endif\n")
]
with warnings.catch_warnings():
warnings.filterwarnings("ignore", category=SymPyDeprecationWarning)
result = codegen(("test", expr), "C", "file", header=False, empty=False)
assert result == expected
def test_multiple_results_c():
x, y, z = symbols('x,y,z')
expr1 = (x + y)*z
expr2 = (x - y)*z
routine = make_routine(
"test",
[expr1, expr2]
)
code_gen = C99CodeGen()
raises(CodeGenError, lambda: get_string(code_gen.dump_h, [routine]))
def test_no_results_c():
raises(ValueError, lambda: make_routine("test", []))
def test_ansi_math1_codegen():
# not included: log10
from sympy import (acos, asin, atan, ceiling, cos, cosh, floor, log, ln,
sin, sinh, sqrt, tan, tanh, Abs)
x = symbols('x')
name_expr = [
("test_fabs", Abs(x)),
("test_acos", acos(x)),
("test_asin", asin(x)),
("test_atan", atan(x)),
("test_ceil", ceiling(x)),
("test_cos", cos(x)),
("test_cosh", cosh(x)),
("test_floor", floor(x)),
("test_log", log(x)),
("test_ln", ln(x)),
("test_sin", sin(x)),
("test_sinh", sinh(x)),
("test_sqrt", sqrt(x)),
("test_tan", tan(x)),
("test_tanh", tanh(x)),
]
result = codegen(name_expr, "C89", "file", header=False, empty=False)
assert result[0][0] == "file.c"
assert result[0][1] == (
'#include "file.h"\n#include <math.h>\n'
'double test_fabs(double x) {\n double test_fabs_result;\n test_fabs_result = fabs(x);\n return test_fabs_result;\n}\n'
'double test_acos(double x) {\n double test_acos_result;\n test_acos_result = acos(x);\n return test_acos_result;\n}\n'
'double test_asin(double x) {\n double test_asin_result;\n test_asin_result = asin(x);\n return test_asin_result;\n}\n'
'double test_atan(double x) {\n double test_atan_result;\n test_atan_result = atan(x);\n return test_atan_result;\n}\n'
'double test_ceil(double x) {\n double test_ceil_result;\n test_ceil_result = ceil(x);\n return test_ceil_result;\n}\n'
'double test_cos(double x) {\n double test_cos_result;\n test_cos_result = cos(x);\n return test_cos_result;\n}\n'
'double test_cosh(double x) {\n double test_cosh_result;\n test_cosh_result = cosh(x);\n return test_cosh_result;\n}\n'
'double test_floor(double x) {\n double test_floor_result;\n test_floor_result = floor(x);\n return test_floor_result;\n}\n'
'double test_log(double x) {\n double test_log_result;\n test_log_result = log(x);\n return test_log_result;\n}\n'
'double test_ln(double x) {\n double test_ln_result;\n test_ln_result = log(x);\n return test_ln_result;\n}\n'
'double test_sin(double x) {\n double test_sin_result;\n test_sin_result = sin(x);\n return test_sin_result;\n}\n'
'double test_sinh(double x) {\n double test_sinh_result;\n test_sinh_result = sinh(x);\n return test_sinh_result;\n}\n'
'double test_sqrt(double x) {\n double test_sqrt_result;\n test_sqrt_result = sqrt(x);\n return test_sqrt_result;\n}\n'
'double test_tan(double x) {\n double test_tan_result;\n test_tan_result = tan(x);\n return test_tan_result;\n}\n'
'double test_tanh(double x) {\n double test_tanh_result;\n test_tanh_result = tanh(x);\n return test_tanh_result;\n}\n'
)
assert result[1][0] == "file.h"
assert result[1][1] == (
'#ifndef PROJECT__FILE__H\n#define PROJECT__FILE__H\n'
'double test_fabs(double x);\ndouble test_acos(double x);\n'
'double test_asin(double x);\ndouble test_atan(double x);\n'
'double test_ceil(double x);\ndouble test_cos(double x);\n'
'double test_cosh(double x);\ndouble test_floor(double x);\n'
'double test_log(double x);\ndouble test_ln(double x);\n'
'double test_sin(double x);\ndouble test_sinh(double x);\n'
'double test_sqrt(double x);\ndouble test_tan(double x);\n'
'double test_tanh(double x);\n#endif\n'
)
def test_ansi_math2_codegen():
# not included: frexp, ldexp, modf, fmod
from sympy import atan2
x, y = symbols('x,y')
name_expr = [
("test_atan2", atan2(x, y)),
("test_pow", x**y),
]
result = codegen(name_expr, "C89", "file", header=False, empty=False)
assert result[0][0] == "file.c"
assert result[0][1] == (
'#include "file.h"\n#include <math.h>\n'
'double test_atan2(double x, double y) {\n double test_atan2_result;\n test_atan2_result = atan2(x, y);\n return test_atan2_result;\n}\n'
'double test_pow(double x, double y) {\n double test_pow_result;\n test_pow_result = pow(x, y);\n return test_pow_result;\n}\n'
)
assert result[1][0] == "file.h"
assert result[1][1] == (
'#ifndef PROJECT__FILE__H\n#define PROJECT__FILE__H\n'
'double test_atan2(double x, double y);\n'
'double test_pow(double x, double y);\n'
'#endif\n'
)
def test_complicated_codegen():
from sympy import sin, cos, tan
x, y, z = symbols('x,y,z')
name_expr = [
("test1", ((sin(x) + cos(y) + tan(z))**7).expand()),
("test2", cos(cos(cos(cos(cos(cos(cos(cos(x + y + z))))))))),
]
result = codegen(name_expr, "C89", "file", header=False, empty=False)
assert result[0][0] == "file.c"
assert result[0][1] == (
'#include "file.h"\n#include <math.h>\n'
'double test1(double x, double y, double z) {\n'
' double test1_result;\n'
' test1_result = '
'pow(sin(x), 7) + '
'7*pow(sin(x), 6)*cos(y) + '
'7*pow(sin(x), 6)*tan(z) + '
'21*pow(sin(x), 5)*pow(cos(y), 2) + '
'42*pow(sin(x), 5)*cos(y)*tan(z) + '
'21*pow(sin(x), 5)*pow(tan(z), 2) + '
'35*pow(sin(x), 4)*pow(cos(y), 3) + '
'105*pow(sin(x), 4)*pow(cos(y), 2)*tan(z) + '
'105*pow(sin(x), 4)*cos(y)*pow(tan(z), 2) + '
'35*pow(sin(x), 4)*pow(tan(z), 3) + '
'35*pow(sin(x), 3)*pow(cos(y), 4) + '
'140*pow(sin(x), 3)*pow(cos(y), 3)*tan(z) + '
'210*pow(sin(x), 3)*pow(cos(y), 2)*pow(tan(z), 2) + '
'140*pow(sin(x), 3)*cos(y)*pow(tan(z), 3) + '
'35*pow(sin(x), 3)*pow(tan(z), 4) + '
'21*pow(sin(x), 2)*pow(cos(y), 5) + '
'105*pow(sin(x), 2)*pow(cos(y), 4)*tan(z) + '
'210*pow(sin(x), 2)*pow(cos(y), 3)*pow(tan(z), 2) + '
'210*pow(sin(x), 2)*pow(cos(y), 2)*pow(tan(z), 3) + '
'105*pow(sin(x), 2)*cos(y)*pow(tan(z), 4) + '
'21*pow(sin(x), 2)*pow(tan(z), 5) + '
'7*sin(x)*pow(cos(y), 6) + '
'42*sin(x)*pow(cos(y), 5)*tan(z) + '
'105*sin(x)*pow(cos(y), 4)*pow(tan(z), 2) + '
'140*sin(x)*pow(cos(y), 3)*pow(tan(z), 3) + '
'105*sin(x)*pow(cos(y), 2)*pow(tan(z), 4) + '
'42*sin(x)*cos(y)*pow(tan(z), 5) + '
'7*sin(x)*pow(tan(z), 6) + '
'pow(cos(y), 7) + '
'7*pow(cos(y), 6)*tan(z) + '
'21*pow(cos(y), 5)*pow(tan(z), 2) + '
'35*pow(cos(y), 4)*pow(tan(z), 3) + '
'35*pow(cos(y), 3)*pow(tan(z), 4) + '
'21*pow(cos(y), 2)*pow(tan(z), 5) + '
'7*cos(y)*pow(tan(z), 6) + '
'pow(tan(z), 7);\n'
' return test1_result;\n'
'}\n'
'double test2(double x, double y, double z) {\n'
' double test2_result;\n'
' test2_result = cos(cos(cos(cos(cos(cos(cos(cos(x + y + z))))))));\n'
' return test2_result;\n'
'}\n'
)
assert result[1][0] == "file.h"
assert result[1][1] == (
'#ifndef PROJECT__FILE__H\n'
'#define PROJECT__FILE__H\n'
'double test1(double x, double y, double z);\n'
'double test2(double x, double y, double z);\n'
'#endif\n'
)
def test_loops_c():
from sympy.tensor import IndexedBase, Idx
from sympy import symbols
n, m = symbols('n m', integer=True)
A = IndexedBase('A')
x = IndexedBase('x')
y = IndexedBase('y')
i = Idx('i', m)
j = Idx('j', n)
(f1, code), (f2, interface) = codegen(
('matrix_vector', Eq(y[i], A[i, j]*x[j])), "C99", "file", header=False, empty=False)
assert f1 == 'file.c'
expected = (
'#include "file.h"\n'
'#include <math.h>\n'
'void matrix_vector(double *A, int m, int n, double *x, double *y) {\n'
' for (int i=0; i<m; i++){\n'
' y[i] = 0;\n'
' }\n'
' for (int i=0; i<m; i++){\n'
' for (int j=0; j<n; j++){\n'
' y[i] = %(rhs)s + y[i];\n'
' }\n'
' }\n'
'}\n'
)
assert (code == expected % {'rhs': 'A[%s]*x[j]' % (i*n + j)} or
code == expected % {'rhs': 'A[%s]*x[j]' % (j + i*n)} or
code == expected % {'rhs': 'x[j]*A[%s]' % (i*n + j)} or
code == expected % {'rhs': 'x[j]*A[%s]' % (j + i*n)})
assert f2 == 'file.h'
assert interface == (
'#ifndef PROJECT__FILE__H\n'
'#define PROJECT__FILE__H\n'
'void matrix_vector(double *A, int m, int n, double *x, double *y);\n'
'#endif\n'
)
def test_dummy_loops_c():
from sympy.tensor import IndexedBase, Idx
i, m = symbols('i m', integer=True, cls=Dummy)
x = IndexedBase('x')
y = IndexedBase('y')
i = Idx(i, m)
expected = (
'#include "file.h"\n'
'#include <math.h>\n'
'void test_dummies(int m_%(mno)i, double *x, double *y) {\n'
' for (int i_%(ino)i=0; i_%(ino)i<m_%(mno)i; i_%(ino)i++){\n'
' y[i_%(ino)i] = x[i_%(ino)i];\n'
' }\n'
'}\n'
) % {'ino': i.label.dummy_index, 'mno': m.dummy_index}
r = make_routine('test_dummies', Eq(y[i], x[i]))
c89 = C89CodeGen()
c99 = C99CodeGen()
code = get_string(c99.dump_c, [r])
assert code == expected
with raises(NotImplementedError):
get_string(c89.dump_c, [r])
def test_partial_loops_c():
# check that loop boundaries are determined by Idx, and array strides
# determined by shape of IndexedBase object.
from sympy.tensor import IndexedBase, Idx
from sympy import symbols
n, m, o, p = symbols('n m o p', integer=True)
A = IndexedBase('A', shape=(m, p))
x = IndexedBase('x')
y = IndexedBase('y')
i = Idx('i', (o, m - 5)) # Note: bounds are inclusive
j = Idx('j', n) # dimension n corresponds to bounds (0, n - 1)
(f1, code), (f2, interface) = codegen(
('matrix_vector', Eq(y[i], A[i, j]*x[j])), "C99", "file", header=False, empty=False)
assert f1 == 'file.c'
expected = (
'#include "file.h"\n'
'#include <math.h>\n'
'void matrix_vector(double *A, int m, int n, int o, int p, double *x, double *y) {\n'
' for (int i=o; i<%(upperi)s; i++){\n'
' y[i] = 0;\n'
' }\n'
' for (int i=o; i<%(upperi)s; i++){\n'
' for (int j=0; j<n; j++){\n'
' y[i] = %(rhs)s + y[i];\n'
' }\n'
' }\n'
'}\n'
) % {'upperi': m - 4, 'rhs': '%(rhs)s'}
assert (code == expected % {'rhs': 'A[%s]*x[j]' % (i*p + j)} or
code == expected % {'rhs': 'A[%s]*x[j]' % (j + i*p)} or
code == expected % {'rhs': 'x[j]*A[%s]' % (i*p + j)} or
code == expected % {'rhs': 'x[j]*A[%s]' % (j + i*p)})
assert f2 == 'file.h'
assert interface == (
'#ifndef PROJECT__FILE__H\n'
'#define PROJECT__FILE__H\n'
'void matrix_vector(double *A, int m, int n, int o, int p, double *x, double *y);\n'
'#endif\n'
)
def test_output_arg_c():
from sympy import sin, cos, Equality
x, y, z = symbols("x,y,z")
r = make_routine("foo", [Equality(y, sin(x)), cos(x)])
c = C89CodeGen()
result = c.write([r], "test", header=False, empty=False)
assert result[0][0] == "test.c"
expected = (
'#include "test.h"\n'
'#include <math.h>\n'
'double foo(double x, double *y) {\n'
' (*y) = sin(x);\n'
' double foo_result;\n'
' foo_result = cos(x);\n'
' return foo_result;\n'
'}\n'
)
assert result[0][1] == expected
def test_output_arg_c_reserved_words():
from sympy import sin, cos, Equality
x, y, z = symbols("if, while, z")
r = make_routine("foo", [Equality(y, sin(x)), cos(x)])
c = C89CodeGen()
result = c.write([r], "test", header=False, empty=False)
assert result[0][0] == "test.c"
expected = (
'#include "test.h"\n'
'#include <math.h>\n'
'double foo(double if_, double *while_) {\n'
' (*while_) = sin(if_);\n'
' double foo_result;\n'
' foo_result = cos(if_);\n'
' return foo_result;\n'
'}\n'
)
assert result[0][1] == expected
def test_ccode_results_named_ordered():
x, y, z = symbols('x,y,z')
B, C = symbols('B,C')
A = MatrixSymbol('A', 1, 3)
expr1 = Equality(A, Matrix([[1, 2, x]]))
expr2 = Equality(C, (x + y)*z)
expr3 = Equality(B, 2*x)
name_expr = ("test", [expr1, expr2, expr3])
expected = (
'#include "test.h"\n'
'#include <math.h>\n'
'void test(double x, double *C, double z, double y, double *A, double *B) {\n'
' (*C) = z*(x + y);\n'
' A[0] = 1;\n'
' A[1] = 2;\n'
' A[2] = x;\n'
' (*B) = 2*x;\n'
'}\n'
)
with warnings.catch_warnings():
warnings.filterwarnings("ignore", category=SymPyDeprecationWarning)
result = codegen(name_expr, "c", "test", header=False, empty=False,
argument_sequence=(x, C, z, y, A, B))
source = result[0][1]
assert source == expected
def test_ccode_matrixsymbol_slice():
A = MatrixSymbol('A', 5, 3)
B = MatrixSymbol('B', 1, 3)
C = MatrixSymbol('C', 1, 3)
D = MatrixSymbol('D', 5, 1)
name_expr = ("test", [Equality(B, A[0, :]),
Equality(C, A[1, :]),
Equality(D, A[:, 2])])
result = codegen(name_expr, "c99", "test", header=False, empty=False)
source = result[0][1]
expected = (
'#include "test.h"\n'
'#include <math.h>\n'
'void test(double *A, double *B, double *C, double *D) {\n'
' B[0] = A[0];\n'
' B[1] = A[1];\n'
' B[2] = A[2];\n'
' C[0] = A[3];\n'
' C[1] = A[4];\n'
' C[2] = A[5];\n'
' D[0] = A[2];\n'
' D[1] = A[5];\n'
' D[2] = A[8];\n'
' D[3] = A[11];\n'
' D[4] = A[14];\n'
'}\n'
)
assert source == expected
def test_empty_f_code():
code_gen = FCodeGen()
source = get_string(code_gen.dump_f95, [])
assert source == ""
def test_empty_f_code_with_header():
code_gen = FCodeGen()
source = get_string(code_gen.dump_f95, [], header=True)
assert source[:82] == (
"!******************************************************************************\n!*"
)
# " Code generated with sympy 0.7.2-git "
assert source[158:] == ( "*\n"
"!* *\n"
"!* See http://www.sympy.org/ for more information. *\n"
"!* *\n"
"!* This file is part of 'project' *\n"
"!******************************************************************************\n"
)
def test_empty_f_header():
code_gen = FCodeGen()
source = get_string(code_gen.dump_h, [])
assert source == ""
def test_simple_f_code():
x, y, z = symbols('x,y,z')
expr = (x + y)*z
routine = make_routine("test", expr)
code_gen = FCodeGen()
source = get_string(code_gen.dump_f95, [routine])
expected = (
"REAL*8 function test(x, y, z)\n"
"implicit none\n"
"REAL*8, intent(in) :: x\n"
"REAL*8, intent(in) :: y\n"
"REAL*8, intent(in) :: z\n"
"test = z*(x + y)\n"
"end function\n"
)
assert source == expected
def test_numbersymbol_f_code():
routine = make_routine("test", pi**Catalan)
code_gen = FCodeGen()
source = get_string(code_gen.dump_f95, [routine])
expected = (
"REAL*8 function test()\n"
"implicit none\n"
"REAL*8, parameter :: Catalan = 0.915965594177219d0\n"
"REAL*8, parameter :: pi = 3.14159265358979d0\n"
"test = pi**Catalan\n"
"end function\n"
)
assert source == expected
def test_erf_f_code():
x = symbols('x')
routine = make_routine("test", erf(x) - erf(-2 * x))
code_gen = FCodeGen()
source = get_string(code_gen.dump_f95, [routine])
expected = (
"REAL*8 function test(x)\n"
"implicit none\n"
"REAL*8, intent(in) :: x\n"
"test = erf(x) + erf(2.0d0*x)\n"
"end function\n"
)
assert source == expected, source
def test_f_code_argument_order():
x, y, z = symbols('x,y,z')
expr = x + y
routine = make_routine("test", expr, argument_sequence=[z, x, y])
code_gen = FCodeGen()
source = get_string(code_gen.dump_f95, [routine])
expected = (
"REAL*8 function test(z, x, y)\n"
"implicit none\n"
"REAL*8, intent(in) :: z\n"
"REAL*8, intent(in) :: x\n"
"REAL*8, intent(in) :: y\n"
"test = x + y\n"
"end function\n"
)
assert source == expected
def test_simple_f_header():
x, y, z = symbols('x,y,z')
expr = (x + y)*z
routine = make_routine("test", expr)
code_gen = FCodeGen()
source = get_string(code_gen.dump_h, [routine])
expected = (
"interface\n"
"REAL*8 function test(x, y, z)\n"
"implicit none\n"
"REAL*8, intent(in) :: x\n"
"REAL*8, intent(in) :: y\n"
"REAL*8, intent(in) :: z\n"
"end function\n"
"end interface\n"
)
assert source == expected
def test_simple_f_codegen():
x, y, z = symbols('x,y,z')
expr = (x + y)*z
result = codegen(
("test", expr), "F95", "file", header=False, empty=False)
expected = [
("file.f90",
"REAL*8 function test(x, y, z)\n"
"implicit none\n"
"REAL*8, intent(in) :: x\n"
"REAL*8, intent(in) :: y\n"
"REAL*8, intent(in) :: z\n"
"test = z*(x + y)\n"
"end function\n"),
("file.h",
"interface\n"
