def f(x):
pi_x = x * np.pi
return array_ops.where_v2(x == 0, array_ops.ones_like(x),
math_ops.sin(pi_x) / pi_x)
def f(x):
# __pow__ can't handle negative base, so we use `abs` here.
rt = math_ops.abs(x)**(1.0 / 3)
return array_ops.where_v2(x < 0, -rt, rt)
def f(x):
return array_ops.where_v2(x < 0, math_ops.ceil(x), math_ops.floor(x))
def f(x1, x2):
return array_ops.where_v2(
x1 < 0, constant_op.constant(0, dtype=x2.dtype),
array_ops.where_v2(x1 > 0, constant_op.constant(1, dtype=x2.dtype),
x2))
def f(x):
if x.dtype in _tf_float_types:
# Workaround for b/147515503
return array_ops.where_v2(x < 0, np.pi, 0)
else:
return math_ops.angle(x)
def false_fn():
return MaskedTensorV1(
array_ops.where_v2(mt.mask, 100, mt.values * 2),
math_ops.logical_not(mt.mask))
def with_default(self, default):
return array_ops.where_v2(self.mask, self.values, default)
def loop_fn(i):
a_i = array_ops.gather(a, i)
b_i = array_ops.gather(b, i)
return array_ops.where_v2(cond, a_i, b_i)
def true_fn():
return MaskedTensorV1(array_ops.where_v2(mt.mask, mt.values, -1),
mt.values > 3)
def norm(tensor,
ord='euclidean',
axis=None,
keepdims=None,
name=None,
keep_dims=None):
r"""Computes the norm of vectors, matrices, and tensors.
This function can compute several different vector norms (the 1-norm, the
Euclidean or 2-norm, the inf-norm, and in general the p-norm for p > 0) and
matrix norms (Frobenius, 1-norm, 2-norm and inf-norm).
Args:
tensor: `Tensor` of types `float32`, `float64`, `complex64`, `complex128`
ord: Order of the norm. Supported values are 'fro', 'euclidean',
`1`, `2`, `np.inf` and any positive real number yielding the corresponding
p-norm. Default is 'euclidean' which is equivalent to Frobenius norm if
`tensor` is a matrix and equivalent to 2-norm for vectors.
Some restrictions apply:
a) The Frobenius norm `fro` is not defined for vectors,
b) If axis is a 2-tuple (matrix norm), only 'euclidean', 'fro', `1`,
`2`, `np.inf` are supported.
See the description of `axis` on how to compute norms for a batch of
vectors or matrices stored in a tensor.
axis: If `axis` is `None` (the default), the input is considered a vector
and a single vector norm is computed over the entire set of values in the
tensor, i.e. `norm(tensor, ord=ord)` is equivalent to
`norm(reshape(tensor, [-1]), ord=ord)`.
If `axis` is a Python integer, the input is considered a batch of vectors,
and `axis` determines the axis in `tensor` over which to compute vector
norms.
If `axis` is a 2-tuple of Python integers it is considered a batch of
matrices and `axis` determines the axes in `tensor` over which to compute
a matrix norm.
Negative indices are supported. Example: If you are passing a tensor that
can be either a matrix or a batch of matrices at runtime, pass
`axis=[-2,-1]` instead of `axis=None` to make sure that matrix norms are
computed.
keepdims: If True, the axis indicated in `axis` are kept with size 1.
Otherwise, the dimensions in `axis` are removed from the output shape.
name: The name of the op.
keep_dims: Deprecated alias for `keepdims`.
Returns:
output: A `Tensor` of the same type as tensor, containing the vector or
matrix norms. If `keepdims` is True then the rank of output is equal to
the rank of `tensor`. Otherwise, if `axis` is none the output is a scalar,
if `axis` is an integer, the rank of `output` is one less than the rank
of `tensor`, if `axis` is a 2-tuple the rank of `output` is two less
than the rank of `tensor`.
Raises:
ValueError: If `ord` or `axis` is invalid.
@compatibility(numpy)
Mostly equivalent to numpy.linalg.norm.
Not supported: ord <= 0, 2-norm for matrices, nuclear norm.
Other differences:
a) If axis is `None`, treats the flattened `tensor` as a vector
regardless of rank.
b) Explicitly supports 'euclidean' norm as the default, including for
higher order tensors.
