def check_cam_coherence(path):
"""Check the coherence of a camera path."""
cam_gt = path + 'cam0_gt.visim'
cam_render = path + 'cam0.render'
lines = tf.string_split([tf.read_file(cam_render)], '\n').values
lines = lines[3:]
lines = tf.strided_slice(lines, [0], [lines.shape_as_list()[0]], [2])
fields = tf.reshape(tf.string_split(lines, ' ').values, [-1, 10])
timestamp_from_render, numbers = tf.split(fields, [1, 9], -1)
numbers = tf.strings.to_number(numbers)
eye, lookat, up = tf.split(numbers, [3, 3, 3], -1)
up_vector = tf.nn.l2_normalize(up - eye)
lookat_vector = tf.nn.l2_normalize(lookat - eye)
rotation_from_lookat = lookat_matrix(up_vector, lookat_vector)
lines = tf.string_split([tf.read_file(cam_gt)], '\n').values
lines = lines[1:]
fields = tf.reshape(tf.string_split(lines, ',').values, [-1, 8])
timestamp_from_gt, numbers = tf.split(fields, [1, 7], -1)
numbers = tf.strings.to_number(numbers)
position, quaternion = tf.split(numbers, [3, 4], -1)
rotation_from_quaternion = from_quaternion(quaternion)
assert tf.reduce_all(tf.equal(timestamp_from_render, timestamp_from_gt))
assert tf.reduce_all(tf.equal(eye, position))
so3_diff = (tf.trace(
tf.matmul(
rotation_from_lookat, rotation_from_quaternion, transpose_a=True)) -
1) / 2
tf.assert_near(so3_diff, tf.ones_like(so3_diff))
def _validate_correlationness(self, x):
if not self.validate_args:
return x
checks = [
tf.assert_less_equal(-1., x, message='Correlations must be >= -1.'),
tf.assert_less_equal(x, 1., message='Correlations must be <= 1.'),
tf.assert_near(
tf.matrix_diag_part(x), 1.,
message='Self-correlations must be = 1.'),
tf.assert_near(
x, tf.matrix_transpose(x),
message='Correlation matrices must be symmetric')
]
with tf.control_dependencies(checks):
return tf.identity(x)
def _assert_valid_sample(self, x):
if not self.validate_args:
return x
return control_flow_ops.with_dependencies([
tf.assert_non_positive(x),
tf.assert_near(tf.zeros([], dtype=self.dtype),
tf.reduce_logsumexp(x, axis=[-1])),
], x)
def _assert_valid_sample(self, x):
if not self.validate_args:
return x
return control_flow_ops.with_dependencies([
tf.assert_non_positive(x),
tf.assert_near(
tf.zeros([], dtype=self.dtype), tf.reduce_logsumexp(x, axis=[-1])),
], x)
def _maybe_assert_valid_sample(self, x):
"""Checks the validity of a sample."""
if not self.validate_args:
return x
return control_flow_ops.with_dependencies([
tf.assert_positive(x, message="samples must be positive"),
tf.assert_near(tf.ones([], dtype=self.dtype),
tf.reduce_sum(x, -1),
message="sample last-dimension must sum to `1`"),
], x)
def _validate_correlationness(self, x):
if not self.validate_args or self.input_output_cholesky:
return x
checks = [
tf.assert_less_equal(tf.cast(-1., dtype=x.dtype.base_dtype),
x,
message='Correlations must be >= -1.'),
tf.assert_less_equal(x,
tf.cast(1., x.dtype.base_dtype),
message='Correlations must be <= 1.'),
tf.assert_near(tf.matrix_diag_part(x),
tf.cast(1., x.dtype.base_dtype),
message='Self-correlations must be = 1.'),
tf.assert_near(x,
tf.matrix_transpose(x),
message='Correlation matrices must be symmetric')
]
with tf.control_dependencies(checks):
return tf.identity(x)
def _maybe_assert_valid_sample(self, x):
"""Checks the validity of a sample."""