"REAL*8 function test(x, y, z)\n"
"implicit none\n"
"REAL*8, intent(in) :: x\n"
"REAL*8, intent(in) :: y\n"
"REAL*8, intent(in) :: z\n"
"end function\n"
"end interface\n")
]
assert result == expected
def test_multiple_results_f():
x, y, z = symbols('x,y,z')
expr1 = (x + y)*z
expr2 = (x - y)*z
routine = make_routine(
"test",
[expr1, expr2]
)
code_gen = FCodeGen()
raises(CodeGenError, lambda: get_string(code_gen.dump_h, [routine]))
def test_no_results_f():
raises(ValueError, lambda: make_routine("test", []))
def test_intrinsic_math_codegen():
# not included: log10
from sympy import (acos, asin, atan, ceiling, cos, cosh, floor, log, ln,
sin, sinh, sqrt, tan, tanh, Abs)
x = symbols('x')
name_expr = [
("test_abs", Abs(x)),
("test_acos", acos(x)),
("test_asin", asin(x)),
("test_atan", atan(x)),
("test_cos", cos(x)),
("test_cosh", cosh(x)),
("test_log", log(x)),
("test_ln", ln(x)),
("test_sin", sin(x)),
("test_sinh", sinh(x)),
("test_sqrt", sqrt(x)),
("test_tan", tan(x)),
("test_tanh", tanh(x)),
]
result = codegen(name_expr, "F95", "file", header=False, empty=False)
assert result[0][0] == "file.f90"
expected = (
'REAL*8 function test_abs(x)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'test_abs = abs(x)\n'
'end function\n'
'REAL*8 function test_acos(x)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'test_acos = acos(x)\n'
'end function\n'
'REAL*8 function test_asin(x)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'test_asin = asin(x)\n'
'end function\n'
'REAL*8 function test_atan(x)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'test_atan = atan(x)\n'
'end function\n'
'REAL*8 function test_cos(x)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'test_cos = cos(x)\n'
'end function\n'
'REAL*8 function test_cosh(x)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'test_cosh = cosh(x)\n'
'end function\n'
'REAL*8 function test_log(x)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'test_log = log(x)\n'
'end function\n'
'REAL*8 function test_ln(x)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'test_ln = log(x)\n'
'end function\n'
'REAL*8 function test_sin(x)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'test_sin = sin(x)\n'
'end function\n'
'REAL*8 function test_sinh(x)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'test_sinh = sinh(x)\n'
'end function\n'
'REAL*8 function test_sqrt(x)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'test_sqrt = sqrt(x)\n'
'end function\n'
'REAL*8 function test_tan(x)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'test_tan = tan(x)\n'
'end function\n'
'REAL*8 function test_tanh(x)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'test_tanh = tanh(x)\n'
'end function\n'
)
assert result[0][1] == expected
assert result[1][0] == "file.h"
expected = (
'interface\n'
'REAL*8 function test_abs(x)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'end function\n'
'end interface\n'
'interface\n'
'REAL*8 function test_acos(x)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'end function\n'
'end interface\n'
'interface\n'
'REAL*8 function test_asin(x)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'end function\n'
'end interface\n'
'interface\n'
'REAL*8 function test_atan(x)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'end function\n'
'end interface\n'
'interface\n'
'REAL*8 function test_cos(x)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'end function\n'
'end interface\n'
'interface\n'
'REAL*8 function test_cosh(x)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'end function\n'
'end interface\n'
'interface\n'
'REAL*8 function test_log(x)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'end function\n'
'end interface\n'
'interface\n'
'REAL*8 function test_ln(x)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'end function\n'
'end interface\n'
'interface\n'
'REAL*8 function test_sin(x)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'end function\n'
'end interface\n'
'interface\n'
'REAL*8 function test_sinh(x)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'end function\n'
'end interface\n'
'interface\n'
'REAL*8 function test_sqrt(x)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'end function\n'
'end interface\n'
'interface\n'
'REAL*8 function test_tan(x)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'end function\n'
'end interface\n'
'interface\n'
'REAL*8 function test_tanh(x)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'end function\n'
'end interface\n'
)
assert result[1][1] == expected
def test_intrinsic_math2_codegen():
# not included: frexp, ldexp, modf, fmod
from sympy import atan2
x, y = symbols('x,y')
name_expr = [
("test_atan2", atan2(x, y)),
("test_pow", x**y),
]
result = codegen(name_expr, "F95", "file", header=False, empty=False)
assert result[0][0] == "file.f90"
expected = (
'REAL*8 function test_atan2(x, y)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'REAL*8, intent(in) :: y\n'
'test_atan2 = atan2(x, y)\n'
'end function\n'
'REAL*8 function test_pow(x, y)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'REAL*8, intent(in) :: y\n'
'test_pow = x**y\n'
'end function\n'
)
assert result[0][1] == expected
assert result[1][0] == "file.h"
expected = (
'interface\n'
'REAL*8 function test_atan2(x, y)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'REAL*8, intent(in) :: y\n'
'end function\n'
'end interface\n'
'interface\n'
'REAL*8 function test_pow(x, y)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'REAL*8, intent(in) :: y\n'
'end function\n'
'end interface\n'
)
assert result[1][1] == expected
def test_complicated_codegen_f95():
from sympy import sin, cos, tan
x, y, z = symbols('x,y,z')
name_expr = [
("test1", ((sin(x) + cos(y) + tan(z))**7).expand()),
("test2", cos(cos(cos(cos(cos(cos(cos(cos(x + y + z))))))))),
]
result = codegen(name_expr, "F95", "file", header=False, empty=False)
assert result[0][0] == "file.f90"
expected = (
'REAL*8 function test1(x, y, z)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'REAL*8, intent(in) :: y\n'
'REAL*8, intent(in) :: z\n'
'test1 = sin(x)**7 + 7*sin(x)**6*cos(y) + 7*sin(x)**6*tan(z) + 21*sin(x) &\n'
' **5*cos(y)**2 + 42*sin(x)**5*cos(y)*tan(z) + 21*sin(x)**5*tan(z) &\n'
' **2 + 35*sin(x)**4*cos(y)**3 + 105*sin(x)**4*cos(y)**2*tan(z) + &\n'
' 105*sin(x)**4*cos(y)*tan(z)**2 + 35*sin(x)**4*tan(z)**3 + 35*sin( &\n'
' x)**3*cos(y)**4 + 140*sin(x)**3*cos(y)**3*tan(z) + 210*sin(x)**3* &\n'
' cos(y)**2*tan(z)**2 + 140*sin(x)**3*cos(y)*tan(z)**3 + 35*sin(x) &\n'
' **3*tan(z)**4 + 21*sin(x)**2*cos(y)**5 + 105*sin(x)**2*cos(y)**4* &\n'
' tan(z) + 210*sin(x)**2*cos(y)**3*tan(z)**2 + 210*sin(x)**2*cos(y) &\n'
' **2*tan(z)**3 + 105*sin(x)**2*cos(y)*tan(z)**4 + 21*sin(x)**2*tan &\n'
' (z)**5 + 7*sin(x)*cos(y)**6 + 42*sin(x)*cos(y)**5*tan(z) + 105* &\n'
' sin(x)*cos(y)**4*tan(z)**2 + 140*sin(x)*cos(y)**3*tan(z)**3 + 105 &\n'
' *sin(x)*cos(y)**2*tan(z)**4 + 42*sin(x)*cos(y)*tan(z)**5 + 7*sin( &\n'
' x)*tan(z)**6 + cos(y)**7 + 7*cos(y)**6*tan(z) + 21*cos(y)**5*tan( &\n'
' z)**2 + 35*cos(y)**4*tan(z)**3 + 35*cos(y)**3*tan(z)**4 + 21*cos( &\n'
' y)**2*tan(z)**5 + 7*cos(y)*tan(z)**6 + tan(z)**7\n'
'end function\n'
'REAL*8 function test2(x, y, z)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'REAL*8, intent(in) :: y\n'
'REAL*8, intent(in) :: z\n'
'test2 = cos(cos(cos(cos(cos(cos(cos(cos(x + y + z))))))))\n'
'end function\n'
)
assert result[0][1] == expected
assert result[1][0] == "file.h"
expected = (
'interface\n'
'REAL*8 function test1(x, y, z)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'REAL*8, intent(in) :: y\n'
'REAL*8, intent(in) :: z\n'
'end function\n'
'end interface\n'
'interface\n'
'REAL*8 function test2(x, y, z)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'REAL*8, intent(in) :: y\n'
'REAL*8, intent(in) :: z\n'
'end function\n'
'end interface\n'
)
assert result[1][1] == expected
def test_loops():
from sympy.tensor import IndexedBase, Idx
from sympy import symbols
n, m = symbols('n,m', integer=True)
A, x, y = map(IndexedBase, 'Axy')
i = Idx('i', m)
j = Idx('j', n)
(f1, code), (f2, interface) = codegen(
('matrix_vector', Eq(y[i], A[i, j]*x[j])), "F95", "file", header=False, empty=False)
assert f1 == 'file.f90'
expected = (
'subroutine matrix_vector(A, m, n, x, y)\n'
'implicit none\n'
'INTEGER*4, intent(in) :: m\n'
'INTEGER*4, intent(in) :: n\n'
'REAL*8, intent(in), dimension(1:m, 1:n) :: A\n'
'REAL*8, intent(in), dimension(1:n) :: x\n'
'REAL*8, intent(out), dimension(1:m) :: y\n'
'INTEGER*4 :: i\n'
'INTEGER*4 :: j\n'
'do i = 1, m\n'
' y(i) = 0\n'
'end do\n'
'do i = 1, m\n'
' do j = 1, n\n'
' y(i) = %(rhs)s + y(i)\n'
' end do\n'
'end do\n'
'end subroutine\n'
)
assert code == expected % {'rhs': 'A(i, j)*x(j)'} or\
code == expected % {'rhs': 'x(j)*A(i, j)'}
assert f2 == 'file.h'
assert interface == (
'interface\n'
'subroutine matrix_vector(A, m, n, x, y)\n'
'implicit none\n'
'INTEGER*4, intent(in) :: m\n'
'INTEGER*4, intent(in) :: n\n'
'REAL*8, intent(in), dimension(1:m, 1:n) :: A\n'
'REAL*8, intent(in), dimension(1:n) :: x\n'
'REAL*8, intent(out), dimension(1:m) :: y\n'
'end subroutine\n'
'end interface\n'
)
def test_dummy_loops_f95():
from sympy.tensor import IndexedBase, Idx
i, m = symbols('i m', integer=True, cls=Dummy)
x = IndexedBase('x')
y = IndexedBase('y')
i = Idx(i, m)
expected = (
'subroutine test_dummies(m_%(mcount)i, x, y)\n'
'implicit none\n'
'INTEGER*4, intent(in) :: m_%(mcount)i\n'
'REAL*8, intent(in), dimension(1:m_%(mcount)i) :: x\n'
'REAL*8, intent(out), dimension(1:m_%(mcount)i) :: y\n'
'INTEGER*4 :: i_%(icount)i\n'
'do i_%(icount)i = 1, m_%(mcount)i\n'
' y(i_%(icount)i) = x(i_%(icount)i)\n'
'end do\n'
'end subroutine\n'
) % {'icount': i.label.dummy_index, 'mcount': m.dummy_index}
r = make_routine('test_dummies', Eq(y[i], x[i]))
c = FCodeGen()
code = get_string(c.dump_f95, [r])
assert code == expected
def test_loops_InOut():
from sympy.tensor import IndexedBase, Idx
from sympy import symbols
i, j, n, m = symbols('i,j,n,m', integer=True)
A, x, y = symbols('A,x,y')
A = IndexedBase(A)[Idx(i, m), Idx(j, n)]
x = IndexedBase(x)[Idx(j, n)]
y = IndexedBase(y)[Idx(i, m)]
(f1, code), (f2, interface) = codegen(
('matrix_vector', Eq(y, y + A*x)), "F95", "file", header=False, empty=False)
assert f1 == 'file.f90'
expected = (
'subroutine matrix_vector(A, m, n, x, y)\n'
'implicit none\n'
'INTEGER*4, intent(in) :: m\n'
'INTEGER*4, intent(in) :: n\n'
'REAL*8, intent(in), dimension(1:m, 1:n) :: A\n'
'REAL*8, intent(in), dimension(1:n) :: x\n'
'REAL*8, intent(inout), dimension(1:m) :: y\n'
'INTEGER*4 :: i\n'
'INTEGER*4 :: j\n'
'do i = 1, m\n'
' do j = 1, n\n'
' y(i) = %(rhs)s + y(i)\n'
' end do\n'
'end do\n'
'end subroutine\n'
)
assert (code == expected % {'rhs': 'A(i, j)*x(j)'} or
code == expected % {'rhs': 'x(j)*A(i, j)'})
assert f2 == 'file.h'
assert interface == (
'interface\n'
'subroutine matrix_vector(A, m, n, x, y)\n'
'implicit none\n'
'INTEGER*4, intent(in) :: m\n'
'INTEGER*4, intent(in) :: n\n'
'REAL*8, intent(in), dimension(1:m, 1:n) :: A\n'
'REAL*8, intent(in), dimension(1:n) :: x\n'
'REAL*8, intent(inout), dimension(1:m) :: y\n'
'end subroutine\n'
'end interface\n'
)
def test_partial_loops_f():
# check that loop boundaries are determined by Idx, and array strides
# determined by shape of IndexedBase object.
from sympy.tensor import IndexedBase, Idx
from sympy import symbols
n, m, o, p = symbols('n m o p', integer=True)
A = IndexedBase('A', shape=(m, p))
x = IndexedBase('x')
y = IndexedBase('y')
i = Idx('i', (o, m - 5)) # Note: bounds are inclusive
j = Idx('j', n) # dimension n corresponds to bounds (0, n - 1)
(f1, code), (f2, interface) = codegen(
('matrix_vector', Eq(y[i], A[i, j]*x[j])), "F95", "file", header=False, empty=False)
expected = (
'subroutine matrix_vector(A, m, n, o, p, x, y)\n'
'implicit none\n'
'INTEGER*4, intent(in) :: m\n'
'INTEGER*4, intent(in) :: n\n'
'INTEGER*4, intent(in) :: o\n'
'INTEGER*4, intent(in) :: p\n'
'REAL*8, intent(in), dimension(1:m, 1:p) :: A\n'
'REAL*8, intent(in), dimension(1:n) :: x\n'
'REAL*8, intent(out), dimension(1:%(iup-ilow)s) :: y\n'
'INTEGER*4 :: i\n'
'INTEGER*4 :: j\n'
'do i = %(ilow)s, %(iup)s\n'
' y(i) = 0\n'
'end do\n'
'do i = %(ilow)s, %(iup)s\n'
' do j = 1, n\n'
' y(i) = %(rhs)s + y(i)\n'
' end do\n'
'end do\n'
'end subroutine\n'
) % {
'rhs': '%(rhs)s',
'iup': str(m - 4),
'ilow': str(1 + o),
'iup-ilow': str(m - 4 - o)
}
assert code == expected % {'rhs': 'A(i, j)*x(j)'} or\
code == expected % {'rhs': 'x(j)*A(i, j)'}
def test_output_arg_f():
from sympy import sin, cos, Equality
x, y, z = symbols("x,y,z")
r = make_routine("foo", [Equality(y, sin(x)), cos(x)])
c = FCodeGen()
result = c.write([r], "test", header=False, empty=False)
assert result[0][0] == "test.f90"
assert result[0][1] == (
'REAL*8 function foo(x, y)\n'
'implicit none\n'
'REAL*8, intent(in) :: x\n'
'REAL*8, intent(out) :: y\n'
'y = sin(x)\n'
'foo = cos(x)\n'
'end function\n'
)
def test_inline_function():
from sympy.tensor import IndexedBase, Idx
from sympy import symbols
n, m = symbols('n m', integer=True)
A, x, y = map(IndexedBase, 'Axy')
i = Idx('i', m)
p = FCodeGen()
func = implemented_function('func', Lambda(n, n*(n + 1)))
routine = make_routine('test_inline', Eq(y[i], func(x[i])))
code = get_string(p.dump_f95, [routine])
expected = (
'subroutine test_inline(m, x, y)\n'
'implicit none\n'
'INTEGER*4, intent(in) :: m\n'
'REAL*8, intent(in), dimension(1:m) :: x\n'
'REAL*8, intent(out), dimension(1:m) :: y\n'
'INTEGER*4 :: i\n'
'do i = 1, m\n'
' y(i) = %s*%s\n'
'end do\n'
'end subroutine\n'
)
args = ('x(i)', '(x(i) + 1)')
assert code == expected % args or\
code == expected % args[::-1]
def test_f_code_call_signature_wrap():
# Issue #7934
x = symbols('x:20')
expr = 0
for sym in x:
expr += sym
routine = make_routine("test", expr)
code_gen = FCodeGen()
source = get_string(code_gen.dump_f95, [routine])
expected = """\
REAL*8 function test(x0, x1, x10, x11, x12, x13, x14, x15, x16, x17, x18, &
x19, x2, x3, x4, x5, x6, x7, x8, x9)
implicit none
REAL*8, intent(in) :: x0
REAL*8, intent(in) :: x1
REAL*8, intent(in) :: x10
REAL*8, intent(in) :: x11
REAL*8, intent(in) :: x12
REAL*8, intent(in) :: x13
REAL*8, intent(in) :: x14
REAL*8, intent(in) :: x15
REAL*8, intent(in) :: x16
REAL*8, intent(in) :: x17
REAL*8, intent(in) :: x18
REAL*8, intent(in) :: x19
REAL*8, intent(in) :: x2
REAL*8, intent(in) :: x3
REAL*8, intent(in) :: x4
REAL*8, intent(in) :: x5
REAL*8, intent(in) :: x6
REAL*8, intent(in) :: x7
REAL*8, intent(in) :: x8
REAL*8, intent(in) :: x9
test = x0 + x1 + x10 + x11 + x12 + x13 + x14 + x15 + x16 + x17 + x18 + &
x19 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9
end function
"""
assert source == expected
def test_check_case():
x, X = symbols('x,X')
raises(CodeGenError, lambda: codegen(('test', x*X), 'f95', 'prefix'))
def test_check_case_false_positive():
# The upper case/lower case exception should not be triggered by SymPy
# objects that differ only because of assumptions. (It may be useful to
# have a check for that as well, but here we only want to test against
# false positives with respect to case checking.)
x1 = symbols('x')
x2 = symbols('x', my_assumption=True)
try:
codegen(('test', x1*x2), 'f95', 'prefix')
except CodeGenError as e:
if e.args[0].startswith("Fortran ignores case."):
raise AssertionError("This exception should not be raised!")
