def testMul_2x3(self):
a = ComplexM(2,3,
[
[(3,2) , (0,0) , (5,-6) ],
[(1,0) , (4,2) , (0,1) ],
]
)
b = ComplexM(3,2,
[
[(5,0) , (2,-1)],
[(0,0) , (4,5)],
[(7,-4) , (2,7)],
]
)
res = ComplexM(2,2,
[
[(26,-52) , (60,24)],
[(9,7) , (1,29)],
]
)
self.assertEqual(a*b, res)
self.assertNotEqual(b*a, a*b)
self.assertIsNone(a.get_identity())
self.assertIsNone(b.get_identity())
self.assertIsNotNone(res.get_identity())
x = Complex(4,-3.5)
self.assertEqual(x * (a*b), (x*a) * b)
self.assertEqual(x * (a*b), a * (x*b))
self.assertEqual((a*b).transpose(), b.transpose() * a.transpose())
self.assertEqual((a*b).adjoint(), b.adjoint() * a.adjoint())
self.assertEqual((a*b).conjugate(), a.conjugate() * b.conjugate())
def testTranspose(self):
a = ComplexM(3, 2, [ [(7, -8), (0,4)], [2, (9.4,3)], [(0,1), (-3,-2)] ])
b = ComplexM(2, 3, [ [(7, -8), 2, (0,1)], [(0,4), (9.4,3), (-3,-2)]])
self.assertEqual(b, a.transpose())
self.assertEqual(a, b.transpose())
self.assertEqual(a, a.transpose().transpose())
self.assertEqual(b, b.transpose().transpose())
def testMul_3x3(self):
a = ComplexM(3,3,
[
[(3,2) , (0,0) , (5,-6) ],
[(1,0) , (4,2) , (0,1) ],
[(4,-1) , (0,0) , (4,0) ],
]
)
b = ComplexM(3,3,
[
[(5,0) , (2,-1) , (6,-4) ],
[(0,0) , (4,5) , (2,0) ],
[(7,-4) , (2,7) , (0,0) ],
]
)
res = ComplexM(3,3,
[
[(26,-52) , (60,24) , (26,0) ],
[(9,7) , (1,29) , (14,0) ],
[(48,-21) , (15,22) , (20,-22) ],
]
)
self.assertEqual(a*b, res)
self.assertNotEqual(b*a, a*b)
ident = a.get_identity()
self.assertEqual(a, a*ident)
self.assertEqual(b, b*ident)
x = Complex(2,-1)
self.assertEqual(x * (a*b), (x*a) * b)
self.assertEqual(x * (a*b), a * (x*b))
c = res
self.assertEqual((a*b)*c, a*(b*c))
self.assertEqual(a*(b+c), (a*b)+(a*c))
self.assertEqual((a*b).transpose(), b.transpose() * a.transpose())
self.assertEqual((a*b).adjoint(), b.adjoint() * a.adjoint())
self.assertEqual((a*b).conjugate(), a.conjugate() * b.conjugate())
