def block_collapse(expr):
"""Evaluates a block matrix expression
>>> from sympy import MatrixSymbol, BlockMatrix, symbols, \
Identity, Matrix, ZeroMatrix, block_collapse
>>> n,m,l = symbols('n m l')
>>> X = MatrixSymbol('X', n, n)
>>> Y = MatrixSymbol('Y', m ,m)
>>> Z = MatrixSymbol('Z', n, m)
>>> B = BlockMatrix([[X, Z], [ZeroMatrix(m, n), Y]])
>>> print B
[X, Z]
[0, Y]
>>> C = BlockMatrix([[Identity(n), Z]])
>>> print C
[I, Z]
>>> print block_collapse(C*B)
[X, Z + Z*Y]
"""
rule = canon(typed({MatAdd: do_one(bc_matadd, bc_block_plus_ident),
MatMul: do_one(bc_matmul, bc_dist),
MatPow: bc_matpow,
BlockMatrix: bc_unpack}))
result = rule(expr)
try:
return result.canonicalize()
except AttributeError:
return result
def block_collapse(expr):
"""Evaluates a block matrix expression
>>> from sympy import MatrixSymbol, BlockMatrix, symbols, \
Identity, Matrix, ZeroMatrix, block_collapse
>>> n,m,l = symbols('n m l')
>>> X = MatrixSymbol('X', n, n)
>>> Y = MatrixSymbol('Y', m ,m)
>>> Z = MatrixSymbol('Z', n, m)
>>> B = BlockMatrix([[X, Z], [ZeroMatrix(m, n), Y]])
>>> print B
[X, Z]
[0, Y]
>>> C = BlockMatrix([[Identity(n), Z]])
>>> print C
[I, Z]
>>> print block_collapse(C*B)
[X, Z + Z*Y]
"""
rule = canon(
typed({
MatAdd: do_one(bc_matadd, bc_block_plus_ident),
MatMul: do_one(bc_matmul, bc_dist),
BlockMatrix: bc_unpack
}))
result = rule(expr)
try:
return result.doit()
except AttributeError:
return result
def test_do_one():
rl1 = lambda x: 2 if x == 1 else x
rl2 = lambda x: 3 if x == 2 else x
rule = do_one(rl1, rl2)
assert rule(1) == 2
assert rule(rule(1)) == 3
def test_do_one():
rl1 = lambda x: 2 if x == 1 else x
rl2 = lambda x: 3 if x == 2 else x
rule = do_one(rl1, rl2)
assert rule(1) == 2
assert rule(rule(1)) == 3
""" Remove Identities from a MatMul
This is a modified version of sympy.rules.rm_id.
This is necesssary because MatMul may contain both MatrixExprs and Exprs
as args.
See Also
--------
sympy.rules.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 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),
factor_in_front, flatten)
canonicalize = exhaust(condition(lambda x: isinstance(x, MatMul),
do_one(*rules)))
""" Remove Identities from a MatMul
This is a modified version of sympy.rules.rm_id.
This is necesssary because MatMul may contain both MatrixExprs and Exprs
as args.
See Also
--------
sympy.rules.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 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), factor_in_front, flatten)
canonicalize = exhaust(condition(lambda x: isinstance(x, MatMul), do_one(*rules)))
def canonicalize(self):
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))
factor_of = lambda arg: arg.as_coeff_mmul()[0]
matrix_of = lambda arg: unpack(arg.as_coeff_mmul()[1])
def combine(cnt, mat):
from matmul import MatMul
if cnt == 1:
return mat
else:
return cnt * mat
rules = (rm_id(lambda x: x == 0 or isinstance(x, ZeroMatrix)), unpack, flatten,
glom(matrix_of, factor_of, combine), sort(str))
canonicalize = exhaust(
condition(lambda x: isinstance(x, MatAdd), do_one(*rules)))