@end_compatibility
"""
keepdims = deprecation.deprecated_argument_lookup('keepdims', keepdims,
'keep_dims', keep_dims)
if keepdims is None:
keepdims = False
is_matrix_norm = ((isinstance(axis, tuple) or isinstance(axis, list)) and
len(axis) == 2)
if is_matrix_norm:
axis = tuple(axis)
if (not isinstance(axis[0], int) or not isinstance(axis[1], int) or
axis[0] == axis[1]):
raise ValueError(
"'axis' must be None, an integer, or a tuple of 2 unique integers")
supported_matrix_norms = ['euclidean', 'fro', 1, 2, np.inf]
if ord not in supported_matrix_norms:
raise ValueError("'ord' must be a supported matrix norm in %s, got %s" %
(supported_matrix_norms, ord))
else:
if not (isinstance(axis, int) or axis is None):
raise ValueError(
"'axis' must be None, an integer, or a tuple of 2 unique integers")
supported_vector_norms = ['euclidean', 1, 2, np.inf]
if (not np.isreal(ord) or ord <= 0) and ord not in supported_vector_norms:
raise ValueError("'ord' must be a supported vector norm, got %s" % ord)
if axis is not None:
axis = (axis,)
with ops.name_scope(name, 'norm', [tensor]):
tensor = ops.convert_to_tensor(tensor)
if ord in ['fro', 'euclidean', 2, 2.0]:
if is_matrix_norm and ord in [2, 2.0]:
rank = array_ops.rank(tensor)
positive_axis = map_fn.map_fn(
lambda i: control_flow_ops.cond(i >= 0, lambda: i, lambda: i + rank),
ops.convert_to_tensor(axis))
axes = math_ops.range(rank)
perm_before = array_ops.concat(
[array_ops.setdiff1d(axes, positive_axis)[0], positive_axis],
axis=0)
perm_after = map_fn.map_fn(
lambda i: math_ops.cast(
array_ops.squeeze(
array_ops.where_v2(math_ops.equal(perm_before, i))),
dtype=dtypes.int32), axes)
permed = array_ops.transpose(tensor, perm=perm_before)
matrix_2_norm = array_ops.expand_dims(
math_ops.reduce_max(
math_ops.abs(gen_linalg_ops.svd(permed, compute_uv=False)[0]),
axis=-1,
keepdims=True),
axis=-1)
result = array_ops.transpose(matrix_2_norm, perm=perm_after)
else:
result = math_ops.sqrt(
math_ops.reduce_sum(
tensor * math_ops.conj(tensor), axis, keepdims=True))
# TODO(rmlarsen): Replace with the following, once gradients are defined
# result = math_ops.reduce_euclidean_norm(tensor, axis, keepdims=True)
else:
result = math_ops.abs(tensor)
if ord == 1:
sum_axis = None if axis is None else axis[0]
result = math_ops.reduce_sum(result, sum_axis, keepdims=True)
if is_matrix_norm:
result = math_ops.reduce_max(result, axis[-1], keepdims=True)
elif ord == np.inf:
if is_matrix_norm:
result = math_ops.reduce_sum(result, axis[1], keepdims=True)
max_axis = None if axis is None else axis[0]
result = math_ops.reduce_max(result, max_axis, keepdims=True)
else:
# General p-norms (positive p only)
result = math_ops.pow(
math_ops.reduce_sum(math_ops.pow(result, ord), axis, keepdims=True),
1.0 / ord)
if not keepdims:
result = array_ops.squeeze(result, axis)
return result
def testCtcLossDenseUniqueFastPathWithBlankIndexIsSameAsCtcLoss(self):
random_seed.set_random_seed(5)
batch_size = 8
num_labels = 6
label_length = 5
num_frames = 12
logits = random_ops.random_uniform([num_frames, batch_size, num_labels])
labels = random_ops.random_uniform([batch_size, label_length],
minval=0,
maxval=num_labels - 1,
dtype=dtypes.int64)
label_lengths = random_ops.random_uniform([batch_size],
minval=2,
maxval=label_length,
dtype=dtypes.int64)
label_mask = array_ops.sequence_mask(
label_lengths, maxlen=label_length, dtype=label_lengths.dtype)
labels *= label_mask
logit_lengths = [num_frames] * batch_size
tf_ctc_loss_labels = math_ops.cast(labels, dtypes.int32)
tf_ctc_loss_labels = ctc_ops.dense_labels_to_sparse(tf_ctc_loss_labels,
label_lengths)
tf_nn_ctc_loss = ctc_ops.ctc_loss(
labels=tf_ctc_loss_labels,
inputs=logits,
sequence_length=logit_lengths,
time_major=True)
tf_nn_ctc_grads = gradients_impl.gradients(tf_nn_ctc_loss, [logits])[0]
