MLPY/Lib/site-packages/sympy/matrices/expressions/tests/test_matmul.py

from sympy.core import I, symbols, Basic, Mul, S
from sympy.core.mul import mul
from sympy.functions import adjoint, transpose
from sympy.matrices.exceptions import ShapeError
from sympy.matrices import (Identity, Inverse, Matrix, MatrixSymbol, ZeroMatrix,
        eye, ImmutableMatrix)
from sympy.matrices.expressions import Adjoint, Transpose, det, MatPow
from sympy.matrices.expressions.special import GenericIdentity
from sympy.matrices.expressions.matmul import (factor_in_front, remove_ids,
        MatMul, combine_powers, any_zeros, unpack, only_squares)
from sympy.strategies import null_safe
from sympy.assumptions.ask import Q
from sympy.assumptions.refine import refine
from sympy.core.symbol import Symbol

from sympy.testing.pytest import XFAIL, raises

n, m, l, k = symbols('n m l k', integer=True)
x = symbols('x')
A = MatrixSymbol('A', n, m)
B = MatrixSymbol('B', m, l)
C = MatrixSymbol('C', n, n)
D = MatrixSymbol('D', n, n)
E = MatrixSymbol('E', m, n)

def test_evaluate():
    assert MatMul(C, C, evaluate=True) == MatMul(C, C).doit()

def test_adjoint():
    assert adjoint(A*B) == Adjoint(B)*Adjoint(A)
    assert adjoint(2*A*B) == 2*Adjoint(B)*Adjoint(A)
    assert adjoint(2*I*C) == -2*I*Adjoint(C)

    M = Matrix(2, 2, [1, 2 + I, 3, 4])
    MA = Matrix(2, 2, [1, 3, 2 - I, 4])
    assert adjoint(M) == MA
    assert adjoint(2*M) == 2*MA
    assert adjoint(MatMul(2, M)) == MatMul(2, MA).doit()


def test_transpose():
    assert transpose(A*B) == Transpose(B)*Transpose(A)
    assert transpose(2*A*B) == 2*Transpose(B)*Transpose(A)
    assert transpose(2*I*C) == 2*I*Transpose(C)

    M = Matrix(2, 2, [1, 2 + I, 3, 4])
    MT = Matrix(2, 2, [1, 3, 2 + I, 4])
    assert transpose(M) == MT
    assert transpose(2*M) == 2*MT
    assert transpose(x*M) == x*MT
    assert transpose(MatMul(2, M)) == MatMul(2, MT).doit()


def test_factor_in_front():
    assert factor_in_front(MatMul(A, 2, B, evaluate=False)) ==\
                           MatMul(2, A, B, evaluate=False)


def test_remove_ids():
    assert remove_ids(MatMul(A, Identity(m), B, evaluate=False)) == \
                      MatMul(A, B, evaluate=False)
    assert null_safe(remove_ids)(MatMul(Identity(n), evaluate=False)) == \
                                 MatMul(Identity(n), evaluate=False)


def test_combine_powers():
    assert combine_powers(MatMul(D, Inverse(D), D, evaluate=False)) == \
                 MatMul(Identity(n), D, evaluate=False)
    assert combine_powers(MatMul(B.T, Inverse(E*A), E, A, B, evaluate=False)) == \
        MatMul(B.T, Identity(m), B, evaluate=False)
    assert combine_powers(MatMul(A, E, Inverse(A*E), D, evaluate=False)) == \
        MatMul(Identity(n), D, evaluate=False)


def test_any_zeros():
    assert any_zeros(MatMul(A, ZeroMatrix(m, k), evaluate=False)) == \
                     ZeroMatrix(n, k)


def test_unpack():
    assert unpack(MatMul(A, evaluate=False)) == A
    x = MatMul(A, B)
    assert unpack(x) == x


def test_only_squares():
    assert only_squares(C) == [C]
    assert only_squares(C, D) == [C, D]
    assert only_squares(C, A, A.T, D) == [C, A*A.T, D]


