def weighted(y_true, y_pred, weights, mask=None):
    """Wrapper function.

    Arguments:
        y_true: `y_true` argument of `fn`.
        y_pred: `y_pred` argument of `fn`.
        weights: Weights tensor.
        mask: Mask tensor.

    Returns:
        Scalar tensor.
    """
    # score_array has ndim >= 2
    score_array = fn(y_true, y_pred)
    if mask is not None:
      # Cast the mask to floatX to avoid float64 upcasting in theano
      mask = math_ops.cast(mask, K.floatx())
      # mask should have the same shape as score_array
      score_array *= mask
      #  the loss per batch should be proportional
      #  to the number of unmasked samples.
      score_array /= K.mean(mask)

    # apply sample weighting
    if weights is not None:
      # reduce score_array to same ndim as weight array
      ndim = K.ndim(score_array)
      weight_ndim = K.ndim(weights)
      score_array = K.mean(score_array, axis=list(range(weight_ndim, ndim)))
      score_array *= weights
      score_array /= K.mean(
          math_ops.cast(math_ops.not_equal(weights, 0), K.floatx()))
    return K.mean(score_array)

    def call(self, x):
        if len(x) != 2:
            raise Exception('input layers must be a list: mean and stddev')
        if len(x[0].shape) != 2 or len(x[1].shape) != 2:
            raise Exception('input shape is not a vector [batchSize, latentSize]')

        mean = x[0]
        stddev = x[1]

        if self.reg == 'bvae':
            # kl divergence:
            latent_loss = -0.5 * K.mean(1 + stddev
                                - K.square(mean)
                                - K.exp(stddev), axis=-1)
            # use beta to force less usage of vector space:
            # also try to use <capacity> dimensions of the space:
            latent_loss = self.beta * K.abs(latent_loss - self.capacity/self.shape.as_list()[1])
            self.add_loss(latent_loss, x)
        elif self.reg == 'vae':
            # kl divergence:
            latent_loss = -0.5 * K.mean(1 + stddev
                                - K.square(mean)
                                - K.exp(stddev), axis=-1)
            self.add_loss(latent_loss, x)

        epsilon = K.random_normal(shape=self.shape,
                              mean=0., stddev=1.)
        if self.random:
            # 'reparameterization trick':
            return mean + K.exp(stddev) * epsilon
        else: # do not perform random sampling, simply grab the impulse value
            return mean + 0*stddev # Keras needs the *0 so the gradinent is not None

  def weighted(y_true, y_pred, weights, mask=None):
    """Wrapper function.

    Arguments:
        y_true: `y_true` argument of `fn`.
        y_pred: `y_pred` argument of `fn`.
        weights: Weights tensor.
        mask: Mask tensor.

    Returns:
        Scalar tensor.
    """
    # score_array has ndim >= 2
    score_array = fn(y_true, y_pred)
    if mask is not None:
      mask = math_ops.cast(mask, y_pred.dtype)
      # Update weights with mask.
      if weights is None:
        weights = mask
      else:
        # Update shape of weights if possible before adding mask.
        # Update dimensions of weights to match with mask if possible.
        mask, _, weights = metrics_module.squeeze_or_expand_dimensions(
            mask, None, weights)
        try:
          # Broadcast weights if possible.
          weights = weights_broadcast_ops.broadcast_weights(weights, mask)
          weights *= mask
        except ValueError:
          score_array *= mask
          score_array /= K.mean(mask)
          # TODO(psv): Handle case when mask and weight shapes are not
          # compatible.

