def test_cosine_similarity(self):
x = tf.fill((10, 10), 1.)
y = tf.fill((10, 10), 2.)
self.assertAllClose(tensor_utils.cosine_similarity(x, y), 1.)
x = tf.fill((10, 10), 1.)
y = tf.fill((10, 10), -2.)
self.assertAllClose(tensor_utils.cosine_similarity(x, y), -1.)
x = tf.concat([tf.random.normal((10, 10)), tf.fill((10, 10), 0.)], axis=0)
y = tf.concat([tf.fill((10, 10), 0.), tf.random.normal((10, 10))], axis=0)
self.assertAllClose(tensor_utils.cosine_similarity(x, y), 0.)
def estimate_scaling(eigvec, matmul_fn, num_samples):
"""Assuming eigvec is an eigenvector of matmul_fn, estimate its eigenvalue.
Args:
eigvec (vector): a vector.
matmul_fn (function): a function defining a matrix-vector product.
num_samples (int): how many samples to estimate the eigenvalue over.
Returns:
total_eigval (float): the estimated eigenvalue for eigvec.
"""
total_eigval = 0.
total_eigvec_hvp = 0.
for _ in range(num_samples):
eigvec_hvp = matmul_fn(eigvec)
estimated_eigval = tf.math.reduce_euclidean_norm(eigvec_hvp)
estimated_eigval = (estimated_eigval if tf.reduce_all(
tf.reduce_sum(tf.multiply(eigvec, eigvec_hvp)) > 0.) else
-estimated_eigval)
total_eigval += estimated_eigval
total_eigvec_hvp += eigvec_hvp
total_eigval /= num_samples
total_eigvec_hvp /= num_samples
logging.info('Eigenvector estimation: difference in norms is %.3lf',
tf.linalg.norm(eigvec - total_eigvec_hvp / total_eigval))
logging.info(
'Eigenvector estimation: cosine is %.3lf',
tensor_utils.cosine_similarity(eigvec,
total_eigvec_hvp / total_eigval))
return total_eigval
def test_deterministic_largest_eigenvalue_estimation_correct(self):
tf.compat.v1.random.set_random_seed(0)
d_ev = 10
mat = tf.random.normal((d_ev, d_ev), stddev=1)
mat = tf.abs((mat + tf.transpose(mat)) / 2.)
e, v = tf.linalg.eigh(mat)
def matmul_fn_largest(v):
return tf.transpose(tf.matmul(mat, v, transpose_b=True))
largest_ev, largest_evec = eigenvalues.iterated_ev(matmul_fn_largest,
200,
d_ev,
print_freq=50)
self.assertAllClose(largest_ev, e[-1], atol=0.01)
self.assertAllClose(tf.abs(largest_evec),
tf.abs(tf.reshape(v[:, -1], [1, -1])),
atol=0.01)
evec_product = matmul_fn_largest(largest_evec)
self.assertAllClose(tensor_utils.cosine_similarity(
evec_product, largest_evec),
1.,
atol=0.1)
self.assertAllClose(evec_product, largest_ev * largest_evec, atol=0.01)