if not self.validate_args:
return x
return control_flow_ops.with_dependencies([
tf.assert_positive(x, message="samples must be positive"),
tf.assert_near(
tf.ones([], dtype=self.dtype),
tf.reduce_sum(x, -1),
message="sample last-dimension must sum to `1`"),
], x)
def _validate_correlationness(self, x):
if not self.validate_args:
return x
checks = [
tf.assert_less_equal(
tf.cast(-1., dtype=x.dtype.base_dtype),
x,
message='Correlations must be >= -1.'),
tf.assert_less_equal(
x,
tf.cast(1., x.dtype.base_dtype),
message='Correlations must be <= 1.'),
tf.assert_near(
tf.matrix_diag_part(x),
tf.cast(1., x.dtype.base_dtype),
message='Self-correlations must be = 1.'),
tf.assert_near(
x, tf.matrix_transpose(x),
message='Correlation matrices must be symmetric')
]
with tf.control_dependencies(checks):
return tf.identity(x)
def _maybe_assert_valid_sample(self, samples):
"""Check counts for proper shape, values, then return tensor version."""
if not self.validate_args:
return samples
with tf.control_dependencies([
tf.assert_near(
1., tf.linalg.norm(samples, axis=-1),
message='samples must be unit length'),
tf.assert_equal(
tf.shape(samples)[-1:], self.event_shape_tensor(),
message=('samples must have innermost dimension matching that of '
'`self.mean_direction`')),
]):
return tf.identity(samples)
def backward_tensor(self, y):
size = np.prod(y.shape.as_list())
N = int(np.sqrt(size / self.num_matrices))
reshaped = tf.reshape(y, shape=(N, N, self.num_matrices))
indices = np.dstack(np.tril_indices(N))[0]
# triangular = tf.reshape(tf.gather_nd(reshaped, indices), shape=[-1])
triangular = tf.transpose(tf.gather_nd(reshaped, indices))
with tf.control_dependencies([
tf.assert_near(y,
self.forward_tensor(triangular),
message='check equal')
]):
triangular = triangular + tf.zeros_like(triangular)
return triangular
def __init__(self,
loc=None,
covariance_matrix=None,
validate_args=False,
allow_nan_stats=True,
name="MultivariateNormalFullCovariance"):
"""Construct Multivariate Normal distribution on `R^k`.
The `batch_shape` is the broadcast shape between `loc` and
`covariance_matrix` arguments.
The `event_shape` is given by last dimension of the matrix implied by
`covariance_matrix`. The last dimension of `loc` (if provided) must
broadcast with this.
A non-batch `covariance_matrix` matrix is a `k x k` symmetric positive
definite matrix. In other words it is (real) symmetric with all eigenvalues
strictly positive.
Additional leading dimensions (if any) will index batches.
Args:
loc: Floating-point `Tensor`. If this is set to `None`, `loc` is
implicitly `0`. When specified, may have shape `[B1, ..., Bb, k]` where
`b >= 0` and `k` is the event size.
covariance_matrix: Floating-point, symmetric positive definite `Tensor` of
same `dtype` as `loc`. The strict upper triangle of `covariance_matrix`
is ignored, so if `covariance_matrix` is not symmetric no error will be
raised (unless `validate_args is True`). `covariance_matrix` has shape
`[B1, ..., Bb, k, k]` where `b >= 0` and `k` is the event size.
validate_args: Python `bool`, default `False`. When `True` distribution
parameters are checked for validity despite possibly degrading runtime
performance. When `False` invalid inputs may silently render incorrect
outputs.
allow_nan_stats: Python `bool`, default `True`. When `True`,
statistics (e.g., mean, mode, variance) use the value "`NaN`" to
indicate the result is undefined. When `False`, an exception is raised
if one or more of the statistic's batch members are undefined.
name: Python `str` name prefixed to Ops created by this class.
Raises:
ValueError: if neither `loc` nor `covariance_matrix` are specified.
