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from sympy.core.assumptions import check_assumptions |
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from sympy.core.logic import fuzzy_and |
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from sympy.core.sympify import _sympify |
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from sympy.matrices.common import MatrixKind |
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from sympy.sets.sets import Set, SetKind |
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from sympy.core.kind import NumberKind |
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from .matexpr import MatrixExpr |
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class MatrixSet(Set): |
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""" |
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MatrixSet represents the set of matrices with ``shape = (n, m)`` over the |
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given set. |
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Examples |
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======== |
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>>> from sympy.matrices import MatrixSet |
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>>> from sympy import S, I, Matrix |
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>>> M = MatrixSet(2, 2, set=S.Reals) |
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>>> X = Matrix([[1, 2], [3, 4]]) |
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>>> X in M |
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True |
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>>> X = Matrix([[1, 2], [I, 4]]) |
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>>> X in M |
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False |
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""" |
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is_empty = False |
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def __new__(cls, n, m, set): |
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n, m, set = _sympify(n), _sympify(m), _sympify(set) |
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cls._check_dim(n) |
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cls._check_dim(m) |
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if not isinstance(set, Set): |
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raise TypeError("{} should be an instance of Set.".format(set)) |
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return Set.__new__(cls, n, m, set) |
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@property |
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def shape(self): |
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return self.args[:2] |
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@property |
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def set(self): |
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return self.args[2] |
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def _contains(self, other): |
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if not isinstance(other, MatrixExpr): |
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raise TypeError("{} should be an instance of MatrixExpr.".format(other)) |
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if other.shape != self.shape: |
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are_symbolic = any(_sympify(x).is_Symbol for x in other.shape + self.shape) |
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if are_symbolic: |
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return None |
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return False |
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return fuzzy_and(self.set.contains(x) for x in other) |
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@classmethod |
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def _check_dim(cls, dim): |
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"""Helper function to check invalid matrix dimensions""" |
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ok = check_assumptions(dim, integer=True, nonnegative=True) |
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if ok is False: |
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raise ValueError( |
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"The dimension specification {} should be " |
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"a nonnegative integer.".format(dim)) |
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def _kind(self): |
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return SetKind(MatrixKind(NumberKind)) |
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