Python tensorflow.python.ops.array_ops.rank() Examples

def _flatten_outer_dims(logits):
  """Flattens logits' outer dimensions and keep its last dimension."""
  rank = array_ops.rank(logits)
  last_dim_size = array_ops.slice(
      array_ops.shape(logits), [math_ops.subtract(rank, 1)], [1])
  output = array_ops.reshape(logits, array_ops.concat([[-1], last_dim_size], 0))

  # Set output shape if known.
  shape = logits.get_shape()
  if shape is not None and shape.dims is not None:
    shape = shape.as_list()
    product = 1
    product_valid = True
    for d in shape[:-1]:
      if d is None:
        product_valid = False
        break
      else:
        product *= d
    if product_valid:
      output_shape = [product, shape[-1]]
      output.set_shape(output_shape)

  return output 

def _transpose_batch_time(x):
    """Transpose the batch and time dimensions of a Tensor.
    Retains as much of the static shape information as possible.
    Args:
        x: A tensor of rank 2 or higher.
    Returns:
        x transposed along the first two dimensions.
    Raises:
        ValueError: if `x` is rank 1 or lower.
    """
    x_static_shape = x.get_shape()
    if x_static_shape.ndims is not None and x_static_shape.ndims < 2:
        raise ValueError(
            "Expected input tensor %s to have rank at least 2, but saw shape: %s" %
            (x, x_static_shape))
    x_rank = array_ops.rank(x)
    x_t = array_ops.transpose(
        x, array_ops.concat(
            ([1, 0], math_ops.range(2, x_rank)), axis=0))
    x_t.set_shape(
        tensor_shape.TensorShape([
            x_static_shape[1].value, x_static_shape[0].value
        ]).concatenate(x_static_shape[2:]))
    return x_t 

def _MatrixSetDiagGrad(op, grad):
  """Gradient for MatrixSetDiag."""
  input_shape = op.inputs[0].get_shape().merge_with(grad.get_shape())
  diag_shape = op.inputs[1].get_shape()
  batch_shape = input_shape[:-2].merge_with(diag_shape[:-1])
  matrix_shape = input_shape[-2:]
  if batch_shape.is_fully_defined() and matrix_shape.is_fully_defined():
    diag_shape = batch_shape.as_list() + [min(matrix_shape.as_list())]
  else:
    with ops.colocate_with(grad):
      grad_shape = array_ops.shape(grad)
      grad_rank = array_ops.rank(grad)
      batch_shape = array_ops.slice(grad_shape, [0], [grad_rank - 2])
      matrix_shape = array_ops.slice(grad_shape, [grad_rank - 2], [2])
      min_dim = math_ops.reduce_min(matrix_shape)
      diag_shape = array_ops.concat([batch_shape, [min_dim]], 0)
  grad_input = array_ops.matrix_set_diag(
      grad, array_ops.zeros(
          diag_shape, dtype=grad.dtype))
  grad_diag = array_ops.matrix_diag_part(grad)
  return (grad_input, grad_diag) 

def _SliceGrad(op, grad):
  """Gradient for Slice op."""
  # Create an Nx2 padding where the first column represents how many
  # zeros are to be prepended for each dimension, and the second
  # column indicates how many zeros are appended.
  #
  # The number of zeros to append is the shape of the input
  # elementwise-subtracted by both the begin vector and sizes vector.
  #
  # Some more reshaping is needed to assemble this tensor with the
  # right dimensions.
  input_vec = op.inputs[0]
  begin_vec = op.inputs[1]
  input_rank = array_ops.rank(input_vec)
  slice_size = array_ops.shape(op.outputs[0])

  shape = array_ops.stack([input_rank, 1])
  before_pad = array_ops.reshape(begin_vec, shape)
  after_pad = array_ops.reshape(
      array_ops.shape(input_vec) - slice_size - begin_vec, shape)
  paddings = array_ops.concat([before_pad, after_pad], 1)
  return array_ops.pad(grad, paddings), None, None 