"""
parameters = dict(locals())
# Convert the covariance_matrix up to a scale_tril and call MVNTriL.
with tf.name_scope(name) as name:
with tf.name_scope("init", values=[loc, covariance_matrix]):
if covariance_matrix is None:
scale_tril = None
else:
covariance_matrix = tf.convert_to_tensor(
covariance_matrix, name="covariance_matrix")
if validate_args:
covariance_matrix = control_flow_ops.with_dependencies(
[
tf.assert_near(
covariance_matrix,
tf.matrix_transpose(covariance_matrix),
message="Matrix was not symmetric")
], covariance_matrix)
# No need to validate that covariance_matrix is non-singular.
# LinearOperatorLowerTriangular has an assert_non_singular method that
# is called by the Bijector.
# However, cholesky() ignores the upper triangular part, so we do need
# to separately assert symmetric.
scale_tril = tf.cholesky(covariance_matrix)
super(MultivariateNormalFullCovariance,
self).__init__(loc=loc,
scale_tril=scale_tril,
validate_args=validate_args,
allow_nan_stats=allow_nan_stats,
name=name)
self._parameters = parameters
def _sample_n(self, n, seed=None):
seed = seed_stream.SeedStream(seed, salt='vom_mises_fisher')
# The sampling strategy relies on the fact that vMF variates are symmetric
# about the mean direction. Accordingly, if we have a sampling strategy for
# the away-from-mean angle, then we can uniformly sample the remaining
# dimensions on the S^{dim-2} sphere for , and rotate these samples from a
# (1, 0, 0, ..., 0)-mode distribution into the target orientation.
#
# This is easy to imagine on the 1-sphere (S^1; in 2-D space): sample a
# von-Mises distributed `x` value in [-1, 1], then uniformly select what
# amounts to a "up" or "down" additional degree of freedom after unit
# normalizing, followed by a final rotation to the desired mean direction
# from a basis of (1, 0).
#
# On S^2 (in 3-D), selecting a vMF `x` identifies a circle in `yz` on the
# unit sphere over which the distribution is uniform, in particular the
# circle where x = \hat{x} intersects the unit sphere. We pick a point on
# that circle, then rotate to the desired mean direction from a basis of
# (1, 0, 0).
event_dim = self.event_shape[0].value or self._event_shape_tensor()[0]
sample_batch_shape = tf.concat([[n], self._batch_shape_tensor()],
axis=0)
dim = tf.cast(event_dim - 1, self.dtype)
if event_dim == 3:
samples_dim0 = self._sample_3d(n, seed=seed)
else:
# Wood'94 provides a rejection algorithm to sample the x coordinate.
# Wood'94 definition of b:
# b = (-2 * kappa + tf.sqrt(4 * kappa**2 + dim**2)) / dim
# https://stats.stackexchange.com/questions/156729 suggests:
b = dim / (2 * self.concentration +
tf.sqrt(4 * self.concentration**2 + dim**2))
# TODO(bjp): Integrate any useful numerical tricks from hyperspherical VAE
# https://github.com/nicola-decao/s-vae-tf/
x = (1 - b) / (1 + b)
c = self.concentration * x + dim * tf.log1p(-x**2)
beta = tf.distributions.Beta(dim / 2, dim / 2)
def cond_fn(w, should_continue):
del w
return tf.reduce_any(should_continue)
def body_fn(w, should_continue):
z = beta.sample(sample_shape=sample_batch_shape, seed=seed())
w = tf.where(should_continue,
(1 - (1 + b) * z) / (1 - (1 - b) * z), w)
w = tf.check_numerics(w, 'w')
should_continue = tf.logical_and(
should_continue,
self.concentration * w + dim * tf.log1p(-x * w) - c <
tf.log(
tf.random_uniform(sample_batch_shape,
seed=seed(),
dtype=self.dtype)))
return w, should_continue
w = tf.zeros(sample_batch_shape, dtype=self.dtype)
should_continue = tf.ones(sample_batch_shape, dtype=tf.bool)
samples_dim0 = tf.while_loop(cond_fn, body_fn,
(w, should_continue))[0]
samples_dim0 = samples_dim0[..., tf.newaxis]
if not self._allow_nan_stats:
