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
