def test_norms():
# matrix norms
A = matrix([[1, -2], [-3, -1], [2, 1]])
assert mnorm(A,1) == 6
assert mnorm(A,inf) == 4
assert mnorm(A,'F') == sqrt(20)
# vector norms
assert norm(-3) == 3
x = [1, -2, 7, -12]
assert norm(x, 1) == 22
assert round(norm(x, 2), 10) == 14.0712472795
assert round(norm(x, 10), 10) == 12.0054633727
assert norm(x, inf) == 12
def test_inverse():
for A in [A1, A2, A5]:
inv = inverse(A)
assert mnorm(A * inv - eye(A.rows), 1) < 1.e-14
def test_cond():
mp.dps = 15
A = matrix([[1.2969, 0.8648], [0.2161, 0.1441]])
assert cond(A, lambda x: mnorm(x, 1)) == mpf('327065209.73817754')
assert cond(A, lambda x: mnorm(x, inf)) == mpf('327065209.73817754')
assert cond(A, lambda x: mnorm(x, 'F')) == mpf('249729266.80008656')
def test_precision():
A = randmatrix(10, 10)
assert mnorm(inverse(inverse(A)) - A, 1) < 1.e-45
def test_factorization():
A = randmatrix(5)
P, L, U = lu(A)
assert mnorm(P * A - L * U, 1) < 1.e-15
def test_inverse():
for A in [A1, A2, A5]:
inv = inverse(A)
assert mnorm(A*inv - eye(A.rows), 1) < 1.e-14
def test_precision():
A = randmatrix(10, 10)
assert mnorm(inverse(inverse(A)) - A, 1) < 1.e-45
def test_cond():
mp.dps = 15
A = matrix([[1.2969, 0.8648], [0.2161, 0.1441]])
assert cond(A, lambda x: mnorm(x,1)) == mpf('327065209.73817754')
assert cond(A, lambda x: mnorm(x,inf)) == mpf('327065209.73817754')
assert cond(A, lambda x: mnorm(x,'F')) == mpf('249729266.80008656')
def test_factorization():
A = randmatrix(5)
P, L, U = lu(A)
assert mnorm(P*A - L*U, 1) < 1.e-15
