# Copyright 2016 The TensorFlow Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
"""Implementation of Loss operations for use in neural networks."""

from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

from tensorflow.python.eager import context
from tensorflow.python.framework import ops
from tensorflow.python.ops import array_ops
from tensorflow.python.ops import confusion_matrix
from tensorflow.python.ops import control_flow_ops
from tensorflow.python.ops import math_ops
from tensorflow.python.ops import nn
from tensorflow.python.ops import nn_ops
from tensorflow.python.ops import weights_broadcast_ops
from tensorflow.python.ops.losses import util
from tensorflow.python.util.deprecation import deprecated_args
from tensorflow.python.util.deprecation import deprecated_argument_lookup
from tensorflow.python.util.tf_export import tf_export


@tf_export("losses.Reduction", "keras.losses.Reduction", v1=[])
class ReductionV2(object):
  """Types of loss reduction.

  Contains the following values:

  * `NONE`: Un-reduced weighted losses with the same shape as input.
  * `SUM`: Scalar sum of weighted losses.
  * `SUM_OVER_BATCH_SIZE`: Scalar `SUM` divided by number of elements in losses.
  """

  NONE = "none"
  SUM = "sum"
  SUM_OVER_BATCH_SIZE = "sum_over_batch_size"

  @classmethod
  def all(cls):
    return (cls.NONE, cls.SUM, cls.SUM_OVER_BATCH_SIZE)

  @classmethod
  def validate(cls, key):
    if key not in cls.all():
      raise ValueError("Invalid Reduction Key %s." % key)


@tf_export(v1=["losses.Reduction"])
class Reduction(object):
  """Types of loss reduction.

  Contains the following values:

  * `NONE`: Un-reduced weighted losses with the same shape as input.
  * `SUM`: Scalar sum of weighted losses.
  * `MEAN`: Scalar `SUM` divided by sum of weights. DEPRECATED.
  * `SUM_OVER_BATCH_SIZE`: Scalar `SUM` divided by number of elements in losses.
  * `SUM_OVER_NONZERO_WEIGHTS`: Scalar `SUM` divided by number of non-zero
     weights. DEPRECATED.
  * `SUM_BY_NONZERO_WEIGHTS`: Same as `SUM_OVER_NONZERO_WEIGHTS`.
  """

  NONE = "none"
  SUM = "weighted_sum"
  SUM_OVER_BATCH_SIZE = "weighted_sum_over_batch_size"
  MEAN = "weighted_mean"
  SUM_BY_NONZERO_WEIGHTS = "weighted_sum_by_nonzero_weights"
  SUM_OVER_NONZERO_WEIGHTS = SUM_BY_NONZERO_WEIGHTS

  @classmethod
  def all(cls):
    return (
        cls.NONE,
        cls.SUM,
        cls.MEAN,
        cls.SUM_OVER_BATCH_SIZE,
        cls.SUM_OVER_NONZERO_WEIGHTS,
        cls.SUM_BY_NONZERO_WEIGHTS)

  @classmethod
  def validate(cls, key):
    if key not in cls.all():
      raise ValueError("Invalid Reduction Key %s." % key)


def _safe_mean(losses, num_present):
  """Computes a safe mean of the losses.

  Args:
    losses: `Tensor` whose elements contain individual loss measurements.
    num_present: The number of measurable elements in `losses`.

  Returns:
    A scalar representing the mean of `losses`. If `num_present` is zero,
      then zero is returned.
  """
  total_loss = math_ops.reduce_sum(losses)
  return math_ops.div_no_nan(total_loss, num_present, name="value")


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.
  """
  if ((isinstance(weights, float) and weights != 0.0) or
      (context.executing_eagerly() and weights._rank() == 0  # pylint: disable=protected-access
       and not math_ops.equal(weights, 0.0))):
    return _num_elements(losses)
  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)),
          keepdims=True,
          name=scope)
    return math_ops.reduce_sum(present, name=scope)


def _num_elements(losses):
  """Computes the number of elements in `losses` tensor."""
  with ops.name_scope(None, "num_elements", values=[losses]) as scope:
    return math_ops.cast(array_ops.size(losses, name=scope), dtype=losses.dtype)


@tf_export(v1=["losses.compute_weighted_loss"])
def compute_weighted_loss(
    losses, weights=1.0, scope=None, loss_collection=ops.GraphKeys.LOSSES,
    reduction=Reduction.SUM_BY_NONZERO_WEIGHTS):
  """Computes the weighted loss.