# Verify samples are w/in -1, 1, with useful error output tensors (top
# value rather than all values).
with tf.control_dependencies([
tf.assert_less_equal(
samples_dim0,
self.dtype.as_numpy_dtype(1.01),
data=[tf.nn.top_k(tf.reshape(samples_dim0, [-1]))[0]]),
tf.assert_greater_equal(
samples_dim0,
self.dtype.as_numpy_dtype(-1.01),
data=[
-tf.nn.top_k(tf.reshape(-samples_dim0, [-1]))[0]
])
]):
samples_dim0 = tf.identity(samples_dim0)
samples_otherdims_shape = tf.concat(
[sample_batch_shape, [event_dim - 1]], axis=0)
unit_otherdims = tf.nn.l2_normalize(tf.random_normal(
samples_otherdims_shape, seed=seed(), dtype=self.dtype),
axis=-1)
samples = tf.concat(
[
samples_dim0, # we must avoid sqrt(1 - (>1)**2)
tf.sqrt(tf.maximum(1 - samples_dim0**2, 0.)) * unit_otherdims
],
axis=-1)
samples = tf.nn.l2_normalize(samples, axis=-1)
if not self._allow_nan_stats:
samples = tf.check_numerics(samples, 'samples')
# Runtime assert that samples are unit length.
if not self._allow_nan_stats:
worst, idx = tf.nn.top_k(
tf.reshape(tf.abs(1 - tf.linalg.norm(samples, axis=-1)), [-1]))
with tf.control_dependencies([
tf.assert_near(self.dtype.as_numpy_dtype(0),
worst,
data=[
worst, idx,
tf.gather(
tf.reshape(samples,
[-1, event_dim]), idx)
],
atol=1e-4,
summarize=100)
]):
samples = tf.identity(samples)
# The samples generated are symmetric around a mode at (1, 0, 0, ...., 0).
# Now, we move the mode to `self.mean_direction` using a rotation matrix.
if not self._allow_nan_stats:
# Assert that the basis vector rotates to the mean direction, as expected.
basis = tf.cast(
tf.concat([[1.], tf.zeros([event_dim - 1])], axis=0),
self.dtype)
with tf.control_dependencies([
tf.assert_less(
tf.linalg.norm(self._rotate(basis) -
self.mean_direction,
axis=-1),
self.dtype.as_numpy_dtype(1e-5))
]):
return self._rotate(samples)
return self._rotate(samples)
def __init__(self,
mean_direction,
concentration,
validate_args=False,
allow_nan_stats=True,
name='VonMisesFisher'):
"""Creates a new `VonMisesFisher` instance.
Args:
mean_direction: Floating-point `Tensor` with shape [B1, ... Bn, D].
A unit vector indicating the mode of the distribution, or the
unit-normalized direction of the mean. (This is *not* in general the
mean of the distribution; the mean is not generally in the support of
the distribution.) NOTE: `D` is currently restricted to <= 5.
concentration: Floating-point `Tensor` having batch shape [B1, ... Bn]
broadcastable with `mean_direction`. The level of concentration of
samples around the `mean_direction`. `concentration=0` indicates a
uniform distribution over the unit hypersphere, and `concentration=+inf`
indicates a `Deterministic` distribution (delta function) at
`mean_direction`.
validate_args: Python `bool`, default `False`. When `True` distribution
parameters are checked for validity despite possibly degrading runtime
performance. When `False` invalid inputs may silently render incorrect
outputs.
allow_nan_stats: Python `bool`, default `True`. When `True`,
statistics (e.g., mean, mode, variance) use the value "`NaN`" to
indicate the result is undefined. When `False`, an exception is raised
if one or more of the statistic's batch members are undefined.
name: Python `str` name prefixed to Ops created by this class.
Raises:
ValueError: For known-bad arguments, i.e. unsupported event dimension.
"""
parameters = dict(locals())
with tf.name_scope(name, values=[mean_direction,
concentration]) as name:
assertions = [
tf.assert_non_negative(
concentration,
message='`concentration` must be non-negative'),
tf.assert_greater(
tf.shape(mean_direction)[-1],
1,
message='`mean_direction` may not have scalar event shape'
),
tf.assert_near(1.,
tf.linalg.norm(mean_direction, axis=-1),
message='`mean_direction` must be unit-length')
] if validate_args else []
if mean_direction.shape.with_rank_at_least(
1)[-1].value is not None:
if mean_direction.shape.with_rank_at_least(1)[-1].value > 5:
raise ValueError(
'vMF ndims > 5 is not currently supported')
elif validate_args:
assertions += [
tf.assert_less_equal(
tf.shape(mean_direction)[-1],
5,
message='vMF ndims > 5 is not currently supported')
]
with tf.control_dependencies(assertions):
self._mean_direction = tf.convert_to_tensor(
mean_direction, name='mean_direction')
self._concentration = tf.convert_to_tensor(
concentration, name='concentration')
tf.assert_same_float_dtype(
[self._mean_direction, self._concentration])