def test_c_fortran_omit_routine_name():
x, y = symbols("x,y")
name_expr = [("foo", 2*x)]
result = codegen(name_expr, "F95", header=False, empty=False)
expresult = codegen(name_expr, "F95", "foo", header=False, empty=False)
assert result[0][1] == expresult[0][1]
name_expr = ("foo", x*y)
result = codegen(name_expr, "F95", header=False, empty=False)
expresult = codegen(name_expr, "F95", "foo", header=False, empty=False)
assert result[0][1] == expresult[0][1]
name_expr = ("foo", Matrix([[x, y], [x+y, x-y]]))
result = codegen(name_expr, "C89", header=False, empty=False)
expresult = codegen(name_expr, "C89", "foo", header=False, empty=False)
assert result[0][1] == expresult[0][1]
def test_fcode_matrix_output():
x, y, z = symbols('x,y,z')
e1 = x + y
e2 = Matrix([[x, y], [z, 16]])
name_expr = ("test", (e1, e2))
result = codegen(name_expr, "f95", "test", header=False, empty=False)
source = result[0][1]
expected = (
"REAL*8 function test(x, y, z, out_%(hash)s)\n"
"implicit none\n"
"REAL*8, intent(in) :: x\n"
"REAL*8, intent(in) :: y\n"
"REAL*8, intent(in) :: z\n"
"REAL*8, intent(out), dimension(1:2, 1:2) :: out_%(hash)s\n"
"out_%(hash)s(1, 1) = x\n"
"out_%(hash)s(2, 1) = z\n"
"out_%(hash)s(1, 2) = y\n"
"out_%(hash)s(2, 2) = 16\n"
"test = x + y\n"
"end function\n"
)
# look for the magic number
a = source.splitlines()[5]
b = a.split('_')
out = b[1]
expected = expected % {'hash': out}
assert source == expected
def test_fcode_results_named_ordered():
x, y, z = symbols('x,y,z')
B, C = symbols('B,C')
A = MatrixSymbol('A', 1, 3)
expr1 = Equality(A, Matrix([[1, 2, x]]))
expr2 = Equality(C, (x + y)*z)
expr3 = Equality(B, 2*x)
name_expr = ("test", [expr1, expr2, expr3])
result = codegen(name_expr, "f95", "test", header=False, empty=False,
argument_sequence=(x, z, y, C, A, B))
source = result[0][1]
expected = (
"subroutine test(x, z, y, C, A, B)\n"
"implicit none\n"
"REAL*8, intent(in) :: x\n"
"REAL*8, intent(in) :: z\n"
"REAL*8, intent(in) :: y\n"
"REAL*8, intent(out) :: C\n"
"REAL*8, intent(out) :: B\n"
"REAL*8, intent(out), dimension(1:1, 1:3) :: A\n"
"C = z*(x + y)\n"
"A(1, 1) = 1\n"
"A(1, 2) = 2\n"
"A(1, 3) = x\n"
"B = 2*x\n"
"end subroutine\n"
)
assert source == expected
def test_fcode_matrixsymbol_slice():
A = MatrixSymbol('A', 2, 3)
B = MatrixSymbol('B', 1, 3)
C = MatrixSymbol('C', 1, 3)
D = MatrixSymbol('D', 2, 1)
name_expr = ("test", [Equality(B, A[0, :]),
Equality(C, A[1, :]),
Equality(D, A[:, 2])])
result = codegen(name_expr, "f95", "test", header=False, empty=False)
source = result[0][1]
expected = (
"subroutine test(A, B, C, D)\n"
"implicit none\n"
"REAL*8, intent(in), dimension(1:2, 1:3) :: A\n"
"REAL*8, intent(out), dimension(1:1, 1:3) :: B\n"
"REAL*8, intent(out), dimension(1:1, 1:3) :: C\n"
"REAL*8, intent(out), dimension(1:2, 1:1) :: D\n"
"B(1, 1) = A(1, 1)\n"
"B(1, 2) = A(1, 2)\n"
"B(1, 3) = A(1, 3)\n"
"C(1, 1) = A(2, 1)\n"
"C(1, 2) = A(2, 2)\n"
"C(1, 3) = A(2, 3)\n"
"D(1, 1) = A(1, 3)\n"
"D(2, 1) = A(2, 3)\n"
"end subroutine\n"
)
assert source == expected
def test_fcode_matrixsymbol_slice_autoname():
# see issue #8093
A = MatrixSymbol('A', 2, 3)
name_expr = ("test", A[:, 1])
result = codegen(name_expr, "f95", "test", header=False, empty=False)
source = result[0][1]
expected = (
"subroutine test(A, out_%(hash)s)\n"
"implicit none\n"
"REAL*8, intent(in), dimension(1:2, 1:3) :: A\n"
"REAL*8, intent(out), dimension(1:2, 1:1) :: out_%(hash)s\n"
"out_%(hash)s(1, 1) = A(1, 2)\n"
"out_%(hash)s(2, 1) = A(2, 2)\n"
"end subroutine\n"
)
# look for the magic number
a = source.splitlines()[3]
b = a.split('_')
out = b[1]
expected = expected % {'hash': out}
assert source == expected
def test_global_vars():
x, y, z, t = symbols("x y z t")
result = codegen(('f', x*y), "F95", header=False, empty=False,
global_vars=(y,))
source = result[0][1]
expected = (
"REAL*8 function f(x)\n"
"implicit none\n"
"REAL*8, intent(in) :: x\n"
"f = x*y\n"
"end function\n"
)
assert source == expected
expected = (
'#include "f.h"\n'
'#include <math.h>\n'
'double f(double x, double y) {\n'
' double f_result;\n'
' f_result = x*y + z;\n'
' return f_result;\n'
'}\n'
)
with warnings.catch_warnings():
warnings.filterwarnings("ignore", category=SymPyDeprecationWarning)
result = codegen(('f', x*y+z), "C", header=False, empty=False,
global_vars=(z, t))
source = result[0][1]
assert source == expected
def test_custom_codegen():
from sympy.printing.ccode import C99CodePrinter
from sympy.functions.elementary.exponential import exp
printer = C99CodePrinter(settings={'user_functions': {'exp': 'fastexp'}})
x, y = symbols('x y')
expr = exp(x + y)
# replace math.h with a different header
gen = C99CodeGen(printer=printer,
preprocessor_statements=['#include "fastexp.h"'])
expected = (
'#include "expr.h"\n'
'#include "fastexp.h"\n'
'double expr(double x, double y) {\n'
' double expr_result;\n'
' expr_result = fastexp(x + y);\n'
' return expr_result;\n'
'}\n'
)
result = codegen(('expr', expr), header=False, empty=False, code_gen=gen)
source = result[0][1]
assert source == expected
# use both math.h and an external header
gen = C99CodeGen(printer=printer)
gen.preprocessor_statements.append('#include "fastexp.h"')
expected = (
'#include "expr.h"\n'
'#include <math.h>\n'
'#include "fastexp.h"\n'
'double expr(double x, double y) {\n'
' double expr_result;\n'
' expr_result = fastexp(x + y);\n'
' return expr_result;\n'
'}\n'
)
result = codegen(('expr', expr), header=False, empty=False, code_gen=gen)
source = result[0][1]
assert source == expected
| 51,143 | 33.324832 | 151 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/tests/test_source.py
|
from sympy.utilities.source import get_mod_func, get_class
def test_get_mod_func():
assert get_mod_func(
'sympy.core.basic.Basic') == ('sympy.core.basic', 'Basic')
def test_get_class():
_basic = get_class('sympy.core.basic.Basic')
assert _basic.__name__ == 'Basic'
| 289 | 23.166667 | 66 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/tests/test_lambdify.py
|
from itertools import product
import math
import mpmath
from sympy.utilities.pytest import XFAIL, raises
from sympy import (
symbols, lambdify, sqrt, sin, cos, tan, pi, acos, acosh, Rational,
Float, Matrix, Lambda, Piecewise, exp, Integral, oo, I, Abs, Function,
true, false, And, Or, Not, ITE, Min, Max, floor, diff, IndexedBase, Sum,
DotProduct, Eq)
from sympy.printing.lambdarepr import LambdaPrinter
from sympy.utilities.lambdify import implemented_function
from sympy.utilities.pytest import skip
from sympy.utilities.decorator import conserve_mpmath_dps
from sympy.external import import_module
from sympy.functions.special.gamma_functions import uppergamma,lowergamma
import sympy
MutableDenseMatrix = Matrix
numpy = import_module('numpy')
numexpr = import_module('numexpr')
tensorflow = import_module('tensorflow')
w, x, y, z = symbols('w,x,y,z')
#================== Test different arguments =======================
def test_no_args():
f = lambdify([], 1)
raises(TypeError, lambda: f(-1))
assert f() == 1
def test_single_arg():
f = lambdify(x, 2*x)
assert f(1) == 2
def test_list_args():
f = lambdify([x, y], x + y)
assert f(1, 2) == 3
def test_str_args():
f = lambdify('x,y,z', 'z,y,x')
assert f(3, 2, 1) == (1, 2, 3)
assert f(1.0, 2.0, 3.0) == (3.0, 2.0, 1.0)
# make sure correct number of args required
raises(TypeError, lambda: f(0))
def test_own_namespace():
myfunc = lambda x: 1
f = lambdify(x, sin(x), {"sin": myfunc})
assert f(0.1) == 1
assert f(100) == 1
def test_own_module():
f = lambdify(x, sin(x), math)
assert f(0) == 0.0
def test_bad_args():
# no vargs given
raises(TypeError, lambda: lambdify(1))
# same with vector exprs
raises(TypeError, lambda: lambdify([1, 2]))
def test_atoms():
# Non-Symbol atoms should not be pulled out from the expression namespace
f = lambdify(x, pi + x, {"pi": 3.14})
assert f(0) == 3.14
f = lambdify(x, I + x, {"I": 1j})
assert f(1) == 1 + 1j
#================== Test different modules =========================
# high precision output of sin(0.2*pi) is used to detect if precision is lost unwanted
@conserve_mpmath_dps
def test_sympy_lambda():
mpmath.mp.dps = 50
sin02 = mpmath.mpf("0.19866933079506121545941262711838975037020672954020")
f = lambdify(x, sin(x), "sympy")
assert f(x) == sin(x)
prec = 1e-15
assert -prec < f(Rational(1, 5)).evalf() - Float(str(sin02)) < prec
# arctan is in numpy module and should not be available
raises(NameError, lambda: lambdify(x, arctan(x), "sympy"))
@conserve_mpmath_dps
def test_math_lambda():
mpmath.mp.dps = 50
sin02 = mpmath.mpf("0.19866933079506121545941262711838975037020672954020")
f = lambdify(x, sin(x), "math")
prec = 1e-15
assert -prec < f(0.2) - sin02 < prec
raises(TypeError, lambda: f(x))
# if this succeeds, it can't be a python math function
@conserve_mpmath_dps
def test_mpmath_lambda():
mpmath.mp.dps = 50
sin02 = mpmath.mpf("0.19866933079506121545941262711838975037020672954020")
f = lambdify(x, sin(x), "mpmath")
prec = 1e-49 # mpmath precision is around 50 decimal places
assert -prec < f(mpmath.mpf("0.2")) - sin02 < prec
raises(TypeError, lambda: f(x))
# if this succeeds, it can't be a mpmath function
@conserve_mpmath_dps
def test_number_precision():
mpmath.mp.dps = 50
sin02 = mpmath.mpf("0.19866933079506121545941262711838975037020672954020")
f = lambdify(x, sin02, "mpmath")
prec = 1e-49 # mpmath precision is around 50 decimal places
assert -prec < f(0) - sin02 < prec
@conserve_mpmath_dps
def test_mpmath_precision():
mpmath.mp.dps = 100
assert str(lambdify((), pi.evalf(100), 'mpmath')()) == str(pi.evalf(100))
#================== Test Translations ==============================
# We can only check if all translated functions are valid. It has to be checked
# by hand if they are complete.
def test_math_transl():
from sympy.utilities.lambdify import MATH_TRANSLATIONS
for sym, mat in MATH_TRANSLATIONS.items():
assert sym in sympy.__dict__
assert mat in math.__dict__
def test_mpmath_transl():
from sympy.utilities.lambdify import MPMATH_TRANSLATIONS
for sym, mat in MPMATH_TRANSLATIONS.items():
assert sym in sympy.__dict__ or sym == 'Matrix'
assert mat in mpmath.__dict__
def test_numpy_transl():
if not numpy:
skip("numpy not installed.")
from sympy.utilities.lambdify import NUMPY_TRANSLATIONS
for sym, nump in NUMPY_TRANSLATIONS.items():
assert sym in sympy.__dict__
assert nump in numpy.__dict__
def test_tensorflow_transl():
if not tensorflow:
skip("tensorflow not installed")
from sympy.utilities.lambdify import TENSORFLOW_TRANSLATIONS
for sym, tens in TENSORFLOW_TRANSLATIONS.items():
assert sym in sympy.__dict__
assert tens in tensorflow.__dict__
def test_numpy_translation_abs():
if not numpy:
skip("numpy not installed.")
f = lambdify(x, Abs(x), "numpy")
assert f(-1) == 1
assert f(1) == 1
def test_numexpr_printer():
if not numexpr:
skip("numexpr not installed.")
# if translation/printing is done incorrectly then evaluating
# a lambdified numexpr expression will throw an exception
from sympy.printing.lambdarepr import NumExprPrinter
from sympy import S
blacklist = ('where', 'complex', 'contains')
arg_tuple = (x, y, z) # some functions take more than one argument
for sym in NumExprPrinter._numexpr_functions.keys():
if sym in blacklist:
continue
ssym = S(sym)
if hasattr(ssym, '_nargs'):
nargs = ssym._nargs[0]
else:
nargs = 1
args = arg_tuple[:nargs]
f = lambdify(args, ssym(*args), modules='numexpr')
assert f(*(1, )*nargs) is not None
def test_issue_9334():
if not numexpr:
skip("numexpr not installed.")
if not numpy:
skip("numpy not installed.")
expr = sympy.S('b*a - sqrt(a**2)')
a, b = sorted(expr.free_symbols, key=lambda s: s.name)
func_numexpr = lambdify((a,b), expr, modules=[numexpr], dummify=False)
foo, bar = numpy.random.random((2, 4))
func_numexpr(foo, bar)
#================== Test some functions ============================
def test_exponentiation():
f = lambdify(x, x**2)
assert f(-1) == 1
assert f(0) == 0
assert f(1) == 1
assert f(-2) == 4
assert f(2) == 4
assert f(2.5) == 6.25
def test_sqrt():
f = lambdify(x, sqrt(x))
assert f(0) == 0.0
assert f(1) == 1.0
assert f(4) == 2.0
assert abs(f(2) - 1.414) < 0.001
assert f(6.25) == 2.5
def test_trig():
f = lambdify([x], [cos(x), sin(x)], 'math')
d = f(pi)
prec = 1e-11
assert -prec < d[0] + 1 < prec
assert -prec < d[1] < prec
d = f(3.14159)
prec = 1e-5
assert -prec < d[0] + 1 < prec
assert -prec < d[1] < prec
#================== Test vectors ===================================
def test_vector_simple():
f = lambdify((x, y, z), (z, y, x))
assert f(3, 2, 1) == (1, 2, 3)
assert f(1.0, 2.0, 3.0) == (3.0, 2.0, 1.0)
# make sure correct number of args required
raises(TypeError, lambda: f(0))
def test_vector_discontinuous():
f = lambdify(x, (-1/x, 1/x))
raises(ZeroDivisionError, lambda: f(0))
assert f(1) == (-1.0, 1.0)
assert f(2) == (-0.5, 0.5)
assert f(-2) == (0.5, -0.5)
def test_trig_symbolic():
f = lambdify([x], [cos(x), sin(x)], 'math')
d = f(pi)
assert abs(d[0] + 1) < 0.0001
assert abs(d[1] - 0) < 0.0001
def test_trig_float():
f = lambdify([x], [cos(x), sin(x)])
d = f(3.14159)
assert abs(d[0] + 1) < 0.0001
assert abs(d[1] - 0) < 0.0001
def test_docs():
f = lambdify(x, x**2)
assert f(2) == 4
f = lambdify([x, y, z], [z, y, x])
assert f(1, 2, 3) == [3, 2, 1]
f = lambdify(x, sqrt(x))
assert f(4) == 2.0
f = lambdify((x, y), sin(x*y)**2)
assert f(0, 5) == 0
def test_math():
f = lambdify((x, y), sin(x), modules="math")
assert f(0, 5) == 0
def test_sin():
f = lambdify(x, sin(x)**2)
assert isinstance(f(2), float)
f = lambdify(x, sin(x)**2, modules="math")
assert isinstance(f(2), float)
def test_matrix():
A = Matrix([[x, x*y], [sin(z) + 4, x**z]])
sol = Matrix([[1, 2], [sin(3) + 4, 1]])
f = lambdify((x, y, z), A, modules="sympy")
assert f(1, 2, 3) == sol
f = lambdify((x, y, z), (A, [A]), modules="sympy")
assert f(1, 2, 3) == (sol, [sol])
J = Matrix((x, x + y)).jacobian((x, y))
v = Matrix((x, y))
sol = Matrix([[1, 0], [1, 1]])
assert lambdify(v, J, modules='sympy')(1, 2) == sol
assert lambdify(v.T, J, modules='sympy')(1, 2) == sol
def test_numpy_matrix():
if not numpy:
skip("numpy not installed.")
A = Matrix([[x, x*y], [sin(z) + 4, x**z]])
sol_arr = numpy.array([[1, 2], [numpy.sin(3) + 4, 1]])
#Lambdify array first, to ensure return to array as default
f = lambdify((x, y, z), A, ['numpy'])
numpy.testing.assert_allclose(f(1, 2, 3), sol_arr)
#Check that the types are arrays and matrices
assert isinstance(f(1, 2, 3), numpy.ndarray)
def test_numpy_transpose():
if not numpy:
skip("numpy not installed.")