  Args:
    losses: `Tensor` of shape `[batch_size, d1, ... dN]`.
    weights: Optional `Tensor` whose rank is either 0, or the same rank as
      `losses`, and must be broadcastable to `losses` (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: the loss will be added to these collections.
    reduction: Type of reduction to apply to loss.

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

  Raises:
    ValueError: If `weights` is `None` or the shape is not compatible with
      `losses`, or if the number of dimensions (rank) of either `losses` or
      `weights` is missing.

  Note:
    When calculating the gradient of a weighted loss contributions from
    both `losses` and `weights` are considered. If your `weights` depend
    on some model parameters but you do not want this to affect the loss
    gradient, you need to apply `tf.stop_gradient` to `weights` before
    passing them to `compute_weighted_loss`.

  @compatibility(eager)
  The `loss_collection` argument is ignored when executing eagerly. Consider
  holding on to the return value or collecting losses via a `tf.keras.Model`.
  @end_compatibility
  """
  Reduction.validate(reduction)
  with ops.name_scope(scope, "weighted_loss", (losses, weights)):
    # Save the `reduction` argument for loss normalization when distributing
    # to multiple replicas.
    # TODO(josh11b): Associate it with the returned op for more precision.
    ops.get_default_graph()._last_loss_reduction = reduction  # pylint: disable=protected-access

    with ops.control_dependencies((
        weights_broadcast_ops.assert_broadcastable(weights, losses),)):
      losses = ops.convert_to_tensor(losses)
      input_dtype = losses.dtype
      losses = math_ops.to_float(losses)
      weights = math_ops.to_float(weights)
      weighted_losses = math_ops.multiply(losses, weights)
      if reduction == Reduction.NONE:
        loss = weighted_losses
      else:
        loss = math_ops.reduce_sum(weighted_losses)
        if reduction == Reduction.MEAN:
          loss = _safe_mean(
              loss,
              math_ops.reduce_sum(array_ops.ones_like(losses) * weights))
        elif (reduction == Reduction.SUM_BY_NONZERO_WEIGHTS or
              reduction == Reduction.SUM_OVER_NONZERO_WEIGHTS):
          loss = _safe_mean(loss, _num_present(losses, weights))
        elif reduction == Reduction.SUM_OVER_BATCH_SIZE:
          loss = _safe_mean(loss, _num_elements(losses))

      # Convert the result back to the input type.
      loss = math_ops.cast(loss, input_dtype)
      util.add_loss(loss, loss_collection)
      return loss


@tf_export(v1=["losses.absolute_difference"])
def absolute_difference(
    labels, predictions, weights=1.0, scope=None,
    loss_collection=ops.GraphKeys.LOSSES,
    reduction=Reduction.SUM_BY_NONZERO_WEIGHTS):
  """Adds an Absolute Difference 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
  shape `[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 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 the shape of `predictions` doesn't match that of
      `labels` or if the shape of `weights` is invalid or if `labels`
      or `predictions` is None.