    # Apply sample weighting.
    if weights is not None:

      # Update dimensions of weights to match with values if possible.
      score_array, _, weights = metrics_module.squeeze_or_expand_dimensions(
          score_array, None, weights)
      try:
        # Broadcast weights if possible.
        weights = weights_broadcast_ops.broadcast_weights(weights, score_array)
      except ValueError:
        # Reduce values to same ndim as weight array.
        ndim = K.ndim(score_array)
        weight_ndim = K.ndim(weights)
        score_array = K.mean(score_array, axis=list(range(weight_ndim, ndim)))

      score_array = math_ops.multiply(score_array, weights)
      score_array = math_ops.reduce_sum(score_array)
      weights = math_ops.reduce_sum(weights)
      score_array = metrics_module.safe_div(score_array, weights)
    return K.mean(score_array)

def correlation_coefficient_loss(y_true, y_pred):
    x = y_true
    y = y_pred
    mx = K.mean(x)
    my = K.mean(y)
    xm, ym = x-mx, y-my
    r_num = K.sum(tf.multiply(xm,ym))
    r_den = K.sqrt(tf.multiply(K.sum(K.square(xm)), K.sum(K.square(ym))))
    r = r_num / r_den

    r = K.maximum(K.minimum(r, 1.0), -1.0)
    return 1 - K.square(r)

def logloss(y_true, y_pred):
  y_pred = ops.convert_to_tensor(y_pred)
  y_true = math_ops.cast(y_true, y_pred.dtype)
  losses = math_ops.multiply(y_true, math_ops.log(y_pred + K.epsilon()))
  losses += math_ops.multiply((1 - y_true),
                              math_ops.log(1 - y_pred + K.epsilon()))
  return K.mean(-losses, axis=-1)

def _eager_metrics_fn(model,
                      outputs,
                      targets,
                      sample_weights=None,
                      masks=None,
                      return_stateful_result=True):
  """Calculates the metrics for each output of the given model.

  Arguments:
      model: The model on which metrics are being calculated.
      outputs: The outputs of the given model.
      targets: The predictions or targets of the given model.
      sample_weights: Optional list of sample weights for each output.
      masks: Optional list of masks for each output.
      return_stateful_result: Boolean, indicates whether the stateful
        (aggregated)/stateless metric result should be returned.

  Returns:
      Returns the metric results for each output of the model.
  """
  outputs = nest.flatten(outputs)
  targets = nest.flatten(targets)
  # TODO(psv): Consider supporting skip target indices in eager mode?
  metric_results = model._handle_metrics(
      outputs,
      targets=targets,
      sample_weights=sample_weights,
      masks=masks,
      return_stateful_result=return_stateful_result)
  return [backend.mean(t) for t in metric_results]

def compute_weighted_loss(losses,
                          sample_weight=None,
                          reduction=ReductionV2.SUM_OVER_BATCH_SIZE,
                          name=None):
  """Computes the weighted loss.

  Args:
    losses: `Tensor` of shape `[batch_size, d1, ... dN]`.
    sample_weight: Optional `Tensor` whose rank is either 0, or the same rank as
      `losses`, or be broadcastable to `losses`.
    reduction: (Optional) Type of `tf.keras.losses.Reduction` to apply to loss.
      Default value is `SUM_OVER_BATCH_SIZE`.
    name: Optional name for the op.

  Raises:
    ValueError: If the shape of `sample_weight` is not compatible with `losses`.

  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.
  """
  ReductionV2.validate(reduction)

  # If this function is called directly, then we just default 'AUTO' to
  # 'SUM_OVER_BATCH_SIZE'. Eg. Canned estimator use cases.
  if reduction == ReductionV2.AUTO:
    reduction = ReductionV2.SUM_OVER_BATCH_SIZE
  if sample_weight is None:
    sample_weight = 1.0
  with K.name_scope(name or 'weighted_loss'):
    # Save the `reduction` argument for loss normalization when distributing
    # to multiple replicas. Used only for estimator + v1 optimizer flow.
    ops.get_default_graph()._last_loss_reduction = reduction  # pylint: disable=protected-access