def _SumGrad(op, grad):
  """Gradient for Sum."""
  # Fast path for when reducing to a scalar and ndims is known: adds only
  # Reshape and Tile ops (and possibly a Shape).
  if (op.inputs[0].get_shape().ndims is not None and
      op.inputs[1].op.type == "Const"):
    rank = op.inputs[0].get_shape().ndims
    axes = tensor_util.MakeNdarray(op.inputs[1].op.get_attr("value"))
    if np.array_equal(axes, np.arange(rank)):  # Reduce all dims.
      grad = array_ops.reshape(grad, [1] * rank)
      # If shape is not fully defined (but rank is), we use Shape.
      if op.inputs[0].get_shape().is_fully_defined():
        input_shape = op.inputs[0].get_shape().as_list()
      else:
        input_shape = array_ops.shape(op.inputs[0])
      return [array_ops.tile(grad, input_shape), None]

  input_shape = array_ops.shape(op.inputs[0])
  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)
  return [array_ops.tile(grad, tile_scaling), None] 

def _event_dims_tensor(self, sample):
    """Return a 1D `int32` tensor: `range(rank(sample))[-event_ndims:]`."""
    if self.event_ndims is None:
      raise ValueError("Jacobian cannot be computed with unknown event_ndims")
    static_event_ndims = tensor_util.constant_value(self.event_ndims)
    static_rank = sample.get_shape().ndims
    if static_event_ndims is not None and static_rank is not None:
      return ops.convert_to_tensor(
          static_rank + np.arange(-static_event_ndims, 0).astype(np.int32))

    if static_event_ndims is not None:
      event_range = np.arange(-static_event_ndims, 0).astype(np.int32)
    else:
      event_range = math_ops.range(-self.event_ndims, 0, dtype=dtypes.int32)

    if static_rank is not None:
      return event_range + static_rank
    else:
      return event_range + array_ops.rank(sample) 

def _ReductionDims(x, axis, reduction_indices):
  """Returns range(0, rank(x)) if reduction_indices is None."""
  # TODO(aselle): Remove this after deprecation
  if reduction_indices is not None:
    if axis is not None:
      raise ValueError("Can't specify both axis' and 'reduction_indices'.")
    axis = reduction_indices
  if axis is not None:
    return axis
  else:
    # Fast path: avoid creating Rank and Range ops if ndims is known.
    if isinstance(x, ops.Tensor) and x.get_shape().ndims is not None:
      return constant_op.constant(
          np.arange(x.get_shape().ndims), dtype=dtypes.int32)
    if (isinstance(x, sparse_tensor.SparseTensor) and
        x.dense_shape.get_shape().is_fully_defined()):
      rank = x.dense_shape.get_shape()[0].value  # sparse.dense_shape is 1-D.
      return constant_op.constant(np.arange(rank), dtype=dtypes.int32)

    # Otherwise, we rely on Range and Rank to do the right thing at run-time.
    return range(0, array_ops.rank(x)) 

def _BiasAddGradV1(unused_bias_op, received_grad):
  """Return the gradients for the 2 inputs of bias_op.

  The first input of unused_bias_op is the tensor t, and its gradient is
  just the gradient the unused_bias_op received.

  The second input of unused_bias_op is the bias vector which has one fewer
  dimension than "received_grad" (the batch dimension.)  Its gradient is the
  received gradient Summed on the batch dimension, which is the first dimension.

  Args:
    unused_bias_op: The BiasOp for which we need to generate gradients.
    received_grad: Tensor.  The gradients passed to the BiasOp.

  Returns:
    Two tensors, the first one for the "tensor" input of the BiasOp,
    the second one for the "bias" input of the BiasOp.
  """
  reduction_dim_tensor = math_ops.range(array_ops.rank(received_grad) - 1)
  return (received_grad, math_ops.reduce_sum(received_grad,
                                             reduction_dim_tensor)) 

def mean_squared_error(
    labels, predictions, weights=1.0, scope=None,
    loss_collection=ops.GraphKeys.LOSSES,
    reduction=Reduction.SUM_BY_NONZERO_WEIGHTS):
  """Adds a Sum-of-Squares loss to the training procedure.

