def test_inversion_reverts_correctly(self):
m1 = Matrix([[3, -9, 7, 3], [3, -8, 2, -9], [-4, 4, 4, 1],
[-6, 5, -1, 1]])
m2 = Matrix([[8, 2, 2, 2], [3, -1, 7, 0], [7, 0, 5, 4], [6, -2, 0, 5]])
m3 = m1 * m2
result = m3 * m2.inverse()
assert self.rounded(m1.data) == self.rounded(result.data)
def lse(data_points, base, lamb):
# print (f'Processing LSE with data points: {data_points} and lambda {lamb}')
A, b = extract_paras(data_points, base)
identity = Matrix.make_identity(A.cols, lamb)
A_reverse = A.reverse()
A = A.reverse().mul(A).add(identity)
A = Matrix.inverse(A)
return A.mul(A_reverse).mul(b).data
def newtons_method(data_points, base, iteration):
A, b = extract_paras(data_points, base)
x = Matrix([[random.randint(1, 100)], [random.randint(1, 100)]])
for i in range(iteration):
gradient = A.reverse().mul(A).mul(x).mul_const(2).sub(
A.reverse().mul(b).mul_const(2))
hessian = A.reverse().mul(A).mul_const(2)
x = x.sub(Matrix.inverse(hessian).mul(gradient))
return x.data
def test_second_4_by_4_inversion(self):
matrix = Matrix([[8, -5, 9, 2], [7, 5, 6, 1], [-6, 0, 9, 6],
[-3, 0, -9, -4]])
result = matrix.inverse()
assert self.rounded(result.data) == [
[-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],
]
def test_inverse_matrix(self):
matrix = Matrix([[-5, 2, 6, -8], [1, -5, 1, 8], [7, 7, -6, -7],
[1, -3, 7, 4]])
result = matrix.inverse()
assert matrix.determinant() == 532
assert matrix.cofactor(2, 3) == -160
assert matrix.cofactor(3, 2) == 105
assert result.at(3, 2) == -160 / 532
assert result.at(2, 3) == 105 / 532
assert self.rounded(result.data) == [
[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],
]