    # Update dimensions of `sample_weight` to match with `losses` if possible.
    losses, _, sample_weight = squeeze_or_expand_dimensions(
        losses, None, sample_weight)
    losses = ops.convert_to_tensor(losses)
    input_dtype = losses.dtype
    losses = math_ops.cast(losses, dtypes.float32)
    sample_weight = math_ops.cast(sample_weight, dtypes.float32)

    try:
      # Broadcast weights if possible.
      sample_weight = weights_broadcast_ops.broadcast_weights(
          sample_weight, losses)
    except ValueError:
      # Reduce values to same ndim as weight array.
      ndim = K.ndim(losses)
      weight_ndim = K.ndim(sample_weight)
      losses = K.mean(losses, axis=list(range(weight_ndim, ndim)))

    sample_weight.shape.assert_is_compatible_with(losses.shape)
    weighted_losses = math_ops.multiply(losses, sample_weight)
    # Apply reduction function to the individual weighted losses.
    loss = reduce_weighted_loss(weighted_losses, reduction)
    # Convert the result back to the input type.
    loss = math_ops.cast(loss, input_dtype)
    return loss

def binary_crossentropy(y_true, y_pred, from_logits=False, label_smoothing=0):

  def _smooth_labels():
    return y_true * (1.0 - label_smoothing) + 0.5 * label_smoothing

  y_true = smart_cond.smart_cond(label_smoothing,
                                 _smooth_labels, lambda: y_true)
  return K.mean(
      K.binary_crossentropy(y_true, y_pred, from_logits=from_logits), axis=-1)

  def weighted(y_true, y_pred, weights, mask=None):
    """Wrapper function.

    Arguments:
        y_true: `y_true` argument of `fn`.
        y_pred: `y_pred` argument of `fn`.
        weights: Weights tensor.
        mask: Mask tensor.

    Returns:
        Scalar tensor.
    """
    # score_array has ndim >= 2
    score_array = fn(y_true, y_pred)
    if mask is not None:
      mask = math_ops.cast(mask, y_pred.dtype)
      # Update weights with mask.
      if weights is None:
        weights = mask
      else:
        # Update dimensions of weights to match with mask if possible.
        mask, _, weights = squeeze_or_expand_dimensions(mask, None, weights)
        weights *= mask

    # Apply sample weighting.
    if weights is not None:

      # Update dimensions of weights to match with values if possible.
      score_array, _, weights = squeeze_or_expand_dimensions(
          score_array, None, weights)
      try:
        # Broadcast weights if possible.
        weights = weights_broadcast_ops.broadcast_weights(weights, score_array)
      except ValueError:
        # Reduce values to same ndim as weight array.
        ndim = K.ndim(score_array)
        weight_ndim = K.ndim(weights)
        score_array = K.mean(score_array, axis=list(range(weight_ndim, ndim)))

      score_array = math_ops.multiply(score_array, weights)
      score_array = math_ops.reduce_sum(score_array)
      weights = math_ops.reduce_sum(weights)
      score_array = math_ops.div_no_nan(score_array, weights)
    return K.mean(score_array)

def compute_weighted_loss(losses,
                          sample_weight=None,
                          reduction=losses_impl.ReductionV2.SUM_OVER_BATCH_SIZE,
                          name=None):
  """Computes the weighted loss.

  Args:
    losses: `Tensor` of shape `[batch_size, d1, ... dN]`.
    sample_weight: Optional `Tensor` whose rank is either 0, or the same rank as
      `losses`, or be broadcastable to `losses`.
    reduction: Type of `tf.losses.Reduction` to apply to loss. Default value is
      `SUM_OVER_BATCH_SIZE`.
    name: Optional name for the op.

  Raises:
    ValueError: If the shape of `sample_weight` is not compatible with `losses`.

  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.
  """
  losses_impl.ReductionV2.validate(reduction)
  if sample_weight is None:
    sample_weight = 1.0
  with ops.name_scope(name, 'weighted_loss', (losses, sample_weight)):
    # 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