  `weights` acts as a coefficient for the loss. If a scalar is provided, then
  the loss is simply scaled by the given value. If `weights` is a tensor of size
  [batch_size], then the total loss for each sample of the batch is rescaled
  by the corresponding element in the `weights` vector. If the shape of
  `weights` matches the shape of `predictions`, then the loss of each
  measurable element of `predictions` is scaled by the corresponding value of
  `weights`.

  Args:
    labels: The ground truth output tensor, same dimensions as 'predictions'.
    predictions: The predicted outputs.
    weights: Optional `Tensor` whose rank is either 0, or the same rank as
      `labels`, and must be broadcastable to `labels` (i.e., all dimensions must
      be either `1`, or the same as the corresponding `losses` dimension).
    scope: The scope for the operations performed in computing the loss.
    loss_collection: collection to which the loss will be added.
    reduction: Type of reduction to apply to loss.

  Returns:
    Weighted loss float `Tensor`. If `reduction` is `NONE`, this has the same
    shape as `labels`; otherwise, it is scalar.

  Raises:
    ValueError: If the shape of `predictions` doesn't match that of `labels` or
      if the shape of `weights` is invalid.
  """
  with ops.name_scope(scope, "mean_squared_error",
                      (predictions, labels, weights)) as scope:
    predictions = math_ops.to_float(predictions)
    labels = math_ops.to_float(labels)
    predictions.get_shape().assert_is_compatible_with(labels.get_shape())
    losses = math_ops.square(math_ops.subtract(predictions, labels))
    return compute_weighted_loss(
        losses, weights, scope, loss_collection, reduction=reduction) 

def trace(x, name=None):
  """Compute the trace of a tensor `x`.

  `trace(x)` returns the sum along the main diagonal of each inner-most matrix
  in x. If x is of rank `k` with shape `[I, J, K, ..., L, M, N]`, then output
  is a tensor of rank `k-2` with dimensions `[I, J, K, ..., L]` where

  `output[i, j, k, ..., l] = trace(x[i, j, i, ..., l, :, :])`

  For example:

  ```python
  # 'x' is [[1, 2],
  #         [3, 4]]
  tf.trace(x) ==> 5

  # 'x' is [[1,2,3],
  #         [4,5,6],
  #         [7,8,9]]
  tf.trace(x) ==> 15

  # 'x' is [[[1,2,3],
  #          [4,5,6],
  #          [7,8,9]],
  #         [[-1,-2,-3],
  #          [-4,-5,-6],
  #          [-7,-8,-9]]]
  tf.trace(x) ==> [15,-15]
  ```

  Args:
    x: tensor.
    name: A name for the operation (optional).

  Returns:
    The trace of input tensor.
  """
  with ops.name_scope(name, "Trace", [x]) as name:
    x = ops.convert_to_tensor(x, name="x")
    return reduce_sum(array_ops.matrix_diag_part(x), [-1], name=name) 

def reduce_max(input_tensor,
               axis=None,
               keep_dims=False,
               name=None,
               reduction_indices=None):
  """Computes the maximum of elements across dimensions of a tensor.

  Reduces `input_tensor` along the dimensions given in `axis`.
  Unless `keep_dims` is true, the rank of the tensor is reduced by 1 for each
  entry in `axis`. If `keep_dims` is true, the reduced dimensions
  are retained with length 1.

  If `axis` has no entries, all dimensions are reduced, and a
  tensor with a single element is returned.

  Args:
    input_tensor: The tensor to reduce. Should have numeric type.
    axis: The dimensions to reduce. If `None` (the default),
      reduces all dimensions.
    keep_dims: If true, retains reduced dimensions with length 1.
    name: A name for the operation (optional).
    reduction_indices: The old (deprecated) name for axis.

  Returns:
    The reduced tensor.

  @compatibility(numpy)
  Equivalent to np.max
  @end_compatibility
  """
  return gen_math_ops._max(
      input_tensor,
      _ReductionDims(input_tensor, axis, reduction_indices),
      keep_dims,
      name=name) 

def reduce_min(input_tensor,
               axis=None,
               keep_dims=False,
               name=None,
               reduction_indices=None):
  """Computes the minimum of elements across dimensions of a tensor.

