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from __future__ import print_function, division
from sympy.core import Mul, sympify
from sympy.strategies import unpack, flatten, condition, exhaust, do_one
from sympy.matrices.expressions.matexpr import MatrixExpr, ShapeError
def hadamard_product(*matrices):
"""
Return the elementwise (aka Hadamard) product of matrices.
Examples
========
>>> from sympy.matrices import hadamard_product, MatrixSymbol
>>> A = MatrixSymbol('A', 2, 3)
>>> B = MatrixSymbol('B', 2, 3)
>>> hadamard_product(A)
A
>>> hadamard_product(A, B)
A.*B
>>> hadamard_product(A, B)[0, 1]
A[0, 1]*B[0, 1]
"""
if not matrices:
raise TypeError("Empty Hadamard product is undefined")
validate(*matrices)
if len(matrices) == 1:
return matrices[0]
else:
return HadamardProduct(*matrices).doit()
class HadamardProduct(MatrixExpr):
"""
Elementwise product of matrix expressions
This is a symbolic object that simply stores its argument without
evaluating it. To actually compute the product, use the function
``hadamard_product()``.
>>> from sympy.matrices import hadamard_product, HadamardProduct, MatrixSymbol
>>> A = MatrixSymbol('A', 5, 5)
>>> B = MatrixSymbol('B', 5, 5)
>>> isinstance(hadamard_product(A, B), HadamardProduct)
True
"""
is_HadamardProduct = True
def __new__(cls, *args, **kwargs):
args = list(map(sympify, args))
check = kwargs.get('check' , True)
if check:
validate(*args)
return super(HadamardProduct, cls).__new__(cls, *args)
@property
def shape(self):
return self.args[0].shape
def _entry(self, i, j):
return Mul(*[arg._entry(i, j) for arg in self.args])
def _eval_transpose(self):
from sympy.matrices.expressions.transpose import transpose
return HadamardProduct(*list(map(transpose, self.args)))
def doit(self, **ignored):
return canonicalize(self)
def validate(*args):
if not all(arg.is_Matrix for arg in args):
raise TypeError("Mix of Matrix and Scalar symbols")
A = args[0]
for B in args[1:]:
if A.shape != B.shape:
raise ShapeError("Matrices %s and %s are not aligned" % (A, B))
rules = (unpack,
flatten)
canonicalize = exhaust(condition(lambda x: isinstance(x, HadamardProduct),
do_one(*rules)))
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