def _normalize(self):
# Normalization of trace of matrix products. Use transposition and
# cyclic properties of traces to make sure the arguments of the matrix
# product are sorted and the first argument is not a trasposition.
from sympy.matrices.expressions.matmul import MatMul
from sympy.matrices.expressions.transpose import Transpose
trace_arg = self.arg
if isinstance(trace_arg, MatMul):
def get_arg_key(x):
a = trace_arg.args[x]
if isinstance(a, Transpose):
a = a.arg
return default_sort_key(a)
indmin = min(range(len(trace_arg.args)), key=get_arg_key)
if isinstance(trace_arg.args[indmin], Transpose):
trace_arg = Transpose(trace_arg).doit()
indmin = min(range(len(trace_arg.args)), key=lambda x: default_sort_key(trace_arg.args[x]))
trace_arg = MatMul.fromiter(trace_arg.args[indmin:] + trace_arg.args[:indmin])
return Trace(trace_arg)
return self
def doit(self, **hints):
from sympy.assumptions import ask, Q
from sympy.matrices.expressions.matmul import MatMul
from sympy.matrices.expressions.transpose import Transpose
from sympy.matrices.dense import eye
from sympy.matrices.matrices import MatrixBase
vector = self._vector
# This accounts for shape (1, 1) and identity matrices, among others:
if ask(Q.diagonal(vector)):
return vector
if isinstance(vector, MatrixBase):
ret = eye(max(vector.shape))
for i in range(ret.shape[0]):
ret[i, i] = vector[i]
return type(vector)(ret)
if vector.is_MatMul:
matrices = [arg for arg in vector.args if arg.is_Matrix]
scalars = [arg for arg in vector.args if arg not in matrices]
if scalars:
return Mul.fromiter(scalars) * DiagMatrix(
MatMul.fromiter(matrices).doit()).doit()
if isinstance(vector, Transpose):
vector = vector.arg
return DiagMatrix(vector)
def convert_matrix_to_array(expr: Basic) -> Basic:
if isinstance(expr, MatMul):
args_nonmat = []
args = []
for arg in expr.args:
if isinstance(arg, MatrixExpr):
args.append(arg)
else:
args_nonmat.append(convert_matrix_to_array(arg))
contractions = [(2*i+1, 2*i+2) for i in range(len(args)-1)]
scalar = _array_tensor_product(*args_nonmat) if args_nonmat else S.One
if scalar == 1:
tprod = _array_tensor_product(
*[convert_matrix_to_array(arg) for arg in args])
else:
tprod = _array_tensor_product(
scalar,
*[convert_matrix_to_array(arg) for arg in args])
return _array_contraction(
tprod,
*contractions
)
elif isinstance(expr, MatAdd):
return _array_add(
*[convert_matrix_to_array(arg) for arg in expr.args]
)
elif isinstance(expr, Transpose):
return _permute_dims(
convert_matrix_to_array(expr.args[0]), [1, 0]
)
elif isinstance(expr, Trace):
inner_expr: MatrixExpr = convert_matrix_to_array(expr.arg) # type: ignore
return _array_contraction(inner_expr, (0, len(inner_expr.shape) - 1))
elif isinstance(expr, Mul):
return _array_tensor_product(*[convert_matrix_to_array(i) for i in expr.args])
elif isinstance(expr, Pow):
base = convert_matrix_to_array(expr.base)
if (expr.exp > 0) == True:
return _array_tensor_product(*[base for i in range(expr.exp)])
else:
return expr
elif isinstance(expr, MatPow):
base = convert_matrix_to_array(expr.base)
if expr.exp.is_Integer != True:
b = symbols("b", cls=Dummy)
return ArrayElementwiseApplyFunc(Lambda(b, b**expr.exp), convert_matrix_to_array(base))
elif (expr.exp > 0) == True:
return convert_matrix_to_array(MatMul.fromiter(base for i in range(expr.exp)))
else:
return expr
elif isinstance(expr, HadamardProduct):
tp = _array_tensor_product(*[convert_matrix_to_array(arg) for arg in expr.args])
diag = [[2*i for i in range(len(expr.args))], [2*i+1 for i in range(len(expr.args))]]
return _array_diagonal(tp, *diag)
elif isinstance(expr, HadamardPower):
base, exp = expr.args
if isinstance(exp, Integer) and exp > 0:
return convert_matrix_to_array(HadamardProduct.fromiter(base for i in range(exp)))
else:
d = Dummy("d")
return ArrayElementwiseApplyFunc(Lambda(d, d**exp), base)
elif isinstance(expr, KroneckerProduct):
kp_args = [convert_matrix_to_array(arg) for arg in expr.args]
permutation = [2*i for i in range(len(kp_args))] + [2*i + 1 for i in range(len(kp_args))]
return Reshape(_permute_dims(_array_tensor_product(*kp_args), permutation), expr.shape)
else:
return expr