  Reduces `input_tensor` along the dimensions given in `axis`.
  Unless `keep_dims` is true, the rank of the tensor is reduced by 1 for each
  entry in `axis`. If `keep_dims` is true, the reduced dimensions
  are retained with length 1.

  If `axis` has no entries, all dimensions are reduced, and a
  tensor with a single element is returned.

  Args:
    input_tensor: The tensor to reduce. Should have numeric type.
    axis: The dimensions to reduce. If `None` (the default),
      reduces all dimensions.
    keep_dims: If true, retains reduced dimensions with length 1.
    name: A name for the operation (optional).
    reduction_indices: The old (deprecated) name for axis.

  Returns:
    The reduced tensor.

  @compatibility(numpy)
  Equivalent to np.min
  @end_compatibility
  """
  return gen_math_ops._min(
      input_tensor,
      _ReductionDims(input_tensor, axis, reduction_indices),
      keep_dims,
      name=name) 

def reduce_prod(input_tensor,
                axis=None,
                keep_dims=False,
                name=None,
                reduction_indices=None):
  """Computes the product of elements across dimensions of a tensor.

  Reduces `input_tensor` along the dimensions given in `axis`.
  Unless `keep_dims` is true, the rank of the tensor is reduced by 1 for each
  entry in `axis`. If `keep_dims` is true, the reduced dimensions
  are retained with length 1.

  If `axis` has no entries, all dimensions are reduced, and a
  tensor with a single element is returned.

  Args:
    input_tensor: The tensor to reduce. Should have numeric type.
    axis: The dimensions to reduce. If `None` (the default),
      reduces all dimensions.
    keep_dims: If true, retains reduced dimensions with length 1.
    name: A name for the operation (optional).
    reduction_indices: The old (deprecated) name for axis.

  Returns:
    The reduced tensor.

  @compatibility(numpy)
  Equivalent to np.prod
  @end_compatibility
  """
  return gen_math_ops._prod(
      input_tensor,
      _ReductionDims(input_tensor, axis, reduction_indices),
      keep_dims,
      name=name) 

def cosine_distance(
    labels, predictions, dim=None, weights=1.0, scope=None,
    loss_collection=ops.GraphKeys.LOSSES,
    reduction=Reduction.SUM_BY_NONZERO_WEIGHTS):
  """Adds a cosine-distance loss to the training procedure.

  Note that the function assumes that `predictions` and `labels` are already
  unit-normalized.

  Args:
    labels: `Tensor` whose shape matches 'predictions'
    predictions: An arbitrary matrix.
    dim: The dimension along which the cosine distance is computed.
    weights: Optional `Tensor` whose rank is either 0, or the same rank as
      `labels`, and must be broadcastable to `labels` (i.e., all dimensions must
      be either `1`, or the same as the corresponding `losses` dimension).
    scope: The scope for the operations performed in computing the loss.
    loss_collection: collection to which this loss will be added.
    reduction: Type of reduction to apply to loss.

  Returns:
    Weighted loss float `Tensor`. If `reduction` is `NONE`, this has the same
    shape as `labels`; otherwise, it is scalar.

  Raises:
    ValueError: If `predictions` shape doesn't match `labels` shape, or
      `weights` is `None`.
  """
  if dim is None:
    raise ValueError("`dim` cannot be None.")
  with ops.name_scope(scope, "cosine_distance_loss",
                      (predictions, labels, weights)) as scope:
    predictions = math_ops.to_float(predictions)
    labels = math_ops.to_float(labels)
    predictions.get_shape().assert_is_compatible_with(labels.get_shape())

    radial_diffs = math_ops.multiply(predictions, labels)
    losses = 1 - math_ops.reduce_sum(radial_diffs, axis=(dim,), keep_dims=True)
    return compute_weighted_loss(
        losses, weights, scope, loss_collection, reduction=reduction) 

def _broadcast_weights(weights, values):
  """Broadcast `weights` to the same shape as `values`.

  This returns a version of `weights` following the same broadcast rules as
  `mul(weights, values)`. When computing a weighted average, use this function
  to broadcast `weights` before summing them; e.g.,
  `reduce_sum(w * v) / reduce_sum(_broadcast_weights(w, v))`.