def test_determinant():
    assert det(2*C) == 2**n*det(C)
    assert det(2*C*D) == 2**n*det(C)*det(D)
    assert det(3*C*A*A.T*D) == 3**n*det(C)*det(A*A.T)*det(D)


def test_doit():
    assert MatMul(C, 2, D).args == (C, 2, D)
    assert MatMul(C, 2, D).doit().args == (2, C, D)
    assert MatMul(C, Transpose(D*C)).args == (C, Transpose(D*C))
    assert MatMul(C, Transpose(D*C)).doit(deep=True).args == (C, C.T, D.T)


def test_doit_drills_down():
    X = ImmutableMatrix([[1, 2], [3, 4]])
    Y = ImmutableMatrix([[2, 3], [4, 5]])
    assert MatMul(X, MatPow(Y, 2)).doit() == X*Y**2
    assert MatMul(C, Transpose(D*C)).doit().args == (C, C.T, D.T)


def test_doit_deep_false_still_canonical():
    assert (MatMul(C, Transpose(D*C), 2).doit(deep=False).args ==
            (2, C, Transpose(D*C)))


def test_matmul_scalar_Matrix_doit():
    # Issue 9053
    X = Matrix([[1, 2], [3, 4]])
    assert MatMul(2, X).doit() == 2*X


def test_matmul_sympify():
    assert isinstance(MatMul(eye(1), eye(1)).args[0], Basic)


def test_collapse_MatrixBase():
    A = Matrix([[1, 1], [1, 1]])
    B = Matrix([[1, 2], [3, 4]])
    assert MatMul(A, B).doit() == ImmutableMatrix([[4, 6], [4, 6]])


def test_refine():
    assert refine(C*C.T*D, Q.orthogonal(C)).doit() == D

    kC = k*C
    assert refine(kC*C.T, Q.orthogonal(C)).doit() == k*Identity(n)
    assert refine(kC* kC.T, Q.orthogonal(C)).doit() == (k**2)*Identity(n)

def test_matmul_no_matrices():
    assert MatMul(1) == 1
    assert MatMul(n, m) == n*m
    assert not isinstance(MatMul(n, m), MatMul)

def test_matmul_args_cnc():
    assert MatMul(n, A, A.T).args_cnc() == [[n], [A, A.T]]
    assert MatMul(A, A.T).args_cnc() == [[], [A, A.T]]

@XFAIL
def test_matmul_args_cnc_symbols():
    # Not currently supported
    a, b = symbols('a b', commutative=False)
    assert MatMul(n, a, b, A, A.T).args_cnc() == [[n], [a, b, A, A.T]]
    assert MatMul(n, a, A, b, A.T).args_cnc() == [[n], [a, A, b, A.T]]

def test_issue_12950():
    M = Matrix([[Symbol("x")]]) * MatrixSymbol("A", 1, 1)
    assert MatrixSymbol("A", 1, 1).as_explicit()[0]*Symbol('x') == M.as_explicit()[0]

def test_construction_with_Mul():
    assert Mul(C, D) == MatMul(C, D)
    assert Mul(D, C) == MatMul(D, C)

def test_construction_with_mul():
    assert mul(C, D) == MatMul(C, D)
    assert mul(D, C) == MatMul(D, C)
    assert mul(C, D) != MatMul(D, C)

def test_generic_identity():
    assert MatMul.identity == GenericIdentity()
    assert MatMul.identity != S.One


def test_issue_23519():
    N = Symbol("N", integer=True)
    M1 = MatrixSymbol("M1", N, N)
    M2 = MatrixSymbol("M2", N, N)
    I = Identity(N)
    z = (M2 + 2 * (M2 + I) * M1 + I)
    assert z.coeff(M1) == 2*I + 2*M2


def test_shape_error():
    A = MatrixSymbol('A', 2, 2)
    B = MatrixSymbol('B', 3, 3)
    raises(ShapeError, lambda: MatMul(A, B))