A = Matrix([[1, x], [0, 1]])
f = lambdify((x), A.T, modules="numpy")
numpy.testing.assert_array_equal(f(2), numpy.array([[1, 0], [2, 1]]))
def test_numpy_dotproduct():
if not numpy:
skip("numpy not installed")
A = Matrix([x, y, z])
f1 = lambdify([x, y, z], DotProduct(A, A), modules='numpy')
f2 = lambdify([x, y, z], DotProduct(A, A.T), modules='numpy')
f3 = lambdify([x, y, z], DotProduct(A.T, A), modules='numpy')
f4 = lambdify([x, y, z], DotProduct(A, A.T), modules='numpy')
assert f1(1, 2, 3) == \
f2(1, 2, 3) == \
f3(1, 2, 3) == \
f4(1, 2, 3) == \
numpy.array([14])
def test_numpy_inverse():
if not numpy:
skip("numpy not installed.")
A = Matrix([[1, x], [0, 1]])
f = lambdify((x), A**-1, modules="numpy")
numpy.testing.assert_array_equal(f(2), numpy.array([[1, -2], [0, 1]]))
def test_numpy_old_matrix():
if not numpy:
skip("numpy not installed.")
A = Matrix([[x, x*y], [sin(z) + 4, x**z]])
sol_arr = numpy.array([[1, 2], [numpy.sin(3) + 4, 1]])
f = lambdify((x, y, z), A, [{'ImmutableDenseMatrix': numpy.matrix}, 'numpy'])
numpy.testing.assert_allclose(f(1, 2, 3), sol_arr)
assert isinstance(f(1, 2, 3), numpy.matrix)
def test_python_div_zero_issue_11306():
if not numpy:
skip("numpy not installed.")
p = Piecewise((1 / x, y < -1), (x, y < 1), (1 / x, True))
f = lambdify([x, y], p, modules='numpy')
numpy.seterr(divide='ignore')
assert str(float(f(0,1))) == 'inf'
numpy.seterr(divide='warn')
def test_issue9474():
mods = [None, 'math']
if numpy:
mods.append('numpy')
if mpmath:
mods.append('mpmath')
for mod in mods:
f = lambdify(x, sympy.S(1)/x, modules=mod)
assert f(2) == 0.5
f = lambdify(x, floor(sympy.S(1)/x), modules=mod)
assert f(2) == 0
if mpmath:
f = lambdify(x, sympy.S(1)/sympy.Abs(x), modules=['mpmath'])
assert isinstance(f(2), mpmath.mpf)
for absfunc, modules in product([Abs, abs], mods):
f = lambdify(x, absfunc(x), modules=modules)
assert f(-1) == 1
assert f(1) == 1
assert f(3+4j) == 5
def test_issue_9871():
if not numexpr:
skip("numexpr not installed.")
if not numpy:
skip("numpy not installed.")
r = sqrt(x**2 + y**2)
expr = diff(1/r, x)
xn = yn = numpy.linspace(1, 10, 16)
# expr(xn, xn) = -xn/(sqrt(2)*xn)^3
fv_exact = -numpy.sqrt(2.)**-3 * xn**-2
fv_numpy = lambdify((x, y), expr, modules='numpy')(xn, yn)
fv_numexpr = lambdify((x, y), expr, modules='numexpr')(xn, yn)
numpy.testing.assert_allclose(fv_numpy, fv_exact, rtol=1e-10)
numpy.testing.assert_allclose(fv_numexpr, fv_exact, rtol=1e-10)
def test_numpy_piecewise():
if not numpy:
skip("numpy not installed.")
pieces = Piecewise((x, x < 3), (x**2, x > 5), (0, True))
f = lambdify(x, pieces, modules="numpy")
numpy.testing.assert_array_equal(f(numpy.arange(10)),
numpy.array([0, 1, 2, 0, 0, 0, 36, 49, 64, 81]))
# If we evaluate somewhere all conditions are False, we should get back NaN
nodef_func = lambdify(x, Piecewise((x, x > 0), (-x, x < 0)))
numpy.testing.assert_array_equal(nodef_func(numpy.array([-1, 0, 1])),
numpy.array([1, numpy.nan, 1]))
def test_numpy_logical_ops():
if not numpy:
skip("numpy not installed.")
and_func = lambdify((x, y), And(x, y), modules="numpy")
or_func = lambdify((x, y), Or(x, y), modules="numpy")
not_func = lambdify((x), Not(x), modules="numpy")
arr1 = numpy.array([True, True])
arr2 = numpy.array([False, True])
numpy.testing.assert_array_equal(and_func(arr1, arr2), numpy.array([False, True]))
numpy.testing.assert_array_equal(or_func(arr1, arr2), numpy.array([True, True]))
numpy.testing.assert_array_equal(not_func(arr2), numpy.array([True, False]))
def test_numpy_matmul():
if not numpy:
skip("numpy not installed.")
xmat = Matrix([[x, y], [z, 1+z]])
ymat = Matrix([[x**2], [Abs(x)]])
mat_func = lambdify((x, y, z), xmat*ymat, modules="numpy")
numpy.testing.assert_array_equal(mat_func(0.5, 3, 4), numpy.array([[1.625], [3.5]]))
numpy.testing.assert_array_equal(mat_func(-0.5, 3, 4), numpy.array([[1.375], [3.5]]))
# Multiple matrices chained together in multiplication
f = lambdify((x, y, z), xmat*xmat*xmat, modules="numpy")
numpy.testing.assert_array_equal(f(0.5, 3, 4), numpy.array([[72.125, 119.25],
[159, 251]]))
def test_numpy_numexpr():
if not numpy:
skip("numpy not installed.")
if not numexpr:
skip("numexpr not installed.")
a, b, c = numpy.random.randn(3, 128, 128)
# ensure that numpy and numexpr return same value for complicated expression
expr = sin(x) + cos(y) + tan(z)**2 + Abs(z-y)*acos(sin(y*z)) + \
Abs(y-z)*acosh(2+exp(y-x))- sqrt(x**2+I*y**2)
npfunc = lambdify((x, y, z), expr, modules='numpy')
nefunc = lambdify((x, y, z), expr, modules='numexpr')
assert numpy.allclose(npfunc(a, b, c), nefunc(a, b, c))
def test_numexpr_userfunctions():
if not numpy:
skip("numpy not installed.")
if not numexpr:
skip("numexpr not installed.")
a, b = numpy.random.randn(2, 10)
uf = type('uf', (Function, ),
{'eval' : classmethod(lambda x, y : y**2+1)})
func = lambdify(x, 1-uf(x), modules='numexpr')
assert numpy.allclose(func(a), -(a**2))
uf = implemented_function(Function('uf'), lambda x, y : 2*x*y+1)
func = lambdify((x, y), uf(x, y), modules='numexpr')
assert numpy.allclose(func(a, b), 2*a*b+1)
def test_tensorflow_basic_math():
if not tensorflow:
skip("tensorflow not installed.")
expr = Max(sin(x), Abs(1/(x+2)))
func = lambdify(x, expr, modules="tensorflow")
a = tensorflow.constant(0, dtype=tensorflow.float32)
s = tensorflow.Session()
assert func(a).eval(session=s) == 0.5
def test_tensorflow_placeholders():
if not tensorflow:
skip("tensorflow not installed.")
expr = Max(sin(x), Abs(1/(x+2)))
func = lambdify(x, expr, modules="tensorflow")
a = tensorflow.placeholder(dtype=tensorflow.float32)
s = tensorflow.Session()
assert func(a).eval(session=s, feed_dict={a: 0}) == 0.5
def test_tensorflow_variables():
if not tensorflow:
skip("tensorflow not installed.")
expr = Max(sin(x), Abs(1/(x+2)))
func = lambdify(x, expr, modules="tensorflow")
a = tensorflow.Variable(0, dtype=tensorflow.float32)
s = tensorflow.Session()
s.run(tensorflow.initialize_all_variables())
assert func(a).eval(session=s) == 0.5
def test_tensorflow_logical_operations():
if not tensorflow:
skip("tensorflow not installed.")
expr = Not(And(Or(x, y), y))
func = lambdify([x, y], expr, modules="tensorflow")
a = tensorflow.constant(False)
b = tensorflow.constant(True)
s = tensorflow.Session()
assert func(a, b).eval(session=s) == 0
def test_tensorflow_piecewise():
if not tensorflow:
skip("tensorflow not installed.")
expr = Piecewise((0, Eq(x,0)), (-1, x < 0), (1, x > 0))
func = lambdify(x, expr, modules="tensorflow")
a = tensorflow.placeholder(dtype=tensorflow.float32)
s = tensorflow.Session()
assert func(a).eval(session=s, feed_dict={a: -1}) == -1
assert func(a).eval(session=s, feed_dict={a: 0}) == 0
assert func(a).eval(session=s, feed_dict={a: 1}) == 1
def test_tensorflow_multi_max():
if not tensorflow:
skip("tensorflow not installed.")
expr = Max(x, -x, x**2)
func = lambdify(x, expr, modules="tensorflow")
a = tensorflow.placeholder(dtype=tensorflow.float32)
s = tensorflow.Session()
assert func(a).eval(session=s, feed_dict={a: -2}) == 4
def test_tensorflow_multi_min():
if not tensorflow:
skip("tensorflow not installed.")
expr = Min(x, -x, x**2)
func = lambdify(x, expr, modules="tensorflow")
a = tensorflow.placeholder(dtype=tensorflow.float32)
s = tensorflow.Session()
assert func(a).eval(session=s, feed_dict={a: -2}) == -2
def test_tensorflow_relational():
if not tensorflow:
skip("tensorflow not installed.")
expr = x >= 0
func = lambdify(x, expr, modules="tensorflow")
a = tensorflow.placeholder(dtype=tensorflow.float32)
s = tensorflow.Session()
assert func(a).eval(session=s, feed_dict={a: 1})
def test_integral():
f = Lambda(x, exp(-x**2))
l = lambdify(x, Integral(f(x), (x, -oo, oo)), modules="sympy")
assert l(x) == Integral(exp(-x**2), (x, -oo, oo))
#================== Test symbolic ==================================
def test_sym_single_arg():
f = lambdify(x, x * y)
assert f(z) == z * y
def test_sym_list_args():
f = lambdify([x, y], x + y + z)
assert f(1, 2) == 3 + z
def test_sym_integral():
f = Lambda(x, exp(-x**2))
l = lambdify(x, Integral(f(x), (x, -oo, oo)), modules="sympy")
assert l(y).doit() == sqrt(pi)
def test_namespace_order():
# lambdify had a bug, such that module dictionaries or cached module
# dictionaries would pull earlier namespaces into themselves.
# Because the module dictionaries form the namespace of the
# generated lambda, this meant that the behavior of a previously
# generated lambda function could change as a result of later calls
# to lambdify.
n1 = {'f': lambda x: 'first f'}
n2 = {'f': lambda x: 'second f',
'g': lambda x: 'function g'}
f = sympy.Function('f')
g = sympy.Function('g')
if1 = lambdify(x, f(x), modules=(n1, "sympy"))
assert if1(1) == 'first f'
if2 = lambdify(x, g(x), modules=(n2, "sympy"))
# previously gave 'second f'
assert if1(1) == 'first f'
def test_imps():
# Here we check if the default returned functions are anonymous - in
# the sense that we can have more than one function with the same name
f = implemented_function('f', lambda x: 2*x)
g = implemented_function('f', lambda x: math.sqrt(x))
l1 = lambdify(x, f(x))
l2 = lambdify(x, g(x))
assert str(f(x)) == str(g(x))
assert l1(3) == 6
assert l2(3) == math.sqrt(3)
# check that we can pass in a Function as input
func = sympy.Function('myfunc')
assert not hasattr(func, '_imp_')
my_f = implemented_function(func, lambda x: 2*x)
assert hasattr(func, '_imp_')
# Error for functions with same name and different implementation
f2 = implemented_function("f", lambda x: x + 101)
raises(ValueError, lambda: lambdify(x, f(f2(x))))
def test_imps_errors():
# Test errors that implemented functions can return, and still be able to
# form expressions.
# See: https://github.com/sympy/sympy/issues/10810
for val, error_class in product((0, 0., 2, 2.0),
(AttributeError, TypeError, ValueError)):
def myfunc(a):
if a == 0:
raise error_class
return 1
f = implemented_function('f', myfunc)
expr = f(val)
assert expr == f(val)
def test_imps_wrong_args():
raises(ValueError, lambda: implemented_function(sin, lambda x: x))
def test_lambdify_imps():
# Test lambdify with implemented functions
# first test basic (sympy) lambdify
f = sympy.cos
assert lambdify(x, f(x))(0) == 1
assert lambdify(x, 1 + f(x))(0) == 2
assert lambdify((x, y), y + f(x))(0, 1) == 2
# make an implemented function and test
f = implemented_function("f", lambda x: x + 100)
assert lambdify(x, f(x))(0) == 100
assert lambdify(x, 1 + f(x))(0) == 101
assert lambdify((x, y), y + f(x))(0, 1) == 101
# Can also handle tuples, lists, dicts as expressions
lam = lambdify(x, (f(x), x))
assert lam(3) == (103, 3)
lam = lambdify(x, [f(x), x])
assert lam(3) == [103, 3]
lam = lambdify(x, [f(x), (f(x), x)])
assert lam(3) == [103, (103, 3)]
lam = lambdify(x, {f(x): x})
assert lam(3) == {103: 3}
lam = lambdify(x, {f(x): x})
assert lam(3) == {103: 3}
lam = lambdify(x, {x: f(x)})
assert lam(3) == {3: 103}
# Check that imp preferred to other namespaces by default
d = {'f': lambda x: x + 99}
lam = lambdify(x, f(x), d)
assert lam(3) == 103
# Unless flag passed
lam = lambdify(x, f(x), d, use_imps=False)
assert lam(3) == 102
def test_dummification():
t = symbols('t')
F = Function('F')
G = Function('G')
#"\alpha" is not a valid python variable name
#lambdify should sub in a dummy for it, and return
#without a syntax error
alpha = symbols(r'\alpha')
some_expr = 2 * F(t)**2 / G(t)
lam = lambdify((F(t), G(t)), some_expr)
assert lam(3, 9) == 2
lam = lambdify(sin(t), 2 * sin(t)**2)
assert lam(F(t)) == 2 * F(t)**2
#Test that \alpha was properly dummified
lam = lambdify((alpha, t), 2*alpha + t)
assert lam(2, 1) == 5
raises(SyntaxError, lambda: lambdify(F(t) * G(t), F(t) * G(t) + 5))
raises(SyntaxError, lambda: lambdify(2 * F(t), 2 * F(t) + 5))
raises(SyntaxError, lambda: lambdify(2 * F(t), 4 * F(t) + 5))
def test_python_keywords():
# Test for issue 7452. The automatic dummification should ensure use of
# Python reserved keywords as symbol names will create valid lambda
# functions. This is an additional regression test.
python_if = symbols('if')
expr = python_if / 2
f = lambdify(python_if, expr)
assert f(4.0) == 2.0
def test_lambdify_docstring():
func = lambdify((w, x, y, z), w + x + y + z)
assert func.__doc__ == (
"Created with lambdify. Signature:\n\n"
"func(w, x, y, z)\n\n"
"Expression:\n\n"
"w + x + y + z")
syms = symbols('a1:26')
func = lambdify(syms, sum(syms))
assert func.__doc__ == (
"Created with lambdify. Signature:\n\n"
"func(a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15,\n"
" a16, a17, a18, a19, a20, a21, a22, a23, a24, a25)\n\n"
"Expression:\n\n"
"a1 + a10 + a11 + a12 + a13 + a14 + a15 + a16 + a17 + a18 + a19 + a2 + a20 +...")
#================== Test special printers ==========================
def test_special_printers():
class IntervalPrinter(LambdaPrinter):
"""Use ``lambda`` printer but print numbers as ``mpi`` intervals. """
def _print_Integer(self, expr):
return "mpi('%s')" % super(IntervalPrinter, self)._print_Integer(expr)
def _print_Rational(self, expr):
return "mpi('%s')" % super(IntervalPrinter, self)._print_Rational(expr)
def intervalrepr(expr):
return IntervalPrinter().doprint(expr)
expr = sympy.sqrt(sympy.sqrt(2) + sympy.sqrt(3)) + sympy.S(1)/2
func0 = lambdify((), expr, modules="mpmath", printer=intervalrepr)
func1 = lambdify((), expr, modules="mpmath", printer=IntervalPrinter)
func2 = lambdify((), expr, modules="mpmath", printer=IntervalPrinter())
mpi = type(mpmath.mpi(1, 2))
assert isinstance(func0(), mpi)
assert isinstance(func1(), mpi)
assert isinstance(func2(), mpi)
def test_true_false():
# We want exact is comparison here, not just ==
assert lambdify([], true)() is True
assert lambdify([], false)() is False
def test_issue_2790():
assert lambdify((x, (y, z)), x + y)(1, (2, 4)) == 3
assert lambdify((x, (y, (w, z))), w + x + y + z)(1, (2, (3, 4))) == 10
assert lambdify(x, x + 1, dummify=False)(1) == 2
def test_issue_12092():
f = implemented_function('f', lambda x: x**2)
assert f(f(2)).evalf() == Float(16)
def test_ITE():
assert lambdify((x, y, z), ITE(x, y, z))(True, 5, 3) == 5
assert lambdify((x, y, z), ITE(x, y, z))(False, 5, 3) == 3
def test_Min_Max():
# see gh-10375
assert lambdify((x, y, z), Min(x, y, z))(1, 2, 3) == 1
assert lambdify((x, y, z), Max(x, y, z))(1, 2, 3) == 3
def test_Indexed():
# Issue #10934
if not numpy:
skip("numpy not installed")
a = IndexedBase('a')
i, j = symbols('i j')
b = numpy.array([[1, 2], [3, 4]])
assert lambdify(a, Sum(a[x, y], (x, 0, 1), (y, 0, 1)))(b) == 10
def test_issue_12173():
#test for issue 12173
exp1 = lambdify((x, y), uppergamma(x, y),"mpmath")(1, 2)
exp2 = lambdify((x, y), lowergamma(x, y),"mpmath")(1, 2)
assert exp1 == uppergamma(1, 2).evalf()
assert exp2 == lowergamma(1, 2).evalf()
| 26,016 | 32.016497 | 93 |
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cba-pipeline-public
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cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/tests/__init__.py
| 0 | 0 | 0 |
py
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cba-pipeline-public
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cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/tests/test_autowrap.py
|
# Tests that require installed backends go into
# sympy/test_external/test_autowrap
import os
import tempfile
import shutil
import warnings
import tempfile
from sympy.core import symbols, Eq
from sympy.core.compatibility import StringIO
from sympy.utilities.exceptions import SymPyDeprecationWarning
from sympy.utilities.pytest import raises
from sympy.utilities.autowrap import (autowrap, binary_function,
CythonCodeWrapper, ufuncify, UfuncifyCodeWrapper, CodeWrapper)
from sympy.utilities.codegen import (
CCodeGen, C99CodeGen, CodeGenArgumentListError, make_routine
)
def get_string(dump_fn, routines, prefix="file", **kwargs):
"""Wrapper for dump_fn. dump_fn writes its results to a stream object and
this wrapper returns the contents of that stream as a string. This
auxiliary function is used by many tests below.
