def _SparseReorderGrad(op, unused_output_indices_grad, output_values_grad):
"""Gradients for the SparseReorder op.
Args:
op: the SparseReorder op
unused_output_indices_grad: the incoming gradients of the output indices
output_values_grad: the incoming gradients of the output values
Returns:
Gradient for each of the 3 input tensors:
(input_indices, input_values, input_shape)
The gradients for input_indices and input_shape is None.
"""
input_indices = op.inputs[0]
input_shape = op.inputs[2]
num_entries = array_ops.shape(input_indices)[0]
entry_indices = math_ops.range(num_entries)
sp_unordered = sparse_tensor.SparseTensor(
input_indices, entry_indices, input_shape)
sp_ordered = sparse_ops.sparse_reorder(sp_unordered)
inverted_permutation = array_ops.invert_permutation(sp_ordered.values)
return (None,
array_ops.gather(output_values_grad, inverted_permutation),
None)
def testInvertPermutation(self):
for dtype in [dtypes.int32, dtypes.int64]:
with self.test_session(use_gpu=True):
x = constant_op.constant([3, 4, 0, 2, 1], dtype=dtype)
y = array_ops.invert_permutation(x)
self.assertAllEqual(y.get_shape(), [5])
self.assertAllEqual(y.eval(), [2, 4, 3, 0, 1])
def _ConjugateTransposeGrad(op, grad):
"""Returns conj(unshuffle(grad))."""
p = op.inputs[1]
return [
array_ops.transpose(
grad, array_ops.invert_permutation(p), conjugate=True), None
]
def reshape_inv(y):
# Expand the extra dims hanging off the end, "b_extra_sh".
# Note we use y_sh[:-1] + [b_main_sh[-1]] rather than b_main_sh, because y
# Could have different batch dims than a and b, because of broadcasting.
y_extra_shape = array_ops.concat(
(array_ops.shape(y)[:-1], [b_main_sh[-1]], b_extra_sh), 0)
y_extra_on_end = array_ops.reshape(y, y_extra_shape)
return array_ops.transpose(
y_extra_on_end, perm=array_ops.invert_permutation(perm))
def _ProdGrad(op, grad):
"""Gradient for Prod."""
# The gradient can be expressed by dividing the product by each entry of the
# input tensor, but this approach can't deal with zeros in the input.
# Here, we avoid this problem by composing the output as a product of two
# cumprod operations.
input_shape = array_ops.shape(op.inputs[0])
# Reshape reduction indices for the case where the parameter is a scalar
reduction_indices = array_ops.reshape(op.inputs[1], [-1])
# Expand grad to full input shape
output_shape_kept_dims = math_ops.reduced_shape(input_shape, op.inputs[1])
tile_scaling = _safe_shape_div(input_shape, output_shape_kept_dims)
grad = array_ops.reshape(grad, output_shape_kept_dims)
grad = array_ops.tile(grad, tile_scaling)
# Pack all reduced dimensions into a single one, so we can perform the
# cumprod ops. If the reduction dims list is empty, it defaults to float32,
# so we need to cast here. We put all the shape-related ops on CPU to avoid
# copying back and forth, and since listdiff is CPU only.
with ops.device("/cpu:0"):
rank = array_ops.rank(op.inputs[0])
reduction_indices = (reduction_indices + rank) % rank
reduced = math_ops.cast(reduction_indices, dtypes.int32)
idx = math_ops.range(0, rank)
other, _ = array_ops.setdiff1d(idx, reduced)
perm = array_ops.concat([reduced, other], 0)
reduced_num = math_ops.reduce_prod(array_ops.gather(input_shape, reduced))
other_num = math_ops.reduce_prod(array_ops.gather(input_shape, other))
permuted = array_ops.transpose(op.inputs[0], perm)
permuted_shape = array_ops.shape(permuted)
reshaped = array_ops.reshape(permuted, (reduced_num, other_num))
# Calculate product, leaving out the current entry
left = math_ops.cumprod(reshaped, axis=0, exclusive=True)
right = math_ops.cumprod(reshaped, axis=0, exclusive=True, reverse=True)
# For complex inputs, the gradient is in the conjugate direction.
y = array_ops.reshape(math_ops.conj(left) * math_ops.conj(right),
permuted_shape)
