metrics.py

# Copyright 2015 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.
# ==============================================================================
# pylint: disable=unused-import
# pylint: disable=g-classes-have-attributes
"""Built-in metrics.
"""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

import tensorflow.compat.v2 as tf

import abc
import types

import numpy as np
import six
from tensorflow.python.eager import def_function
from keras import activations
from keras import backend as K
from keras.engine import base_layer
from keras.engine import base_layer_utils
from keras.engine import keras_tensor
from keras.losses import binary_crossentropy
from keras.losses import categorical_crossentropy
from keras.losses import categorical_hinge
from keras.losses import hinge
from keras.losses import kullback_leibler_divergence
from keras.losses import logcosh
from keras.losses import mean_absolute_error
from keras.losses import mean_absolute_percentage_error
from keras.losses import mean_squared_error
from keras.losses import mean_squared_logarithmic_error
from keras.losses import poisson
from keras.losses import sparse_categorical_crossentropy
from keras.losses import squared_hinge
from keras.saving.saved_model import metric_serialization
from keras.utils import losses_utils
from keras.utils import metrics_utils
from keras.utils import tf_inspect
from keras.utils.generic_utils import deserialize_keras_object
from keras.utils.generic_utils import serialize_keras_object
from keras.utils.generic_utils import to_list
from keras.utils.tf_utils import is_tensor_or_variable
from tensorflow.python.util.tf_export import keras_export
from tensorflow.tools.docs import doc_controls


@keras_export('keras.metrics.Metric')
@six.add_metaclass(abc.ABCMeta)
class Metric(base_layer.Layer):
  """Encapsulates metric logic and state.

  Args:
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.
    **kwargs: Additional layer keywords arguments.

  Standalone usage:

  ```python
  m = SomeMetric(...)
  for input in ...:
    m.update_state(input)
  print('Final result: ', m.result().numpy())
  ```

  Usage with `compile()` API:

  ```python
  model = tf.keras.Sequential()
  model.add(tf.keras.layers.Dense(64, activation='relu'))
  model.add(tf.keras.layers.Dense(64, activation='relu'))
  model.add(tf.keras.layers.Dense(10, activation='softmax'))

  model.compile(optimizer=tf.keras.optimizers.RMSprop(0.01),
                loss=tf.keras.losses.CategoricalCrossentropy(),
                metrics=[tf.keras.metrics.CategoricalAccuracy()])

  data = np.random.random((1000, 32))
  labels = np.random.random((1000, 10))

  dataset = tf.data.Dataset.from_tensor_slices((data, labels))
  dataset = dataset.batch(32)

  model.fit(dataset, epochs=10)
  ```

  To be implemented by subclasses:
  * `__init__()`: All state variables should be created in this method by
    calling `self.add_weight()` like: `self.var = self.add_weight(...)`
  * `update_state()`: Has all updates to the state variables like:
    self.var.assign_add(...).
  * `result()`: Computes and returns a value for the metric
    from the state variables.

  Example subclass implementation:

  ```python
  class BinaryTruePositives(tf.keras.metrics.Metric):

    def __init__(self, name='binary_true_positives', **kwargs):
      super(BinaryTruePositives, self).__init__(name=name, **kwargs)
      self.true_positives = self.add_weight(name='tp', initializer='zeros')

    def update_state(self, y_true, y_pred, sample_weight=None):
      y_true = tf.cast(y_true, tf.bool)
      y_pred = tf.cast(y_pred, tf.bool)

      values = tf.logical_and(tf.equal(y_true, True), tf.equal(y_pred, True))
      values = tf.cast(values, self.dtype)
      if sample_weight is not None:
        sample_weight = tf.cast(sample_weight, self.dtype)
        sample_weight = tf.broadcast_to(sample_weight, values.shape)
        values = tf.multiply(values, sample_weight)
      self.true_positives.assign_add(tf.reduce_sum(values))

    def result(self):
      return self.true_positives
  ```
  """

  def __init__(self, name=None, dtype=None, **kwargs):
    super(Metric, self).__init__(name=name, dtype=dtype, **kwargs)
    self.stateful = True  # All metric layers are stateful.
    self.built = True
    if not base_layer_utils.v2_dtype_behavior_enabled():
      # We only do this when the V2 behavior is not enabled, as when it is
      # enabled, the dtype already defaults to floatx.
      self._dtype = K.floatx() if dtype is None else tf.as_dtype(dtype).name

  def __new__(cls, *args, **kwargs):
    obj = super(Metric, cls).__new__(cls)

    # If `update_state` is not in eager/tf.function and it is not from a
    # built-in metric, wrap it in `tf.function`. This is so that users writing
    # custom metrics in v1 need not worry about control dependencies and
    # return ops.
    if (base_layer_utils.is_in_eager_or_tf_function() or
        is_built_in(cls)):
      obj_update_state = obj.update_state

      def update_state_fn(*args, **kwargs):
        control_status = tf.__internal__.autograph.control_status_ctx()
        ag_update_state = tf.__internal__.autograph.tf_convert(obj_update_state, control_status)
        return ag_update_state(*args, **kwargs)
    else:
      if isinstance(obj.update_state, def_function.Function):
        update_state_fn = obj.update_state
      else:
        update_state_fn = tf.function(obj.update_state)

    obj.update_state = types.MethodType(
        metrics_utils.update_state_wrapper(update_state_fn), obj)

    obj_result = obj.result

    def result_fn(*args, **kwargs):
      control_status = tf.__internal__.autograph.control_status_ctx()
      ag_result = tf.__internal__.autograph.tf_convert(obj_result, control_status)
      return ag_result(*args, **kwargs)

    obj.result = types.MethodType(metrics_utils.result_wrapper(result_fn), obj)

    return obj

  def __call__(self, *args, **kwargs):
    """Accumulates statistics and then computes metric result value.

    Args:
      *args:
      **kwargs: A mini-batch of inputs to the Metric,
        passed on to `update_state()`.

    Returns:
      The metric value tensor.
    """

    def replica_local_fn(*args, **kwargs):
      """Updates the state of the metric in a replica-local context."""
      if any(
          isinstance(arg, keras_tensor.KerasTensor)
          for arg in tf.nest.flatten((args, kwargs))):
        update_op = None
      else:
        update_op = self.update_state(*args, **kwargs)  # pylint: disable=not-callable
      update_ops = []
      if update_op is not None:
        update_ops.append(update_op)
      with tf.control_dependencies(update_ops):
        result_t = self.result()  # pylint: disable=not-callable

        # We are adding the metric object as metadata on the result tensor.
        # This is required when we want to use a metric with `add_metric` API on
        # a Model/Layer in graph mode. This metric instance will later be used
        # to reset variable state after each epoch of training.
        # Example:
        #   model = Model()
        #   mean = Mean()
        #   model.add_metric(mean(values), name='mean')
        result_t._metric_obj = self  # pylint: disable=protected-access
        return result_t

    from keras.distribute import distributed_training_utils  # pylint:disable=g-import-not-at-top
    return distributed_training_utils.call_replica_local_fn(
        replica_local_fn, *args, **kwargs)

  @property
  def dtype(self):
    return self._dtype

  def get_config(self):
    """Returns the serializable config of the metric."""
    return {'name': self.name, 'dtype': self.dtype}

  def reset_states(self):
    """Resets all of the metric state variables.

    This function is called between epochs/steps,
    when a metric is evaluated during training.
    """
    K.batch_set_value([(v, 0) for v in self.variables])

  @abc.abstractmethod
  def update_state(self, *args, **kwargs):
    """Accumulates statistics for the metric.

    Note: This function is executed as a graph function in graph mode.
    This means:
      a) Operations on the same resource are executed in textual order.
         This should make it easier to do things like add the updated
         value of a variable to another, for example.
      b) You don't need to worry about collecting the update ops to execute.
         All update ops added to the graph by this function will be executed.
      As a result, code should generally work the same way with graph or
      eager execution.

    Args:
      *args:
      **kwargs: A mini-batch of inputs to the Metric.
    """
    raise NotImplementedError('Must be implemented in subclasses.')

  @abc.abstractmethod
  def result(self):
    """Computes and returns the metric value tensor.

    Result computation is an idempotent operation that simply calculates the
    metric value using the state variables.
    """
    raise NotImplementedError('Must be implemented in subclasses.')