The header and the empty lines are not generator to facilitate the
testing of the output.
"""
output = StringIO()
dump_fn(routines, output, prefix, **kwargs)
source = output.getvalue()
output.close()
return source
def test_cython_wrapper_scalar_function():
x, y, z = symbols('x,y,z')
expr = (x + y)*z
routine = make_routine("test", expr)
with warnings.catch_warnings():
warnings.filterwarnings('ignore', category=SymPyDeprecationWarning)
code_gen = CythonCodeWrapper(CCodeGen())
source = get_string(code_gen.dump_pyx, [routine])
expected = (
"cdef extern from 'file.h':\n"
" double test(double x, double y, double z)\n"
"\n"
"def test_c(double x, double y, double z):\n"
"\n"
" return test(x, y, z)")
assert source == expected
def test_cython_wrapper_outarg():
from sympy import Equality
x, y, z = symbols('x,y,z')
code_gen = CythonCodeWrapper(C99CodeGen())
routine = make_routine("test", Equality(z, x + y))
source = get_string(code_gen.dump_pyx, [routine])
expected = (
"cdef extern from 'file.h':\n"
" void test(double x, double y, double *z)\n"
"\n"
"def test_c(double x, double y):\n"
"\n"
" cdef double z = 0\n"
" test(x, y, &z)\n"
" return z")
assert source == expected
def test_cython_wrapper_inoutarg():
from sympy import Equality
x, y, z = symbols('x,y,z')
code_gen = CythonCodeWrapper(C99CodeGen())
routine = make_routine("test", Equality(z, x + y + z))
source = get_string(code_gen.dump_pyx, [routine])
expected = (
"cdef extern from 'file.h':\n"
" void test(double x, double y, double *z)\n"
"\n"
"def test_c(double x, double y, double z):\n"
"\n"
" test(x, y, &z)\n"
" return z")
assert source == expected
def test_cython_wrapper_compile_flags():
from sympy import Equality
x, y, z = symbols('x,y,z')
routine = make_routine("test", Equality(z, x + y))
code_gen = CythonCodeWrapper(CCodeGen())
expected = """\
try:
from setuptools import setup
from setuptools import Extension
except ImportError:
from distutils.core import setup
from distutils.extension import Extension
from Cython.Build import cythonize
cy_opts = {}
ext_mods = [Extension(
'wrapper_module_%(num)s', ['wrapper_module_%(num)s.pyx', 'wrapped_code_%(num)s.c'],
include_dirs=[],
library_dirs=[],
libraries=[],
extra_compile_args=['-std=c99'],
extra_link_args=[]
)]
setup(ext_modules=cythonize(ext_mods, **cy_opts))
""" % {'num': CodeWrapper._module_counter}
temp_dir = tempfile.mkdtemp()
setup_file_path = os.path.join(temp_dir, 'setup.py')
code_gen._prepare_files(routine, build_dir=temp_dir)
with open(setup_file_path) as f:
setup_text = f.read()
assert setup_text == expected
code_gen = CythonCodeWrapper(CCodeGen(),
include_dirs=['/usr/local/include', '/opt/booger/include'],
library_dirs=['/user/local/lib'],
libraries=['thelib', 'nilib'],
extra_compile_args=['-slow-math'],
extra_link_args=['-lswamp', '-ltrident'],
cythonize_options={'compiler_directives': {'boundscheck': False}}
)
expected = """\
try:
from setuptools import setup
from setuptools import Extension
except ImportError:
from distutils.core import setup
from distutils.extension import Extension
from Cython.Build import cythonize
cy_opts = {'compiler_directives': {'boundscheck': False}}
ext_mods = [Extension(
'wrapper_module_%(num)s', ['wrapper_module_%(num)s.pyx', 'wrapped_code_%(num)s.c'],
include_dirs=['/usr/local/include', '/opt/booger/include'],
library_dirs=['/user/local/lib'],
libraries=['thelib', 'nilib'],
extra_compile_args=['-slow-math', '-std=c99'],
extra_link_args=['-lswamp', '-ltrident']
)]
setup(ext_modules=cythonize(ext_mods, **cy_opts))
""" % {'num': CodeWrapper._module_counter}
code_gen._prepare_files(routine, build_dir=temp_dir)
with open(setup_file_path) as f:
setup_text = f.read()
assert setup_text == expected
expected = """\
try:
from setuptools import setup
from setuptools import Extension
except ImportError:
from distutils.core import setup
from distutils.extension import Extension
from Cython.Build import cythonize
cy_opts = {'compiler_directives': {'boundscheck': False}}
import numpy as np
ext_mods = [Extension(
'wrapper_module_%(num)s', ['wrapper_module_%(num)s.pyx', 'wrapped_code_%(num)s.c'],
include_dirs=['/usr/local/include', '/opt/booger/include', np.get_include()],
library_dirs=['/user/local/lib'],
libraries=['thelib', 'nilib'],
extra_compile_args=['-slow-math', '-std=c99'],
extra_link_args=['-lswamp', '-ltrident']
)]
setup(ext_modules=cythonize(ext_mods, **cy_opts))
""" % {'num': CodeWrapper._module_counter}
code_gen._need_numpy = True
code_gen._prepare_files(routine, build_dir=temp_dir)
with open(setup_file_path) as f:
setup_text = f.read()
assert setup_text == expected
def test_autowrap_dummy():
x, y, z = symbols('x y z')
# Uses DummyWrapper to test that codegen works as expected
f = autowrap(x + y, backend='dummy')
assert f() == str(x + y)
assert f.args == "x, y"
assert f.returns == "nameless"
f = autowrap(Eq(z, x + y), backend='dummy')
assert f() == str(x + y)
assert f.args == "x, y"
assert f.returns == "z"
f = autowrap(Eq(z, x + y + z), backend='dummy')
assert f() == str(x + y + z)
assert f.args == "x, y, z"
assert f.returns == "z"
def test_autowrap_args():
x, y, z = symbols('x y z')
raises(CodeGenArgumentListError, lambda: autowrap(Eq(z, x + y),
backend='dummy', args=[x]))
f = autowrap(Eq(z, x + y), backend='dummy', args=[y, x])
assert f() == str(x + y)
assert f.args == "y, x"
assert f.returns == "z"
raises(CodeGenArgumentListError, lambda: autowrap(Eq(z, x + y + z),
backend='dummy', args=[x, y]))
f = autowrap(Eq(z, x + y + z), backend='dummy', args=[y, x, z])
assert f() == str(x + y + z)
assert f.args == "y, x, z"
assert f.returns == "z"
f = autowrap(Eq(z, x + y + z), backend='dummy', args=(y, x, z))
assert f() == str(x + y + z)
assert f.args == "y, x, z"
assert f.returns == "z"
def test_autowrap_store_files():
x, y = symbols('x y')
tmp = tempfile.mkdtemp()
try:
f = autowrap(x + y, backend='dummy', tempdir=tmp)
assert f() == str(x + y)
assert os.access(tmp, os.F_OK)
finally:
shutil.rmtree(tmp)
def test_binary_function():
x, y = symbols('x y')
f = binary_function('f', x + y, backend='dummy')
assert f._imp_() == str(x + y)
def test_ufuncify_source():
x, y, z = symbols('x,y,z')
code_wrapper = UfuncifyCodeWrapper(C99CodeGen("ufuncify"))
CodeWrapper._module_counter = 0
routine = make_routine("test", x + y + z)
source = get_string(code_wrapper.dump_c, [routine])
expected = """\
#include "Python.h"
#include "math.h"
#include "numpy/ndarraytypes.h"
#include "numpy/ufuncobject.h"
#include "numpy/halffloat.h"
#include "file.h"
static PyMethodDef wrapper_module_0Methods[] = {
{NULL, NULL, 0, NULL}
};
static void test_ufunc(char **args, npy_intp *dimensions, npy_intp* steps, void* data)
{
npy_intp i;
npy_intp n = dimensions[0];
char *in0 = args[0];
char *in1 = args[1];
char *in2 = args[2];
char *out0 = args[3];
npy_intp in0_step = steps[0];
npy_intp in1_step = steps[1];
npy_intp in2_step = steps[2];
npy_intp out0_step = steps[3];
for (i = 0; i < n; i++) {
*((double *)out0) = test(*(double *)in0, *(double *)in1, *(double *)in2);
in0 += in0_step;
in1 += in1_step;
in2 += in2_step;
out0 += out0_step;
}
}
PyUFuncGenericFunction test_funcs[1] = {&test_ufunc};
static char test_types[4] = {NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE};
static void *test_data[1] = {NULL};
#if PY_VERSION_HEX >= 0x03000000
static struct PyModuleDef moduledef = {
PyModuleDef_HEAD_INIT,
"wrapper_module_0",
NULL,
-1,
wrapper_module_0Methods,
NULL,
NULL,
NULL,
NULL
};
PyMODINIT_FUNC PyInit_wrapper_module_0(void)
{
PyObject *m, *d;
PyObject *ufunc0;
m = PyModule_Create(&moduledef);
if (!m) {
return NULL;
}
import_array();
import_umath();
d = PyModule_GetDict(m);
ufunc0 = PyUFunc_FromFuncAndData(test_funcs, test_data, test_types, 1, 3, 1,
PyUFunc_None, "wrapper_module_0", "Created in SymPy with Ufuncify", 0);
PyDict_SetItemString(d, "test", ufunc0);
Py_DECREF(ufunc0);
return m;
}
#else
PyMODINIT_FUNC initwrapper_module_0(void)
{
PyObject *m, *d;
PyObject *ufunc0;
m = Py_InitModule("wrapper_module_0", wrapper_module_0Methods);
if (m == NULL) {
return;
}
import_array();
import_umath();
d = PyModule_GetDict(m);
ufunc0 = PyUFunc_FromFuncAndData(test_funcs, test_data, test_types, 1, 3, 1,
PyUFunc_None, "wrapper_module_0", "Created in SymPy with Ufuncify", 0);
PyDict_SetItemString(d, "test", ufunc0);
Py_DECREF(ufunc0);
}
#endif"""
assert source == expected
def test_ufuncify_source_multioutput():
x, y, z = symbols('x,y,z')
var_symbols = (x, y, z)
expr = x + y**3 + 10*z**2
code_wrapper = UfuncifyCodeWrapper(C99CodeGen("ufuncify"))
CodeWrapper._module_counter = 0
routines = [make_routine("func{}".format(i), expr.diff(var_symbols[i]), var_symbols) for i in range(len(var_symbols))]
source = get_string(code_wrapper.dump_c, routines, funcname='multitest')
expected = """\
#include "Python.h"
#include "math.h"
#include "numpy/ndarraytypes.h"
#include "numpy/ufuncobject.h"
#include "numpy/halffloat.h"
#include "file.h"
static PyMethodDef wrapper_module_0Methods[] = {
{NULL, NULL, 0, NULL}
};
static void multitest_ufunc(char **args, npy_intp *dimensions, npy_intp* steps, void* data)
{
npy_intp i;
npy_intp n = dimensions[0];
char *in0 = args[0];
char *in1 = args[1];
char *in2 = args[2];
char *out0 = args[3];
char *out1 = args[4];
char *out2 = args[5];
npy_intp in0_step = steps[0];
npy_intp in1_step = steps[1];
npy_intp in2_step = steps[2];
npy_intp out0_step = steps[3];
npy_intp out1_step = steps[4];
npy_intp out2_step = steps[5];
for (i = 0; i < n; i++) {
*((double *)out0) = func0(*(double *)in0, *(double *)in1, *(double *)in2);
*((double *)out1) = func1(*(double *)in0, *(double *)in1, *(double *)in2);
*((double *)out2) = func2(*(double *)in0, *(double *)in1, *(double *)in2);
in0 += in0_step;
in1 += in1_step;
in2 += in2_step;
out0 += out0_step;
out1 += out1_step;
out2 += out2_step;
}
}
PyUFuncGenericFunction multitest_funcs[1] = {&multitest_ufunc};
static char multitest_types[6] = {NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE};
static void *multitest_data[1] = {NULL};
#if PY_VERSION_HEX >= 0x03000000
static struct PyModuleDef moduledef = {
PyModuleDef_HEAD_INIT,
"wrapper_module_0",
NULL,
-1,
wrapper_module_0Methods,
NULL,
NULL,
NULL,
NULL
};
PyMODINIT_FUNC PyInit_wrapper_module_0(void)
{
PyObject *m, *d;
PyObject *ufunc0;
m = PyModule_Create(&moduledef);
if (!m) {
return NULL;
}
import_array();
import_umath();
d = PyModule_GetDict(m);
ufunc0 = PyUFunc_FromFuncAndData(multitest_funcs, multitest_data, multitest_types, 1, 3, 3,
PyUFunc_None, "wrapper_module_0", "Created in SymPy with Ufuncify", 0);
PyDict_SetItemString(d, "multitest", ufunc0);
Py_DECREF(ufunc0);
return m;
}
#else
PyMODINIT_FUNC initwrapper_module_0(void)
{
PyObject *m, *d;
PyObject *ufunc0;
m = Py_InitModule("wrapper_module_0", wrapper_module_0Methods);
if (m == NULL) {
return;
}
import_array();
import_umath();
d = PyModule_GetDict(m);
ufunc0 = PyUFunc_FromFuncAndData(multitest_funcs, multitest_data, multitest_types, 1, 3, 3,
PyUFunc_None, "wrapper_module_0", "Created in SymPy with Ufuncify", 0);
PyDict_SetItemString(d, "multitest", ufunc0);
Py_DECREF(ufunc0);
}
#endif"""
assert source == expected
| 13,607 | 29.78733 | 122 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/tests/test_decorator.py
|
from sympy.utilities.decorator import threaded, xthreaded
from sympy import Eq, Matrix
from sympy.abc import x, y
from sympy.core.decorators import wraps
def test_threaded():
@threaded
def function(expr, *args):
return 2*expr + sum(args)
assert function(Matrix([[x, y], [1, x]]), 1, 2) == \
Matrix([[2*x + 3, 2*y + 3], [5, 2*x + 3]])
assert function(Eq(x, y), 1, 2) == Eq(2*x + 3, 2*y + 3)
assert function([x, y], 1, 2) == [2*x + 3, 2*y + 3]
assert function((x, y), 1, 2) == (2*x + 3, 2*y + 3)
assert function({x, y}, 1, 2) == {2*x + 3, 2*y + 3}
@threaded
def function(expr, n):
return expr**n
assert function(x + y, 2) == x**2 + y**2
assert function(x, 2) == x**2
def test_xthreaded():
@xthreaded
def function(expr, n):
return expr**n
assert function(x + y, 2) == (x + y)**2
def test_wraps():
def my_func(x):
"""My function. """
my_func.is_my_func = True
new_my_func = threaded(my_func)
new_my_func = wraps(my_func)(new_my_func)
assert new_my_func.__name__ == 'my_func'
assert new_my_func.__doc__ == 'My function. '
assert hasattr(new_my_func, 'is_my_func')
assert new_my_func.is_my_func is True
| 1,243 | 22.471698 | 59 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/utilities/mathml/__init__.py
|
"""Module with some functions for MathML, like transforming MathML
content in MathML presentation.
To use this module, you will need lxml.
"""
from sympy.utilities.pkgdata import get_resource
from sympy.utilities.decorator import doctest_depends_on
import xml.dom.minidom
def add_mathml_headers(s):
return """<math xmlns:mml="http://www.w3.org/1998/Math/MathML"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
xsi:schemaLocation="http://www.w3.org/1998/Math/MathML
http://www.w3.org/Math/XMLSchema/mathml2/mathml2.xsd">""" + s + "</math>"
@doctest_depends_on(modules=('lxml',))
def apply_xsl(mml, xsl):
"""Apply a xsl to a MathML string
@param mml: a string with MathML code
@param xsl: a string representing a path to a xsl (xml stylesheet)
file. This file name is relative to the PYTHONPATH
>>> from sympy.utilities.mathml import apply_xsl
>>> xsl = 'mathml/data/simple_mmlctop.xsl'
>>> mml = '<apply> <plus/> <ci>a</ci> <ci>b</ci> </apply>'
>>> res = apply_xsl(mml,xsl)
>>> ''.join(res.splitlines())
'<?xml version="1.0"?><mrow xmlns="http://www.w3.org/1998/Math/MathML"> <mi>a</mi> <mo> + </mo> <mi>b</mi></mrow>'
"""
from lxml import etree
s = etree.XML(get_resource(xsl).read())
transform = etree.XSLT(s)
doc = etree.XML(mml)
result = transform(doc)
s = str(result)
return s
@doctest_depends_on(modules=('lxml',))
def c2p(mml, simple=False):
"""Transforms a document in MathML content (like the one that sympy produces)
in one document in MathML presentation, more suitable for printing, and more
widely accepted
>>> from sympy.utilities.mathml import c2p
>>> mml = '<apply> <exp/> <cn>2</cn> </apply>'
>>> c2p(mml,simple=True) != c2p(mml,simple=False)
True
"""
if not mml.startswith('<math'):
mml = add_mathml_headers(mml)
if simple:
return apply_xsl(mml, 'mathml/data/simple_mmlctop.xsl')
return apply_xsl(mml, 'mathml/data/mmlctop.xsl')
| 2,030 | 31.238095 | 121 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/calculus/singularities.py
|
"""
Singularities
=============
This module implements algorithms for finding singularities for a function
and identifying types of functions.
The differential calculus methods in this module include methods to identify
the following function types in the given ``Interval``:
- Increasing
- Strictly Increasing
- Decreasing
- Strictly Decreasing
- Monotonic
"""
from sympy.core.sympify import sympify
from sympy.solvers.solveset import solveset
from sympy.simplify import simplify
from sympy import S, Symbol
def singularities(expression, symbol):
"""
Find singularities of a given function.
Currently supported functions are:
- univariate rational (real or complex) functions
Examples
========
>>> from sympy.calculus.singularities import singularities
>>> from sympy import Symbol
>>> x = Symbol('x', real=True)
>>> y = Symbol('y', real=False)
>>> singularities(x**2 + x + 1, x)
EmptySet()
>>> singularities(1/(x + 1), x)
{-1}
>>> singularities(1/(y**2 + 1), y)
{-I, I}
>>> singularities(1/(y**3 + 1), y)
{-1, 1/2 - sqrt(3)*I/2, 1/2 + sqrt(3)*I/2}
Notes
=====
This function does not find nonisolated singularities
nor does it find branch points of the expression.