  Args:
    weights: `Tensor` whose rank is either 0, or the same rank as `values`, and
      must be broadcastable to `values` (i.e., all dimensions must be either
      `1`, or the same as the corresponding `values` dimension).
    values: `Tensor` of any shape.

  Returns:
    `weights` broadcast to `values` shape.
  """
  with ops.name_scope(None, 'broadcast_weights', (values, weights)) as scope:
    weights_shape = weights.get_shape()
    values_shape = values.get_shape()
    if (weights_shape.is_fully_defined() and
        values_shape.is_fully_defined() and
        weights_shape.is_compatible_with(values_shape)):
      return weights
    with ops.control_dependencies((_assert_weights_rank(weights, values),)):
      return math_ops.multiply(
          weights, array_ops.ones_like(values), name=scope) 

def streaming_false_negatives(predictions, labels, weights=None,
                              metrics_collections=None,
                              updates_collections=None,
                              name=None):
  """Computes the total number of false negatives.

  If `weights` is `None`, weights default to 1. Use weights of 0 to mask values.

  Args:
    predictions: The predicted values, a `Tensor` of arbitrary dimensions. Will
      be cast to `bool`.
    labels: The ground truth values, a `Tensor` whose dimensions must match
      `predictions`. Will be cast to `bool`.
    weights: Optional `Tensor` whose rank is either 0, or the same rank as
      `labels`, and must be broadcastable to `labels` (i.e., all dimensions
      must be either `1`, or the same as the corresponding `labels`
      dimension).
    metrics_collections: An optional list of collections that the metric
      value variable should be added to.
    updates_collections: An optional list of collections that the metric update
      ops should be added to.
    name: An optional variable_scope name.

  Returns:
    value_tensor: A `Tensor` representing the current value of the metric.
    update_op: An operation that accumulates the error from a batch of data.

  Raises:
    ValueError: If `weights` is not `None` and its shape doesn't match `values`,
      or if either `metrics_collections` or `updates_collections` are not a list
      or tuple.
  """
  return metrics.false_negatives(
      predictions=predictions, labels=labels, weights=weights,
      metrics_collections=metrics_collections,
      updates_collections=updates_collections, name=name)


# TODO(ptucker): Move this somewhere common, to share with ops/losses/losses.py. 

def project_col_factors(self,
                          sp_input=None,
                          transpose_input=False,
                          projection_weights=None):
    """Projects the column factors.

    This computes the column embedding v_j for an observed column a_j by solving
    one iteration of the update equations.

    Args:
      sp_input: A SparseTensor representing a set of columns. Please note that
        the row indices of this SparseTensor must match the model row feature
        indexing while the column indices are ignored. The returned results will
        be in the same ordering as the input columns.
      transpose_input: If true, the input will be logically transposed and the
        columns corresponding to the transposed input are projected.
      projection_weights: The column weights to be used for the projection. If
        None then 1.0 is used. This can be either a scaler or a rank-1 tensor
        with the number of elements matching the number of columns to be
        projected. Note that the row weights will be determined by the
        underlying WALS model.

    Returns:
      Projected column factors.
    """
    if projection_weights is None:
      projection_weights = 1
    return self._process_input_helper(False, sp_input=sp_input,
                                      transpose_input=transpose_input,
                                      row_weights=projection_weights)[0] 

def _check_labels_and_scores(boolean_labels, scores, check_shape):
  """Check the rank of labels/scores, return tensor versions."""
  with ops.name_scope('_check_labels_and_scores',
                      values=[boolean_labels, scores]):
    boolean_labels = ops.convert_to_tensor(boolean_labels,
                                           name='boolean_labels')
    scores = ops.convert_to_tensor(scores, name='scores')

    if boolean_labels.dtype != dtypes.bool:
      raise ValueError(
          'Argument boolean_labels should have dtype bool.  Found: %s',
          boolean_labels.dtype)

    if check_shape:
      labels_rank_1 = control_flow_ops.Assert(
          math_ops.equal(1, array_ops.rank(boolean_labels)),
          ['Argument boolean_labels should have rank 1.  Found: ',
           boolean_labels.name, array_ops.shape(boolean_labels)])

      scores_rank_1 = control_flow_ops.Assert(
          math_ops.equal(1, array_ops.rank(scores)),
          ['Argument scores should have rank 1.  Found: ', scores.name,
           array_ops.shape(scores)])

      with ops.control_dependencies([labels_rank_1, scores_rank_1]):
        return boolean_labels, scores
    else:
      return boolean_labels, scores 

def hinge_loss(labels, logits, weights=1.0, scope=None,
               loss_collection=ops.GraphKeys.LOSSES,
               reduction=Reduction.SUM_BY_NONZERO_WEIGHTS):
  """Adds a hinge loss to the training procedure.