# mean_direction is always reparameterized.
# concentration is only for event_dim==3, via an inversion sampler.
reparameterization_type = (
tf.distributions.FULLY_REPARAMETERIZED
if mean_direction.shape.with_rank_at_least(1)[-1].value == 3
else tf.distributions.NOT_REPARAMETERIZED)
super(VonMisesFisher, self).__init__(
dtype=self._concentration.dtype,
validate_args=validate_args,
allow_nan_stats=allow_nan_stats,
reparameterization_type=reparameterization_type,
parameters=parameters,
graph_parents=[self._mean_direction, self._concentration],
name=name)
def _sample_n(self, n, seed=None):
seed = seed_stream.SeedStream(seed, salt='vom_mises_fisher')
# The sampling strategy relies on the fact that vMF variates are symmetric
# about the mean direction. Accordingly, if we have a sampling strategy for
# the away-from-mean angle, then we can uniformly sample the remaining
# dimensions on the S^{dim-2} sphere for , and rotate these samples from a
# (1, 0, 0, ..., 0)-mode distribution into the target orientation.
#
# This is easy to imagine on the 1-sphere (S^1; in 2-D space): sample a
# von-Mises distributed `x` value in [-1, 1], then uniformly select what
# amounts to a "up" or "down" additional degree of freedom after unit
# normalizing, followed by a final rotation to the desired mean direction
# from a basis of (1, 0).
#
# On S^2 (in 3-D), selecting a vMF `x` identifies a circle in `yz` on the
# unit sphere over which the distribution is uniform, in particular the
# circle where x = \hat{x} intersects the unit sphere. We pick a point on
# that circle, then rotate to the desired mean direction from a basis of
# (1, 0, 0).
event_dim = self.event_shape[0].value or self._event_shape_tensor()[0]
sample_batch_shape = tf.concat([[n], self._batch_shape_tensor()], axis=0)
dim = tf.cast(event_dim - 1, self.dtype)
if event_dim == 3:
samples_dim0 = self._sample_3d(n, seed=seed)
else:
# Wood'94 provides a rejection algorithm to sample the x coordinate.
# Wood'94 definition of b:
# b = (-2 * kappa + tf.sqrt(4 * kappa**2 + dim**2)) / dim
# https://stats.stackexchange.com/questions/156729 suggests:
b = dim / (2 * self.concentration +
tf.sqrt(4 * self.concentration**2 + dim**2))
# TODO(bjp): Integrate any useful numerical tricks from hyperspherical VAE
# https://github.com/nicola-decao/s-vae-tf/
x = (1 - b) / (1 + b)
c = self.concentration * x + dim * tf.log1p(-x**2)
beta = beta_lib.Beta(dim / 2, dim / 2)
def cond_fn(w, should_continue):
del w
return tf.reduce_any(should_continue)
def body_fn(w, should_continue):
z = beta.sample(sample_shape=sample_batch_shape, seed=seed())
w = tf.where(should_continue, (1 - (1 + b) * z) / (1 - (1 - b) * z), w)
w = tf.check_numerics(w, 'w')
should_continue = tf.logical_and(
should_continue,
self.concentration * w + dim * tf.log1p(-x * w) - c <
tf.log(tf.random_uniform(sample_batch_shape, seed=seed(),
dtype=self.dtype)))
return w, should_continue
w = tf.zeros(sample_batch_shape, dtype=self.dtype)
should_continue = tf.ones(sample_batch_shape, dtype=tf.bool)
samples_dim0 = tf.while_loop(cond_fn, body_fn, (w, should_continue))[0]
samples_dim0 = samples_dim0[..., tf.newaxis]
if not self._allow_nan_stats:
# Verify samples are w/in -1, 1, with useful error output tensors (top
# value rather than all values).
with tf.control_dependencies([
tf.assert_less_equal(
samples_dim0, self.dtype.as_numpy_dtype(1.01),
data=[tf.nn.top_k(tf.reshape(samples_dim0, [-1]))[0]]),
tf.assert_greater_equal(
samples_dim0, self.dtype.as_numpy_dtype(-1.01),
data=[-tf.nn.top_k(tf.reshape(-samples_dim0, [-1]))[0]])]):
samples_dim0 = tf.identity(samples_dim0)
samples_otherdims_shape = tf.concat([sample_batch_shape, [event_dim - 1]],
axis=0)
unit_otherdims = tf.nn.l2_normalize(
tf.random_normal(samples_otherdims_shape, seed=seed(),
dtype=self.dtype),
axis=-1)
samples = tf.concat([
samples_dim0, # we must avoid sqrt(1 - (>1)**2)
tf.sqrt(tf.maximum(1 - samples_dim0**2, 0.)) * unit_otherdims
], axis=-1)
samples = tf.nn.l2_normalize(samples, axis=-1)
if not self._allow_nan_stats:
samples = tf.check_numerics(samples, 'samples')
# Runtime assert that samples are unit length.
if not self._allow_nan_stats:
worst, idx = tf.nn.top_k(
tf.reshape(tf.abs(1 - tf.linalg.norm(samples, axis=-1)), [-1]))
with tf.control_dependencies([
tf.assert_near(
self.dtype.as_numpy_dtype(0), worst,
data=[worst, idx,
tf.gather(tf.reshape(samples, [-1, event_dim]), idx)],
atol=1e-4, summarize=100)]):
samples = tf.identity(samples)
# The samples generated are symmetric around a mode at (1, 0, 0, ...., 0).
# Now, we move the mode to `self.mean_direction` using a rotation matrix.
if not self._allow_nan_stats:
# Assert that the basis vector rotates to the mean direction, as expected.
basis = tf.cast(tf.concat([[1.], tf.zeros([event_dim - 1])], axis=0),
self.dtype)
with tf.control_dependencies([
tf.assert_less(
tf.linalg.norm(self._rotate(basis) - self.mean_direction,
axis=-1),
self.dtype.as_numpy_dtype(1e-5))
]):
return self._rotate(samples)
return self._rotate(samples)
def __init__(self,
mean_direction,
concentration,
validate_args=False,
allow_nan_stats=True,
name='VonMisesFisher'):
"""Creates a new `VonMisesFisher` instance.
Args:
mean_direction: Floating-point `Tensor` with shape [B1, ... Bn, D].
A unit vector indicating the mode of the distribution, or the
unit-normalized direction of the mean. (This is *not* in general the
mean of the distribution; the mean is not generally in the support of
the distribution.) NOTE: `D` is currently restricted to <= 5.
concentration: Floating-point `Tensor` having batch shape [B1, ... Bn]
broadcastable with `mean_direction`. The level of concentration of
samples around the `mean_direction`. `concentration=0` indicates a
uniform distribution over the unit hypersphere, and `concentration=+inf`
indicates a `Deterministic` distribution (delta function) at
`mean_direction`.
validate_args: Python `bool`, default `False`. When `True` distribution
parameters are checked for validity despite possibly degrading runtime
performance. When `False` invalid inputs may silently render incorrect
outputs.
allow_nan_stats: Python `bool`, default `True`. When `True`,
statistics (e.g., mean, mode, variance) use the value "`NaN`" to
indicate the result is undefined. When `False`, an exception is raised
if one or more of the statistic's batch members are undefined.
name: Python `str` name prefixed to Ops created by this class.
Raises:
ValueError: For known-bad arguments, i.e. unsupported event dimension.
"""
parameters = dict(locals())
with tf.name_scope(name, values=[mean_direction, concentration]) as name:
dtype = dtype_util.common_dtype([mean_direction, concentration],
tf.float32)
mean_direction = tf.convert_to_tensor(
mean_direction, name='mean_direction', dtype=dtype)
concentration = tf.convert_to_tensor(
concentration, name='concentration', dtype=dtype)
assertions = [
tf.assert_non_negative(
concentration, message='`concentration` must be non-negative'),
tf.assert_greater(
tf.shape(mean_direction)[-1], 1,
message='`mean_direction` may not have scalar event shape'),
tf.assert_near(
1., tf.linalg.norm(mean_direction, axis=-1),
message='`mean_direction` must be unit-length')
] if validate_args else []
if mean_direction.shape.with_rank_at_least(1)[-1].value is not None:
if mean_direction.shape.with_rank_at_least(1)[-1].value > 5:
raise ValueError('vMF ndims > 5 is not currently supported')
elif validate_args:
assertions += [tf.assert_less_equal(
tf.shape(mean_direction)[-1], 5,
message='vMF ndims > 5 is not currently supported')]
with tf.control_dependencies(assertions):
self._mean_direction = tf.identity(mean_direction)
self._concentration = tf.identity(concentration)
tf.assert_same_float_dtype([self._mean_direction, self._concentration])
