def sympy_key(expr):
"""Get the key for ordering SymPy expressions.
This function assumes that the given expression is already sympified.
"""
return count_ops(expr), default_sort_key(expr)
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 import MatMul, Transpose, default_sort_key
trace_arg = self.arg
if isinstance(trace_arg, MatMul):
indmin = min(range(len(trace_arg.args)),
key=lambda x: default_sort_key(trace_arg.args[x]))
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 _sort_fully_contracted_args(cls, expr, contraction_indices):
if expr.shape is None:
return expr, contraction_indices
cumul = list(accumulate([0] + expr.subranks))
index_blocks = [list(range(cumul[i], cumul[i+1])) for i in range(len(expr.args))]
contraction_indices_flat = {j for i in contraction_indices for j in i}
fully_contracted = [all(j in contraction_indices_flat for j in range(cumul[i], cumul[i+1])) for i, arg in enumerate(expr.args)]
new_pos = sorted(range(len(expr.args)), key=lambda x: (0, default_sort_key(expr.args[x])) if fully_contracted[x] else (1,))
new_args = [expr.args[i] for i in new_pos]
new_index_blocks_flat = [j for i in new_pos for j in index_blocks[i]]
index_permutation_array_form = _af_invert(new_index_blocks_flat)
new_contraction_indices = [tuple(index_permutation_array_form[j] for j in i) for i in contraction_indices]
new_contraction_indices = _sort_contraction_indices(new_contraction_indices)
return ArrayTensorProduct(*new_args), new_contraction_indices
def sort_args_by_name(self):
"""
Sort arguments in the tensor product so that their order is lexicographical.
Examples
========
>>> from sympy.tensor.array.expressions.conv_matrix_to_array import convert_matrix_to_array
>>> from sympy import MatrixSymbol
>>> from sympy.abc import N
>>> A = MatrixSymbol("A", N, N)
>>> B = MatrixSymbol("B", N, N)
>>> C = MatrixSymbol("C", N, N)
>>> D = MatrixSymbol("D", N, N)
>>> cg = convert_matrix_to_array(C*D*A*B)
>>> cg
ArrayContraction(ArrayTensorProduct(A, D, C, B), (0, 3), (1, 6), (2, 5))
>>> cg.sort_args_by_name()
ArrayContraction(ArrayTensorProduct(A, D, B, C), (0, 3), (1, 4), (2, 7))
"""
expr = self.expr
if not isinstance(expr, ArrayTensorProduct):
return self
args = expr.args
sorted_data = sorted(enumerate(args), key=lambda x: default_sort_key(x[1]))
pos_sorted, args_sorted = zip(*sorted_data)
reordering_map = {i: pos_sorted.index(i) for i, arg in enumerate(args)}
contraction_tuples = self._get_contraction_tuples()
contraction_tuples = [[(reordering_map[j], k) for j, k in i] for i in contraction_tuples]
c_tp = ArrayTensorProduct(*args_sorted)
new_contr_indices = self._contraction_tuples_to_contraction_indices(
c_tp,
contraction_tuples
)
return ArrayContraction(c_tp, *new_contr_indices)
def eqn_simplicity(eqn):
return len(eqn.lhs.free_symbols), default_sort_key(eqn)
def get_arg_key(x):
a = trace_arg.args[x]
if isinstance(a, Transpose):
a = a.arg
return default_sort_key(a)
def _entity_sort_key(entity):
return sympy.default_sort_key(entity.value)