  @compatibility(eager)
  The `loss_collection` argument is ignored when executing eagerly. Consider
  holding on to the return value or collecting losses via a `tf.keras.Model`.
  @end_compatibility
  """
  if labels is None:
    raise ValueError("labels must not be None.")
  if predictions is None:
    raise ValueError("predictions must not be None.")
  with ops.name_scope(scope, "absolute_difference",
                      (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.abs(math_ops.subtract(predictions, labels))
    return compute_weighted_loss(
        losses, weights, scope, loss_collection, reduction=reduction)


@tf_export(v1=["losses.cosine_distance"])
@deprecated_args(None, "dim is deprecated, use axis instead", "dim")
def cosine_distance(
    labels, predictions, axis=None, weights=1.0, scope=None,
    loss_collection=ops.GraphKeys.LOSSES,
    reduction=Reduction.SUM_BY_NONZERO_WEIGHTS,
    dim=None):
  """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.
    axis: 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.
    dim: The old (deprecated) name for `axis`.

  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
      `axis`, `labels`, `predictions` or `weights` is `None`.

  @compatibility(eager)
  The `loss_collection` argument is ignored when executing eagerly. Consider
  holding on to the return value or collecting losses via a `tf.keras.Model`.
  @end_compatibility
  """
  axis = deprecated_argument_lookup("axis", axis, "dim", dim)
  if axis is None:
    raise ValueError("You must specify 'axis'.")
  if labels is None:
    raise ValueError("labels must not be None.")
  if predictions is None:
    raise ValueError("predictions must not 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=(axis,), keepdims=True)
    return compute_weighted_loss(
        losses, weights, scope, loss_collection, reduction=reduction)


@tf_export(v1=["losses.hinge_loss"])
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. Internally
      the {0,1} labels are converted to {-1,1} when calculating the hinge loss.
    logits: The logits, a float tensor. Note that logits are assumed to be
      unbounded and 0-centered. A value > 0 (resp. < 0) is considered a positive
      (resp. negative) binary prediction.
    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 or
      if `labels` or `logits` is None.

  @compatibility(eager)
  The `loss_collection` argument is ignored when executing eagerly. Consider
  holding on to the return value or collecting losses via a `tf.keras.Model`.
  @end_compatibility
  """
  if labels is None:
    raise ValueError("labels must not be None.")
  if logits is None:
    raise ValueError("logits must not be None.")
  with ops.name_scope(scope, "hinge_loss", (logits, labels, weights)) 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)


@tf_export(v1=["losses.huber_loss"])
def huber_loss(labels, predictions, weights=1.0, delta=1.0, scope=None,
               loss_collection=ops.GraphKeys.LOSSES,
               reduction=Reduction.SUM_BY_NONZERO_WEIGHTS):
  """Adds a Huber Loss term to the training procedure.

  For each value x in `error=labels-predictions`, the following is calculated:

  ```
    0.5 * x^2                  if |x| <= d
    0.5 * d^2 + d * (|x| - d)  if |x| > d
  ```

  where d is `delta`.

  See: https://en.wikipedia.org/wiki/Huber_loss

  `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).
    delta: `float`, the point where the huber loss function
      changes from a quadratic to linear.
    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.  Also if `labels` or
     `predictions` is None.

  @compatibility(eager)
  The `loss_collection` argument is ignored when executing eagerly. Consider
  holding on to the return value or collecting losses via a `tf.keras.Model`.
  @end_compatibility
  """
  if labels is None:
    raise ValueError("labels must not be None.")
  if predictions is None:
    raise ValueError("predictions must not be None.")
  with ops.name_scope(scope, "huber_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())
    error = math_ops.subtract(predictions, labels)
    abs_error = math_ops.abs(error)
    quadratic = math_ops.minimum(abs_error, delta)
    # The following expression is the same in value as
    # tf.maximum(abs_error - delta, 0), but importantly the gradient for the
    # expression when abs_error == delta is 0 (for tf.maximum it would be 1).
    # This is necessary to avoid doubling the gradient, since there is already a
    # nonzero contribution to the gradient from the quadratic term.
    linear = math_ops.subtract(abs_error, quadratic)
    losses = math_ops.add(
        math_ops.multiply(
            ops.convert_to_tensor(0.5, dtype=quadratic.dtype),
            math_ops.multiply(quadratic, quadratic)),
        math_ops.multiply(delta, linear))
    return compute_weighted_loss(
        losses, weights, scope, loss_collection, reduction=reduction)