    # Update dimensions of `sample_weight` to match with `losses` if possible.
    losses, _, sample_weight = squeeze_or_expand_dimensions(
        losses, None, sample_weight)
    losses = ops.convert_to_tensor(losses)
    input_dtype = losses.dtype
    losses = math_ops.to_float(losses)
    sample_weight = math_ops.to_float(sample_weight)

    try:
      # Broadcast weights if possible.
      sample_weight = weights_broadcast_ops.broadcast_weights(
          sample_weight, losses)
    except ValueError:
      # Reduce values to same ndim as weight array.
      ndim = K.ndim(losses)
      weight_ndim = K.ndim(sample_weight)
      losses = K.mean(losses, axis=list(range(weight_ndim, ndim)))

    sample_weight.get_shape().assert_is_compatible_with(losses.get_shape())
    weighted_losses = math_ops.multiply(losses, sample_weight)
    # Apply reduction function to the individual weighted losses.
    loss = _reduce_weighted_loss(weighted_losses, reduction)
    # Convert the result back to the input type.
    loss = math_ops.cast(loss, input_dtype)
    return loss

def binary_crossentropy(y_true, y_pred, from_logits=False, label_smoothing=0):  # pylint: disable=missing-docstring
  y_pred = ops.convert_to_tensor(y_pred)
  y_true = math_ops.cast(y_true, y_pred.dtype)
  label_smoothing = ops.convert_to_tensor(label_smoothing, dtype=K.floatx())

  def _smooth_labels():
    return y_true * (1.0 - label_smoothing) + 0.5 * label_smoothing

  y_true = smart_cond.smart_cond(label_smoothing,
                                 _smooth_labels, lambda: y_true)
  return K.mean(
      K.binary_crossentropy(y_true, y_pred, from_logits=from_logits), axis=-1)

 def call(self, inputs, mask=None):
   steps_axis = 1 if self.data_format == 'channels_last' else 2
   if mask is not None:
     mask = math_ops.cast(mask, backend.floatx())
     input_shape = inputs.shape.as_list()
     broadcast_shape = [-1, input_shape[steps_axis], 1]
     mask = array_ops.reshape(mask, broadcast_shape)
     inputs *= mask
     return backend.sum(inputs, axis=steps_axis) / math_ops.reduce_sum(
         mask, axis=steps_axis)
   else:
     return backend.mean(inputs, axis=steps_axis)

def compute_weighted_loss(losses,
                          sample_weight=None,
                          reduction=ReductionV2.SUM_OVER_BATCH_SIZE,
                          name=None):
  """Computes the weighted loss.

  Args:
    losses: `Tensor` of shape `[batch_size, d1, ... dN]`.
    sample_weight: Optional `Tensor` whose rank is either 0, or the same rank as
      `losses`, or be broadcastable to `losses`.
    reduction: (Optional) Type of `tf.keras.losses.Reduction` to apply to loss.
      Default value is `SUM_OVER_BATCH_SIZE`.
    name: Optional name for the op.

  Raises:
    ValueError: If the shape of `sample_weight` is not compatible with `losses`.

  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.
  """
  ReductionV2.validate(reduction)
  if sample_weight is None:
    sample_weight = 1.0
  with ops.name_scope(name, 'weighted_loss', (losses, sample_weight)):
    # Update dimensions of `sample_weight` to match with `losses` if possible.
    losses, _, sample_weight = squeeze_or_expand_dimensions(
        losses, None, sample_weight)
    losses = ops.convert_to_tensor(losses)
    input_dtype = losses.dtype
    losses = math_ops.cast(losses, dtypes.float32)
    sample_weight = math_ops.cast(sample_weight, dtypes.float32)

    try:
      # Broadcast weights if possible.
      sample_weight = weights_broadcast_ops.broadcast_weights(
          sample_weight, losses)
    except ValueError:
      # Reduce values to same ndim as weight array.
      ndim = K.ndim(losses)
      weight_ndim = K.ndim(sample_weight)
      losses = K.mean(losses, axis=list(range(weight_ndim, ndim)))

    sample_weight.shape.assert_is_compatible_with(losses.shape)
    weighted_losses = math_ops.multiply(losses, sample_weight)
    # Apply reduction function to the individual weighted losses.
    loss = reduce_weighted_loss(weighted_losses, reduction)
    # Convert the result back to the input type.
    loss = math_ops.cast(loss, input_dtype)
    return loss

def hinge(y_true, y_pred):
  """Computes the hinge loss between `y_true` and `y_pred`.

