def test_inversion(self):
m = Matrix(vals=[
[6, 4, 4, 4],
[5, 5, 7, 6],
[4, -9, 3, -7],
[9, 1, 7, -6],
])
self.assertEqual(m._determinant(), -2120)
# verify exception if determinant is zero
m = Matrix(
vals=[[-4, 2, -2, -3], [9, 6, 2, 6], [0, -5, 1, -5], [0, 0, 0, 0]])
self.assertEqual(m._determinant(), 0)
with self.assertRaises(ValueError):
m.inverse()
m = Matrix(vals=[
[-5, 2, 6, -8],
[1, -5, 1, 8],
[7, 7, -6, -7],
[1, -3, 7, 4],
])
self.assertMatrixEqual(
m.inverse(),
Matrix(vals=[[0.21805, 0.45113, 0.24060, -0.04511],
[-0.80827, -1.45677, -0.44361, 0.52068],
[-0.07895, -0.22368, -0.05263, 0.19737],
[-0.52256, -0.81391, -0.30075, 0.30639]]))
m = Matrix(
vals=[[8, -5, 9, 2], [7, 5, 6, 1], [-6, 0, 9, 6], [-3, 0, -9, -4]])
self.assertMatrixEqual(
m.inverse(),
Matrix(vals=[[-0.15385, -0.15385, -0.28205, -0.53846],
[-0.07692, 0.12308, 0.02564, 0.03077],
[0.35897, 0.35897, 0.43590, 0.92308],
[-0.69231, -0.69231, -0.76923, -1.92308]]))
m = Matrix(vals=[[9, 3, 0, 9], [-5, -2, -6, -3], [-4, 9, 6, 4],
[-7, 6, 6, 2]])
self.assertMatrixEqual(
m.inverse(),
Matrix(vals=[[-0.04074, -0.07778, 0.14444, -0.22222],
[-0.07778, 0.03333, 0.36667, -0.33333],
[-0.02901, -0.14630, -0.10926, 0.12963],
[0.17778, 0.06667, -0.26667, 0.33333]]))
a = Matrix(vals=[[3, -9, 7, 3], [3, -8, 2, -9], [-4, 4, 4, 1],
[-6, 5, -1, 1]])
b = Matrix(
vals=[[8, 2, 2, 2], [3, -1, 7, 0], [7, 0, 5, 4], [6, -2, 0, 5]])
c = a * b
self.assertMatrixEqual(c * b.inverse(), a)
def test_determinant_3x3(self):
m = Matrix(vals=[[1, 2, 6], [-5, 8, -4], [2, 6, 4]])
self.assertEqual(m._determinant(), -196)
def test_determinant_4x4(self):
m = Matrix(vals=[[-2, -8, 3, 5], [-3, 1, 7, 3], [1, 2, -9, 6],
[-6, 7, 7, -9]])
self.assertEqual(m._determinant(), -4071)
def test_determinant_2x2(self):
m = Matrix(vals=[[1, 5], [-3, 2]])
self.assertEqual(m._determinant(), 17)