References
==========
.. [1] http://en.wikipedia.org/wiki/Mathematical_singularity
"""
if not expression.is_rational_function(symbol):
raise NotImplementedError(
"Algorithms finding singularities for non-rational"
" functions are not yet implemented."
)
else:
return solveset(simplify(1 / expression), symbol)
###########################################################################
###################### DIFFERENTIAL CALCULUS METHODS ######################
###########################################################################
def monotonicity_helper(expression, predicate, interval=S.Reals, symbol=None):
"""
Helper function for functions checking function monotonicity.
It returns a boolean indicating whether the interval in which
the function's derivative satisfies given predicate is a superset
of the given interval.
"""
expression = sympify(expression)
free = expression.free_symbols
if symbol is None:
if len(free) > 1:
raise NotImplementedError(
'The function has not yet been implemented'
' for all multivariate expressions.'
)
x = symbol or (free.pop() if free else Symbol('x'))
derivative = expression.diff(x)
predicate_interval = solveset(predicate(derivative), x, S.Reals)
return interval.is_subset(predicate_interval)
def is_increasing(expression, interval=S.Reals, symbol=None):
"""
Return whether the function is increasing in the given interval.
Examples
========
>>> from sympy import is_increasing
>>> from sympy.abc import x, y
>>> from sympy import S, Interval, oo
>>> is_increasing(x**3 - 3*x**2 + 4*x, S.Reals)
True
>>> is_increasing(-x**2, Interval(-oo, 0))
True
>>> is_increasing(-x**2, Interval(0, oo))
False
>>> is_increasing(4*x**3 - 6*x**2 - 72*x + 30, Interval(-2, 3))
False
>>> is_increasing(x**2 + y, Interval(1, 2), x)
True
"""
return monotonicity_helper(expression, lambda x: x >= 0, interval, symbol)
def is_strictly_increasing(expression, interval=S.Reals, symbol=None):
"""
Return whether the function is strictly increasing in the given interval.
Examples
========
>>> from sympy import is_strictly_increasing
>>> from sympy.abc import x, y
>>> from sympy import Interval, oo
>>> is_strictly_increasing(4*x**3 - 6*x**2 - 72*x + 30, Interval.Ropen(-oo, -2))
True
>>> is_strictly_increasing(4*x**3 - 6*x**2 - 72*x + 30, Interval.Lopen(3, oo))
True
>>> is_strictly_increasing(4*x**3 - 6*x**2 - 72*x + 30, Interval.open(-2, 3))
False
>>> is_strictly_increasing(-x**2, Interval(0, oo))
False
>>> is_strictly_increasing(-x**2 + y, Interval(-oo, 0), x)
False
"""
return monotonicity_helper(expression, lambda x: x > 0, interval, symbol)
def is_decreasing(expression, interval=S.Reals, symbol=None):
"""
Return whether the function is decreasing in the given interval.
Examples
========
>>> from sympy import is_decreasing
>>> from sympy.abc import x, y
>>> from sympy import S, Interval, oo
>>> is_decreasing(1/(x**2 - 3*x), Interval.open(1.5, 3))
True
>>> is_decreasing(1/(x**2 - 3*x), Interval.Lopen(3, oo))
True
>>> is_decreasing(1/(x**2 - 3*x), Interval.Ropen(-oo, S(3)/2))
False
>>> is_decreasing(-x**2, Interval(-oo, 0))
False
>>> is_decreasing(-x**2 + y, Interval(-oo, 0), x)
False
"""
return monotonicity_helper(expression, lambda x: x <= 0, interval, symbol)
def is_strictly_decreasing(expression, interval=S.Reals, symbol=None):
"""
Return whether the function is strictly decreasing in the given interval.
Examples
========
>>> from sympy import is_strictly_decreasing
>>> from sympy.abc import x, y
>>> from sympy import S, Interval, oo
>>> is_strictly_decreasing(1/(x**2 - 3*x), Interval.Lopen(3, oo))
True
>>> is_strictly_decreasing(1/(x**2 - 3*x), Interval.Ropen(-oo, S(3)/2))
False
>>> is_strictly_decreasing(-x**2, Interval(-oo, 0))
False
>>> is_strictly_decreasing(-x**2 + y, Interval(-oo, 0), x)
False
"""
return monotonicity_helper(expression, lambda x: x < 0, interval, symbol)
def is_monotonic(expression, interval=S.Reals, symbol=None):
"""
Return whether the function is monotonic in the given interval.
Examples
========
>>> from sympy import is_monotonic
>>> from sympy.abc import x, y
>>> from sympy import S, Interval, oo
>>> is_monotonic(1/(x**2 - 3*x), Interval.open(1.5, 3))
True
>>> is_monotonic(1/(x**2 - 3*x), Interval.Lopen(3, oo))
True
>>> is_monotonic(x**3 - 3*x**2 + 4*x, S.Reals)
True
>>> is_monotonic(-x**2, S.Reals)
False
>>> is_monotonic(x**2 + y + 1, Interval(1, 2), x)
True
"""
expression = sympify(expression)
free = expression.free_symbols
if symbol is None and len(free) > 1:
raise NotImplementedError(
'is_monotonic has not yet been implemented'
' for all multivariate expressions.'
)
x = symbol or (free.pop() if free else Symbol('x'))
turning_points = solveset(expression.diff(x), x, interval)
return interval.intersection(turning_points) is S.EmptySet
| 6,668 | 28.122271 | 84 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/calculus/finite_diff.py
|
"""
Finite difference weights
=========================
This module implements an algorithm for efficient generation of finite
difference weights for ordinary differentials of functions for
derivatives from 0 (interpolation) up to arbitrary order.
The core algorithm is provided in the finite difference weight generating
function (``finite_diff_weights``), and two convenience functions are provided
for:
- estimating a derivative (or interpolate) directly from a series of points
is also provided (``apply_finite_diff``).
- differentiating by using finite difference approximations
(``differentiate_finite``).
"""
from sympy import Derivative, S
from sympy.core.compatibility import iterable, range
from sympy.core.decorators import deprecated
def finite_diff_weights(order, x_list, x0=S.One):
"""
Calculates the finite difference weights for an arbitrarily spaced
one-dimensional grid (``x_list``) for derivatives at ``x0`` of order
0, 1, ..., up to ``order`` using a recursive formula. Order of accuracy
is at least ``len(x_list) - order``, if ``x_list`` is defined correctly.
Parameters
==========
order: int
Up to what derivative order weights should be calculated.
0 corresponds to interpolation.
x_list: sequence
Sequence of (unique) values for the independent variable.
It is useful (but not necessary) to order ``x_list`` from
nearest to furthest from ``x0``; see examples below.
x0: Number or Symbol
Root or value of the independent variable for which the finite
difference weights should be generated. Default is ``S.One``.
Returns
=======
list
A list of sublists, each corresponding to coefficients for
increasing derivative order, and each containing lists of
coefficients for increasing subsets of x_list.
Examples
========
>>> from sympy import S
>>> from sympy.calculus import finite_diff_weights
>>> res = finite_diff_weights(1, [-S(1)/2, S(1)/2, S(3)/2, S(5)/2], 0)
>>> res
[[[1, 0, 0, 0],
[1/2, 1/2, 0, 0],
[3/8, 3/4, -1/8, 0],
[5/16, 15/16, -5/16, 1/16]],
[[0, 0, 0, 0],
[-1, 1, 0, 0],
[-1, 1, 0, 0],
[-23/24, 7/8, 1/8, -1/24]]]
>>> res[0][-1] # FD weights for 0th derivative, using full x_list
[5/16, 15/16, -5/16, 1/16]
>>> res[1][-1] # FD weights for 1st derivative
[-23/24, 7/8, 1/8, -1/24]
>>> res[1][-2] # FD weights for 1st derivative, using x_list[:-1]
[-1, 1, 0, 0]
>>> res[1][-1][0] # FD weight for 1st deriv. for x_list[0]
-23/24
>>> res[1][-1][1] # FD weight for 1st deriv. for x_list[1], etc.
7/8
Each sublist contains the most accurate formula at the end.
Note, that in the above example ``res[1][1]`` is the same as ``res[1][2]``.
Since res[1][2] has an order of accuracy of
``len(x_list[:3]) - order = 3 - 1 = 2``, the same is true for ``res[1][1]``!
>>> from sympy import S
>>> from sympy.calculus import finite_diff_weights
>>> res = finite_diff_weights(1, [S(0), S(1), -S(1), S(2), -S(2)], 0)[1]
>>> res
[[0, 0, 0, 0, 0],
[-1, 1, 0, 0, 0],
[0, 1/2, -1/2, 0, 0],
[-1/2, 1, -1/3, -1/6, 0],
[0, 2/3, -2/3, -1/12, 1/12]]
>>> res[0] # no approximation possible, using x_list[0] only
[0, 0, 0, 0, 0]
>>> res[1] # classic forward step approximation
[-1, 1, 0, 0, 0]
>>> res[2] # classic centered approximation
[0, 1/2, -1/2, 0, 0]
>>> res[3:] # higher order approximations
[[-1/2, 1, -1/3, -1/6, 0], [0, 2/3, -2/3, -1/12, 1/12]]
Let us compare this to a differently defined ``x_list``. Pay attention to
``foo[i][k]`` corresponding to the gridpoint defined by ``x_list[k]``.
>>> from sympy import S
>>> from sympy.calculus import finite_diff_weights
>>> foo = finite_diff_weights(1, [-S(2), -S(1), S(0), S(1), S(2)], 0)[1]
>>> foo
[[0, 0, 0, 0, 0],
[-1, 1, 0, 0, 0],
[1/2, -2, 3/2, 0, 0],
[1/6, -1, 1/2, 1/3, 0],
[1/12, -2/3, 0, 2/3, -1/12]]
>>> foo[1] # not the same and of lower accuracy as res[1]!
[-1, 1, 0, 0, 0]
>>> foo[2] # classic double backward step approximation
[1/2, -2, 3/2, 0, 0]
>>> foo[4] # the same as res[4]
[1/12, -2/3, 0, 2/3, -1/12]
Note that, unless you plan on using approximations based on subsets of
``x_list``, the order of gridpoints does not matter.
The capability to generate weights at arbitrary points can be
used e.g. to minimize Runge's phenomenon by using Chebyshev nodes:
>>> from sympy import cos, symbols, pi, simplify
>>> from sympy.calculus import finite_diff_weights
>>> N, (h, x) = 4, symbols('h x')
>>> x_list = [x+h*cos(i*pi/(N)) for i in range(N,-1,-1)] # chebyshev nodes
>>> print(x_list)
[-h + x, -sqrt(2)*h/2 + x, x, sqrt(2)*h/2 + x, h + x]
>>> mycoeffs = finite_diff_weights(1, x_list, 0)[1][4]
>>> [simplify(c) for c in mycoeffs] #doctest: +NORMALIZE_WHITESPACE
[(h**3/2 + h**2*x - 3*h*x**2 - 4*x**3)/h**4,
(-sqrt(2)*h**3 - 4*h**2*x + 3*sqrt(2)*h*x**2 + 8*x**3)/h**4,
6*x/h**2 - 8*x**3/h**4,
(sqrt(2)*h**3 - 4*h**2*x - 3*sqrt(2)*h*x**2 + 8*x**3)/h**4,
(-h**3/2 + h**2*x + 3*h*x**2 - 4*x**3)/h**4]
Notes
=====
If weights for a finite difference approximation of 3rd order
derivative is wanted, weights for 0th, 1st and 2nd order are
calculated "for free", so are formulae using subsets of ``x_list``.
This is something one can take advantage of to save computational cost.
Be aware that one should define ``x_list`` from nearest to farest from
``x0``. If not, subsets of ``x_list`` will yield poorer approximations,
which might not grand an order of accuracy of ``len(x_list) - order``.
See also
========
sympy.calculus.finite_diff.apply_finite_diff
References
==========
.. [1] Generation of Finite Difference Formulas on Arbitrarily Spaced
Grids, Bengt Fornberg; Mathematics of computation; 51; 184;
(1988); 699-706; doi:10.1090/S0025-5718-1988-0935077-0
"""
# The notation below closely corresponds to the one used in the paper.
if order < 0:
raise ValueError("Negative derivative order illegal.")
if int(order) != order:
raise ValueError("Non-integer order illegal")
M = order
N = len(x_list) - 1
delta = [[[0 for nu in range(N+1)] for n in range(N+1)] for
m in range(M+1)]
delta[0][0][0] = S(1)
c1 = S(1)
for n in range(1, N+1):
c2 = S(1)
for nu in range(0, n):
c3 = x_list[n]-x_list[nu]
c2 = c2 * c3
if n <= M:
delta[n][n-1][nu] = 0
for m in range(0, min(n, M)+1):
delta[m][n][nu] = (x_list[n]-x0)*delta[m][n-1][nu] -\
m*delta[m-1][n-1][nu]
delta[m][n][nu] /= c3
for m in range(0, min(n, M)+1):
delta[m][n][n] = c1/c2*(m*delta[m-1][n-1][n-1] -
(x_list[n-1]-x0)*delta[m][n-1][n-1])
c1 = c2
return delta
def apply_finite_diff(order, x_list, y_list, x0=S(0)):
"""
Calculates the finite difference approximation of
the derivative of requested order at ``x0`` from points
provided in ``x_list`` and ``y_list``.
Parameters
==========
order: int
order of derivative to approximate. 0 corresponds to interpolation.
x_list: sequence
Sequence of (unique) values for the independent variable.
y_list: sequence
The function value at corresponding values for the independent
variable in x_list.
x0: Number or Symbol
At what value of the independent variable the derivative should be
evaluated. Defaults to S(0).
Returns
=======
sympy.core.add.Add or sympy.core.numbers.Number
The finite difference expression approximating the requested
derivative order at ``x0``.
Examples
========
>>> from sympy.calculus import apply_finite_diff
>>> cube = lambda arg: (1.0*arg)**3
>>> xlist = range(-3,3+1)
>>> apply_finite_diff(2, xlist, map(cube, xlist), 2) - 12 # doctest: +SKIP
-3.55271367880050e-15
we see that the example above only contain rounding errors.
apply_finite_diff can also be used on more abstract objects:
>>> from sympy import IndexedBase, Idx
>>> from sympy.calculus import apply_finite_diff
>>> x, y = map(IndexedBase, 'xy')
>>> i = Idx('i')
>>> x_list, y_list = zip(*[(x[i+j], y[i+j]) for j in range(-1,2)])
>>> apply_finite_diff(1, x_list, y_list, x[i])
((x[i + 1] - x[i])/(-x[i - 1] + x[i]) - 1)*y[i]/(x[i + 1] - x[i]) - \
(x[i + 1] - x[i])*y[i - 1]/((x[i + 1] - x[i - 1])*(-x[i - 1] + x[i])) + \
(-x[i - 1] + x[i])*y[i + 1]/((x[i + 1] - x[i - 1])*(x[i + 1] - x[i]))
Notes
=====
Order = 0 corresponds to interpolation.
Only supply so many points you think makes sense
to around x0 when extracting the derivative (the function
need to be well behaved within that region). Also beware
of Runge's phenomenon.
See also
========
sympy.calculus.finite_diff.finite_diff_weights
References
==========
Fortran 90 implementation with Python interface for numerics: finitediff_
.. _finitediff: https://github.com/bjodah/finitediff
"""
# In the original paper the following holds for the notation:
# M = order
# N = len(x_list) - 1
N = len(x_list) - 1
if len(x_list) != len(y_list):
raise ValueError("x_list and y_list not equal in length.")
delta = finite_diff_weights(order, x_list, x0)
derivative = 0
for nu in range(0, len(x_list)):
derivative += delta[order][N][nu]*y_list[nu]
return derivative
def _as_finite_diff(derivative, points=1, x0=None, wrt=None):
"""
Returns an approximation of a derivative of a function in
the form of a finite difference formula. The expression is a
weighted sum of the function at a number of discrete values of
(one of) the independent variable(s).
Parameters
==========
derivative: a Derivative instance
points: sequence or coefficient, optional
If sequence: discrete values (length >= order+1) of the
independent variable used for generating the finite
difference weights.
If it is a coefficient, it will be used as the step-size
for generating an equidistant sequence of length order+1
centered around ``x0``. default: 1 (step-size 1)
x0: number or Symbol, optional
the value of the independent variable (``wrt``) at which the
derivative is to be approximated. Default: same as ``wrt``.
wrt: Symbol, optional
"with respect to" the variable for which the (partial)
derivative is to be approximated for. If not provided it
is required that the Derivative is ordinary. Default: ``None``.
Examples
========
>>> from sympy import symbols, Function, exp, sqrt, Symbol, as_finite_diff
>>> from sympy.utilities.exceptions import SymPyDeprecationWarning
>>> import warnings
>>> warnings.simplefilter("ignore", SymPyDeprecationWarning)
>>> x, h = symbols('x h')
>>> f = Function('f')
>>> as_finite_diff(f(x).diff(x))
-f(x - 1/2) + f(x + 1/2)
The default step size and number of points are 1 and ``order + 1``
respectively. We can change the step size by passing a symbol
as a parameter:
>>> as_finite_diff(f(x).diff(x), h)
-f(-h/2 + x)/h + f(h/2 + x)/h
We can also specify the discretized values to be used in a sequence:
>>> as_finite_diff(f(x).diff(x), [x, x+h, x+2*h])
-3*f(x)/(2*h) + 2*f(h + x)/h - f(2*h + x)/(2*h)
The algorithm is not restricted to use equidistant spacing, nor
do we need to make the approximation around ``x0``, but we can get
an expression estimating the derivative at an offset:
>>> e, sq2 = exp(1), sqrt(2)
>>> xl = [x-h, x+h, x+e*h]
>>> as_finite_diff(f(x).diff(x, 1), xl, x+h*sq2)
2*h*((h + sqrt(2)*h)/(2*h) - (-sqrt(2)*h + h)/(2*h))*f(E*h + x)/\
((-h + E*h)*(h + E*h)) + (-(-sqrt(2)*h + h)/(2*h) - \
(-sqrt(2)*h + E*h)/(2*h))*f(-h + x)/(h + E*h) + \
(-(h + sqrt(2)*h)/(2*h) + (-sqrt(2)*h + E*h)/(2*h))*f(h + x)/(-h + E*h)
Partial derivatives are also supported:
>>> y = Symbol('y')
>>> d2fdxdy=f(x,y).diff(x,y)
>>> as_finite_diff(d2fdxdy, wrt=x)
-Derivative(f(x - 1/2, y), y) + Derivative(f(x + 1/2, y), y)
See also
========
sympy.calculus.finite_diff.apply_finite_diff
sympy.calculus.finite_diff.finite_diff_weights
"""
if derivative.is_Derivative:
pass
elif derivative.is_Atom:
return derivative
else:
return derivative.fromiter(
[_as_finite_diff(ar, points, x0, wrt) for ar
in derivative.args], **derivative.assumptions0)
if wrt is None:
old = None
for v in derivative.variables:
if old is v:
continue
derivative = _as_finite_diff(derivative, points, x0, v)
old = v
return derivative
order = derivative.variables.count(wrt)
if x0 is None:
x0 = wrt
if not iterable(points):
# points is simply the step-size, let's make it a
# equidistant sequence centered around x0
if order % 2 == 0:
# even order => odd number of points, grid point included
points = [x0 + points*i for i
in range(-order//2, order//2 + 1)]
else:
# odd order => even number of points, half-way wrt grid point
points = [x0 + points*S(i)/2 for i
in range(-order, order + 1, 2)]
others = [wrt, 0]
for v in set(derivative.variables):
if v == wrt:
continue
others += [v, derivative.variables.count(v)]
if len(points) < order+1:
raise ValueError("Too few points for order %d" % order)
return apply_finite_diff(order, points, [
Derivative(derivative.expr.subs({wrt: x}), *others) for
x in points], x0)
as_finite_diff = deprecated(
useinstead="Derivative.as_finite_difference",
deprecated_since_version="1.1", issue=11410)(_as_finite_diff)
def differentiate_finite(expr, *symbols,
# points=1, x0=None, wrt=None, evaluate=True, #Py2:
**kwargs):
r""" Differentiate expr and replace Derivatives with finite differences.