  Args:
    labels: The ground truth output tensor. Its shape should match the shape of
      logits. The values of the tensor are expected to be 0.0 or 1.0.
    logits: The logits, a float tensor.
    weights: Optional `Tensor` whose rank is either 0, or the same rank as
      `labels`, and must be broadcastable to `labels` (i.e., all dimensions must
      be either `1`, or the same as the corresponding `losses` dimension).
    scope: The scope for the operations performed in computing the loss.
    loss_collection: collection to which the loss will be added.
    reduction: Type of reduction to apply to loss.

  Returns:
    Weighted loss float `Tensor`. If `reduction` is `NONE`, this has the same
    shape as `labels`; otherwise, it is scalar.

  Raises:
    ValueError: If the shapes of `logits` and `labels` don't match.
  """
  with ops.name_scope(scope, "hinge_loss", (logits, labels)) as scope:
    logits = math_ops.to_float(logits)
    labels = math_ops.to_float(labels)
    logits.get_shape().assert_is_compatible_with(labels.get_shape())
    # We first need to convert binary labels to -1/1 labels (as floats).
    all_ones = array_ops.ones_like(labels)
    labels = math_ops.subtract(2 * labels, all_ones)
    losses = nn_ops.relu(
        math_ops.subtract(all_ones, math_ops.multiply(labels, logits)))
    return compute_weighted_loss(
        losses, weights, scope, loss_collection, reduction=reduction) 

def _transpose_batch_time(x):
  """Transpose the batch and time dimensions of a Tensor.

  Retains as much of the static shape information as possible.

  Args:
    x: A tensor of rank 2 or higher.

  Returns:
    x transposed along the first two dimensions.

  Raises:
    ValueError: if `x` is rank 1 or lower.
  """
  x_static_shape = x.get_shape()
  if x_static_shape.ndims is not None and x_static_shape.ndims < 2:
    raise ValueError(
        "Expected input tensor %s to have rank at least 2, but saw shape: %s" %
        (x, x_static_shape))
  x_rank = array_ops.rank(x)
  x_t = array_ops.transpose(
      x, array_ops.concat(
          ([1, 0], math_ops.range(2, x_rank)), axis=0))
  x_t.set_shape(
      tensor_shape.TensorShape([
          x_static_shape[1].value, x_static_shape[0].value
      ]).concatenate(x_static_shape[2:]))
  return x_t 

def _num_present(losses, weights, per_batch=False):
  """Computes the number of elements in the loss function induced by `weights`.

  A given weights tensor induces different numbers of usable elements in the
  `losses` tensor. The `weights` tensor is broadcast across `losses` for all
  possible dimensions. For example, if `losses` is a tensor of dimension
  `[4, 5, 6, 3]` and `weights` is a tensor of shape `[4, 5]`, then `weights` is,
  in effect, tiled to match the shape of `losses`. Following this effective
  tile, the total number of present elements is the number of non-zero weights.

  Args:
    losses: `Tensor` of shape `[batch_size, d1, ... dN]`.
    weights: `Tensor` of shape `[]`, `[batch_size]` or
      `[batch_size, d1, ... dK]`, where K < N.
    per_batch: Whether to return the number of elements per batch or as a sum
      total.

