def _get_distribution_over_matrix(dims, cfg):
"""Get the distribution over a matrix given a config.
Args:
dims: int dimensions of the matrix.
cfg: Config generated from `get_distribution_over_matrix` or
`sample_matrix_noise_dist`.
Returns:
The corresponding tfp.distribution.Distribution for the matrix.
"""
name, params = cfg
if name == "linspace_eigen":
# Generates a random matrix whose spectrum is sampled uniformly from the
# range (min, max).
spectrum = np.linspace(params["min"], params["max"],
dims).astype(np.float32)
return quadratic_helper.FixedEigenSpectrumMatrixDistribution(spectrum)
elif name == "logspace_eigen":
# Generates a random matrix whose spectrum is sampled logrithmically from
# the range (min, max).
spectrum = np.logspace(np.log10(params["min"]),
np.log10(params["max"]),
dims).astype(np.float32)
return quadratic_helper.FixedEigenSpectrumMatrixDistribution(spectrum)
elif name == "normal":
# Generates a random matrix whose values are randomly sampled from a normal
# with mean and std.
return tfp.distributions.Normal(
tf.ones([dims, dims]) * params["mean"],
tf.ones([dims, dims]) * params["std"])
elif name == "uniform":
# Generates a random matrix whose values are randomly sampled from a uniform
# with mean and std.
return tfp.distributions.Uniform(
tf.ones([dims, dims]) * params["min"],
tf.ones([dims, dims]) * params["max"])
else:
raise ValueError("Name of matrix distribution [%s] not supported." %
name)
def test_eigen_spectrum_matrix_distribution(self):
"""Ensures that the sampled matrix has the correct eigen spectrum."""
dims = 5
specturm = np.linspace(1.0, 2.0, dims).astype(np.float32)
A_dist = quadratic_helper.FixedEigenSpectrumMatrixDistribution(
specturm)
s = A_dist.sample()
with self.test_session() as sess:
mat = sess.run(s)
# Ensure the matrix is not simply a diagonal.
sum_square_not_diag = np.sum(np.square(mat - np.eye(dims) * mat))
self.assertGreater(sum_square_not_diag, 1e-3)
eig_value, _ = np.linalg.eig(mat)
np.testing.assert_allclose(np.linspace(1, 2, 5),
sorted(eig_value),
rtol=1e-5)