@tf_export(v1=["losses.log_loss"])
def log_loss(labels, predictions, weights=1.0, epsilon=1e-7, scope=None,
             loss_collection=ops.GraphKeys.LOSSES,
             reduction=Reduction.SUM_BY_NONZERO_WEIGHTS):
  """Adds a Log Loss term 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).
    epsilon: A small increment to add to avoid taking a log of zero.
    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.  Also if `labels` or `predictions`
      is None.

  @compatibility(eager)
  The `loss_collection` argument is ignored when executing eagerly. Consider
  holding on to the return value or collecting losses via a `tf.keras.Model`.
  @end_compatibility
  """
  if labels is None:
    raise ValueError("labels must not be None.")
  if predictions is None:
    raise ValueError("predictions must not be None.")
  with ops.name_scope(scope, "log_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())
    losses = -math_ops.multiply(
        labels,
        math_ops.log(predictions + epsilon)) - math_ops.multiply(
            (1 - labels), math_ops.log(1 - predictions + epsilon))
    return compute_weighted_loss(
        losses, weights, scope, loss_collection, reduction=reduction)


# TODO(b/37208492): Add reduction arg.
@tf_export(v1=["losses.mean_pairwise_squared_error"])
def mean_pairwise_squared_error(
    labels, predictions, weights=1.0, scope=None,
    loss_collection=ops.GraphKeys.LOSSES):
  """Adds a pairwise-errors-squared loss to the training procedure.

  Unlike `mean_squared_error`, which is a measure of the differences between
  corresponding elements of `predictions` and `labels`,
  `mean_pairwise_squared_error` is a measure of the differences between pairs of
  corresponding elements of `predictions` and `labels`.

  For example, if `labels`=[a, b, c] and `predictions`=[x, y, z], there are
  three pairs of differences are summed to compute the loss:
    loss = [ ((a-b) - (x-y)).^2 + ((a-c) - (x-z)).^2 + ((b-c) - (y-z)).^2 ] / 3

  Note that since the inputs are of shape `[batch_size, d0, ... dN]`, the
  corresponding pairs are computed within each batch sample but not across
  samples within a batch. For example, if `predictions` represents a batch of
  16 grayscale images of dimension [batch_size, 100, 200], then the set of pairs
  is drawn from each image, but not across images.

  `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.

  Args:
    labels: The ground truth output tensor, whose shape must match the shape of
      `predictions`.
    predictions: The predicted outputs, a tensor of size
      `[batch_size, d0, .. dN]` where N+1 is the total number of dimensions in
      `predictions`.
    weights: Coefficients for the loss a scalar, a tensor of shape
      `[batch_size]` or a tensor whose shape matches `predictions`.
    scope: The scope for the operations performed in computing the loss.
    loss_collection: collection to which the loss will be added.

  Returns:
    A scalar `Tensor` that returns the weighted loss.

  Raises:
    ValueError: If the shape of `predictions` doesn't match that of `labels` or
      if the shape of `weights` is invalid.  Also if `labels` or `predictions`
      is None.

  @compatibility(eager)
  The `loss_collection` argument is ignored when executing eagerly. Consider
  holding on to the return value or collecting losses via a `tf.keras.Model`.
  @end_compatibility
  """
  if labels is None:
    raise ValueError("labels must not be None.")
  if predictions is None:
    raise ValueError("predictions must not be None.")
  with ops.name_scope(scope, "mean_pairwise_squared_error",
                      (predictions, labels, weights)) as scope:
    weights = math_ops.to_float(weights)
    labels = math_ops.to_float(labels)
    with ops.control_dependencies((
        weights_broadcast_ops.assert_broadcastable(weights, labels),)):
      predictions = math_ops.to_float(predictions)
      predictions.get_shape().assert_is_compatible_with(labels.get_shape())

