def test_sparse_consistent_when_stacked(self):
m = 100
nnz = m * 10
n = 10
p = 5
rng = tf.random.Generator.from_seed(0)
A = random_sparse((m, m), nnz, rng=rng)
b = rng.normal((m, p))
bs = tf.split( # pylint: disable=no-value-for-parameter,redundant-keyword-arg
b, p, axis=-1
)
Q_stacked, h_stacked = arnoldi_iteration_tf(A, b, n)
Q_sep, h_sep = zip(*(arnoldi_iteration_tf(A, bi, n) for bi in bs))
Q_sep = tf.concat( # pylint: disable=no-value-for-parameter,unexpected-keyword-arg
Q_sep, axis=-1
)
h_sep = tf.concat( # pylint: disable=no-value-for-parameter,unexpected-keyword-arg
h_sep, axis=-1
)
self.assertAllClose(Q_stacked, Q_sep)
self.assertAllClose(h_stacked, h_sep)
def test_symmetric_case(self):
m = 100
nnz = m * 10
n = 20
p = 5
rng = tf.random.Generator.from_seed(0)
A = random_sparse((m, m), nnz, rng=rng)
A = tf.sparse.add(A, tf.sparse.transpose(A, (1, 0))) # make symmetric
b = rng.normal((m, p))
Qs, hs = arnoldi_iteration_tf(A, b, n, symmetric=True)
Q, h = arnoldi_iteration_tf(A, b, n)
self.assertAllClose(Q, Qs, atol=1e-4)
self.assertAllClose(h, hs, atol=1e-4)
def test_dense_consistent_with_numpy(self):
m = 10
n = 3
rng = tf.random.Generator.from_seed(0)
A = rng.normal((m, m))
b = rng.normal((m, 1))
Q_tf, h_tf = arnoldi_iteration_tf(A, b, n)
Q_np, h_np = arnoldi_iteration_np(A.numpy(), tf.squeeze(b, 1).numpy(), n)
self.assertAllClose(tf.squeeze(Q_tf, axis=-1), Q_np)
self.assertAllClose(tf.squeeze(h_tf, axis=-1), h_np)