  ### For use by subclasses ###
  @doc_controls.for_subclass_implementers
  def add_weight(self,
                 name,
                 shape=(),
                 aggregation=tf.compat.v1.VariableAggregation.SUM,
                 synchronization=tf.VariableSynchronization.ON_READ,
                 initializer=None,
                 dtype=None):
    """Adds state variable. Only for use by subclasses."""
    if tf.distribute.has_strategy():
      strategy = tf.distribute.get_strategy()
    else:
      strategy = None

    # TODO(b/120571621): Make `ON_READ` work with Keras metrics on TPU.
    if K.is_tpu_strategy(strategy):
      synchronization = tf.VariableSynchronization.ON_WRITE

    with tf.init_scope():
      return super(Metric, self).add_weight(
          name=name,
          shape=shape,
          dtype=self._dtype if dtype is None else dtype,
          trainable=False,
          initializer=initializer,
          collections=[],
          synchronization=synchronization,
          aggregation=aggregation)

  ### End: For use by subclasses ###

  @property
  def trainable_weights(self):
    # Overridden from Layer class to track submetric weights.
    if self.trainable:
      trainable_weights = self._trainable_weights
      for m in self._metrics:
        trainable_weights += m.trainable_weights
      return self._dedup_weights(trainable_weights)
    else:
      return []

  @property
  def non_trainable_weights(self):
    # Overridden from Layer class to track submetric weights.
    if self.trainable:
      non_trainable_weights = self._non_trainable_weights
      for m in self._metrics:
        non_trainable_weights += m.non_trainable_weights
    else:
      non_trainable_weights = (
          self._non_trainable_weights + self._trainable_weights)
      for m in self._metrics:
        non_trainable_weights += m.weights
    return self._dedup_weights(non_trainable_weights)

  @property
  def _trackable_saved_model_saver(self):
    return metric_serialization.MetricSavedModelSaver(self)


class Reduce(Metric):
  """Encapsulates metrics that perform a reduce operation on the values.

  Args:
    reduction: a `tf.keras.metrics.Reduction` enum value.
    name: string name of the metric instance.
    dtype: (Optional) data type of the metric result.
  """

  def __init__(self, reduction, name, dtype=None):
    super(Reduce, self).__init__(name=name, dtype=dtype)
    self.reduction = reduction
    self.total = self.add_weight(
        'total', initializer=tf.compat.v1.zeros_initializer)
    if reduction in [metrics_utils.Reduction.SUM_OVER_BATCH_SIZE,
                     metrics_utils.Reduction.WEIGHTED_MEAN]:
      self.count = self.add_weight(
          'count', initializer=tf.compat.v1.zeros_initializer)

  def update_state(self, values, sample_weight=None):
    """Accumulates statistics for computing the metric.

    Args:
      values: Per-example value.
      sample_weight: Optional weighting of each example. Defaults to 1.

    Returns:
      Update op.
    """
    [values], sample_weight = \
        metrics_utils.ragged_assert_compatible_and_get_flat_values(
            [values], sample_weight)
    values = tf.cast(values, self._dtype)
    if sample_weight is not None:
      sample_weight = tf.cast(sample_weight, self._dtype)
      # Update dimensions of weights to match with values if possible.
      values, _, sample_weight = losses_utils.squeeze_or_expand_dimensions(
          values, sample_weight=sample_weight)
      try:
        # Broadcast weights if possible.
        sample_weight = tf.__internal__.ops.broadcast_weights(
            sample_weight, values)
      except ValueError:
        # Reduce values to same ndim as weight array
        ndim = K.ndim(values)
        weight_ndim = K.ndim(sample_weight)
        if self.reduction == metrics_utils.Reduction.SUM:
          values = tf.reduce_sum(
              values, axis=list(range(weight_ndim, ndim)))
        else:
          values = tf.reduce_mean(
              values, axis=list(range(weight_ndim, ndim)))
      values = tf.multiply(values, sample_weight)

    value_sum = tf.reduce_sum(values)
    with tf.control_dependencies([value_sum]):
      update_total_op = self.total.assign_add(value_sum)

    # Exit early if the reduction doesn't have a denominator.
    if self.reduction == metrics_utils.Reduction.SUM:
      return update_total_op

    # Update `count` for reductions that require a denominator.
    if self.reduction == metrics_utils.Reduction.SUM_OVER_BATCH_SIZE:
      num_values = tf.cast(tf.compat.v1.size(values), self._dtype)
    elif self.reduction == metrics_utils.Reduction.WEIGHTED_MEAN:
      if sample_weight is None:
        num_values = tf.cast(tf.compat.v1.size(values), self._dtype)
      else:
        num_values = tf.reduce_sum(sample_weight)
    else:
      raise NotImplementedError(
          'reduction [%s] not implemented' % self.reduction)

    with tf.control_dependencies([update_total_op]):
      return self.count.assign_add(num_values)

  def result(self):
    if self.reduction == metrics_utils.Reduction.SUM:
      return tf.identity(self.total)
    elif self.reduction in [
        metrics_utils.Reduction.WEIGHTED_MEAN,
        metrics_utils.Reduction.SUM_OVER_BATCH_SIZE
    ]:
      return tf.math.divide_no_nan(self.total, self.count)
    else:
      raise NotImplementedError(
          'reduction [%s] not implemented' % self.reduction)


@keras_export('keras.metrics.Sum')
class Sum(Reduce):
  """Computes the (weighted) sum of the given values.

  For example, if values is [1, 3, 5, 7] then the sum is 16.
  If the weights were specified as [1, 1, 0, 0] then the sum would be 4.

  This metric creates one variable, `total`, that is used to compute the sum of
  `values`. This is ultimately returned as `sum`.

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

  Args:
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> m = tf.keras.metrics.Sum()
  >>> m.update_state([1, 3, 5, 7])
  >>> m.result().numpy()
  16.0

  Usage with `compile()` API:

  ```python
  model.add_metric(tf.keras.metrics.Sum(name='sum_1')(outputs))
  model.compile(optimizer='sgd', loss='mse')
  ```
  """

  def __init__(self, name='sum', dtype=None):
    super(Sum, self).__init__(reduction=metrics_utils.Reduction.SUM,
                              name=name, dtype=dtype)


@keras_export('keras.metrics.Mean')
class Mean(Reduce):
  """Computes the (weighted) mean of the given values.

  For example, if values is [1, 3, 5, 7] then the mean is 4.
  If the weights were specified as [1, 1, 0, 0] then the mean would be 2.

  This metric creates two variables, `total` and `count` that are used to
  compute the average of `values`. This average is ultimately returned as `mean`
  which is an idempotent operation that simply divides `total` by `count`.

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

  Args:
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> m = tf.keras.metrics.Mean()
  >>> m.update_state([1, 3, 5, 7])
  >>> m.result().numpy()
  4.0
  >>> m.reset_states()
  >>> m.update_state([1, 3, 5, 7], sample_weight=[1, 1, 0, 0])
  >>> m.result().numpy()
  2.0

  Usage with `compile()` API:

  ```python
  model.add_metric(tf.keras.metrics.Mean(name='mean_1')(outputs))
  model.compile(optimizer='sgd', loss='mse')
  ```
  """

  def __init__(self, name='mean', dtype=None):
    super(Mean, self).__init__(
        reduction=metrics_utils.Reduction.WEIGHTED_MEAN, name=name, dtype=dtype)


@keras_export('keras.metrics.MeanRelativeError')
class MeanRelativeError(Mean):
  """Computes the mean relative error by normalizing with the given values.

  This metric creates two local variables, `total` and `count` that are used to
  compute the mean relative error. This is weighted by `sample_weight`, and
  it is ultimately returned as `mean_relative_error`:
  an idempotent operation that simply divides `total` by `count`.

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

  Args:
    normalizer: The normalizer values with same shape as predictions.
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> m = tf.keras.metrics.MeanRelativeError(normalizer=[1, 3, 2, 3])
  >>> m.update_state([1, 3, 2, 3], [2, 4, 6, 8])

  >>> # metric = mean(|y_pred - y_true| / normalizer)
  >>> #        = mean([1, 1, 4, 5] / [1, 3, 2, 3]) = mean([1, 1/3, 2, 5/3])
  >>> #        = 5/4 = 1.25
  >>> m.result().numpy()
  1.25

  Usage with `compile()` API:

  ```python
  model.compile(
    optimizer='sgd',
    loss='mse',
    metrics=[tf.keras.metrics.MeanRelativeError(normalizer=[1, 3])])
  ```
  """

  def __init__(self, normalizer, name=None, dtype=None):
    super(MeanRelativeError, self).__init__(name=name, dtype=dtype)
    normalizer = tf.cast(normalizer, self._dtype)
    self.normalizer = normalizer

  def update_state(self, y_true, y_pred, sample_weight=None):
    """Accumulates metric statistics.

    Args:
      y_true: The ground truth values.
      y_pred: The predicted values.
      sample_weight: Optional weighting of each example. Defaults to 1. Can be a
        `Tensor` whose rank is either 0, or the same rank as `y_true`, and must
        be broadcastable to `y_true`.

