def block_collapse(expr):
"""Evaluates a block matrix expression
>>> 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]])
>>> B
Matrix([
[X, Z],
[0, Y]])
>>> C = BlockMatrix([[Identity(n), Z]])
>>> C
Matrix([[I, Z]])
>>> block_collapse(C*B)
Matrix([[X, Z + Z*Y]])
"""
def hasbm(expr):
return isinstance(expr, MatrixExpr) and expr.has(BlockMatrix)
rule = exhaust(
bottom_up(exhaust(condition(hasbm, typed(
{MatAdd: do_one([bc_matadd, bc_block_plus_ident]),
MatMul: do_one([bc_matmul, bc_dist]),
Transpose: bc_transpose,
Inverse: bc_inverse,
BlockMatrix: do_one([bc_unpack, deblock])})))))
result = rule(expr)
return result.doit()
def block_collapse(expr):
"""Evaluates a block matrix expression
>>> 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]])
>>> B
Matrix([
[X, Z],
[0, Y]])
>>> C = BlockMatrix([[Identity(n), Z]])
>>> C
Matrix([[I, Z]])
>>> block_collapse(C*B)
Matrix([[X, Z + Z*Y]])
"""
def hasbm(expr):
return isinstance(expr, MatrixExpr) and expr.has(BlockMatrix)
rule = exhaust(
bottom_up(exhaust(condition(hasbm, typed(
{MatAdd: do_one([bc_matadd, bc_block_plus_ident]),
MatMul: do_one([bc_matmul, bc_dist]),
Transpose: bc_transpose,
Inverse: bc_inverse,
BlockMatrix: do_one([bc_unpack, deblock])})))))
result = rule(expr)
return result.doit()
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
return out
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
return out