      diffs = math_ops.subtract(predictions, labels)

      axis = math_ops.range(1, array_ops.rank(diffs))

      sum_squares_diff_per_batch = math_ops.reduce_sum(
          math_ops.square(diffs), axis=axis, keepdims=True)
      num_present_per_batch = _num_present(diffs, weights, per_batch=True)

      term1 = 2.0 * math_ops.div_no_nan(
          sum_squares_diff_per_batch,
          math_ops.maximum(num_present_per_batch - 1, 0),
          name="value")

      sum_diff = math_ops.reduce_sum(diffs, axis=axis, keepdims=True)
      term2 = 2.0 * math_ops.div_no_nan(
          math_ops.square(sum_diff),
          math_ops.maximum(
              math_ops.multiply(num_present_per_batch,
                                num_present_per_batch - 1), 0),
          name="value")

      weighted_losses = math_ops.multiply(term1 - term2, weights)
      loss = math_ops.reduce_sum(weighted_losses)

      mean_loss = array_ops.where(
          math_ops.reduce_sum(num_present_per_batch) > 0,
          loss,
          array_ops.zeros_like(loss),
          name="value")
      util.add_loss(mean_loss, loss_collection)
      return mean_loss


@tf_export(v1=["losses.mean_squared_error"])
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.  Also if `labels` or `predictions`
      is None.

  @compatibility(eager)
  The `loss_collection` argument is ignored when executing eagerly. Consider
  holding on to the return value or collecting losses via a `tf.keras.Model`.
  @end_compatibility
  """
  if labels is None:
    raise ValueError("labels must not be None.")
  if predictions is None:
    raise ValueError("predictions must not be None.")
  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.squared_difference(predictions, labels)
    return compute_weighted_loss(
        losses, weights, scope, loss_collection, reduction=reduction)


@tf_export(v1=["losses.sigmoid_cross_entropy"])
def sigmoid_cross_entropy(
    multi_class_labels, logits, weights=1.0, label_smoothing=0, scope=None,
    loss_collection=ops.GraphKeys.LOSSES,
    reduction=Reduction.SUM_BY_NONZERO_WEIGHTS):
  """Creates a cross-entropy loss using tf.nn.sigmoid_cross_entropy_with_logits.

  `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 shape `[batch_size]`, then the loss weights apply to each
  corresponding sample.

  If `label_smoothing` is nonzero, smooth the labels towards 1/2:

      new_multiclass_labels = multiclass_labels * (1 - label_smoothing)
                              + 0.5 * label_smoothing

  Args:
    multi_class_labels: `[batch_size, num_classes]` target integer labels in
      `{0, 1}`.
    logits: Float `[batch_size, num_classes]` logits outputs of the network.
    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).
    label_smoothing: If greater than `0` then smooth the labels.
    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 `Tensor` of the same type as `logits`. If `reduction` is
    `NONE`, this has the same shape as `logits`; otherwise, it is scalar.

  Raises:
    ValueError: If the shape of `logits` doesn't match that of
      `multi_class_labels` or if the shape of `weights` is invalid, or if
      `weights` is None.  Also if `multi_class_labels` or `logits` is None.

  @compatibility(eager)
  The `loss_collection` argument is ignored when executing eagerly. Consider
  holding on to the return value or collecting losses via a `tf.keras.Model`.
  @end_compatibility
  """
  if multi_class_labels is None:
    raise ValueError("multi_class_labels must not be None.")
  if logits is None:
    raise ValueError("logits must not be None.")
  with ops.name_scope(scope, "sigmoid_cross_entropy_loss",
                      (logits, multi_class_labels, weights)) as scope:
    logits = ops.convert_to_tensor(logits)
    multi_class_labels = math_ops.cast(multi_class_labels, logits.dtype)
    logits.get_shape().assert_is_compatible_with(multi_class_labels.get_shape())

    if label_smoothing > 0:
      multi_class_labels = (multi_class_labels * (1 - label_smoothing) +
                            0.5 * label_smoothing)

    losses = nn.sigmoid_cross_entropy_with_logits(labels=multi_class_labels,
                                                  logits=logits,
                                                  name="xentropy")
    return compute_weighted_loss(
        losses, weights, scope, loss_collection, reduction=reduction)