    Returns:
      Update op.
    """
    y_true = tf.cast(y_true, self._dtype)
    y_pred = tf.cast(y_pred, self._dtype)
    [y_pred, y_true], sample_weight = \
        metrics_utils.ragged_assert_compatible_and_get_flat_values(
            [y_pred, y_true], sample_weight)
    y_pred, y_true = losses_utils.squeeze_or_expand_dimensions(
        y_pred, y_true)

    y_pred, self.normalizer = losses_utils.remove_squeezable_dimensions(
        y_pred, self.normalizer)
    y_pred.shape.assert_is_compatible_with(y_true.shape)
    relative_errors = tf.math.divide_no_nan(
        tf.abs(y_true - y_pred), self.normalizer)

    return super(MeanRelativeError, self).update_state(
        relative_errors, sample_weight=sample_weight)

  def get_config(self):
    n = self.normalizer
    config = {'normalizer': K.eval(n) if is_tensor_or_variable(n) else n}
    base_config = super(MeanRelativeError, self).get_config()
    return dict(list(base_config.items()) + list(config.items()))


class MeanMetricWrapper(Mean):
  """Wraps a stateless metric function with the Mean metric.

  Args:
    fn: The metric function to wrap, with signature `fn(y_true, y_pred,
      **kwargs)`.
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.
    **kwargs: The keyword arguments that are passed on to `fn`.
  """

  def __init__(self, fn, name=None, dtype=None, **kwargs):
    super(MeanMetricWrapper, self).__init__(name=name, dtype=dtype)
    self._fn = fn
    self._fn_kwargs = kwargs

  def update_state(self, y_true, y_pred, sample_weight=None):
    """Accumulates metric statistics.

    `y_true` and `y_pred` should have the same shape.

    Args:
      y_true: Ground truth values. shape = `[batch_size, d0, .. dN]`.
      y_pred: The predicted values. shape = `[batch_size, d0, .. dN]`.
      sample_weight: Optional `sample_weight` acts as a
        coefficient for the metric. If a scalar is provided, then the metric is
        simply scaled by the given value. If `sample_weight` is a tensor of size
        `[batch_size]`, then the metric for each sample of the batch is rescaled
        by the corresponding element in the `sample_weight` vector. If the shape
        of `sample_weight` is `[batch_size, d0, .. dN-1]` (or can be broadcasted
        to this shape), then each metric element of `y_pred` is scaled by the
        corresponding value of `sample_weight`. (Note on `dN-1`: all metric
        functions reduce by 1 dimension, usually the last axis (-1)).

    Returns:
      Update op.
    """
    y_true = tf.cast(y_true, self._dtype)
    y_pred = tf.cast(y_pred, self._dtype)
    [y_true, y_pred], sample_weight = \
        metrics_utils.ragged_assert_compatible_and_get_flat_values(
            [y_true, y_pred], sample_weight)
    y_pred, y_true = losses_utils.squeeze_or_expand_dimensions(
        y_pred, y_true)

    ag_fn = tf.__internal__.autograph.tf_convert(self._fn, tf.__internal__.autograph.control_status_ctx())
    matches = ag_fn(y_true, y_pred, **self._fn_kwargs)
    return super(MeanMetricWrapper, self).update_state(
        matches, sample_weight=sample_weight)

  def get_config(self):
    config = {}

    if type(self) is MeanMetricWrapper:  # pylint: disable=unidiomatic-typecheck
      # Only include function argument when the object is a MeanMetricWrapper
      # and not a subclass.
      config['fn'] = self._fn

    for k, v in six.iteritems(self._fn_kwargs):
      config[k] = K.eval(v) if is_tensor_or_variable(v) else v
    base_config = super(MeanMetricWrapper, self).get_config()
    return dict(list(base_config.items()) + list(config.items()))

  @classmethod
  def from_config(cls, config):
    # Note that while MeanMetricWrapper itself isn't public, objects of this
    # class may be created and added to the model by calling model.compile.
    fn = config.pop('fn', None)
    if cls is MeanMetricWrapper:
      return cls(get(fn), **config)
    return super(MeanMetricWrapper, cls).from_config(config)


@keras_export('keras.metrics.Accuracy')
class Accuracy(MeanMetricWrapper):
  """Calculates how often predictions equal labels.

  This metric creates two local variables, `total` and `count` that are used to
  compute the frequency with which `y_pred` matches `y_true`. This frequency is
  ultimately returned as `binary accuracy`: an idempotent operation that simply
  divides `total` by `count`.

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

  Args:
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> m = tf.keras.metrics.Accuracy()
  >>> m.update_state([[1], [2], [3], [4]], [[0], [2], [3], [4]])
  >>> m.result().numpy()
  0.75

  >>> m.reset_states()
  >>> m.update_state([[1], [2], [3], [4]], [[0], [2], [3], [4]],
  ...                sample_weight=[1, 1, 0, 0])
  >>> m.result().numpy()
  0.5

  Usage with `compile()` API:

  ```python
  model.compile(optimizer='sgd',
                loss='mse',
                metrics=[tf.keras.metrics.Accuracy()])
  ```
  """

  def __init__(self, name='accuracy', dtype=None):
    super(Accuracy, self).__init__(accuracy, name, dtype=dtype)


@keras_export('keras.metrics.BinaryAccuracy')
class BinaryAccuracy(MeanMetricWrapper):
  """Calculates how often predictions match binary labels.

  This metric creates two local variables, `total` and `count` that are used to
  compute the frequency with which `y_pred` matches `y_true`. This frequency is
  ultimately returned as `binary accuracy`: an idempotent operation that simply
  divides `total` by `count`.

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

  Args:
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.
    threshold: (Optional) Float representing the threshold for deciding
    whether prediction values are 1 or 0.

  Standalone usage:

  >>> m = tf.keras.metrics.BinaryAccuracy()
  >>> m.update_state([[1], [1], [0], [0]], [[0.98], [1], [0], [0.6]])
  >>> m.result().numpy()
  0.75

  >>> m.reset_states()
  >>> m.update_state([[1], [1], [0], [0]], [[0.98], [1], [0], [0.6]],
  ...                sample_weight=[1, 0, 0, 1])
  >>> m.result().numpy()
  0.5

  Usage with `compile()` API:

  ```python
  model.compile(optimizer='sgd',
                loss='mse',
                metrics=[tf.keras.metrics.BinaryAccuracy()])
  ```
  """

  def __init__(self, name='binary_accuracy', dtype=None, threshold=0.5):
    super(BinaryAccuracy, self).__init__(
        binary_accuracy, name, dtype=dtype, threshold=threshold)


@keras_export('keras.metrics.CategoricalAccuracy')
class CategoricalAccuracy(MeanMetricWrapper):
  """Calculates how often predictions match one-hot labels.

  You can provide logits of classes as `y_pred`, since argmax of
  logits and probabilities are same.

  This metric creates two local variables, `total` and `count` that are used to
  compute the frequency with which `y_pred` matches `y_true`. This frequency is
  ultimately returned as `categorical accuracy`: an idempotent operation that
  simply divides `total` by `count`.

  `y_pred` and `y_true` should be passed in as vectors of probabilities, rather
  than as labels. If necessary, use `tf.one_hot` to expand `y_true` as a vector.

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

  Args:
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> m = tf.keras.metrics.CategoricalAccuracy()
  >>> m.update_state([[0, 0, 1], [0, 1, 0]], [[0.1, 0.9, 0.8],
  ...                 [0.05, 0.95, 0]])
  >>> m.result().numpy()
  0.5

  >>> m.reset_states()
  >>> m.update_state([[0, 0, 1], [0, 1, 0]], [[0.1, 0.9, 0.8],
  ...                 [0.05, 0.95, 0]],
  ...                sample_weight=[0.7, 0.3])
  >>> m.result().numpy()
  0.3

  Usage with `compile()` API:

  ```python
  model.compile(
    optimizer='sgd',
    loss='mse',
    metrics=[tf.keras.metrics.CategoricalAccuracy()])
  ```
  """

  def __init__(self, name='categorical_accuracy', dtype=None):
    super(CategoricalAccuracy, self).__init__(
        categorical_accuracy, name, dtype=dtype)


@keras_export('keras.metrics.SparseCategoricalAccuracy')
class SparseCategoricalAccuracy(MeanMetricWrapper):
  """Calculates how often predictions match integer labels.

  ```python
  acc = np.dot(sample_weight, np.equal(y_true, np.argmax(y_pred, axis=1))
  ```

  You can provide logits of classes as `y_pred`, since argmax of
  logits and probabilities are same.

  This metric creates two local variables, `total` and `count` that are used to
  compute the frequency with which `y_pred` matches `y_true`. This frequency is
  ultimately returned as `sparse categorical accuracy`: an idempotent operation
  that simply divides `total` by `count`.

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

  Args:
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> m = tf.keras.metrics.SparseCategoricalAccuracy()
  >>> m.update_state([[2], [1]], [[0.1, 0.6, 0.3], [0.05, 0.95, 0]])
  >>> m.result().numpy()
  0.5

  >>> m.reset_states()
  >>> m.update_state([[2], [1]], [[0.1, 0.6, 0.3], [0.05, 0.95, 0]],
  ...                sample_weight=[0.7, 0.3])
  >>> m.result().numpy()
  0.3

  Usage with `compile()` API:

  ```python
  model.compile(
      optimizer='sgd',
      loss='mse',
      metrics=[tf.keras.metrics.SparseCategoricalAccuracy()])
  ```
  """

  def __init__(self, name='sparse_categorical_accuracy', dtype=None):
    super(SparseCategoricalAccuracy, self).__init__(
        sparse_categorical_accuracy, name, dtype=dtype)


@keras_export('keras.metrics.TopKCategoricalAccuracy')
class TopKCategoricalAccuracy(MeanMetricWrapper):
  """Computes how often targets are in the top `K` predictions.

