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import pytest
import numpy as np
from numpy.testing import assert_allclose, assert_equal
import scipy.special as sc
class TestHyperu:
def test_negative_x(self):
a, b, x = np.meshgrid(
[-1, -0.5, 0, 0.5, 1],
[-1, -0.5, 0, 0.5, 1],
np.linspace(-100, -1, 10),
)
assert np.all(np.isnan(sc.hyperu(a, b, x)))
def test_special_cases(self):
assert sc.hyperu(0, 1, 1) == 1.0
@pytest.mark.parametrize('a', [0.5, 1, np.nan])
@pytest.mark.parametrize('b', [1, 2, np.nan])
@pytest.mark.parametrize('x', [0.25, 3, np.nan])
def test_nan_inputs(self, a, b, x):
assert np.isnan(sc.hyperu(a, b, x)) == np.any(np.isnan([a, b, x]))
class TestHyp1f1:
@pytest.mark.parametrize('a, b, x', [
(np.nan, 1, 1),
(1, np.nan, 1),
(1, 1, np.nan)
])
def test_nan_inputs(self, a, b, x):
assert np.isnan(sc.hyp1f1(a, b, x))
def test_poles(self):
assert_equal(sc.hyp1f1(1, [0, -1, -2, -3, -4], 0.5), np.inf)
@pytest.mark.parametrize('a, b, x, result', [
(-1, 1, 0.5, 0.5),
(1, 1, 0.5, 1.6487212707001281468),
(2, 1, 0.5, 2.4730819060501922203),
(1, 2, 0.5, 1.2974425414002562937),
(-10, 1, 0.5, -0.38937441413785204475)
])
def test_special_cases(self, a, b, x, result):
# Hit all the special case branches at the beginning of the
# function. Desired answers computed using Mpmath.
assert_allclose(sc.hyp1f1(a, b, x), result, atol=0, rtol=1e-15)
@pytest.mark.parametrize('a, b, x, result', [
(1, 1, 0.44, 1.5527072185113360455),
(-1, 1, 0.44, 0.55999999999999999778),
(100, 100, 0.89, 2.4351296512898745592),
(-100, 100, 0.89, 0.40739062490768104667),
(1.5, 100, 59.99, 3.8073513625965598107),
(-1.5, 100, 59.99, 0.25099240047125826943)
])
def test_geometric_convergence(self, a, b, x, result):
# Test the region where we are relying on the ratio of
#
# (|a| + 1) * |x| / |b|
#
# being small. Desired answers computed using Mpmath
assert_allclose(sc.hyp1f1(a, b, x), result, atol=0, rtol=1e-15)
@pytest.mark.parametrize('a, b, x, result', [
(-1, 1, 1.5, -0.5),
(-10, 1, 1.5, 0.41801777430943080357),
(-25, 1, 1.5, 0.25114491646037839809),
(-50, 1, 1.5, -0.25683643975194756115),
(-80, 1, 1.5, -0.24554329325751503601),
(-150, 1, 1.5, -0.173364795515420454496),
])
def test_a_negative_integer(self, a, b, x, result):
# Desired answers computed using Mpmath.
assert_allclose(sc.hyp1f1(a, b, x), result, atol=0, rtol=2e-14)
@pytest.mark.parametrize('a, b, x, expected', [
(0.01, 150, -4, 0.99973683897677527773), # gh-3492
(1, 5, 0.01, 1.0020033381011970966), # gh-3593
(50, 100, 0.01, 1.0050126452421463411), # gh-3593
(1, 0.3, -1e3, -7.011932249442947651455e-04), # gh-14149
(1, 0.3, -1e4, -7.001190321418937164734e-05), # gh-14149
(9, 8.5, -350, -5.224090831922378361082e-20), # gh-17120
(9, 8.5, -355, -4.595407159813368193322e-20), # gh-17120
(75, -123.5, 15, 3.425753920814889017493e+06),
])
def test_assorted_cases(self, a, b, x, expected):
# Expected values were computed with mpmath.hyp1f1(a, b, x).
assert_allclose(sc.hyp1f1(a, b, x), expected, atol=0, rtol=1e-14)
def test_a_neg_int_and_b_equal_x(self):
# This is a case where the Boost wrapper will call hypergeometric_pFq
# instead of hypergeometric_1F1. When we use a version of Boost in
# which https://github.com/boostorg/math/issues/833 is fixed, this
# test case can probably be moved into test_assorted_cases.
# The expected value was computed with mpmath.hyp1f1(a, b, x).
a = -10.0
b = 2.5
x = 2.5
expected = 0.0365323664364104338721
computed = sc.hyp1f1(a, b, x)
assert_allclose(computed, expected, atol=0, rtol=1e-13)
@pytest.mark.parametrize('a, b, x, desired', [
(-1, -2, 2, 2),
(-1, -4, 10, 3.5),
(-2, -2, 1, 2.5)
])
def test_gh_11099(self, a, b, x, desired):
# All desired results computed using Mpmath
assert sc.hyp1f1(a, b, x) == desired
@pytest.mark.parametrize('a', [-3, -2])
def test_x_zero_a_and_b_neg_ints_and_a_ge_b(self, a):
assert sc.hyp1f1(a, -3, 0) == 1
# The "legacy edge cases" mentioned in the comments in the following
# tests refers to the behavior of hyp1f1(a, b, x) when b is a nonpositive
# integer. In some subcases, the behavior of SciPy does not match that
# of Boost (1.81+), mpmath and Mathematica (via Wolfram Alpha online).
# If the handling of these edges cases is changed to agree with those
# libraries, these test will have to be updated.
@pytest.mark.parametrize('b', [0, -1, -5])
def test_legacy_case1(self, b):
# Test results of hyp1f1(0, n, x) for n <= 0.
# This is a legacy edge case.
# Boost (versions greater than 1.80), Mathematica (via Wolfram Alpha
# online) and mpmath all return 1 in this case, but SciPy's hyp1f1
# returns inf.
assert_equal(sc.hyp1f1(0, b, [-1.5, 0, 1.5]), [np.inf, np.inf, np.inf])
def test_legacy_case2(self):
# This is a legacy edge case.
# In software such as boost (1.81+), mpmath and Mathematica,
# the value is 1.
assert sc.hyp1f1(-4, -3, 0) == np.inf
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