def combine_powers(mul):
"""Combine consecutive powers with the same base into one
e.g. A*A**2 -> A**3
This also cancels out the possible matrix inverses using the
knowledgebase of ``Inverse``.
e.g. Y * X * X.I -> Y
"""
factor, args = mul.as_coeff_matrices()
new_args = [args[0]]
for B in args[1:]:
A = new_args[-1]
if A.is_square == False or B.is_square == False:
new_args.append(B)
continue
if isinstance(A, MatPow):
A_base, A_exp = A.args
else:
A_base, A_exp = A, S.One
if isinstance(B, MatPow):
B_base, B_exp = B.args
else:
B_base, B_exp = B, S.One
if A_base == B_base:
new_exp = A_exp + B_exp
new_args[-1] = MatPow(A_base, new_exp).doit(deep=False)
continue
elif not isinstance(B_base, MatrixBase):
try:
B_base_inv = B_base.inverse()
except NonInvertibleMatrixError:
B_base_inv = None
if B_base_inv is not None and A_base == B_base_inv:
new_exp = A_exp - B_exp
new_args[-1] = MatPow(A_base, new_exp).doit(deep=False)
continue
new_args.append(B)
return newmul(factor, *new_args)
def combine_one_matrices(mul):
"""
Combine products of OneMatrix
e.g. OneMatrix(2, 3) * OneMatrix(3, 4) -> 3 * OneMatrix(2, 4)
"""
factor, args = mul.as_coeff_matrices()
new_args = [args[0]]
for B in args[1:]:
A = new_args[-1]
if not isinstance(A, OneMatrix) or not isinstance(B, OneMatrix):
new_args.append(B)
continue
new_args.pop()
new_args.append(OneMatrix(A.shape[0], B.shape[1]))
factor *= A.shape[1]
return newmul(factor, *new_args)
def combine_powers(mul):
r"""Combine consecutive powers with the same base into one, e.g.
$$A \times A^2 \Rightarrow A^3$$
This also cancels out the possible matrix inverses using the
knowledgebase of :class:`~.Inverse`, e.g.,
$$ Y \times X \times X^{-1} \Rightarrow Y $$
"""
factor, args = mul.as_coeff_matrices()
new_args = [args[0]]
for B in args[1:]:
A = new_args[-1]
if A.is_square == False or B.is_square == False:
new_args.append(B)
continue
if isinstance(A, MatPow):
A_base, A_exp = A.args
else:
A_base, A_exp = A, S.One
if isinstance(B, MatPow):
B_base, B_exp = B.args
else:
B_base, B_exp = B, S.One
if A_base == B_base:
new_exp = A_exp + B_exp
new_args[-1] = MatPow(A_base, new_exp).doit(deep=False)
continue
elif not isinstance(B_base, MatrixBase):
try:
B_base_inv = B_base.inverse()
except NonInvertibleMatrixError:
B_base_inv = None
if B_base_inv is not None and A_base == B_base_inv:
new_exp = A_exp - B_exp
new_args[-1] = MatPow(A_base, new_exp).doit(deep=False)
continue
new_args.append(B)
return newmul(factor, *new_args)
def combine_powers(mul):
r"""Combine consecutive powers with the same base into one, e.g.
$$A \times A^2 \Rightarrow A^3$$
This also cancels out the possible matrix inverses using the
knowledgebase of :class:`~.Inverse`, e.g.,
$$ Y \times X \times X^{-1} \Rightarrow Y $$
"""
factor, args = mul.as_coeff_matrices()
new_args = [args[0]]
for i in range(1, len(args)):
A = new_args[-1]
B = args[i]
if isinstance(B, Inverse) and isinstance(B.arg, MatMul):
Bargs = B.arg.args
l = len(Bargs)
if list(Bargs) == new_args[-l:]:
new_args = new_args[:-l] + [Identity(B.shape[0])]
continue
if isinstance(A, Inverse) and isinstance(A.arg, MatMul):
Aargs = A.arg.args
l = len(Aargs)
if list(Aargs) == args[i:i + l]:
identity = Identity(A.shape[0])
new_args[-1] = identity
for j in range(i, i + l):
args[j] = identity
continue
if A.is_square == False or B.is_square == False:
new_args.append(B)
continue
if isinstance(A, MatPow):
A_base, A_exp = A.args
else:
A_base, A_exp = A, S.One
if isinstance(B, MatPow):
B_base, B_exp = B.args
else:
B_base, B_exp = B, S.One
if A_base == B_base:
new_exp = A_exp + B_exp
new_args[-1] = MatPow(A_base, new_exp).doit(deep=False)
continue
elif not isinstance(B_base, MatrixBase):
try:
B_base_inv = B_base.inverse()
except NonInvertibleMatrixError:
B_base_inv = None
if B_base_inv is not None and A_base == B_base_inv:
new_exp = A_exp - B_exp
new_args[-1] = MatPow(A_base, new_exp).doit(deep=False)
continue
new_args.append(B)
return newmul(factor, *new_args)
def factor_in_front(mul):
factor, matrices = mul.as_coeff_matrices()
if factor != 1:
return newmul(factor, *matrices)
return mul
