def test_norms(): # matrix norms A = matrix([[1, -2], [-3, -1], [2, 1]]) assert mnorm_1(A) == 6 assert mnorm_oo(A) == 4 assert mnorm_F(A) == sqrt(20) # vector norms x = [1, -2, 7, -12] assert norm_p(x, 1) == 22 assert round(norm_p(x, 2), 10) == 14.0712472795 assert round(norm_p(x, 10), 10) == 12.0054633727 assert norm_p(x, inf) == 12
def test_norms(): # matrix norms A = matrix([[1, -2], [-3, -1], [2, 1]]) assert mnorm_1(A) == 6 assert mnorm_oo(A) == 4 assert mnorm_F(A) == sqrt(20) # vector norms x = [1, -2, 7, -12] assert norm_p(x, 1) == 22 assert round(norm_p(x, 2), 10) == 14.0712472795 assert round(norm_p(x, 10), 10) == 12.0054633727 assert norm_p(x, inf) == 12
def test_inverse(): for A in [A1, A2, A5]: inv = inverse(A) assert mnorm_1(A*inv - eye(A.rows)) < 1.e-14
def test_precision(): A = randmatrix(10, 10) assert mnorm_1(inverse(inverse(A)) - A) < 1.e-45
def test_factorization(): A = randmatrix(5) P, L, U = lu(A) assert mnorm_1(P*A - L*U) < 1.e-15
def test_inverse(): for A in [A1, A2, A5]: inv = inverse(A) assert mnorm_1(A * inv - eye(A.rows)) < 1.e-14
def test_precision(): A = randmatrix(10, 10) assert mnorm_1(inverse(inverse(A)) - A) < 1.e-45
def test_factorization(): A = randmatrix(5) P, L, U = lu(A) assert mnorm_1(P * A - L * U) < 1.e-15