  Returns:
    The number of present (non-zero) elements in the losses tensor. If
      `per_batch` is `True`, the value is returned as a tensor of size
      `[batch_size]`. Otherwise, a single scalar tensor is returned.
  """
  with ops.name_scope(None, "num_present", (losses, weights)) as scope:
    weights = math_ops.to_float(weights)
    present = array_ops.where(
        math_ops.equal(weights, 0.0),
        array_ops.zeros_like(weights),
        array_ops.ones_like(weights))
    present = weights_broadcast_ops.broadcast_weights(present, losses)
    if per_batch:
      return math_ops.reduce_sum(
          present, axis=math_ops.range(1, array_ops.rank(present)),
          keep_dims=True, name=scope)
    return math_ops.reduce_sum(present, name=scope) 

def _IRFFTGradHelper(rank, rfft_fn):
  """Returns a gradient function for an IRFFT of the provided rank."""
  # Can't happen because we don't register a gradient for IRFFT3D.
  assert rank in (1, 2), "Gradient for IRFFT3D is not implemented."

  def _Grad(op, grad):
    """A gradient function for IRFFT with the provided `rank` and `rfft_fn`."""
    # Generate a simple mask like [1.0, 2.0, ..., 2.0, 1.0] for even-length FFTs
    # and [1.0, 2.0, ..., 2.0] for odd-length FFTs. To reduce extra ops in the
    # graph we special-case the situation where the FFT length and last
    # dimension of the input are known at graph construction time.
    fft_length = op.inputs[1]
    is_odd = math_ops.mod(fft_length[-1], 2)
    input_last_dimension = array_ops.shape(op.inputs[0])[-1]
    mask = array_ops.concat(
        [[1.0], 2.0 * array_ops.ones([input_last_dimension - 2 + is_odd]),
         array_ops.ones([1 - is_odd])], 0)

    rsize = math_ops.reciprocal(math_ops.to_float(_FFTSizeForGrad(grad, rank)))

    # The gradient of IRFFT is the RFFT of the incoming gradient times a scaling
    # factor and a mask. The mask scales the gradient for the Hermitian
    # symmetric components of the RFFT by a factor of two, since these
    # components are de-duplicated in the RFFT.
    rfft = rfft_fn(grad, fft_length)
    return rfft * math_ops.cast(rsize * mask, dtypes.complex64), None

  return _Grad 

def same_dynamic_shape(a, b):
  """Returns whether a and b have the same dynamic shape.

  Args:
    a: `Tensor`
    b: `Tensor`

  Returns:
    `bool` `Tensor` representing if both tensors have the same shape.
  """
  a = ops.convert_to_tensor(a, name="a")
  b = ops.convert_to_tensor(b, name="b")

  # Here we can't just do math_ops.equal(a.shape, b.shape), since
  # static shape inference may break the equality comparison between
  # shape(a) and shape(b) in math_ops.equal.
  def all_shapes_equal():
    return math_ops.reduce_all(math_ops.equal(
        array_ops.concat([array_ops.shape(a), array_ops.shape(b)], 0),
        array_ops.concat([array_ops.shape(b), array_ops.shape(a)], 0)))

  # One of the shapes isn't fully defined, so we need to use the dynamic
  # shape.
  return control_flow_ops.cond(
      math_ops.equal(array_ops.rank(a), array_ops.rank(b)),
      all_shapes_equal,
      lambda: constant_op.constant(False)) 

def _ndims_from_shape(shape):
  """Returns `Tensor`'s `rank` implied by a `Tensor` shape."""
  if shape.get_shape().ndims not in (None, 1):
    raise ValueError("input is not a valid shape: not 1D")
  if not shape.dtype.is_integer:
    raise TypeError("input is not a valid shape: wrong dtype")
  if shape.get_shape().is_fully_defined():
    return constant_op.constant(shape.get_shape().as_list()[0])
  return array_ops.shape(shape)[0] 

def _maybe_rotate_dims(self, x, rotate_right=False):
    """Helper which rolls left event_dims left or right event_dims right."""
    needs_rotation_const = tensor_util.constant_value(self._needs_rotation)
    if needs_rotation_const is not None and not needs_rotation_const:
      return x
    ndims = array_ops.rank(x)
    n = (ndims - self._rotate_ndims) if rotate_right else self._rotate_ndims
    return array_ops.transpose(
        x, _concat_vectors(math_ops.range(n, ndims), math_ops.range(0, n))) 