# Invert the transpose and reshape operations.
# Make sure to set the statically known shape information through a reshape.
out = grad * array_ops.transpose(y, array_ops.invert_permutation(perm))
return array_ops.reshape(out, input_shape), None
def _ProdGrad(op, grad): """Gradient for Prod.""" # The gradient can be expressed by dividing the product by each entry of the # input tensor, but this approach can't deal with zeros in the input. # Here, we avoid this problem by composing the output as a product of two # cumprod operations. input_shape = array_ops.shape(op.inputs[0]) # Expand grad to full input shape output_shape_kept_dims = math_ops.reduced_shape(input_shape, op.inputs[1]) tile_scaling = _safe_shape_div(input_shape, output_shape_kept_dims) grad = array_ops.reshape(grad, output_shape_kept_dims) grad = array_ops.tile(grad, tile_scaling) # Pack all reduced dimensions into a single one, so we can perform the # cumprod ops. If the reduction dims list is empty, it defaults to float32, # so we need to cast here. reduced = math_ops.cast(op.inputs[1], dtypes.int32) idx = math_ops.range(0, array_ops.rank(op.inputs[0])) other, _ = array_ops.listdiff(idx, reduced) perm = array_ops.concat(0, [reduced, other]) reduced_num = math_ops.reduce_prod(array_ops.gather(input_shape, reduced)) other_num = math_ops.reduce_prod(array_ops.gather(input_shape, other)) permuted = array_ops.transpose(op.inputs[0], perm) permuted_shape = array_ops.shape(permuted) reshaped = array_ops.reshape(permuted, (reduced_num, other_num)) # Calculate product, leaving out the current entry left = math_ops.cumprod(reshaped, axis=0, exclusive=True) right = math_ops.cumprod(reshaped, axis=0, exclusive=True, reverse=True) y = array_ops.reshape(left * right, permuted_shape) # Invert the transpose and reshape operations. # Make sure to set the statically known shape information through a reshape. out = grad * array_ops.transpose(y, array_ops.invert_permutation(perm)) return array_ops.reshape(out, input_shape), None
def _TransposeGrad(op, grad): """Returns unshuffle(grad).""" p = op.inputs[1] return [array_ops.transpose(grad, array_ops.invert_permutation(p)), None]
def _TransposeGrad(op, grad):
"""Returns unshuffle(grad)."""
p = op.inputs[1]
return [array_ops.transpose(grad, array_ops.invert_permutation(p)), None]
def testInvertPermutationTwiceIsNoop(self):
self._assertOpOutputMatchesExpected(
lambda x: array_ops.invert_permutation(array_ops.invert_permutation(x)),
np.array([1, 2, 0], np.int32),
expected=np.array([1, 2, 0], dtype=np.int32))
def lu_reconstruct(lower_upper, perm, validate_args=False, name=None):
"""The reconstruct one or more matrices from their LU decomposition(s).
Args:
lower_upper: `lu` as returned by `tf.linalg.lu`, i.e., if `matmul(P,
matmul(L, U)) = X` then `lower_upper = L + U - eye`.
perm: `p` as returned by `tf.linag.lu`, i.e., if `matmul(P, matmul(L, U)) =
X` then `perm = argmax(P)`.
validate_args: Python `bool` indicating whether arguments should be checked
for correctness.
Default value: `False` (i.e., don't validate arguments).
name: Python `str` name given to ops managed by this object.
Default value: `None` (i.e., 'lu_reconstruct').
Returns:
x: The original input to `tf.linalg.lu`, i.e., `x` as in,
`lu_reconstruct(*tf.linalg.lu(x))`.
#### Examples
```python
import numpy as np
import tensorflow as tf
import tensorflow_probability as tfp
x = [[[3., 4], [1, 2]],
[[7., 8], [3, 4]]]
x_reconstructed = tf.linalg.lu_reconstruct(*tf.linalg.lu(x))
tf.assert_near(x, x_reconstructed)
# ==> True
```
"""
with ops.name_scope(name or 'lu_reconstruct'):
lower_upper = ops.convert_to_tensor(lower_upper,
dtype_hint=dtypes.float32,
name='lower_upper')
perm = ops.convert_to_tensor(perm,
dtype_hint=dtypes.int32,
name='perm')
assertions = lu_reconstruct_assertions(lower_upper, perm,
validate_args)
if assertions:
with ops.control_dependencies(assertions):
lower_upper = array_ops.identity(lower_upper)
perm = array_ops.identity(perm)
shape = array_ops.shape(lower_upper)
lower = set_diag(band_part(lower_upper, num_lower=-1, num_upper=0),
array_ops.ones(shape[:-1], dtype=lower_upper.dtype))
upper = band_part(lower_upper, num_lower=0, num_upper=-1)
x = math_ops.matmul(lower, upper)
if (lower_upper.shape is None or lower_upper.shape.rank is None
or lower_upper.shape.rank != 2):
# We either don't know the batch rank or there are >0 batch dims.
batch_size = math_ops.reduce_prod(shape[:-2])
d = shape[-1]
x = array_ops.reshape(x, [batch_size, d, d])
perm = array_ops.reshape(perm, [batch_size, d])
perm = map_fn.map_fn(array_ops.invert_permutation, perm)
batch_indices = array_ops.broadcast_to(
math_ops.range(batch_size)[:, array_ops.newaxis],
[batch_size, d])
x = array_ops.gather_nd(
x, array_ops.stack([batch_indices, perm], axis=-1))
x = array_ops.reshape(x, shape)
else:
x = array_ops.gather(x, array_ops.invert_permutation(perm))
x.set_shape(lower_upper.shape)
return x
def invert_twice(x): return array_ops.invert_permutation(array_ops.invert_permutation(x))
def testInvertPermutationTwiceIsNoop(self):
self._assertOpOutputMatchesExpected(
lambda x: array_ops.invert_permutation(array_ops.invert_permutation(x)),
np.array([1, 2, 0], np.int32),
expected=np.array([1, 2, 0], dtype=np.int32))
def _inverse(self, y):
return array_ops.gather(y,
array_ops.invert_permutation(self.permutation),
axis=-1)
def _inverse(self, y):
return array_ops.gather(
y,
array_ops.invert_permutation(self.permutation),
axis=-1)