@tf_export(v1=["losses.softmax_cross_entropy"])
def softmax_cross_entropy(
    onehot_labels, logits, weights=1.0, label_smoothing=0, scope=None,
    loss_collection=ops.GraphKeys.LOSSES,
    reduction=Reduction.SUM_BY_NONZERO_WEIGHTS):
  """Creates a cross-entropy loss using tf.nn.softmax_cross_entropy_with_logits_v2.

  `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 shape `[batch_size]`, then the loss weights apply to each
  corresponding sample.

  If `label_smoothing` is nonzero, smooth the labels towards 1/num_classes:
      new_onehot_labels = onehot_labels * (1 - label_smoothing)
                          + label_smoothing / num_classes

  Note that `onehot_labels` and `logits` must have the same shape,
  e.g. `[batch_size, num_classes]`. The shape of `weights` must be
  broadcastable to loss, whose shape is decided by the shape of `logits`.
  In case the shape of `logits` is `[batch_size, num_classes]`, loss is
  a `Tensor` of shape `[batch_size]`.

  Args:
    onehot_labels: One-hot-encoded labels.
    logits: Logits outputs of the network.
    weights: Optional `Tensor` that is broadcastable to loss.
    label_smoothing: If greater than 0 then smooth the labels.
    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 `Tensor` of the same type as `logits`. If `reduction` is
    `NONE`, this has shape `[batch_size]`; otherwise, it is scalar.

  Raises:
    ValueError: If the shape of `logits` doesn't match that of `onehot_labels`
      or if the shape of `weights` is invalid or if `weights` is None.  Also if
      `onehot_labels` or `logits` is None.

  @compatibility(eager)
  The `loss_collection` argument is ignored when executing eagerly. Consider
  holding on to the return value or collecting losses via a `tf.keras.Model`.
  @end_compatibility
  """
  if onehot_labels is None:
    raise ValueError("onehot_labels must not be None.")
  if logits is None:
    raise ValueError("logits must not be None.")
  with ops.name_scope(scope, "softmax_cross_entropy_loss",
                      (logits, onehot_labels, weights)) as scope:
    logits = ops.convert_to_tensor(logits)
    onehot_labels = math_ops.cast(onehot_labels, logits.dtype)
    logits.get_shape().assert_is_compatible_with(onehot_labels.get_shape())

    if label_smoothing > 0:
      num_classes = math_ops.cast(
          array_ops.shape(onehot_labels)[1], logits.dtype)
      smooth_positives = 1.0 - label_smoothing
      smooth_negatives = label_smoothing / num_classes
      onehot_labels = onehot_labels * smooth_positives + smooth_negatives

    onehot_labels = array_ops.stop_gradient(
        onehot_labels, name="labels_stop_gradient")
    losses = nn.softmax_cross_entropy_with_logits_v2(
        labels=onehot_labels, logits=logits, name="xentropy")

    return compute_weighted_loss(
        losses, weights, scope, loss_collection, reduction=reduction)


# TODO(ptucker): Merge this with similar method in metrics_impl.
def _remove_squeezable_dimensions(
    labels, predictions, weights=None, expected_rank_diff=0):
  """Internal version of _remove_squeezable_dimensions which handles weights.

  Squeezes `predictions` and `labels` if their ranks differ from expected by
  exactly 1.
  Squeezes `weights` if its rank is 1 more than the new rank of `predictions`

  This will use static shape if available. Otherwise, it will add graph
  operations, which could result in a performance hit.