  Args:
    k: (Optional) Number of top elements to look at for computing accuracy.
      Defaults to 5.
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> m = tf.keras.metrics.TopKCategoricalAccuracy(k=1)
  >>> m.update_state([[0, 0, 1], [0, 1, 0]],
  ...                [[0.1, 0.9, 0.8], [0.05, 0.95, 0]])
  >>> m.result().numpy()
  0.5

  >>> m.reset_states()
  >>> m.update_state([[0, 0, 1], [0, 1, 0]],
  ...                [[0.1, 0.9, 0.8], [0.05, 0.95, 0]],
  ...                sample_weight=[0.7, 0.3])
  >>> m.result().numpy()
  0.3

  Usage with `compile()` API:

  ```python
  model.compile(optimizer='sgd',
                loss='mse',
                metrics=[tf.keras.metrics.TopKCategoricalAccuracy()])
  ```
  """

  def __init__(self, k=5, name='top_k_categorical_accuracy', dtype=None):
    super(TopKCategoricalAccuracy, self).__init__(
        top_k_categorical_accuracy, name, dtype=dtype, k=k)


@keras_export('keras.metrics.SparseTopKCategoricalAccuracy')
class SparseTopKCategoricalAccuracy(MeanMetricWrapper):
  """Computes how often integer targets are in the top `K` predictions.

  Args:
    k: (Optional) Number of top elements to look at for computing accuracy.
      Defaults to 5.
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> m = tf.keras.metrics.SparseTopKCategoricalAccuracy(k=1)
  >>> m.update_state([2, 1], [[0.1, 0.9, 0.8], [0.05, 0.95, 0]])
  >>> m.result().numpy()
  0.5

  >>> m.reset_states()
  >>> m.update_state([2, 1], [[0.1, 0.9, 0.8], [0.05, 0.95, 0]],
  ...                sample_weight=[0.7, 0.3])
  >>> m.result().numpy()
  0.3

  Usage with `compile()` API:

  ```python
  model.compile(
    optimizer='sgd',
    loss='mse',
    metrics=[tf.keras.metrics.SparseTopKCategoricalAccuracy()])
  ```
  """

  def __init__(self, k=5, name='sparse_top_k_categorical_accuracy', dtype=None):
    super(SparseTopKCategoricalAccuracy, self).__init__(
        sparse_top_k_categorical_accuracy, name, dtype=dtype, k=k)


class _ConfusionMatrixConditionCount(Metric):
  """Calculates the number of the given confusion matrix condition.

  Args:
    confusion_matrix_cond: One of `metrics_utils.ConfusionMatrix` conditions.
    thresholds: (Optional) Defaults to 0.5. A float value or a python list/tuple
      of float threshold values in [0, 1]. A threshold is compared with
      prediction values to determine the truth value of predictions (i.e., above
      the threshold is `true`, below is `false`). One metric value is generated
      for each threshold value.
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.
  """

  def __init__(self,
               confusion_matrix_cond,
               thresholds=None,
               name=None,
               dtype=None):
    super(_ConfusionMatrixConditionCount, self).__init__(name=name, dtype=dtype)
    self._confusion_matrix_cond = confusion_matrix_cond
    self.init_thresholds = thresholds
    self.thresholds = metrics_utils.parse_init_thresholds(
        thresholds, default_threshold=0.5)
    self.accumulator = self.add_weight(
        'accumulator',
        shape=(len(self.thresholds),),
        initializer=tf.compat.v1.zeros_initializer)

  def update_state(self, y_true, y_pred, sample_weight=None):
    """Accumulates the metric statistics.

    Args:
      y_true: The ground truth values.
      y_pred: The predicted values.
      sample_weight: Optional weighting of each example. Defaults to 1. Can be a
        `Tensor` whose rank is either 0, or the same rank as `y_true`, and must
        be broadcastable to `y_true`.

    Returns:
      Update op.
    """
    return metrics_utils.update_confusion_matrix_variables(
        {self._confusion_matrix_cond: self.accumulator},
        y_true,
        y_pred,
        thresholds=self.thresholds,
        sample_weight=sample_weight)

  def result(self):
    if len(self.thresholds) == 1:
      result = self.accumulator[0]
    else:
      result = self.accumulator
    return tf.convert_to_tensor(result)

  def reset_states(self):
    num_thresholds = len(to_list(self.thresholds))
    K.batch_set_value(
        [(v, np.zeros((num_thresholds,))) for v in self.variables])

  def get_config(self):
    config = {'thresholds': self.init_thresholds}
    base_config = super(_ConfusionMatrixConditionCount, self).get_config()
    return dict(list(base_config.items()) + list(config.items()))


@keras_export('keras.metrics.FalsePositives')
class FalsePositives(_ConfusionMatrixConditionCount):
  """Calculates the number of false positives.

  If `sample_weight` is given, calculates the sum of the weights of
  false positives. This metric creates one local variable, `accumulator`
  that is used to keep track of the number of false positives.

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

  Args:
    thresholds: (Optional) Defaults to 0.5. A float value or a python
      list/tuple of float threshold values in [0, 1]. A threshold is compared
      with prediction values to determine the truth value of predictions
      (i.e., above the threshold is `true`, below is `false`). One metric
      value is generated for each threshold value.
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> m = tf.keras.metrics.FalsePositives()
  >>> m.update_state([0, 1, 0, 0], [0, 0, 1, 1])
  >>> m.result().numpy()
  2.0

  >>> m.reset_states()
  >>> m.update_state([0, 1, 0, 0], [0, 0, 1, 1], sample_weight=[0, 0, 1, 0])
  >>> m.result().numpy()
  1.0

  Usage with `compile()` API:

  ```python
  model.compile(optimizer='sgd',
                loss='mse',
                metrics=[tf.keras.metrics.FalsePositives()])
  ```
  """

  def __init__(self, thresholds=None, name=None, dtype=None):
    super(FalsePositives, self).__init__(
        confusion_matrix_cond=metrics_utils.ConfusionMatrix.FALSE_POSITIVES,
        thresholds=thresholds,
        name=name,
        dtype=dtype)


@keras_export('keras.metrics.FalseNegatives')
class FalseNegatives(_ConfusionMatrixConditionCount):
  """Calculates the number of false negatives.

  If `sample_weight` is given, calculates the sum of the weights of
  false negatives. This metric creates one local variable, `accumulator`
  that is used to keep track of the number of false negatives.

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

  Args:
    thresholds: (Optional) Defaults to 0.5. A float value or a python
      list/tuple of float threshold values in [0, 1]. A threshold is compared
      with prediction values to determine the truth value of predictions
      (i.e., above the threshold is `true`, below is `false`). One metric
      value is generated for each threshold value.
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> m = tf.keras.metrics.FalseNegatives()
  >>> m.update_state([0, 1, 1, 1], [0, 1, 0, 0])
  >>> m.result().numpy()
  2.0

  >>> m.reset_states()
  >>> m.update_state([0, 1, 1, 1], [0, 1, 0, 0], sample_weight=[0, 0, 1, 0])
  >>> m.result().numpy()
  1.0

  Usage with `compile()` API:

  ```python
  model.compile(optimizer='sgd',
                loss='mse',
                metrics=[tf.keras.metrics.FalseNegatives()])
  ```
  """

  def __init__(self, thresholds=None, name=None, dtype=None):
    super(FalseNegatives, self).__init__(
        confusion_matrix_cond=metrics_utils.ConfusionMatrix.FALSE_NEGATIVES,
        thresholds=thresholds,
        name=name,
        dtype=dtype)


@keras_export('keras.metrics.TrueNegatives')
class TrueNegatives(_ConfusionMatrixConditionCount):
  """Calculates the number of true negatives.

  If `sample_weight` is given, calculates the sum of the weights of
  true negatives. This metric creates one local variable, `accumulator`
  that is used to keep track of the number of true negatives.

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

  Args:
    thresholds: (Optional) Defaults to 0.5. A float value or a python
      list/tuple of float threshold values in [0, 1]. A threshold is compared
      with prediction values to determine the truth value of predictions
      (i.e., above the threshold is `true`, below is `false`). One metric
      value is generated for each threshold value.
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> m = tf.keras.metrics.TrueNegatives()
  >>> m.update_state([0, 1, 0, 0], [1, 1, 0, 0])
  >>> m.result().numpy()
  2.0

  >>> m.reset_states()
  >>> m.update_state([0, 1, 0, 0], [1, 1, 0, 0], sample_weight=[0, 0, 1, 0])
  >>> m.result().numpy()
  1.0

  Usage with `compile()` API:

  ```python
  model.compile(optimizer='sgd',
                loss='mse',
                metrics=[tf.keras.metrics.TrueNegatives()])
  ```
  """

  def __init__(self, thresholds=None, name=None, dtype=None):
    super(TrueNegatives, self).__init__(
        confusion_matrix_cond=metrics_utils.ConfusionMatrix.TRUE_NEGATIVES,
        thresholds=thresholds,
        name=name,
        dtype=dtype)


@keras_export('keras.metrics.TruePositives')
class TruePositives(_ConfusionMatrixConditionCount):
  """Calculates the number of true positives.