# mean_direction is always reparameterized.
# concentration is only for event_dim==3, via an inversion sampler.
reparameterization_type = (
reparameterization.FULLY_REPARAMETERIZED
if mean_direction.shape.with_rank_at_least(1)[-1].value == 3 else
reparameterization.NOT_REPARAMETERIZED)
super(VonMisesFisher, self).__init__(
dtype=self._concentration.dtype,
validate_args=validate_args,
allow_nan_stats=allow_nan_stats,
reparameterization_type=reparameterization_type,
parameters=parameters,
graph_parents=[self._mean_direction, self._concentration],
name=name)
def __init__(self,
loc=None,
covariance_matrix=None,
validate_args=False,
allow_nan_stats=True,
name="MultivariateNormalFullCovariance"):
"""Construct Multivariate Normal distribution on `R^k`.
The `batch_shape` is the broadcast shape between `loc` and
`covariance_matrix` arguments.
The `event_shape` is given by last dimension of the matrix implied by
`covariance_matrix`. The last dimension of `loc` (if provided) must
broadcast with this.
A non-batch `covariance_matrix` matrix is a `k x k` symmetric positive
definite matrix. In other words it is (real) symmetric with all eigenvalues
strictly positive.
Additional leading dimensions (if any) will index batches.
Args:
loc: Floating-point `Tensor`. If this is set to `None`, `loc` is
implicitly `0`. When specified, may have shape `[B1, ..., Bb, k]` where
`b >= 0` and `k` is the event size.
covariance_matrix: Floating-point, symmetric positive definite `Tensor` of
same `dtype` as `loc`. The strict upper triangle of `covariance_matrix`
is ignored, so if `covariance_matrix` is not symmetric no error will be
raised (unless `validate_args is True`). `covariance_matrix` has shape
`[B1, ..., Bb, k, k]` where `b >= 0` and `k` is the event size.
validate_args: Python `bool`, default `False`. When `True` distribution
parameters are checked for validity despite possibly degrading runtime
performance. When `False` invalid inputs may silently render incorrect
outputs.
allow_nan_stats: Python `bool`, default `True`. When `True`,
statistics (e.g., mean, mode, variance) use the value "`NaN`" to
indicate the result is undefined. When `False`, an exception is raised
if one or more of the statistic's batch members are undefined.
name: Python `str` name prefixed to Ops created by this class.
Raises:
ValueError: if neither `loc` nor `covariance_matrix` are specified.
"""
parameters = dict(locals())
# Convert the covariance_matrix up to a scale_tril and call MVNTriL.
with tf.name_scope(name) as name:
with tf.name_scope("init", values=[loc, covariance_matrix]):
dtype = dtype_util.common_dtype([loc, covariance_matrix], tf.float32)
loc = loc if loc is None else tf.convert_to_tensor(
loc, name="loc", dtype=dtype)
if covariance_matrix is None:
scale_tril = None
else:
covariance_matrix = tf.convert_to_tensor(
covariance_matrix, name="covariance_matrix", dtype=dtype)
if validate_args:
covariance_matrix = control_flow_ops.with_dependencies([
tf.assert_near(
covariance_matrix,
tf.matrix_transpose(covariance_matrix),
message="Matrix was not symmetric")
], covariance_matrix)
# No need to validate that covariance_matrix is non-singular.
# LinearOperatorLowerTriangular has an assert_non_singular method that
# is called by the Bijector.
# However, cholesky() ignores the upper triangular part, so we do need
# to separately assert symmetric.
scale_tril = tf.cholesky(covariance_matrix)
super(MultivariateNormalFullCovariance, self).__init__(
loc=loc,
scale_tril=scale_tril,
validate_args=validate_args,
allow_nan_stats=allow_nan_stats,
name=name)
self._parameters = parameters
