35 lines
1.0 KiB
Python
35 lines
1.0 KiB
Python
|
from sympy.core import symbols, S
|
||
|
|
from sympy.functions import adjoint, conjugate, transpose
|
||
|
|
from sympy.matrices.expressions import MatrixSymbol, Adjoint, trace, Transpose
|
||
|
|
from sympy.matrices import eye, Matrix
|
||
|
|
|
||
|
|
n, m, l, k, p = symbols('n m l k p', integer=True)
|
||
|
|
A = MatrixSymbol('A', n, m)
|
||
|
|
B = MatrixSymbol('B', m, l)
|
||
|
|
C = MatrixSymbol('C', n, n)
|
||
|
|
|
||
|
|
|
||
|
|
def test_adjoint():
|
||
|
|
Sq = MatrixSymbol('Sq', n, n)
|
||
|
|
|
||
|
|
assert Adjoint(A).shape == (m, n)
|
||
|
|
assert Adjoint(A*B).shape == (l, n)
|
||
|
|
assert adjoint(Adjoint(A)) == A
|
||
|
|
assert isinstance(Adjoint(Adjoint(A)), Adjoint)
|
||
|
|
|
||
|
|
assert conjugate(Adjoint(A)) == Transpose(A)
|
||
|
|
assert transpose(Adjoint(A)) == Adjoint(Transpose(A))
|
||
|
|
|
||
|
|
assert Adjoint(eye(3)).doit() == eye(3)
|
||
|
|
|
||
|
|
assert Adjoint(S(5)).doit() == S(5)
|
||
|
|
|
||
|
|
assert Adjoint(Matrix([[1, 2], [3, 4]])).doit() == Matrix([[1, 3], [2, 4]])
|
||
|
|
|
||
|
|
assert adjoint(trace(Sq)) == conjugate(trace(Sq))
|
||
|
|
assert trace(adjoint(Sq)) == conjugate(trace(Sq))
|
||
|
|
|
||
|
|
assert Adjoint(Sq)[0, 1] == conjugate(Sq[1, 0])
|
||
|
|
|
||
|
|
assert Adjoint(A*B).doit() == Adjoint(B) * Adjoint(A)
|