  Args:
    labels: Label values, a `Tensor` whose dimensions match `predictions`.
    predictions: Predicted values, a `Tensor` of arbitrary dimensions.
    weights: Optional weight `Tensor`. It will be squeezed if it's not scalar,
      and its rank is 1 more than the new rank of `labels`.
    expected_rank_diff: Expected result of `rank(predictions) - rank(labels)`.

  Returns:
    Tuple of `predictions`, `labels` and `weights`, possibly with the last
    dimension squeezed.
  """
  labels, predictions = confusion_matrix.remove_squeezable_dimensions(
      labels, predictions, expected_rank_diff=expected_rank_diff)

  if weights is not None:
    weights = ops.convert_to_tensor(weights)
    labels_rank = labels.get_shape().ndims
    weights_shape = weights.get_shape()
    weights_rank = weights_shape.ndims

    if (labels_rank is not None) and (weights_rank is not None):
      # Use static rank.
      rank_diff = weights_rank - labels_rank
      if rank_diff == 1:
        weights = array_ops.squeeze(weights, [-1])
      return labels, predictions, weights

    # Use dynamic rank.
    rank_diff = array_ops.rank(weights) - array_ops.rank(labels)
    if (weights_rank is None) or (
        weights_rank > 0 and weights_shape.dims[-1].is_compatible_with(1)):
      weights = control_flow_ops.cond(
          math_ops.equal(1, rank_diff),
          lambda: array_ops.squeeze(weights, [-1]),
          lambda: weights)

  return labels, predictions, weights


@tf_export(v1=["losses.sparse_softmax_cross_entropy"])
def sparse_softmax_cross_entropy(
    labels, logits, weights=1.0, scope=None,
    loss_collection=ops.GraphKeys.LOSSES,
    reduction=Reduction.SUM_BY_NONZERO_WEIGHTS):
  """Cross-entropy loss using `tf.nn.sparse_softmax_cross_entropy_with_logits`.

  `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 shape `[batch_size]`, then the loss weights apply to each
  corresponding sample.

  Args:
    labels: `Tensor` of shape `[d_0, d_1, ..., d_{r-1}]` (where `r` is rank of
      `labels` and result) and dtype `int32` or `int64`. Each entry in `labels`
      must be an index in `[0, num_classes)`. Other values will raise an
      exception when this op is run on CPU, and return `NaN` for corresponding
      loss and gradient rows on GPU.
    logits: Unscaled log probabilities of shape
      `[d_0, d_1, ..., d_{r-1}, num_classes]` and dtype `float16`, `float32` or
      `float64`.
    weights: Coefficients for the loss. This must be scalar or broadcastable to
      `labels` (i.e. same rank and each dimension is either 1 or the same).
    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 `Tensor` of the same type as `logits`. If `reduction` is
    `NONE`, this has the same shape as `labels`; otherwise, it is scalar.

  Raises:
    ValueError: If the shapes of `logits`, `labels`, and `weights` are
      incompatible, or if any of them are None.

  @compatibility(eager)
  The `loss_collection` argument is ignored when executing eagerly. Consider
  holding on to the return value or collecting losses via a `tf.keras.Model`.
  @end_compatibility
  """
  if labels is None:
    raise ValueError("labels must not be None.")
  if logits is None:
    raise ValueError("logits must not be None.")
  with ops.name_scope(scope, "sparse_softmax_cross_entropy_loss",
                      (logits, labels, weights)) as scope:
    # As documented above in Args, labels contain class IDs and logits contains
    # 1 probability per class ID, so we expect rank(logits) - rank(labels) == 1;
    # therefore, expected_rank_diff=1.
    labels, logits, weights = _remove_squeezable_dimensions(
        labels, logits, weights, expected_rank_diff=1)
    losses = nn.sparse_softmax_cross_entropy_with_logits(labels=labels,
                                                         logits=logits,
                                                         name="xentropy")
    return compute_weighted_loss(
        losses, weights, scope, loss_collection, reduction=reduction)