  If `sample_weight` is given, calculates the sum of the weights of
  true positives. This metric creates one local variable, `true_positives`
  that is used to keep track of the number of true positives.

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

  Args:
    thresholds: (Optional) Defaults to 0.5. A float value or a python
      list/tuple of float threshold values in [0, 1]. A threshold is compared
      with prediction values to determine the truth value of predictions
      (i.e., above the threshold is `true`, below is `false`). One metric
      value is generated for each threshold value.
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> m = tf.keras.metrics.TruePositives()
  >>> m.update_state([0, 1, 1, 1], [1, 0, 1, 1])
  >>> m.result().numpy()
  2.0

  >>> m.reset_states()
  >>> m.update_state([0, 1, 1, 1], [1, 0, 1, 1], sample_weight=[0, 0, 1, 0])
  >>> m.result().numpy()
  1.0

  Usage with `compile()` API:

  ```python
  model.compile(optimizer='sgd',
                loss='mse',
                metrics=[tf.keras.metrics.TruePositives()])
  ```
  """

  def __init__(self, thresholds=None, name=None, dtype=None):
    super(TruePositives, self).__init__(
        confusion_matrix_cond=metrics_utils.ConfusionMatrix.TRUE_POSITIVES,
        thresholds=thresholds,
        name=name,
        dtype=dtype)


@keras_export('keras.metrics.Precision')
class Precision(Metric):
  """Computes the precision of the predictions with respect to the labels.

  The metric creates two local variables, `true_positives` and `false_positives`
  that are used to compute the precision. This value is ultimately returned as
  `precision`, an idempotent operation that simply divides `true_positives`
  by the sum of `true_positives` and `false_positives`.

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

  If `top_k` is set, we'll calculate precision as how often on average a class
  among the top-k classes with the highest predicted values of a batch entry is
  correct and can be found in the label for that entry.

  If `class_id` is specified, we calculate precision by considering only the
  entries in the batch for which `class_id` is above the threshold and/or in the
  top-k highest predictions, and computing the fraction of them for which
  `class_id` is indeed a correct label.

  Args:
    thresholds: (Optional) A float value or a python list/tuple of float
      threshold values in [0, 1]. A threshold is compared with prediction
      values to determine the truth value of predictions (i.e., above the
      threshold is `true`, below is `false`). One metric value is generated
      for each threshold value. If neither thresholds nor top_k are set, the
      default is to calculate precision with `thresholds=0.5`.
    top_k: (Optional) Unset by default. An int value specifying the top-k
      predictions to consider when calculating precision.
    class_id: (Optional) Integer class ID for which we want binary metrics.
      This must be in the half-open interval `[0, num_classes)`, where
      `num_classes` is the last dimension of predictions.
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> m = tf.keras.metrics.Precision()
  >>> m.update_state([0, 1, 1, 1], [1, 0, 1, 1])
  >>> m.result().numpy()
  0.6666667

  >>> m.reset_states()
  >>> m.update_state([0, 1, 1, 1], [1, 0, 1, 1], sample_weight=[0, 0, 1, 0])
  >>> m.result().numpy()
  1.0

  >>> # With top_k=2, it will calculate precision over y_true[:2] and y_pred[:2]
  >>> m = tf.keras.metrics.Precision(top_k=2)
  >>> m.update_state([0, 0, 1, 1], [1, 1, 1, 1])
  >>> m.result().numpy()
  0.0

  >>> # With top_k=4, it will calculate precision over y_true[:4] and y_pred[:4]
  >>> m = tf.keras.metrics.Precision(top_k=4)
  >>> m.update_state([0, 0, 1, 1], [1, 1, 1, 1])
  >>> m.result().numpy()
  0.5

  Usage with `compile()` API:

  ```python
  model.compile(optimizer='sgd',
                loss='mse',
                metrics=[tf.keras.metrics.Precision()])
  ```
  """

  def __init__(self,
               thresholds=None,
               top_k=None,
               class_id=None,
               name=None,
               dtype=None):
    super(Precision, self).__init__(name=name, dtype=dtype)
    self.init_thresholds = thresholds
    self.top_k = top_k
    self.class_id = class_id

    default_threshold = 0.5 if top_k is None else metrics_utils.NEG_INF
    self.thresholds = metrics_utils.parse_init_thresholds(
        thresholds, default_threshold=default_threshold)
    self.true_positives = self.add_weight(
        'true_positives',
        shape=(len(self.thresholds),),
        initializer=tf.compat.v1.zeros_initializer)
    self.false_positives = self.add_weight(
        'false_positives',
        shape=(len(self.thresholds),),
        initializer=tf.compat.v1.zeros_initializer)

  def update_state(self, y_true, y_pred, sample_weight=None):
    """Accumulates true positive and false positive statistics.

    Args:
      y_true: The ground truth values, with the same dimensions as `y_pred`.
        Will be cast to `bool`.
      y_pred: The predicted values. Each element must be in the range `[0, 1]`.
      sample_weight: Optional weighting of each example. Defaults to 1. Can be a
        `Tensor` whose rank is either 0, or the same rank as `y_true`, and must
        be broadcastable to `y_true`.

    Returns:
      Update op.
    """
    return metrics_utils.update_confusion_matrix_variables(
        {
            metrics_utils.ConfusionMatrix.TRUE_POSITIVES: self.true_positives,
            metrics_utils.ConfusionMatrix.FALSE_POSITIVES: self.false_positives
        },
        y_true,
        y_pred,
        thresholds=self.thresholds,
        top_k=self.top_k,
        class_id=self.class_id,
        sample_weight=sample_weight)

  def result(self):
    result = tf.math.divide_no_nan(self.true_positives,
                                 self.true_positives + self.false_positives)
    return result[0] if len(self.thresholds) == 1 else result

  def reset_states(self):
    num_thresholds = len(to_list(self.thresholds))
    K.batch_set_value(
        [(v, np.zeros((num_thresholds,))) for v in self.variables])

  def get_config(self):
    config = {
        'thresholds': self.init_thresholds,
        'top_k': self.top_k,
        'class_id': self.class_id
    }
    base_config = super(Precision, self).get_config()
    return dict(list(base_config.items()) + list(config.items()))


@keras_export('keras.metrics.Recall')
class Recall(Metric):
  """Computes the recall of the predictions with respect to the labels.

  This metric creates two local variables, `true_positives` and
  `false_negatives`, that are used to compute the recall. This value is
  ultimately returned as `recall`, an idempotent operation that simply divides
  `true_positives` by the sum of `true_positives` and `false_negatives`.

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

  If `top_k` is set, recall will be computed as how often on average a class
  among the labels of a batch entry is in the top-k predictions.

  If `class_id` is specified, we calculate recall by considering only the
  entries in the batch for which `class_id` is in the label, and computing the
  fraction of them for which `class_id` is above the threshold and/or in the
  top-k predictions.

  Args:
    thresholds: (Optional) A float value or a python list/tuple of float
      threshold values in [0, 1]. A threshold is compared with prediction
      values to determine the truth value of predictions (i.e., above the
      threshold is `true`, below is `false`). One metric value is generated
      for each threshold value. If neither thresholds nor top_k are set, the
      default is to calculate recall with `thresholds=0.5`.
    top_k: (Optional) Unset by default. An int value specifying the top-k
      predictions to consider when calculating recall.
    class_id: (Optional) Integer class ID for which we want binary metrics.
      This must be in the half-open interval `[0, num_classes)`, where
      `num_classes` is the last dimension of predictions.
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> m = tf.keras.metrics.Recall()
  >>> m.update_state([0, 1, 1, 1], [1, 0, 1, 1])
  >>> m.result().numpy()
  0.6666667

  >>> m.reset_states()
  >>> m.update_state([0, 1, 1, 1], [1, 0, 1, 1], sample_weight=[0, 0, 1, 0])
  >>> m.result().numpy()
  1.0

  Usage with `compile()` API:

  ```python
  model.compile(optimizer='sgd',
                loss='mse',
                metrics=[tf.keras.metrics.Recall()])
  ```
  """

  def __init__(self,
               thresholds=None,
               top_k=None,
               class_id=None,
               name=None,
               dtype=None):
    super(Recall, self).__init__(name=name, dtype=dtype)
    self.init_thresholds = thresholds
    self.top_k = top_k
    self.class_id = class_id

    default_threshold = 0.5 if top_k is None else metrics_utils.NEG_INF
    self.thresholds = metrics_utils.parse_init_thresholds(
        thresholds, default_threshold=default_threshold)
    self.true_positives = self.add_weight(
        'true_positives',
        shape=(len(self.thresholds),),
        initializer=tf.compat.v1.zeros_initializer)
    self.false_negatives = self.add_weight(
        'false_negatives',
        shape=(len(self.thresholds),),
        initializer=tf.compat.v1.zeros_initializer)

  def update_state(self, y_true, y_pred, sample_weight=None):
    """Accumulates true positive and false negative statistics.

