def remove_ids(mul):
""" Remove Identities from a MatMul
This is a modified version of diofant.core.strategies.rm_id.
This is necesssary because MatMul may contain both MatrixExprs and Exprs
as args.
See Also
--------
diofant.core.strategies.rm_id
"""
# Separate Exprs from MatrixExprs in args
factor, mmul = mul.as_coeff_mmul()
# Apply standard rm_id for MatMuls
result = rm_id(lambda x: x.is_Identity is True)(mmul)
if result != mmul:
return newmul(factor, *result.args) # Recombine and return
else:
return mul
def test_rm_id():
rmzeros = rm_id(lambda x: x == 0)
assert rmzeros(Basic(0, 1)) == Basic(1)
assert rmzeros(Basic(0, 0)) == Basic(0)
assert rmzeros(Basic(2, 1)) == Basic(2, 1)
""" Merge explicit MatrixBase arguments
>>> from diofant import MatrixSymbol, eye, Matrix, MatAdd, pprint
>>> from diofant.matrices.expressions.matadd import merge_explicit
>>> A = MatrixSymbol('A', 2, 2)
>>> B = eye(2)
>>> C = Matrix([[1, 2], [3, 4]])
>>> X = MatAdd(A, B, C)
>>> pprint(X, use_unicode=False)
A + [1 0] + [1 2]
[ ] [ ]
[0 1] [3 4]
>>> pprint(merge_explicit(X), use_unicode=False)
A + [2 2]
[ ]
[3 5]
"""
groups = sift(matadd.args, lambda arg: isinstance(arg, MatrixBase))
if len(groups[True]) > 1:
return MatAdd(*(groups[False] + [reduce(add, groups[True])]))
else:
return matadd
rules = (rm_id(lambda x: x == 0 or isinstance(x, ZeroMatrix)), unpack, flatten,
glom(matrix_of, factor_of,
combine), merge_explicit, sort(default_sort_key))
canonicalize = exhaust(
condition(lambda x: isinstance(x, MatAdd), do_one(rules)))
def test_rm_id():
rmzeros = rm_id(lambda x: x == 0)
assert rmzeros(Basic(0, 1)) == Basic(1)
assert rmzeros(Basic(0, 0)) == Basic(0)
assert rmzeros(Basic(2, 1)) == Basic(2, 1)
# Apply standard rm_id for MatMuls
result = rm_id(lambda x: x.is_Identity is True)(mmul)
if result != mmul:
return newmul(factor, *result.args) # Recombine and return
else:
return mul
def factor_in_front(mul):
factor, matrices = mul.as_coeff_matrices()
if factor != 1:
return newmul(factor, *matrices)
return mul
rules = (any_zeros, remove_ids, xxinv, unpack, rm_id(lambda x: x == 1),
merge_explicit, factor_in_front, flatten)
canonicalize = exhaust(typed({MatMul: do_one(rules)}))
def only_squares(*matrices):
""" factor matrices only if they are square """
if matrices[0].rows != matrices[-1].cols:
raise RuntimeError("Invalid matrices being multiplied")
out = []
start = 0
for i, M in enumerate(matrices):
if M.cols == matrices[start].rows:
out.append(MatMul(*matrices[start:i + 1]).doit())
start = i + 1