# Shift the blank logits/labels to be somewhere in the middle.
blank_index = 2
shifted_logits = array_ops.concat([
logits[:, :, :blank_index],
logits[:, :, -1:],
logits[:, :, blank_index:-1],
],
axis=2)
shifted_labels = array_ops.where_v2(labels < blank_index, labels,
labels + 1)
ctc_loss = ctc_ops.ctc_loss_dense(
labels=shifted_labels,
logits=shifted_logits,
label_length=label_lengths,
logit_length=logit_lengths,
blank_index=blank_index,
unique=ctc_ops.ctc_unique_labels(shifted_labels))
ctc_loss_grads = gradients_impl.gradients(ctc_loss, [logits])[0]
with self.cached_session() as sess:
for _ in range(32):
self.assertAllClose(*self.evaluate([ctc_loss, tf_nn_ctc_loss]))
self.assertAllClose(
*self.evaluate([ctc_loss_grads, tf_nn_ctc_grads]),
rtol=2e-06,
atol=2e-06)
def training_graph(self,
input_data,
input_labels,
num_trainers=1,
trainer_id=0,
**tree_kwargs):
"""Constructs a TF graph for training a random forest.
Args:
input_data: A tensor or dict of string->Tensor for input data.
input_labels: A tensor or placeholder for labels associated with
input_data.
num_trainers: Number of parallel trainers to split trees among.
trainer_id: Which trainer this instance is.
**tree_kwargs: Keyword arguments passed to each tree's training_graph.
Returns:
The last op in the random forest training graph.
Raises:
NotImplementedError: If trying to use bagging with sparse features.
"""
processed_dense_features, processed_sparse_features, data_spec = (
data_ops.ParseDataTensorOrDict(input_data))
if input_labels is not None:
labels = data_ops.ParseLabelTensorOrDict(input_labels)
data_spec = data_spec or self.get_default_data_spec(input_data)
tree_graphs = []
trees_per_trainer = self.params.num_trees / num_trainers
tree_start = int(trainer_id * trees_per_trainer)
tree_end = int((trainer_id + 1) * trees_per_trainer)
for i in range(tree_start, tree_end):
with ops.device(self.variables.device_dummies[i].device):
seed = self.params.base_random_seed
if seed != 0:
seed += i
# If using bagging, randomly select some of the input.
tree_data = processed_dense_features
tree_labels = labels
if self.params.bagging_fraction < 1.0:
# TODO(gilberth): Support bagging for sparse features.
if processed_sparse_features is not None:
raise NotImplementedError(
'Bagging not supported with sparse features.')
# TODO(thomaswc): This does sampling without replacement. Consider
# also allowing sampling with replacement as an option.
batch_size = array_ops.strided_slice(
array_ops.shape(processed_dense_features), [0], [1])
r = random_ops.random_uniform(batch_size, seed=seed)
mask = math_ops.less(
r,
array_ops.ones_like(r) * self.params.bagging_fraction)
gather_indices = array_ops.squeeze(
array_ops.where_v2(mask), axis=[1])
# TODO(thomaswc): Calculate out-of-bag data and labels, and store
# them for use in calculating statistics later.
tree_data = array_ops.gather(processed_dense_features,
gather_indices)
tree_labels = array_ops.gather(labels, gather_indices)
if self.params.bagged_features:
if processed_sparse_features is not None:
raise NotImplementedError(
'Feature bagging not supported with sparse features.'
)
tree_data = self._bag_features(i, tree_data)
tree_graphs.append(self.trees[i].training_graph(
tree_data,
tree_labels,
seed,
data_spec=data_spec,
sparse_features=processed_sparse_features,
**tree_kwargs))
return control_flow_ops.group(*tree_graphs, name='train')
def pinv(a, rcond=None, validate_args=False, name=None):
"""Compute the Moore-Penrose pseudo-inverse of one or more matrices.
Calculate the [generalized inverse of a matrix](
https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_inverse) using its
singular-value decomposition (SVD) and including all large singular values.
The pseudo-inverse of a matrix `A`, is defined as: 'the matrix that 'solves'
[the least-squares problem] `A @ x = b`,' i.e., if `x_hat` is a solution, then
`A_pinv` is the matrix such that `x_hat = A_pinv @ b`. It can be shown that if
`U @ Sigma @ V.T = A` is the singular value decomposition of `A`, then
`A_pinv = V @ inv(Sigma) U^T`. [(Strang, 1980)][1]
This function is analogous to [`numpy.linalg.pinv`](
https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.pinv.html).
It differs only in default value of `rcond`. In `numpy.linalg.pinv`, the
default `rcond` is `1e-15`. Here the default is
`10. * max(num_rows, num_cols) * np.finfo(dtype).eps`.