    Args:
      y_true: The ground truth values, with the same dimensions as `y_pred`.
        Will be cast to `bool`.
      y_pred: The predicted values. Each element must be in the range `[0, 1]`.
      sample_weight: Optional weighting of each example. Defaults to 1. Can be a
        `Tensor` whose rank is either 0, or the same rank as `y_true`, and must
        be broadcastable to `y_true`.

    Returns:
      Update op.
    """
    return metrics_utils.update_confusion_matrix_variables(
        {
            metrics_utils.ConfusionMatrix.TRUE_POSITIVES: self.true_positives,
            metrics_utils.ConfusionMatrix.FALSE_NEGATIVES: self.false_negatives
        },
        y_true,
        y_pred,
        thresholds=self.thresholds,
        top_k=self.top_k,
        class_id=self.class_id,
        sample_weight=sample_weight)

  def result(self):
    result = tf.math.divide_no_nan(self.true_positives,
                                 self.true_positives + self.false_negatives)
    return result[0] if len(self.thresholds) == 1 else result

  def reset_states(self):
    num_thresholds = len(to_list(self.thresholds))
    K.batch_set_value(
        [(v, np.zeros((num_thresholds,))) for v in self.variables])

  def get_config(self):
    config = {
        'thresholds': self.init_thresholds,
        'top_k': self.top_k,
        'class_id': self.class_id
    }
    base_config = super(Recall, self).get_config()
    return dict(list(base_config.items()) + list(config.items()))


@six.add_metaclass(abc.ABCMeta)
class SensitivitySpecificityBase(Metric):
  """Abstract base class for computing sensitivity and specificity.

  For additional information about specificity and sensitivity, see
  [the following](https://en.wikipedia.org/wiki/Sensitivity_and_specificity).
  """

  def __init__(self, value, num_thresholds=200, name=None, dtype=None):
    super(SensitivitySpecificityBase, self).__init__(name=name, dtype=dtype)
    if num_thresholds <= 0:
      raise ValueError('`num_thresholds` must be > 0.')
    self.value = value
    self.true_positives = self.add_weight(
        'true_positives',
        shape=(num_thresholds,),
        initializer=tf.compat.v1.zeros_initializer)
    self.true_negatives = self.add_weight(
        'true_negatives',
        shape=(num_thresholds,),
        initializer=tf.compat.v1.zeros_initializer)
    self.false_positives = self.add_weight(
        'false_positives',
        shape=(num_thresholds,),
        initializer=tf.compat.v1.zeros_initializer)
    self.false_negatives = self.add_weight(
        'false_negatives',
        shape=(num_thresholds,),
        initializer=tf.compat.v1.zeros_initializer)

    # Compute `num_thresholds` thresholds in [0, 1]
    if num_thresholds == 1:
      self.thresholds = [0.5]
    else:
      thresholds = [(i + 1) * 1.0 / (num_thresholds - 1)
                    for i in range(num_thresholds - 2)]
      self.thresholds = [0.0] + thresholds + [1.0]

  def update_state(self, y_true, y_pred, sample_weight=None):
    """Accumulates confusion matrix statistics.

    Args:
      y_true: The ground truth values.
      y_pred: The predicted values.
      sample_weight: Optional weighting of each example. Defaults to 1. Can be a
        `Tensor` whose rank is either 0, or the same rank as `y_true`, and must
        be broadcastable to `y_true`.

    Returns:
      Update op.
    """
    return metrics_utils.update_confusion_matrix_variables(
        {
            metrics_utils.ConfusionMatrix.TRUE_POSITIVES: self.true_positives,
            metrics_utils.ConfusionMatrix.TRUE_NEGATIVES: self.true_negatives,
            metrics_utils.ConfusionMatrix.FALSE_POSITIVES: self.false_positives,
            metrics_utils.ConfusionMatrix.FALSE_NEGATIVES: self.false_negatives,
        },
        y_true,
        y_pred,
        thresholds=self.thresholds,
        sample_weight=sample_weight)

  def reset_states(self):
    num_thresholds = len(self.thresholds)
    K.batch_set_value(
        [(v, np.zeros((num_thresholds,))) for v in self.variables])

  def _find_max_under_constraint(self, constrained, dependent, predicate):
    """Returns the maximum of dependent_statistic that satisfies the constraint.

    Args:
      constrained: Over these values the constraint
        is specified. A rank-1 tensor.
      dependent: From these values the maximum that satiesfies the
        constraint is selected. Values in this tensor and in
        `constrained` are linked by having the same threshold at each
        position, hence this tensor must have the same shape.
      predicate: A binary boolean functor to be applied to arguments
      `constrained` and `self.value`, e.g. `tf.greater`.

    Returns maximal dependent value, if no value satiesfies the constraint 0.0.
    """
    feasible = tf.compat.v1.where(predicate(constrained, self.value))
    feasible_exists = tf.greater(tf.compat.v1.size(feasible), 0)

    def get_max():
      return tf.reduce_max(tf.compat.v1.gather(dependent, feasible))

    return tf.compat.v1.cond(feasible_exists, get_max, lambda: 0.0)


@keras_export('keras.metrics.SensitivityAtSpecificity')
class SensitivityAtSpecificity(SensitivitySpecificityBase):
  """Computes best sensitivity where specificity is >= specified value.

  the sensitivity at a given specificity.

  `Sensitivity` measures the proportion of actual positives that are correctly
  identified as such (tp / (tp + fn)).
  `Specificity` measures the proportion of actual negatives that are correctly
  identified as such (tn / (tn + fp)).

  This metric creates four local variables, `true_positives`, `true_negatives`,
  `false_positives` and `false_negatives` that are used to compute the
  sensitivity at the given specificity. The threshold for the given specificity
  value is computed and used to evaluate the corresponding sensitivity.

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

  For additional information about specificity and sensitivity, see
  [the following](https://en.wikipedia.org/wiki/Sensitivity_and_specificity).

  Args:
    specificity: A scalar value in range `[0, 1]`.
    num_thresholds: (Optional) Defaults to 200. The number of thresholds to
      use for matching the given specificity.
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> m = tf.keras.metrics.SensitivityAtSpecificity(0.5)
  >>> m.update_state([0, 0, 0, 1, 1], [0, 0.3, 0.8, 0.3, 0.8])
  >>> m.result().numpy()
  0.5

  >>> m.reset_states()
  >>> m.update_state([0, 0, 0, 1, 1], [0, 0.3, 0.8, 0.3, 0.8],
  ...                sample_weight=[1, 1, 2, 2, 1])
  >>> m.result().numpy()
  0.333333

  Usage with `compile()` API:

  ```python
  model.compile(
      optimizer='sgd',
      loss='mse',
      metrics=[tf.keras.metrics.SensitivityAtSpecificity()])
  ```
  """

  def __init__(self, specificity, num_thresholds=200, name=None, dtype=None):
    if specificity < 0 or specificity > 1:
      raise ValueError('`specificity` must be in the range [0, 1].')
    self.specificity = specificity
    self.num_thresholds = num_thresholds
    super(SensitivityAtSpecificity, self).__init__(
        specificity, num_thresholds=num_thresholds, name=name, dtype=dtype)

  def result(self):
    specificities = tf.math.divide_no_nan(
        self.true_negatives, self.true_negatives + self.false_positives)
    sensitivities = tf.math.divide_no_nan(
        self.true_positives, self.true_positives + self.false_negatives)
    return self._find_max_under_constraint(
        specificities, sensitivities, tf.greater_equal)

  def get_config(self):
    config = {
        'num_thresholds': self.num_thresholds,
        'specificity': self.specificity
    }
    base_config = super(SensitivityAtSpecificity, self).get_config()
    return dict(list(base_config.items()) + list(config.items()))


@keras_export('keras.metrics.SpecificityAtSensitivity')
class SpecificityAtSensitivity(SensitivitySpecificityBase):
  """Computes best specificity where sensitivity is >= specified value.

  `Sensitivity` measures the proportion of actual positives that are correctly
  identified as such (tp / (tp + fn)).
  `Specificity` measures the proportion of actual negatives that are correctly
  identified as such (tn / (tn + fp)).

  This metric creates four local variables, `true_positives`, `true_negatives`,
  `false_positives` and `false_negatives` that are used to compute the
  specificity at the given sensitivity. The threshold for the given sensitivity
  value is computed and used to evaluate the corresponding specificity.

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

  For additional information about specificity and sensitivity, see
  [the following](https://en.wikipedia.org/wiki/Sensitivity_and_specificity).

