def test_matrix_multiplication():
A = Matrix(3, 3)
B = Matrix(3, 3)
AB = Matrix(3, 3)
BA = Matrix(3, 3)
A[0, :] = [1, 0, 0]
A[1, :] = [0, 0, 1]
A[2, :] = [0, 1, 0]
B[0, :] = [1, 2, 3]
B[1, :] = [4, 5, 6]
B[2, :] = [7, 8, 9]
AB[0, :] = [1, 2, 3]
AB[1, :] = [7, 8, 9]
AB[2, :] = [4, 5, 6]
assert (A * B == AB)
BA[0, :] = [1, 3, 2]
BA[1, :] = [4, 6, 5]
BA[2, :] = [7, 9, 8]
assert (B * A == BA)
def test_matrix_identities():
A = Matrix.identity(3, 3)
A[0, 1] = 1
assert (A + Matrix.zero(3, 3) == A)
assert (Matrix.zero(3, 3) + A == A)
assert (A * Matrix.identity(3, 3) == A)
assert (Matrix.identity(3, 3) * A == A)
def test_matrix_approx():
A = Matrix(3, 3)
B = Matrix(3, 3)
A[0, :] = B[0, :] = [1, 2, 3]
A[1, :] = B[1, :] = [4, 5, 6]
A[2, :] = B[2, :] = [7, 8, 9]
assert (approx(A, B, tol=0.001))
A[0, 0] += 0.002
assert (not approx(A, B, tol=0.001))
def test_matrix_subtraction():
A = Matrix(3, 3)
B = Matrix(3, 3)
C = Matrix(3, 3)
A[0, 1] = 1
B[1, 0] = 2
C[0, 1] = 1
C[1, 0] = 2
assert (C - A == B)
assert (C - B == A)
def test_matrix_addition():
A = Matrix(3, 3)
B = Matrix(3, 3)
C = Matrix(3, 3)
A[0, 1] = 1
B[1, 0] = 2
C[0, 1] = 1
C[1, 0] = 2
assert (A + B == C)
assert (B + A == C)
def test_approx_jacobian_identity():
def f(x):
return x
x = Vector(0, 0, 0)
assert(approx(approx_jacobian(f, x), Matrix.identity(3)))
def test_matrix_svd():
A = Matrix(3, 3)
A[0, :] = [1, 2, 3]
A[1, :] = [4, 5, 6]
A[2, :] = [7, 8, 9]
U, S, V = svd(A)
assert (approx(U * S * V.transposed(), A))
def test_approx_jacobian_permutation():
def f(x):
return Vector(x[0], x[2], x[1])
x = Vector(0, 0, 0)
J = Matrix(3, 3)
J[0, 0] = 1
J[2, 1] = 1
J[1, 2] = 1
assert(approx(approx_jacobian(f, x), J))
def test_approx_jacobian_lorenz():
def f(x):
vx = x[1] - x[0]
vy = x[0] * (1 - x[2]) - x[1]
vz = x[0] * x[1] - x[2]
return Vector(vx, vy, vz)
x = Vector(1, 2, 3)
J = Matrix(3, 3)
J[0, :] = [-1, 1 - x[2], x[1]]
J[1, :] = [1, -1, x[0]]
J[2, :] = [0, -x[0], -1]
assert(approx(approx_jacobian(f, x), J))
def test_matrix_equality():
A = Matrix(3, 3)
B = Matrix(3, 3)
assert (A == B)
A = Matrix.identity(3, 3)
B = Matrix.identity(3, 3)
assert (A == B)
A = Matrix.zero(3, 3)
B = Matrix.zero(3, 3)
assert (A == B)