  Args:
    y_true: The ground truth values. `y_true` values are expected to be -1 or 1.
      If binary (0 or 1) labels are provided we will convert them to -1 or 1.
    y_pred: The predicted values.

  Returns:
    Tensor with one scalar loss entry per sample.
  """
  y_pred = ops.convert_to_tensor(y_pred)
  y_true = math_ops.cast(y_true, y_pred.dtype)
  y_true = _maybe_convert_labels(y_true)
  return K.mean(math_ops.maximum(1. - y_true * y_pred, 0.), axis=-1)

def _eager_metrics_fn(model, outputs, targets, sample_weights=None, masks=None):
  """Calculates the metrics for each output of the given model.

  Arguments:
      model: The model on which metrics are being calculated.
      outputs: The outputs of the given model.
      targets: The predictions or targets of the given model.
      sample_weights: Optional list of sample weights for each output.
      masks: Optional list of masks for each output.

  Returns:
      Returns the metric results for each output of the model.
  """
  outputs = generic_utils.to_list(outputs)
  targets = generic_utils.to_list(targets)
  # TODO(psv): Consider supporting skip target indices in eager mode?
  metric_results = model._handle_metrics(
      outputs, targets=targets, sample_weights=sample_weights, masks=masks)
  return [backend.mean(t) for t in metric_results]

def logcosh(y_true, y_pred):
  """Logarithm of the hyperbolic cosine of the prediction error.

  `log(cosh(x))` is approximately equal to `(x ** 2) / 2` for small `x` and
  to `abs(x) - log(2)` for large `x`. This means that 'logcosh' works mostly
  like the mean squared error, but will not be so strongly affected by the
  occasional wildly incorrect prediction.

  Arguments:
      y_true: tensor of true targets.
      y_pred: tensor of predicted targets.

  Returns:
      Tensor with one scalar loss entry per sample.
  """

  def _logcosh(x):
    return x + nn.softplus(-2. * x) - math_ops.log(2.)

  return K.mean(_logcosh(y_pred - y_true), axis=-1)

def _eager_metrics_fn(model, outputs, targets):
  """Calculates the metrics for each output of the given model.

  Arguments:
      model: The model on which metrics are being calculated.
      outputs: The outputs of the given model.
      targets: The predictions or targets of the given model.

  Returns:
      Returns the metric names and metric results for each output of the model.
  """
  metric_names = []
  metric_results = []
  if not isinstance(outputs, list):
    outputs = [outputs]

  if not isinstance(targets, list):
    targets = [targets]

  for i in range(len(model.outputs)):
    output_metrics = model.nested_metrics[i]
    for nested_output_metric in output_metrics:
      metric_name, metric_fn = _get_metrics_info(
          nested_output_metric, backend.int_shape(model.outputs[i]),
          model.loss_functions[i])

      if len(model.output_names) > 1:
        metric_name = model.output_names[i] + '_' + metric_name
        if metric_name not in model.metrics_names:
          model.metrics_names.append(metric_name)

      with backend.name_scope(metric_name):
        metric_result = metric_fn(targets[i], outputs[i])
        metric_names.append(metric_name)
        metric_results.append(backend.mean(metric_result))

  return metric_results

def top_k_categorical_accuracy(y_true, y_pred, k=5):
  return K.mean(
      nn.in_top_k(y_pred, math_ops.argmax(y_true, axis=-1), k), axis=-1)

def sparse_top_k_categorical_accuracy(y_true, y_pred, k=5):
  # If the shape of y_true is (num_samples, 1), squeeze to (num_samples,)
  if (len(K.int_shape(y_true)) == len(K.int_shape(y_pred))):
    y_true = array_ops.squeeze(y_true, [-1])

  return K.mean(nn.in_top_k(y_pred, math_ops.cast(y_true, 'int32'), k), axis=-1)

def binary_accuracy(y_true, y_pred, threshold=0.5):
  threshold = math_ops.cast(threshold, y_pred.dtype)
  y_pred = math_ops.cast(y_pred > threshold, y_pred.dtype)
  return K.mean(math_ops.equal(y_true, y_pred), axis=-1)