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 __new__(cls, *computations):
computations = tuple(unique(computations))
computations = exhaust(flatten)(computations)
computations = exhaust(rm_identity)(computations)
if len(computations) == 1:
return computations[0]
else:
obj = object.__new__(cls)
obj.computations = tuple(computations)
return obj
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
>>> A = MatrixSymbol('A', 2, 2)
>>> B = eye(2)
>>> C = Matrix([[1, 2], [3, 4]])
>>> X = MatAdd(A, B, C)
>>> pprint(X, use_unicode=False)
[1 0] [1 2]
A + [ ] + [ ]
[0 1] [3 4]
>>> pprint(merge_explicit(X), use_unicode=False)
[2 2]
A + [ ]
[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)))
>>> 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)))
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
return super().__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 .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)))
return super().__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 .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)))