63 lines
2.0 KiB
Python
63 lines
2.0 KiB
Python
from sympy.core import symbols, S
|
|
from sympy.matrices.expressions import MatrixSymbol, Inverse, MatPow, ZeroMatrix, OneMatrix
|
|
from sympy.matrices.common import NonInvertibleMatrixError, NonSquareMatrixError
|
|
from sympy.matrices import eye, Identity
|
|
from sympy.testing.pytest import raises
|
|
from sympy.assumptions.ask import Q
|
|
from sympy.assumptions.refine import refine
|
|
|
|
n, m, l = symbols('n m l', integer=True)
|
|
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_inverse():
|
|
assert Inverse(C).args == (C, S.NegativeOne)
|
|
assert Inverse(C).shape == (n, n)
|
|
assert Inverse(A*E).shape == (n, n)
|
|
assert Inverse(E*A).shape == (m, m)
|
|
assert Inverse(C).inverse() == C
|
|
assert Inverse(Inverse(C)).doit() == C
|
|
assert isinstance(Inverse(Inverse(C)), Inverse)
|
|
|
|
assert Inverse(*Inverse(E*A).args) == Inverse(E*A)
|
|
|
|
assert C.inverse().inverse() == C
|
|
|
|
assert C.inverse()*C == Identity(C.rows)
|
|
|
|
assert Identity(n).inverse() == Identity(n)
|
|
assert (3*Identity(n)).inverse() == Identity(n)/3
|
|
|
|
# Simplifies Muls if possible (i.e. submatrices are square)
|
|
assert (C*D).inverse() == D.I*C.I
|
|
# But still works when not possible
|
|
assert isinstance((A*E).inverse(), Inverse)
|
|
assert Inverse(C*D).doit(inv_expand=False) == Inverse(C*D)
|
|
|
|
assert Inverse(eye(3)).doit() == eye(3)
|
|
assert Inverse(eye(3)).doit(deep=False) == eye(3)
|
|
|
|
assert OneMatrix(1, 1).I == Identity(1)
|
|
assert isinstance(OneMatrix(n, n).I, Inverse)
|
|
|
|
def test_inverse_non_invertible():
|
|
raises(NonInvertibleMatrixError, lambda: ZeroMatrix(n, n).I)
|
|
raises(NonInvertibleMatrixError, lambda: OneMatrix(2, 2).I)
|
|
|
|
def test_refine():
|
|
assert refine(C.I, Q.orthogonal(C)) == C.T
|
|
|
|
|
|
def test_inverse_matpow_canonicalization():
|
|
A = MatrixSymbol('A', 3, 3)
|
|
assert Inverse(MatPow(A, 3)).doit() == MatPow(Inverse(A), 3).doit()
|
|
|
|
|
|
def test_nonsquare_error():
|
|
A = MatrixSymbol('A', 3, 4)
|
|
raises(NonSquareMatrixError, lambda: Inverse(A))
|