def _expand_sample_shape_to_vector(self, x, name):
    """Helper to `sample` which ensures input is 1D."""
    x_static_val = tensor_util.constant_value(x)
    if x_static_val is None:
      prod = math_ops.reduce_prod(x)
    else:
      prod = np.prod(x_static_val, dtype=x.dtype.as_numpy_dtype())

    ndims = x.get_shape().ndims  # != sample_ndims
    if ndims is None:
      # Maybe expand_dims.
      ndims = array_ops.rank(x)
      expanded_shape = util.pick_vector(
          math_ops.equal(ndims, 0),
          np.array([1], dtype=np.int32), array_ops.shape(x))
      x = array_ops.reshape(x, expanded_shape)
    elif ndims == 0:
      # Definitely expand_dims.
      if x_static_val is not None:
        x = ops.convert_to_tensor(
            np.array([x_static_val], dtype=x.dtype.as_numpy_dtype()),
            name=name)
      else:
        x = array_ops.reshape(x, [1])
    elif ndims != 1:
      raise ValueError("Input is neither scalar nor vector.")

    return x, prod 

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"):
    reduced = math_ops.cast(reduction_indices, dtypes.int32)
    idx = math_ops.range(0, array_ops.rank(op.inputs[0]))
    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)
  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 _SegmentMeanGrad(op, grad):
  """Gradient for SegmentMean."""
  input_rank = array_ops.rank(op.inputs[0])
  ones_shape = array_ops.concat([
      array_ops.shape(op.inputs[1]),
      array_ops.fill(array_ops.expand_dims(input_rank - 1, 0), 1)
  ], 0)
  ones = array_ops.fill(ones_shape,
                        constant_op.constant(1, dtype=grad.dtype))
  scaled_grad = math_ops.div(grad, math_ops.segment_sum(ones, op.inputs[1]))
  return array_ops.gather(scaled_grad, op.inputs[1]), None 

def _BiasAddGradGrad(op, received_grad):
  """Gradient for the BiasAddGrad op.

  Args:
    op: BiasAddGrad op for which we are calculating gradients.
    received_grad: The gradients passed to the BiasAddGrad op.

  Returns:
    A single gradient Tensor for the input to BiasAddGrad (which
    is the gradient of the bias term in BiasAdd)
  """

  try:
    data_format = op.get_attr("data_format")
  except ValueError:
    data_format = None

  shape = array_ops.shape(op.inputs[0])
  rank = array_ops.rank(op.inputs[0])
  bias_shape = array_ops.shape(received_grad)

  if data_format == b"NCHW":
    expanded_shape = array_ops.concat([
        array_ops.ones_like(shape[:-3]), bias_shape,
        array_ops.ones_like(shape[-2:])
    ], 0)
    tile_mults = array_ops.concat([shape[:-3], [1], shape[-2:]], 0)
  else:
    expanded_shape = array_ops.concat(
        [array_ops.ones_like(shape[:-1]), bias_shape], 0)
    tile_mults = array_ops.concat([shape[:-1], [1]], 0)

  expanded_grad = array_ops.reshape(received_grad, expanded_shape)
  return array_ops.tile(expanded_grad, tile_mults) 

def _SoftmaxGrad(op, grad_softmax):
  """The derivative of the softmax nonlinearity.

  We assume that probs is of shape [batch_size * dim]
  The formula for dsoftmax / dx = (diag(softmax) - softmax * softmax').
  This matrix is diagonal minus a rank one matrix, so it is easy to implement
  as follows:

    grad_x = grad_softmax * softmax - sum(grad_softmax * softmax) * softmax

  Args:
     op: the Softmax op.
     grad_softmax:  the tensor representing the gradient w.r.t. the
       softmax output.

  Returns:
     gradient w.r.t the input to the softmax

  """
  # TODO(ilyasu): assert that the tensor has two dimensions at
  # graph-construction time?  Alternatively: do different things
  # depending on the dimensionality of the input tensors.
  softmax = op.outputs[0]
  grad_x = ((grad_softmax - array_ops.reshape(
      math_ops.reduce_sum(grad_softmax * softmax, [1]), [-1, 1])) * softmax)
  return grad_x