Parameters
==========
expr : expression
\*symbols : differentiate with respect to symbols
points: sequence or coefficient, optional
see ``Derivative.as_finite_difference``
x0: number or Symbol, optional
see ``Derivative.as_finite_difference``
wrt: Symbol, optional
see ``Derivative.as_finite_difference``
evaluate : bool
kwarg passed on to ``diff``, whether or not to
evaluate the Derivative intermediately (default: ``False``).
Examples
========
>>> from sympy import cos, sin, Function, differentiate_finite
>>> from sympy.abc import x, y, h
>>> f, g = Function('f'), Function('g')
>>> differentiate_finite(f(x)*g(x), x, points=[x-h, x+h])
-f(-h + x)*g(-h + x)/(2*h) + f(h + x)*g(h + x)/(2*h)
Note that the above form preserves the product rule in discrete form.
If we want we can pass ``evaluate=True`` to get another form (which is
usually not what we want):
>>> differentiate_finite(f(x)*g(x), x, points=[x-h, x+h], evaluate=True).simplify()
-((f(-h + x) - f(h + x))*g(x) + (g(-h + x) - g(h + x))*f(x))/(2*h)
``differentiate_finite`` works on any expression:
>>> differentiate_finite(f(x) + sin(x), x, 2)
-2*f(x) + f(x - 1) + f(x + 1) - 2*sin(x) + sin(x - 1) + sin(x + 1)
>>> differentiate_finite(f(x) + sin(x), x, 2, evaluate=True)
-2*f(x) + f(x - 1) + f(x + 1) - sin(x)
>>> differentiate_finite(f(x, y), x, y)
f(x - 1/2, y - 1/2) - f(x - 1/2, y + 1/2) - f(x + 1/2, y - 1/2) + f(x + 1/2, y + 1/2)
"""
# Key-word only arguments only available in Python 3
points = kwargs.pop('points', 1)
x0 = kwargs.pop('x0', None)
wrt = kwargs.pop('wrt', None)
evaluate = kwargs.pop('evaluate', False)
if kwargs != {}:
raise ValueError("Unknown kwargs: %s" % kwargs)
Dexpr = expr.diff(*symbols, evaluate=evaluate)
return Dexpr.replace(
lambda arg: arg.is_Derivative,
lambda arg: arg.as_finite_difference(points=points, x0=x0, wrt=wrt))
| 16,659 | 34.073684 | 89 |
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|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/calculus/util.py
|
from sympy import Order, S, log, limit, lcm_list, pi, Abs
from sympy.core.basic import Basic
from sympy.core import Add, Mul, Pow
from sympy.logic.boolalg import And
from sympy.core.expr import AtomicExpr, Expr
from sympy.core.numbers import _sympifyit, oo
from sympy.core.sympify import _sympify
from sympy.sets.sets import (Interval, Intersection, FiniteSet, Union,
Complement, EmptySet)
from sympy.functions.elementary.miscellaneous import Min, Max
from sympy.utilities import filldedent
def continuous_domain(f, symbol, domain):
"""
Returns the intervals in the given domain for which the function
is continuous.
This method is limited by the ability to determine the various
singularities and discontinuities of the given function.
Examples
========
>>> from sympy import Symbol, S, tan, log, pi, sqrt
>>> from sympy.sets import Interval
>>> from sympy.calculus.util import continuous_domain
>>> x = Symbol('x')
>>> continuous_domain(1/x, x, S.Reals)
Union(Interval.open(-oo, 0), Interval.open(0, oo))
>>> continuous_domain(tan(x), x, Interval(0, pi))
Union(Interval.Ropen(0, pi/2), Interval.Lopen(pi/2, pi))
>>> continuous_domain(sqrt(x - 2), x, Interval(-5, 5))
Interval(2, 5)
>>> continuous_domain(log(2*x - 1), x, S.Reals)
Interval.open(1/2, oo)
"""
from sympy.solvers.inequalities import solve_univariate_inequality
from sympy.solvers.solveset import solveset, _has_rational_power
if domain.is_subset(S.Reals):
constrained_interval = domain
for atom in f.atoms(Pow):
predicate, denom = _has_rational_power(atom, symbol)
constraint = S.EmptySet
if predicate and denom == 2:
constraint = solve_univariate_inequality(atom.base >= 0,
symbol).as_set()
constrained_interval = Intersection(constraint,
constrained_interval)
for atom in f.atoms(log):
constraint = solve_univariate_inequality(atom.args[0] > 0,
symbol).as_set()
constrained_interval = Intersection(constraint,
constrained_interval)
domain = constrained_interval
try:
sings = S.EmptySet
if f.has(Abs):
sings = solveset(1/f, symbol, domain)
else:
for atom in f.atoms(Pow):
predicate, denom = _has_rational_power(atom, symbol)
if predicate and denom == 2:
sings = solveset(1/f, symbol, domain)
break
else:
sings = Intersection(solveset(1/f, symbol), domain)
except BaseException:
raise NotImplementedError(
"Methods for determining the continuous domains"
" of this function have not been developed.")
return domain - sings
def function_range(f, symbol, domain):
"""
Finds the range of a function in a given domain.
This method is limited by the ability to determine the singularities and
determine limits.
Examples
========
>>> from sympy import Symbol, S, exp, log, pi, sqrt, sin, tan
>>> from sympy.sets import Interval
>>> from sympy.calculus.util import function_range
>>> x = Symbol('x')
>>> function_range(sin(x), x, Interval(0, 2*pi))
Interval(-1, 1)
>>> function_range(tan(x), x, Interval(-pi/2, pi/2))
Interval(-oo, oo)
>>> function_range(1/x, x, S.Reals)
Interval(-oo, oo)
>>> function_range(exp(x), x, S.Reals)
Interval.open(0, oo)
>>> function_range(log(x), x, S.Reals)
Interval(-oo, oo)
>>> function_range(sqrt(x), x , Interval(-5, 9))
Interval(0, 3)
"""
from sympy.solvers.solveset import solveset
vals = S.EmptySet
period = periodicity(f, symbol)
if not any(period is i for i in (None, S.Zero)):
inf = domain.inf
inf_period = S.Zero if inf.is_infinite else inf
sup_period = inf_period + period
periodic_interval = Interval(inf_period, sup_period)
domain = domain.intersect(periodic_interval)
intervals = continuous_domain(f, symbol, domain)
range_int = S.EmptySet
if isinstance(intervals, Interval):
interval_iter = (intervals,)
else:
interval_iter = intervals.args
for interval in interval_iter:
critical_points = S.EmptySet
critical_values = S.EmptySet
bounds = ((interval.left_open, interval.inf, '+'),
(interval.right_open, interval.sup, '-'))
for is_open, limit_point, direction in bounds:
if is_open:
critical_values += FiniteSet(limit(f, symbol, limit_point, direction))
vals += critical_values
else:
vals += FiniteSet(f.subs(symbol, limit_point))
critical_points += solveset(f.diff(symbol), symbol, domain)
for critical_point in critical_points:
vals += FiniteSet(f.subs(symbol, critical_point))
left_open, right_open = False, False
if critical_values is not S.EmptySet:
if critical_values.inf == vals.inf:
left_open = True
if critical_values.sup == vals.sup:
right_open = True
range_int += Interval(vals.inf, vals.sup, left_open, right_open)
return range_int
def not_empty_in(finset_intersection, *syms):
""" Finds the domain of the functions in `finite_set` in which the
`finite_set` is not-empty
Parameters
==========
finset_intersection: The unevaluated intersection of FiniteSet containing
real-valued functions with Union of Sets
syms: Tuple of symbols
Symbol for which domain is to be found
Raises
======
NotImplementedError
The algorithms to find the non-emptiness of the given FiniteSet are
not yet implemented.
ValueError
The input is not valid.
RuntimeError
It is a bug, please report it to the github issue tracker
(https://github.com/sympy/sympy/issues).
Examples
========
>>> from sympy import FiniteSet, Interval, not_empty_in, oo
>>> from sympy.abc import x
>>> not_empty_in(FiniteSet(x/2).intersect(Interval(0, 1)), x)
Interval(0, 2)
>>> not_empty_in(FiniteSet(x, x**2).intersect(Interval(1, 2)), x)
Union(Interval(-sqrt(2), -1), Interval(1, 2))
>>> not_empty_in(FiniteSet(x**2/(x + 2)).intersect(Interval(1, oo)), x)
Union(Interval.Lopen(-2, -1), Interval(2, oo))
"""
# TODO: handle piecewise defined functions
# TODO: handle transcendental functions
# TODO: handle multivariate functions
if len(syms) == 0:
raise ValueError("One or more symbols must be given in syms.")
if finset_intersection.is_EmptySet:
return EmptySet()
if isinstance(finset_intersection, Union):
elm_in_sets = finset_intersection.args[0]
return Union(not_empty_in(finset_intersection.args[1], *syms),
elm_in_sets)
if isinstance(finset_intersection, FiniteSet):
finite_set = finset_intersection
_sets = S.Reals
else:
finite_set = finset_intersection.args[1]
_sets = finset_intersection.args[0]
if not isinstance(finite_set, FiniteSet):
raise ValueError('A FiniteSet must be given, not %s: %s' %
(type(finite_set), finite_set))
if len(syms) == 1:
symb = syms[0]
else:
raise NotImplementedError('more than one variables %s not handled' %
(syms,))
def elm_domain(expr, intrvl):
""" Finds the domain of an expression in any given interval """
from sympy.solvers.solveset import solveset
_start = intrvl.start
_end = intrvl.end
_singularities = solveset(expr.as_numer_denom()[1], symb,
domain=S.Reals)
if intrvl.right_open:
if _end is S.Infinity:
_domain1 = S.Reals
else:
_domain1 = solveset(expr < _end, symb, domain=S.Reals)
else:
_domain1 = solveset(expr <= _end, symb, domain=S.Reals)
if intrvl.left_open:
if _start is S.NegativeInfinity:
_domain2 = S.Reals
else:
_domain2 = solveset(expr > _start, symb, domain=S.Reals)
else:
_domain2 = solveset(expr >= _start, symb, domain=S.Reals)
# domain in the interval
expr_with_sing = Intersection(_domain1, _domain2)
expr_domain = Complement(expr_with_sing, _singularities)
return expr_domain
if isinstance(_sets, Interval):
return Union(*[elm_domain(element, _sets) for element in finite_set])
if isinstance(_sets, Union):
_domain = S.EmptySet
for intrvl in _sets.args:
_domain_element = Union(*[elm_domain(element, intrvl)
for element in finite_set])
_domain = Union(_domain, _domain_element)
return _domain
def periodicity(f, symbol, check=False):
"""
Tests the given function for periodicity in the given symbol.
Parameters
==========
f : Expr.
The concerned function.
symbol : Symbol
The variable for which the period is to be determined.
check : Boolean
The flag to verify whether the value being returned is a period or not.
Returns
=======
period
The period of the function is returned.
`None` is returned when the function is aperiodic or has a complex period.
The value of `0` is returned as the period of a constant function.
Raises
======
NotImplementedError
The value of the period computed cannot be verified.
Notes
=====
Currently, we do not support functions with a complex period.
The period of functions having complex periodic values such
as `exp`, `sinh` is evaluated to `None`.
The value returned might not be the "fundamental" period of the given
function i.e. it may not be the smallest periodic value of the function.
The verification of the period through the `check` flag is not reliable
due to internal simplification of the given expression. Hence, it is set
to `False` by default.
Examples
========
>>> from sympy import Symbol, sin, cos, tan, exp
>>> from sympy.calculus.util import periodicity
>>> x = Symbol('x')
>>> f = sin(x) + sin(2*x) + sin(3*x)
>>> periodicity(f, x)
2*pi
>>> periodicity(sin(x)*cos(x), x)
pi
>>> periodicity(exp(tan(2*x) - 1), x)
pi/2
>>> periodicity(sin(4*x)**cos(2*x), x)
pi
>>> periodicity(exp(x), x)
"""
from sympy import simplify, lcm_list
from sympy.functions.elementary.trigonometric import TrigonometricFunction
from sympy.solvers.decompogen import decompogen
orig_f = f
f = simplify(orig_f)
period = None
if not f.has(symbol):
return S.Zero
if isinstance(f, TrigonometricFunction):
try:
period = f.period(symbol)
except NotImplementedError:
pass
if f.is_Pow:
base, expo = f.args
base_has_sym = base.has(symbol)
expo_has_sym = expo.has(symbol)
if base_has_sym and not expo_has_sym:
period = periodicity(base, symbol)
elif expo_has_sym and not base_has_sym:
period = periodicity(expo, symbol)
else:
period = _periodicity(f.args, symbol)
elif f.is_Mul:
coeff, g = f.as_independent(symbol, as_Add=False)
if isinstance(g, TrigonometricFunction) or coeff is not S.One:
period = periodicity(g, symbol)
else:
period = _periodicity(g.args, symbol)
elif f.is_Add:
k, g = f.as_independent(symbol)
if k is not S.Zero:
return periodicity(g, symbol)
period = _periodicity(g.args, symbol)
elif period is None:
from sympy.solvers.decompogen import compogen
g_s = decompogen(f, symbol)
num_of_gs = len(g_s)
if num_of_gs > 1:
for index, g in enumerate(reversed(g_s)):
start_index = num_of_gs - 1 - index
g = compogen(g_s[start_index:], symbol)
if g != orig_f and g != f: # Fix for issue 12620
period = periodicity(g, symbol)
if period is not None:
break
if period is not None:
if check:
if orig_f.subs(symbol, symbol + period) == orig_f:
return period
else:
raise NotImplementedError(filldedent('''
The period of the given function cannot be verified.
Set check=False to obtain the value.'''))
return period
return None
def _periodicity(args, symbol):
"""Helper for periodicity to find the period of a list of simpler
functions. It uses the `lcim` method to find the least common period of
all the functions.
"""
periods = []
for f in args:
period = periodicity(f, symbol)
if period is None:
return None
if period is not S.Zero:
periods.append(period)
if len(periods) > 1:
return lcim(periods)
return periods[0]
def lcim(numbers):
"""Returns the least common integral multiple of a list of numbers.
The numbers can be rational or irrational or a mixture of both.
`None` is returned for incommensurable numbers.
Examples
========
>>> from sympy import S, pi
>>> from sympy.calculus.util import lcim
>>> lcim([S(1)/2, S(3)/4, S(5)/6])
15/2
>>> lcim([2*pi, 3*pi, pi, pi/2])
6*pi
>>> lcim([S(1), 2*pi])
"""
result = None
if all(num.is_irrational for num in numbers):
factorized_nums = list(map(lambda num: num.factor(), numbers))
factors_num = list(
map(lambda num: num.as_coeff_Mul(),
factorized_nums))
term = factors_num[0][1]
if all(factor == term for coeff, factor in factors_num):
common_term = term
coeffs = [coeff for coeff, factor in factors_num]
result = lcm_list(coeffs) * common_term
elif all(num.is_rational for num in numbers):
result = lcm_list(numbers)
else:
pass
return result
class AccumulationBounds(AtomicExpr):
r"""
# Note AccumulationBounds has an alias: AccumBounds
AccumulationBounds represent an interval `[a, b]`, which is always closed
at the ends. Here `a` and `b` can be any value from extended real numbers.
The intended meaning of AccummulationBounds is to give an approximate
location of the accumulation points of a real function at a limit point.
Let `a` and `b` be reals such that a <= b.
`\langle a, b\rangle = \{x \in \mathbb{R} \mid a \le x \le b\}`
`\langle -\infty, b\rangle = \{x \in \mathbb{R} \mid x \le b\} \cup \{-\infty, \infty\}`
`\langle a, \infty \rangle = \{x \in \mathbb{R} \mid a \le x\} \cup \{-\infty, \infty\}`
`\langle -\infty, \infty \rangle = \mathbb{R} \cup \{-\infty, \infty\}`
`oo` and `-oo` are added to the second and third definition respectively,
since if either `-oo` or `oo` is an argument, then the other one should
be included (though not as an end point). This is forced, since we have,
for example, `1/AccumBounds(0, 1) = AccumBounds(1, oo)`, and the limit at
`0` is not one-sided. As x tends to `0-`, then `1/x -> -oo`, so `-oo`
should be interpreted as belonging to `AccumBounds(1, oo)` though it need
not appear explicitly.
In many cases it suffices to know that the limit set is bounded.
However, in some other cases more exact information could be useful.
For example, all accumulation values of cos(x) + 1 are non-negative.
(AccumBounds(-1, 1) + 1 = AccumBounds(0, 2))
A AccumulationBounds object is defined to be real AccumulationBounds,
if its end points are finite reals.
Let `X`, `Y` be real AccumulationBounds, then their sum, difference,
product are defined to be the following sets:
`X + Y = \{ x+y \mid x \in X \cap y \in Y\}`
`X - Y = \{ x-y \mid x \in X \cap y \in Y\}`
`X * Y = \{ x*y \mid x \in X \cap y \in Y\}`
There is, however, no consensus on Interval division.
`X / Y = \{ z \mid \exists x \in X, y \in Y \mid y \neq 0, z = x/y\}`
Note: According to this definition the quotient of two AccumulationBounds
may not be a AccumulationBounds object but rather a union of
AccumulationBounds.
Note
====
The main focus in the interval arithmetic is on the simplest way to
calculate upper and lower endpoints for the range of values of a
function in one or more variables. These barriers are not necessarily
the supremum or infimum, since the precise calculation of those values
can be difficult or impossible.
