def test_streaming_gram_schmidt(self):
X0 = numpy.array([[1, 0.5, 10., 5., -2.], [0, 0.4, 20, 4., 2.],
[0, 0.4, 19, 4.2, 2.], [0, 0.7, 18, 4.1, 1.4]],
dtype=float).T
for dim in (3, 2, 4):
X = X0[:, :dim]
Xt = X.T
algo1 = []
algo1_t = []
idd = numpy.identity(dim)
for i in range(dim, Xt.shape[1] + 1):
t, p = gram_schmidt(Xt[:, :i], change=True)
algo1_t.append(t)
algo1.append(p)
t_ = X[:i] @ p.T
self.assertEqualArray(t @ t.T, idd)
self.assertEqualArray(t_.T @ t_, idd)
algo2 = []
self.assertRaise(
lambda: list(streaming_gram_schmidt(X)), # pylint: disable=W0640
RuntimeError)
for i, p in enumerate(streaming_gram_schmidt(Xt)):
p2 = p.copy()
t2 = X[:i + dim] @ p2.T
algo2.append(p2)
self.assertNotEmpty(t2)
self.assertNotEmpty(p2)
self.assertEqualArray(t2.T @ t2, idd)
self.assertEqual(len(algo1), len(algo2))
def test_gram_schmidt(self):
mat1 = numpy.array([[1, 0], [0, 1]], dtype=float)
res = gram_schmidt(mat1)
self.assertEqual(res, mat1)
mat = numpy.array([[1, 0.5], [0.5, 1]], dtype=float)
res = gram_schmidt(mat)
self.assertEqualArray(mat1, res @ res.T)
res2 = gram_schmidt(mat.T).T
res2, change2 = gram_schmidt(mat, change=True)
self.assertEqual(res, res2)
res3 = change2 @ mat
self.assertEqual(res3, res2)
mat1 = numpy.array([[1, 0, 0], [0, 0, 1]], dtype=float)
res = gram_schmidt(mat1)
self.assertEqual(res, mat1)
mat1 = numpy.array([[1, 0.5, 0], [0, 0.5, 1]], dtype=float)
res = gram_schmidt(mat1)
self.assertEqual(res[0, 2], 0)
mat1 = numpy.array([[1, 0.5, 0], [0, 0.5, 1], [1, 0.5, 1]],
dtype=float)
res = gram_schmidt(mat1)
self.assertEqualArray(numpy.identity(3), res @ res.T)
def test_gram_schmidt(self):
mat1 = numpy.array([[1, 0], [0, 1]], dtype=float)
res = gram_schmidt(mat1)
self.assertEqual(res, mat1)
mat = numpy.array([[1, 0.5], [0.5, 1]], dtype=float)
res = gram_schmidt(mat)
self.assertEqualArray(mat1, res @ res.T)
res2 = gram_schmidt(mat.T).T
res2, change2 = gram_schmidt(mat, change=True)
self.assertEqual(res, res2)
res3 = change2 @ mat
self.assertEqual(res3, res2)
mat1 = numpy.array([[1, 0, 0], [0, 0, 1]], dtype=float)
res = gram_schmidt(mat1)
self.assertEqual(res, mat1)
mat1 = numpy.array([[1, 0.5, 0], [0, 0.5, 1]], dtype=float)
res = gram_schmidt(mat1)
self.assertEqual(res[0, 2], 0)
mat1 = numpy.array(
[[1, 0.5, 0], [0, 0.5, 1], [1, 0.5, 1]], dtype=float)
res = gram_schmidt(mat1)
self.assertEqualArray(numpy.identity(3), res @ res.T)
def test_gram_schmidt_xx(self):
X = numpy.array([[1, 0.5, 0], [0, 0.4, 2]], dtype=float).T
T, P = gram_schmidt(X.T, change=True)
P = P.T
T = T.T
m = P.T @ X.T
z = m @ m.T
self.assertEqual(z, numpy.identity(2))
m = X @ P
self.assertEqual(m, T)
z2 = m.T @ m
self.assertEqual(z2, numpy.identity(2))
def test_gram_schmidt_xx(self):
X = numpy.array([[1, 0.5, 0], [0, 0.4, 2]], dtype=float).T
U, P = gram_schmidt(X.T, change=True)
P = P.T
U = U.T
m = P.T @ X.T
z = m @ m.T
self.assertEqual(z, numpy.identity(2))
m = X @ P
self.assertEqual(m, U)
z2 = m.T @ m
self.assertEqual(z2, numpy.identity(2))