  Args:
    sensitivity: A scalar value in range `[0, 1]`.
    num_thresholds: (Optional) Defaults to 200. The number of thresholds to
      use for matching the given sensitivity.
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> m = tf.keras.metrics.SpecificityAtSensitivity(0.5)
  >>> m.update_state([0, 0, 0, 1, 1], [0, 0.3, 0.8, 0.3, 0.8])
  >>> m.result().numpy()
  0.66666667

  >>> m.reset_states()
  >>> m.update_state([0, 0, 0, 1, 1], [0, 0.3, 0.8, 0.3, 0.8],
  ...                sample_weight=[1, 1, 2, 2, 2])
  >>> m.result().numpy()
  0.5

  Usage with `compile()` API:

  ```python
  model.compile(
      optimizer='sgd',
      loss='mse',
      metrics=[tf.keras.metrics.SpecificityAtSensitivity()])
  ```
  """

  def __init__(self, sensitivity, num_thresholds=200, name=None, dtype=None):
    if sensitivity < 0 or sensitivity > 1:
      raise ValueError('`sensitivity` must be in the range [0, 1].')
    self.sensitivity = sensitivity
    self.num_thresholds = num_thresholds
    super(SpecificityAtSensitivity, self).__init__(
        sensitivity, num_thresholds=num_thresholds, name=name, dtype=dtype)

  def result(self):
    sensitivities = tf.math.divide_no_nan(
        self.true_positives, self.true_positives + self.false_negatives)
    specificities = tf.math.divide_no_nan(
        self.true_negatives, self.true_negatives + self.false_positives)
    return self._find_max_under_constraint(
        sensitivities, specificities, tf.greater_equal)

  def get_config(self):
    config = {
        'num_thresholds': self.num_thresholds,
        'sensitivity': self.sensitivity
    }
    base_config = super(SpecificityAtSensitivity, self).get_config()
    return dict(list(base_config.items()) + list(config.items()))


@keras_export('keras.metrics.PrecisionAtRecall')
class PrecisionAtRecall(SensitivitySpecificityBase):
  """Computes best precision where recall is >= specified value.

  This metric creates four local variables, `true_positives`, `true_negatives`,
  `false_positives` and `false_negatives` that are used to compute the
  precision at the given recall. The threshold for the given recall
  value is computed and used to evaluate the corresponding precision.

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

  Args:
    recall: A scalar value in range `[0, 1]`.
    num_thresholds: (Optional) Defaults to 200. The number of thresholds to
      use for matching the given recall.
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> m = tf.keras.metrics.PrecisionAtRecall(0.5)
  >>> m.update_state([0, 0, 0, 1, 1], [0, 0.3, 0.8, 0.3, 0.8])
  >>> m.result().numpy()
  0.5

  >>> m.reset_states()
  >>> m.update_state([0, 0, 0, 1, 1], [0, 0.3, 0.8, 0.3, 0.8],
  ...                sample_weight=[2, 2, 2, 1, 1])
  >>> m.result().numpy()
  0.33333333

  Usage with `compile()` API:

  ```python
  model.compile(
      optimizer='sgd',
      loss='mse',
      metrics=[tf.keras.metrics.PrecisionAtRecall(recall=0.8)])
  ```
  """

  def __init__(self, recall, num_thresholds=200, name=None, dtype=None):
    if recall < 0 or recall > 1:
      raise ValueError('`recall` must be in the range [0, 1].')
    self.recall = recall
    self.num_thresholds = num_thresholds
    super(PrecisionAtRecall, self).__init__(
        value=recall,
        num_thresholds=num_thresholds,
        name=name,
        dtype=dtype)

  def result(self):
    recalls = tf.math.divide_no_nan(
        self.true_positives, self.true_positives + self.false_negatives)
    precisions = tf.math.divide_no_nan(
        self.true_positives, self.true_positives + self.false_positives)
    return self._find_max_under_constraint(
        recalls, precisions, tf.greater_equal)

  def get_config(self):
    config = {'num_thresholds': self.num_thresholds, 'recall': self.recall}
    base_config = super(PrecisionAtRecall, self).get_config()
    return dict(list(base_config.items()) + list(config.items()))


@keras_export('keras.metrics.RecallAtPrecision')
class RecallAtPrecision(SensitivitySpecificityBase):
  """Computes best recall where precision is >= specified value.

  For a given score-label-distribution the required precision might not
  be achievable, in this case 0.0 is returned as recall.

  This metric creates four local variables, `true_positives`, `true_negatives`,
  `false_positives` and `false_negatives` that are used to compute the
  recall at the given precision. The threshold for the given precision
  value is computed and used to evaluate the corresponding recall.

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

  Args:
    precision: A scalar value in range `[0, 1]`.
    num_thresholds: (Optional) Defaults to 200. The number of thresholds to
      use for matching the given precision.
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> m = tf.keras.metrics.RecallAtPrecision(0.8)
  >>> m.update_state([0, 0, 1, 1], [0, 0.5, 0.3, 0.9])
  >>> m.result().numpy()
  0.5

  >>> m.reset_states()
  >>> m.update_state([0, 0, 1, 1], [0, 0.5, 0.3, 0.9],
  ...                sample_weight=[1, 0, 0, 1])
  >>> m.result().numpy()
  1.0

  Usage with `compile()` API:

  ```python
  model.compile(
      optimizer='sgd',
      loss='mse',
      metrics=[tf.keras.metrics.RecallAtPrecision(precision=0.8)])
  ```
  """

  def __init__(self, precision, num_thresholds=200, name=None, dtype=None):
    if precision < 0 or precision > 1:
      raise ValueError('`precision` must be in the range [0, 1].')
    self.precision = precision
    self.num_thresholds = num_thresholds
    super(RecallAtPrecision, self).__init__(
        value=precision,
        num_thresholds=num_thresholds,
        name=name,
        dtype=dtype)

  def result(self):
    precisions = tf.math.divide_no_nan(
        self.true_positives, self.true_positives + self.false_positives)
    recalls = tf.math.divide_no_nan(
        self.true_positives, self.true_positives + self.false_negatives)
    return self._find_max_under_constraint(
        precisions, recalls, tf.greater_equal)

  def get_config(self):
    config = {'num_thresholds': self.num_thresholds,
              'precision': self.precision}
    base_config = super(RecallAtPrecision, self).get_config()
    return dict(list(base_config.items()) + list(config.items()))


@keras_export('keras.metrics.AUC')
class AUC(Metric):
  """Approximates the AUC (Area under the curve) of the ROC or PR curves.

  The AUC (Area under the curve) of the ROC (Receiver operating
  characteristic; default) or PR (Precision Recall) curves are quality measures
  of binary classifiers. Unlike the accuracy, and like cross-entropy
  losses, ROC-AUC and PR-AUC evaluate all the operational points of a model.

  This classes approximates AUCs using a Riemann sum: During the metric
  accumulation phrase, predictions are accumulated within predefined buckets
  by value. The AUC is then computed by interpolating per-bucket averages. These
  buckets define the evaluated operational points.

  This metric creates four local variables, `true_positives`, `true_negatives`,
  `false_positives` and `false_negatives` that are used to compute the AUC.
  To discretize the AUC curve, a linearly spaced set of thresholds is used to
  compute pairs of recall and precision values. The area under the ROC-curve is
  therefore computed using the height of the recall values by the false positive
  rate, while the area under the PR-curve is the computed using the height of
  the precision values by the recall.

  This value is ultimately returned as `auc`, an idempotent operation that
  computes the area under a discretized curve of precision versus recall values
  (computed using the aforementioned variables). The `num_thresholds` variable
  controls the degree of discretization with larger numbers of thresholds more
  closely approximating the true AUC. The quality of the approximation may vary
  dramatically depending on `num_thresholds`. The `thresholds` parameter can be
  used to manually specify thresholds which split the predictions more evenly.

  For a best approximation of the real AUC, `predictions` should be distributed
  approximately uniformly in the range [0, 1] (if `from_logits=False`). The
  quality of the AUC approximation may be poor if this is not the case. Setting
  `summation_method` to 'minoring' or 'majoring' can help quantify the error in
  the approximation by providing lower or upper bound estimate of the AUC.