Args:
a: (Batch of) `float`-like matrix-shaped `Tensor`(s) which are to be
pseudo-inverted.
rcond: `Tensor` of small singular value cutoffs. Singular values smaller
(in modulus) than `rcond` * largest_singular_value (again, in modulus) are
set to zero. Must broadcast against `tf.shape(a)[:-2]`.
Default value: `10. * max(num_rows, num_cols) * np.finfo(a.dtype).eps`.
validate_args: When `True`, additional assertions might be embedded in the
graph.
Default value: `False` (i.e., no graph assertions are added).
name: Python `str` prefixed to ops created by this function.
Default value: 'pinv'.
Returns:
a_pinv: (Batch of) pseudo-inverse of input `a`. Has same shape as `a` except
rightmost two dimensions are transposed.
Raises:
TypeError: if input `a` does not have `float`-like `dtype`.
ValueError: if input `a` has fewer than 2 dimensions.
#### Examples
```python
import tensorflow as tf
import tensorflow_probability as tfp
a = tf.constant([[1., 0.4, 0.5],
[0.4, 0.2, 0.25],
[0.5, 0.25, 0.35]])
tf.matmul(tf.linalg..pinv(a), a)
# ==> array([[1., 0., 0.],
[0., 1., 0.],
[0., 0., 1.]], dtype=float32)
a = tf.constant([[1., 0.4, 0.5, 1.],
[0.4, 0.2, 0.25, 2.],
[0.5, 0.25, 0.35, 3.]])
tf.matmul(tf.linalg..pinv(a), a)
# ==> array([[ 0.76, 0.37, 0.21, -0.02],
[ 0.37, 0.43, -0.33, 0.02],
[ 0.21, -0.33, 0.81, 0.01],
[-0.02, 0.02, 0.01, 1. ]], dtype=float32)
```
#### References
[1]: G. Strang. 'Linear Algebra and Its Applications, 2nd Ed.' Academic Press,
Inc., 1980, pp. 139-142.
"""
with ops.name_scope(name or 'pinv'):
a = ops.convert_to_tensor(a, name='a')
assertions = _maybe_validate_matrix(a, validate_args)
if assertions:
with ops.control_dependencies(assertions):
a = array_ops.identity(a)
dtype = a.dtype.as_numpy_dtype
if rcond is None:
def get_dim_size(dim):
dim_val = tensor_shape.dimension_value(a.shape[dim])
if dim_val is not None:
return dim_val
return array_ops.shape(a)[dim]
num_rows = get_dim_size(-2)
num_cols = get_dim_size(-1)
if isinstance(num_rows, int) and isinstance(num_cols, int):
max_rows_cols = float(max(num_rows, num_cols))
else:
max_rows_cols = math_ops.cast(
math_ops.maximum(num_rows, num_cols), dtype)
rcond = 10. * max_rows_cols * np.finfo(dtype).eps
rcond = ops.convert_to_tensor(rcond, dtype=dtype, name='rcond')
# Calculate pseudo inverse via SVD.
# Note: if a is Hermitian then u == v. (We might observe additional
# performance by explicitly setting `v = u` in such cases.)
[
singular_values, # Sigma
left_singular_vectors, # U
right_singular_vectors, # V
] = svd(a, full_matrices=False, compute_uv=True)
# Saturate small singular values to inf. This has the effect of make
# `1. / s = 0.` while not resulting in `NaN` gradients.
cutoff = rcond * math_ops.reduce_max(singular_values, axis=-1)
singular_values = array_ops.where_v2(
singular_values > array_ops.expand_dims_v2(cutoff, -1),
singular_values, np.array(np.inf, dtype))
# By the definition of the SVD, `a == u @ s @ v^H`, and the pseudo-inverse
# is defined as `pinv(a) == v @ inv(s) @ u^H`.
a_pinv = math_ops.matmul(right_singular_vectors /
array_ops.expand_dims_v2(singular_values, -2),
left_singular_vectors,
adjoint_b=True)
if a.shape is not None and a.shape.rank is not None:
a_pinv.set_shape(a.shape[:-2].concatenate(
[a.shape[-1], a.shape[-2]]))
return a_pinv
def _cdf(self, x):
# Take Abs(scale) to make subsequent where work correctly.
y = (x - self.loc) / math_ops.abs(self.scale)
x_t = self.df / (y**2. + self.df)
neg_cdf = 0.5 * math_ops.betainc(0.5 * self.df, 0.5, x_t)
return array_ops.where_v2(math_ops.less(y, 0.), neg_cdf, 1. - neg_cdf)