Examples
========
>>> from sympy import AccumBounds, sin, exp, log, pi, E, S, oo
>>> from sympy.abc import x
>>> AccumBounds(0, 1) + AccumBounds(1, 2)
<1, 3>
>>> AccumBounds(0, 1) - AccumBounds(0, 2)
<-2, 1>
>>> AccumBounds(-2, 3)*AccumBounds(-1, 1)
<-3, 3>
>>> AccumBounds(1, 2)*AccumBounds(3, 5)
<3, 10>
The exponentiation of AccumulationBounds is defined
as follows:
If 0 does not belong to `X` or `n > 0` then
`X^n = \{ x^n \mid x \in X\}`
otherwise
`X^n = \{ x^n \mid x \neq 0, x \in X\} \cup \{-\infty, \infty\}`
Here for fractional `n`, the part of `X` resulting in a complex
AccumulationBounds object is neglected.
>>> AccumBounds(-1, 4)**(S(1)/2)
<0, 2>
>>> AccumBounds(1, 2)**2
<1, 4>
>>> AccumBounds(-1, oo)**(-1)
<-oo, oo>
Note: `<a, b>^2` is not same as `<a, b>*<a, b>`
>>> AccumBounds(-1, 1)**2
<0, 1>
>>> AccumBounds(1, 3) < 4
True
>>> AccumBounds(1, 3) < -1
False
Some elementary functions can also take AccumulationBounds as input.
A function `f` evaluated for some real AccumulationBounds `<a, b>`
is defined as `f(\langle a, b\rangle) = \{ f(x) \mid a \le x \le b \}`
>>> sin(AccumBounds(pi/6, pi/3))
<1/2, sqrt(3)/2>
>>> exp(AccumBounds(0, 1))
<1, E>
>>> log(AccumBounds(1, E))
<0, 1>
Some symbol in an expression can be substituted for a AccumulationBounds
object. But it doesn't necessarily evaluate the AccumulationBounds for
that expression.
Same expression can be evaluated to different values depending upon
the form it is used for substituion. For example:
>>> (x**2 + 2*x + 1).subs(x, AccumBounds(-1, 1))
<-1, 4>
>>> ((x + 1)**2).subs(x, AccumBounds(-1, 1))
<0, 4>
References
==========
.. [1] https://en.wikipedia.org/wiki/Interval_arithmetic
.. [2] http://fab.cba.mit.edu/classes/S62.12/docs/Hickey_interval.pdf
Notes
=====
Do not use ``AccumulationBounds`` for floating point interval arithmetic
calculations, use ``mpmath.iv`` instead.
"""
is_real = True
def __new__(cls, min, max):
min = _sympify(min)
max = _sympify(max)
inftys = [S.Infinity, S.NegativeInfinity]
# Only allow real intervals (use symbols with 'is_real=True').
if not (min.is_real or min in inftys) \
or not (max.is_real or max in inftys):
raise ValueError("Only real AccumulationBounds are supported")
# Make sure that the created AccumBounds object will be valid.
if max.is_comparable and min.is_comparable:
if max < min:
raise ValueError(
"Lower limit should be smaller than upper limit")
if max == min:
return max
return Basic.__new__(cls, min, max)
# setting the operation priority
_op_priority = 11.0
@property
def min(self):
"""
Returns the minimum possible value attained by AccumulationBounds
object.
Examples
========
>>> from sympy import AccumBounds
>>> AccumBounds(1, 3).min
1
"""
return self.args[0]
@property
def max(self):
"""
Returns the maximum possible value attained by AccumulationBounds
object.
Examples
========
>>> from sympy import AccumBounds
>>> AccumBounds(1, 3).max
3
"""
return self.args[1]
@property
def delta(self):
"""
Returns the difference of maximum possible value attained by
AccumulationBounds object and minimum possible value attained
by AccumulationBounds object.
Examples
========
>>> from sympy import AccumBounds
>>> AccumBounds(1, 3).delta
2
"""
return self.max - self.min
@property
def mid(self):
"""
Returns the mean of maximum possible value attained by
AccumulationBounds object and minimum possible value
attained by AccumulationBounds object.
Examples
========
>>> from sympy import AccumBounds
>>> AccumBounds(1, 3).mid
2
"""
return (self.min + self.max) / 2
@_sympifyit('other', NotImplemented)
def _eval_power(self, other):
return self.__pow__(other)
@_sympifyit('other', NotImplemented)
def __add__(self, other):
if isinstance(other, Expr):
if isinstance(other, AccumBounds):
return AccumBounds(
Add(self.min, other.min),
Add(self.max, other.max))
if other is S.Infinity and self.min is S.NegativeInfinity or \
other is S.NegativeInfinity and self.max is S.Infinity:
return AccumBounds(-oo, oo)
elif other.is_real:
return AccumBounds(Add(self.min, other), Add(self.max, other))
return Add(self, other, evaluate=False)
return NotImplemented
__radd__ = __add__
def __neg__(self):
return AccumBounds(-self.max, -self.min)
@_sympifyit('other', NotImplemented)
def __sub__(self, other):
if isinstance(other, Expr):
if isinstance(other, AccumBounds):
return AccumBounds(
Add(self.min, -other.max),
Add(self.max, -other.min))
if other is S.NegativeInfinity and self.min is S.NegativeInfinity or \
other is S.Infinity and self.max is S.Infinity:
return AccumBounds(-oo, oo)
elif other.is_real:
return AccumBounds(
Add(self.min, -other),
Add(self.max, -other))
return Add(self, -other, evaluate=False)
return NotImplemented
@_sympifyit('other', NotImplemented)
def __rsub__(self, other):
return self.__neg__() + other
@_sympifyit('other', NotImplemented)
def __mul__(self, other):
if isinstance(other, Expr):
if isinstance(other, AccumBounds):
return AccumBounds(Min(Mul(self.min, other.min),
Mul(self.min, other.max),
Mul(self.max, other.min),
Mul(self.max, other.max)),
Max(Mul(self.min, other.min),
Mul(self.min, other.max),
Mul(self.max, other.min),
Mul(self.max, other.max)))
if other is S.Infinity:
if self.min.is_zero:
return AccumBounds(0, oo)
if self.max.is_zero:
return AccumBounds(-oo, 0)
if other is S.NegativeInfinity:
if self.min.is_zero:
return AccumBounds(-oo, 0)
if self.max.is_zero:
return AccumBounds(0, oo)
if other.is_real:
if other.is_zero:
if self == AccumBounds(-oo, oo):
return AccumBounds(-oo, oo)
if self.max is S.Infinity:
return AccumBounds(0, oo)
if self.min is S.NegativeInfinity:
return AccumBounds(-oo, 0)
return S.Zero
if other.is_positive:
return AccumBounds(
Mul(self.min, other),
Mul(self.max, other))
elif other.is_negative:
return AccumBounds(
Mul(self.max, other),
Mul(self.min, other))
if isinstance(other, Order):
return other
return Mul(self, other, evaluate=False)
return NotImplemented
__rmul__ = __mul__
@_sympifyit('other', NotImplemented)
def __div__(self, other):
if isinstance(other, Expr):
if isinstance(other, AccumBounds):
if S.Zero not in other:
return self * AccumBounds(1/other.max, 1/other.min)
if S.Zero in self and S.Zero in other:
if self.min.is_zero and other.min.is_zero:
return AccumBounds(0, oo)
if self.max.is_zero and other.min.is_zero:
return AccumBounds(-oo, 0)
return AccumBounds(-oo, oo)
if self.max.is_negative:
if other.min.is_negative:
if other.max.is_zero:
return AccumBounds(self.max / other.min, oo)
if other.max.is_positive:
# the actual answer is a Union of AccumBounds,
# Union(AccumBounds(-oo, self.max/other.max),
# AccumBounds(self.max/other.min, oo))
return AccumBounds(-oo, oo)
if other.min.is_zero and other.max.is_positive:
return AccumBounds(-oo, self.max / other.max)
if self.min.is_positive:
if other.min.is_negative:
if other.max.is_zero:
return AccumBounds(-oo, self.min / other.min)
if other.max.is_positive:
# the actual answer is a Union of AccumBounds,
# Union(AccumBounds(-oo, self.min/other.min),
# AccumBounds(self.min/other.max, oo))
return AccumBounds(-oo, oo)
if other.min.is_zero and other.max.is_positive:
return AccumBounds(self.min / other.max, oo)
elif other.is_real:
if other is S.Infinity or other is S.NegativeInfinity:
if self == AccumBounds(-oo, oo):
return AccumBounds(-oo, oo)
if self.max is S.Infinity:
return AccumBounds(Min(0, other), Max(0, other))
if self.min is S.NegativeInfinity:
return AccumBounds(Min(0, -other), Max(0, -other))
if other.is_positive:
return AccumBounds(self.min / other, self.max / other)
elif other.is_negative:
return AccumBounds(self.max / other, self.min / other)
return Mul(self, 1 / other, evaluate=False)
return NotImplemented
__truediv__ = __div__
@_sympifyit('other', NotImplemented)
def __rdiv__(self, other):
if isinstance(other, Expr):
if other.is_real:
if other.is_zero:
return S.Zero
if S.Zero in self:
if self.min == S.Zero:
if other.is_positive:
return AccumBounds(Mul(other, 1 / self.max), oo)
if other.is_negative:
return AccumBounds(-oo, Mul(other, 1 / self.max))
if self.max == S.Zero:
if other.is_positive:
return AccumBounds(-oo, Mul(other, 1 / self.min))
if other.is_negative:
return AccumBounds(Mul(other, 1 / self.min), oo)
return AccumBounds(-oo, oo)
else:
return AccumBounds(Min(other / self.min, other / self.max),
Max(other / self.min, other / self.max))
return Mul(other, 1 / self, evaluate=False)
else:
return NotImplemented
__rtruediv__ = __rdiv__
@_sympifyit('other', NotImplemented)
def __pow__(self, other):
from sympy.functions.elementary.miscellaneous import real_root
if isinstance(other, Expr):
if other is S.Infinity:
if self.min.is_nonnegative:
if self.max < 1:
return S.Zero
if self.min > 1:
return S.Infinity
return AccumBounds(0, oo)
elif self.max.is_negative:
if self.min > -1:
return S.Zero
if self.max < -1:
return FiniteSet(-oo, oo)
return AccumBounds(-oo, oo)
else:
if self.min > -1:
if self.max < 1:
return S.Zero
return AccumBounds(0, oo)
return AccumBounds(-oo, oo)
if other is S.NegativeInfinity:
return (1 / self)**oo
if other.is_real and other.is_number:
if other.is_zero:
return S.One
if other.is_Integer:
if self.min.is_positive:
return AccumBounds(
Min(self.min ** other, self.max ** other),
Max(self.min ** other, self.max ** other))
elif self.max.is_negative:
return AccumBounds(
Min(self.max ** other, self.min ** other),
Max(self.max ** other, self.min ** other))
if other % 2 == 0:
if other.is_negative:
if self.min.is_zero:
return AccumBounds(self.max**other, oo)
if self.max.is_zero:
return AccumBounds(self.min**other, oo)
return AccumBounds(0, oo)
return AccumBounds(
S.Zero, Max(self.min**other, self.max**other))
else:
if other.is_negative:
if self.min.is_zero:
return AccumBounds(self.max**other, oo)
if self.max.is_zero:
return AccumBounds(-oo, self.min**other)
return AccumBounds(-oo, oo)
return AccumBounds(self.min**other, self.max**other)
num, den = other.as_numer_denom()
if num == S(1):
if den % 2 == 0:
if S.Zero in self:
if self.min.is_negative:
return AccumBounds(0, real_root(self.max, den))
return AccumBounds(real_root(self.min, den),
real_root(self.max, den))
num_pow = self**num
return num_pow**(1 / den)
return Pow(self, other, evaluate=False)
return NotImplemented
def __abs__(self):
if self.max.is_negative:
return self.__neg__()
elif self.min.is_negative:
return AccumBounds(S.Zero, Max(abs(self.min), self.max))
else:
return self
def __lt__(self, other):
"""
Returns True if range of values attained by `self` AccumulationBounds
object is less than the range of values attained by `other`, where
other may be any value of type AccumulationBounds object or extended
real number value, False is returned if `other` satisfies the same
property,None if the values attained by AccumulationBounds object
intersect.
Examples
========
>>> from sympy import AccumBounds, oo
>>> AccumBounds(1, 3) < AccumBounds(4, oo)
True
>>> AccumBounds(1, 4) < AccumBounds(3, 4)
>>> AccumBounds(1, oo) < -1
False
"""
other = _sympify(other)
if isinstance(other, AccumBounds):
if self.max < other.min:
return True
if self.min >= other.max:
return False
return None
if not(other.is_real or other is S.Infinity or
other is S.NegativeInfinity):
raise TypeError(
"Invalid comparison of %s %s" %
(type(other), other))
if other.is_comparable:
if self.max < other:
return True
if self.min >= other:
return False
return None
def __le__(self, other):
"""
Returns True if range of values attained by `self` AccumulationBounds
object is less than or equal to the range of values attained by
`other`, where other may be any value of type AccumulationBounds
object or extended real number value, AccumulationBounds object,
False is returned if `other` satisfies the same property, None if
the values attained by AccumulationBounds object intersect.
Examples
========
>>> from sympy import AccumBounds, oo
>>> AccumBounds(1, 3) <= AccumBounds(4, oo)
True
>>> AccumBounds(1, 4) <= AccumBounds(3, 4)
>>> AccumBounds(1, 3) <= 3
True
"""
other = _sympify(other)
if isinstance(other, AccumBounds):
if self.max <= other.min:
return True
if self.min > other.max:
return False
return None
if not(other.is_real or other is S.Infinity or
other is S.NegativeInfinity):
raise TypeError(
"Invalid comparison of %s %s" %
(type(other), other))
if other.is_comparable:
if self.max <= other:
return True
if self.min > other:
return False
return None
def __gt__(self, other):
"""
Returns True if range of values attained by `self` AccumulationBounds
object is greater than the range of values attained by `other`,
where other may be any value of type AccumulationBounds object or
extended real number value, False is returned if `other` satisfies
the same property, None if the values attained by AccumulationBounds
object intersect.
Examples
========
>>> from sympy import AccumBounds, oo
>>> AccumBounds(1, 3) > AccumBounds(4, oo)
False
>>> AccumBounds(1, 4) > AccumBounds(3, 4)
>>> AccumBounds(1, oo) > -1
True
"""
other = _sympify(other)
if isinstance(other, AccumBounds):
if self.min > other.max:
return True
if self.max <= other.min:
return False
return
if not(other.is_real or other is S.Infinity or
other is S.NegativeInfinity):
raise TypeError(
"Invalid comparison of %s %s" %
(type(other), other))
if other.is_comparable:
if self.min > other:
return True
if self.max <= other:
return False
return None
def __ge__(self, other):
"""
Returns True if range of values attained by `self` AccumulationBounds
object is less that the range of values attained by `other`, where
other may be any value of type AccumulationBounds object or extended
real number value, False is returned if `other` satisfies the same
property, None if the values attained by AccumulationBounds object
intersect.
Examples
========
>>> from sympy import AccumBounds, oo
>>> AccumBounds(1, 3) >= AccumBounds(4, oo)
False
>>> AccumBounds(1, 4) >= AccumBounds(3, 4)
>>> AccumBounds(1, oo) >= 1
True
"""
other = _sympify(other)
if isinstance(other, AccumBounds):
if self.min >= other.max:
return True
if self.max < other.min:
return False
return None
if not(other.is_real or other is S.Infinity or
other is S.NegativeInfinity):
raise TypeError(
"Invalid comparison of %s %s" %
(type(other), other))
if other.is_comparable:
if self.min >= other:
return True
if self.max < other:
return False
return None
def __contains__(self, other):
"""
Returns True if other is contained in self, where other
belongs to extended real numbers, False if not contained,
otherwise TypeError is raised.
Examples
========
>>> from sympy import AccumBounds, oo
>>> 1 in AccumBounds(-1, 3)
True
-oo and oo go together as limits (in AccumulationBounds).
>>> -oo in AccumBounds(1, oo)
True
>>> oo in AccumBounds(-oo, 0)
True
"""
other = _sympify(other)
if not (other.is_Symbol or other.is_number):
raise TypeError("Input of type real symbol or Number expected")
if other is S.Infinity or other is S.NegativeInfinity:
if self.min is S.NegativeInfinity or self.max is S.Infinity:
return True
return False
return And(self.min <= other and self.max >= other)
def intersection(self, other):
"""
Returns the intersection of 'self' and 'other'.
Here other can be an instance of FiniteSet or AccumulationBounds.
Examples
========
>>> from sympy import AccumBounds, FiniteSet
>>> AccumBounds(1, 3).intersection(AccumBounds(2, 4))
<2, 3>
>>> AccumBounds(1, 3).intersection(AccumBounds(4, 6))
EmptySet()
>>> AccumBounds(1, 4).intersection(FiniteSet(1, 2, 5))
{1, 2}
"""
if not isinstance(other, (AccumBounds, FiniteSet)):
raise TypeError(
"Input must be AccumulationBounds or FiniteSet object")
if isinstance(other, FiniteSet):
fin_set = S.EmptySet
for i in other:
if i in self:
fin_set = fin_set + FiniteSet(i)
return fin_set
if self.max < other.min or self.min > other.max:
return S.EmptySet
if self.min <= other.min:
if self.max <= other.max:
return AccumBounds(other.min, self.max)
if self.max > other.max:
return other
if other.min <= self.min:
if other.max < self.max:
return AccumBounds(self.min, other.max)
if other.max > self.max:
return self
def union(self, other):
# TODO : Devise a better method for Union of AccumBounds
# this method is not actually correct and
# can be made better
if not isinstance(other, AccumBounds):
raise TypeError(
"Input must be AccumulationBounds or FiniteSet object")
if self.min <= other.min and self.max >= other.min:
return AccumBounds(self.min, Max(self.max, other.max))
if other.min <= self.min and other.max >= self.min:
return AccumBounds(other.min, Max(self.max, other.max))
# setting an alias for AccumulationBounds
AccumBounds = AccumulationBounds
| 41,010 | 32.39658 | 92 |
py
|
cba-pipeline-public
|
cba-pipeline-public-master/containernet/ndn-containers/ndn_headless-player/bandits/venv/lib/python3.6/site-packages/sympy/calculus/__init__.py
|
"""Calculus-related methods."""
from .euler import euler_equations
from .singularities import (singularities, is_increasing,
is_strictly_increasing, is_decreasing,
is_strictly_decreasing, is_monotonic)
from .finite_diff import finite_diff_weights, apply_finite_diff, as_finite_diff, differentiate_finite
from .util import periodicity, not_empty_in, AccumBounds
__all__ = [
'euler_equations',
'singularities', 'is_increasing',
'is_strictly_increasing', 'is_decreasing',
'is_strictly_decreasing', 'is_monotonic',
'finite_diff_weights', 'apply_finite_diff', 'as_finite_diff', 'differentiate_finite',
'periodicity', 'not_empty_in', 'AccumBounds',
]
| 706 | 32.666667 | 101 |
py
|
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