Sources_For_Win/ParaView/Lib/site-packages/sympy/matrices/expressions/matadd.py

from functools import reduce
import operator

from sympy.core import Basic, sympify
from sympy.core.add import add, Add, _could_extract_minus_sign
from sympy.core.sorting import default_sort_key
from sympy.functions import adjoint
from sympy.matrices.common import ShapeError
from sympy.matrices.matrices import MatrixBase
from sympy.matrices.expressions.transpose import transpose
from sympy.strategies import (rm_id, unpack, flatten, sort, condition,
    exhaust, do_one, glom)
from sympy.matrices.expressions.matexpr import MatrixExpr
from sympy.matrices.expressions.special import ZeroMatrix, GenericZeroMatrix
from sympy.utilities import sift

# XXX: MatAdd should perhaps not subclass directly from Add
class MatAdd(MatrixExpr, Add):
    """A Sum of Matrix Expressions

    MatAdd inherits from and operates like SymPy Add

    Examples
    ========

    >>> from sympy import MatAdd, MatrixSymbol
    >>> A = MatrixSymbol('A', 5, 5)
    >>> B = MatrixSymbol('B', 5, 5)
    >>> C = MatrixSymbol('C', 5, 5)
    >>> MatAdd(A, B, C)
    A + B + C
    """
    is_MatAdd = True

    identity = GenericZeroMatrix()

    def __new__(cls, *args, evaluate=False, check=False, _sympify=True):
        if not args:
            return cls.identity

        # This must be removed aggressively in the constructor to avoid
        # TypeErrors from GenericZeroMatrix().shape
        args = list(filter(lambda i: cls.identity != i, args))
        if _sympify:
            args = list(map(sympify, args))

        obj = Basic.__new__(cls, *args)

        if check:
            if not any(isinstance(i, MatrixExpr) for i in args):
                return Add.fromiter(args)
            validate(*args)

        if evaluate:
            if not any(isinstance(i, MatrixExpr) for i in args):
                return Add(*args, evaluate=True)
            obj = canonicalize(obj)

        return obj

    @property
    def shape(self):
        return self.args[0].shape

    def could_extract_minus_sign(self):
        return _could_extract_minus_sign(self)

    def _entry(self, i, j, **kwargs):
        return Add(*[arg._entry(i, j, **kwargs) for arg in self.args])

    def _eval_transpose(self):
        return MatAdd(*[transpose(arg) for arg in self.args]).doit()

    def _eval_adjoint(self):
        return MatAdd(*[adjoint(arg) for arg in self.args]).doit()

    def _eval_trace(self):
        from .trace import trace
        return Add(*[trace(arg) for arg in self.args]).doit()

    def doit(self, **kwargs):
        deep = kwargs.get('deep', True)
        if deep:
            args = [arg.doit(**kwargs) for arg in self.args]
        else:
            args = self.args
        return canonicalize(MatAdd(*args))

    def _eval_derivative_matrix_lines(self, x):
        add_lines = [arg._eval_derivative_matrix_lines(x) for arg in self.args]
        return [j for i in add_lines for j in i]

add.register_handlerclass((Add, MatAdd), MatAdd)

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):
    if cnt == 1:
        return mat
    else:
        return cnt * mat


def merge_explicit(matadd):
    """ Merge explicit MatrixBase arguments

    Examples
    ========

    >>> from sympy import MatrixSymbol, eye, Matrix, MatAdd, pprint
    >>> from sympy.matrices.expressions.matadd import merge_explicit
    >>> A = MatrixSymbol('A', 2, 2)
    >>> B = eye(2)
    >>> C = Matrix([[1, 2], [3, 4]])
    >>> X = MatAdd(A, B, C)
    >>> pprint(X)
        [1  0]   [1  2]
    A + [    ] + [    ]
        [0  1]   [3  4]
    >>> pprint(merge_explicit(X))
        [2  2]
    A + [    ]
        [3  5]
    """
    groups = sift(matadd.args, lambda arg: isinstance(arg, MatrixBase))
    if len(groups[True]) > 1:
        return MatAdd(*(groups[False] + [reduce(operator.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)))