Spaces:
Running
Running
File size: 2,320 Bytes
6a86ad5 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 |
from sympy.core import symbols, S
from sympy.matrices.expressions import MatrixSymbol, Inverse, MatPow, ZeroMatrix, OneMatrix
from sympy.matrices.exceptions 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))
def test_adjoint_trnaspose_conjugate():
A = MatrixSymbol('A', n, n)
assert A.transpose().inverse() == A.inverse().transpose()
assert A.conjugate().inverse() == A.inverse().conjugate()
assert A.adjoint().inverse() == A.inverse().adjoint()
|