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

  Args:
    num_thresholds: (Optional) Defaults to 200. The number of thresholds to
      use when discretizing the roc curve. Values must be > 1.
    curve: (Optional) Specifies the name of the curve to be computed, 'ROC'
      [default] or 'PR' for the Precision-Recall-curve.
    summation_method: (Optional) Specifies the [Riemann summation method](
        https://en.wikipedia.org/wiki/Riemann_sum) used.
        'interpolation' (default) applies mid-point summation scheme for `ROC`.
        For PR-AUC, interpolates (true/false) positives but not the ratio that
        is precision (see Davis & Goadrich 2006 for details);
        'minoring' applies left summation
        for increasing intervals and right summation for decreasing intervals;
        'majoring' does the opposite.
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.
    thresholds: (Optional) A list of floating point values to use as the
      thresholds for discretizing the curve. If set, the `num_thresholds`
      parameter is ignored. Values should be in [0, 1]. Endpoint thresholds
      equal to {-epsilon, 1+epsilon} for a small positive epsilon value will
      be automatically included with these to correctly handle predictions
      equal to exactly 0 or 1.
    multi_label: boolean indicating whether multilabel data should be
      treated as such, wherein AUC is computed separately for each label and
      then averaged across labels, or (when False) if the data should be
      flattened into a single label before AUC computation. In the latter
      case, when multilabel data is passed to AUC, each label-prediction pair
      is treated as an individual data point. Should be set to False for
      multi-class data.
    num_labels: (Optional) The number of labels, used when `multi_label' is
      True. If `num_labels` is not specified, then state variables get created
      on the first call to `update_state`.
    label_weights: (Optional) list, array, or tensor of non-negative weights
      used to compute AUCs for multilabel data. When `multi_label` is True,
      the weights are applied to the individual label AUCs when they are
      averaged to produce the multi-label AUC. When it's False, they are used
      to weight the individual label predictions in computing the confusion
      matrix on the flattened data. Note that this is unlike class_weights in
      that class_weights weights the example depending on the value of its
      label, whereas label_weights depends only on the index of that label
      before flattening; therefore `label_weights` should not be used for
      multi-class data.
    from_logits: boolean indicating whether the predictions (`y_pred` in
      `update_state`) are probabilities or sigmoid logits. As a rule of thumb,
      when using a keras loss, the `from_logits` constructor argument of the
      loss should match the AUC `from_logits` constructor argument.

  Standalone usage:

  >>> m = tf.keras.metrics.AUC(num_thresholds=3)
  >>> m.update_state([0, 0, 1, 1], [0, 0.5, 0.3, 0.9])
  >>> # threshold values are [0 - 1e-7, 0.5, 1 + 1e-7]
  >>> # tp = [2, 1, 0], fp = [2, 0, 0], fn = [0, 1, 2], tn = [0, 2, 2]
  >>> # recall = [1, 0.5, 0], fp_rate = [1, 0, 0]
  >>> # auc = ((((1+0.5)/2)*(1-0))+ (((0.5+0)/2)*(0-0))) = 0.75
  >>> m.result().numpy()
  0.75

  >>> m.reset_states()
  >>> m.update_state([0, 0, 1, 1], [0, 0.5, 0.3, 0.9],
  ...                sample_weight=[1, 0, 0, 1])
  >>> m.result().numpy()
  1.0

  Usage with `compile()` API:

  ```python
  # Reports the AUC of a model outputing a probability.
  model.compile(optimizer='sgd',
                loss=tf.keras.losses.BinaryCrossentropy(),
                metrics=[tf.keras.metrics.AUC()])

  # Reports the AUC of a model outputing a logit.
  model.compile(optimizer='sgd',
                loss=tf.keras.losses.BinaryCrossentropy(from_logits=True),
                metrics=[tf.keras.metrics.AUC(from_logits=True)])
  ```
  """

  def __init__(self,
               num_thresholds=200,
               curve='ROC',
               summation_method='interpolation',
               name=None,
               dtype=None,
               thresholds=None,
               multi_label=False,
               num_labels=None,
               label_weights=None,
               from_logits=False):
    # Validate configurations.
    if isinstance(curve, metrics_utils.AUCCurve) and curve not in list(
        metrics_utils.AUCCurve):
      raise ValueError('Invalid curve: "{}". Valid options are: "{}"'.format(
          curve, list(metrics_utils.AUCCurve)))
    if isinstance(
        summation_method,
        metrics_utils.AUCSummationMethod) and summation_method not in list(
            metrics_utils.AUCSummationMethod):
      raise ValueError(
          'Invalid summation method: "{}". Valid options are: "{}"'.format(
              summation_method, list(metrics_utils.AUCSummationMethod)))

    # Update properties.
    if thresholds is not None:
      # If specified, use the supplied thresholds.
      self.num_thresholds = len(thresholds) + 2
      thresholds = sorted(thresholds)
    else:
      if num_thresholds <= 1:
        raise ValueError('`num_thresholds` must be > 1.')

      # Otherwise, linearly interpolate (num_thresholds - 2) thresholds in
      # (0, 1).
      self.num_thresholds = num_thresholds
      thresholds = [(i + 1) * 1.0 / (num_thresholds - 1)
                    for i in range(num_thresholds - 2)]

    # Add an endpoint "threshold" below zero and above one for either
    # threshold method to account for floating point imprecisions.
    self._thresholds = np.array([0.0 - K.epsilon()] + thresholds +
                                [1.0 + K.epsilon()])

    if isinstance(curve, metrics_utils.AUCCurve):
      self.curve = curve
    else:
      self.curve = metrics_utils.AUCCurve.from_str(curve)
    if isinstance(summation_method, metrics_utils.AUCSummationMethod):
      self.summation_method = summation_method
    else:
      self.summation_method = metrics_utils.AUCSummationMethod.from_str(
          summation_method)
    super(AUC, self).__init__(name=name, dtype=dtype)

    # Handle multilabel arguments.
    self.multi_label = multi_label
    if label_weights is not None:
      label_weights = tf.constant(label_weights, dtype=self.dtype)
      checks = [
          tf.compat.v1.assert_non_negative(
              label_weights,
              message='All values of `label_weights` must be non-negative.')
      ]
      with tf.control_dependencies(checks):
        self.label_weights = label_weights

    else:
      self.label_weights = None

    self._from_logits = from_logits

    self._built = False
    if self.multi_label:
      if num_labels:
        shape = tf.TensorShape([None, num_labels])
        self._build(shape)
    else:
      if num_labels:
        raise ValueError(
            '`num_labels` is needed only when `multi_label` is True.')
      self._build(None)

  @property
  def thresholds(self):
    """The thresholds used for evaluating AUC."""
    return list(self._thresholds)

  def _build(self, shape):
    """Initialize TP, FP, TN, and FN tensors, given the shape of the data."""
    if self.multi_label:
      if shape.ndims != 2:
        raise ValueError('`y_true` must have rank=2 when `multi_label` is '
                         'True. Found rank %s.' % shape.ndims)
      self._num_labels = shape[1]
      variable_shape = tf.TensorShape(
          [tf.compat.v1.Dimension(self.num_thresholds), self._num_labels])

    else:
      variable_shape = tf.TensorShape(
          [tf.compat.v1.Dimension(self.num_thresholds)])
    self._build_input_shape = shape
    # Create metric variables
    self.true_positives = self.add_weight(
        'true_positives',
        shape=variable_shape,
        initializer=tf.compat.v1.zeros_initializer)
    self.true_negatives = self.add_weight(
        'true_negatives',
        shape=variable_shape,
        initializer=tf.compat.v1.zeros_initializer)
    self.false_positives = self.add_weight(
        'false_positives',
        shape=variable_shape,
        initializer=tf.compat.v1.zeros_initializer)
    self.false_negatives = self.add_weight(
        'false_negatives',
        shape=variable_shape,
        initializer=tf.compat.v1.zeros_initializer)

    if self.multi_label:
      with tf.init_scope():
        # This should only be necessary for handling v1 behavior. In v2, AUC
        # should be initialized outside of any tf.functions, and therefore in
        # eager mode.
        if not tf.executing_eagerly():
          K._initialize_variables(K._get_session())  # pylint: disable=protected-access

    self._built = True

  def update_state(self, y_true, y_pred, sample_weight=None):
    """Accumulates confusion matrix statistics.

    Args:
      y_true: The ground truth values.
      y_pred: The predicted values.
      sample_weight: Optional weighting of each example. Defaults to 1. Can be a
        `Tensor` whose rank is either 0, or the same rank as `y_true`, and must
        be broadcastable to `y_true`.

    Returns:
      Update op.
    """
    deps = []
    if not self._built:
      self._build(tf.TensorShape(y_pred.shape))

    if self.multi_label or (self.label_weights is not None):
      # y_true should have shape (number of examples, number of labels).
      shapes = [
          (y_true, ('N', 'L'))
      ]
      if self.multi_label:
        # TP, TN, FP, and FN should all have shape
        # (number of thresholds, number of labels).
        shapes.extend([(self.true_positives, ('T', 'L')),
                       (self.true_negatives, ('T', 'L')),
                       (self.false_positives, ('T', 'L')),
                       (self.false_negatives, ('T', 'L'))])
      if self.label_weights is not None:
        # label_weights should be of length equal to the number of labels.
        shapes.append((self.label_weights, ('L',)))
      deps = [
          tf.compat.v1.debugging.assert_shapes(
              shapes, message='Number of labels is not consistent.')
      ]

    # Only forward label_weights to update_confusion_matrix_variables when
    # multi_label is False. Otherwise the averaging of individual label AUCs is
    # handled in AUC.result
    label_weights = None if self.multi_label else self.label_weights

    if self._from_logits:
      y_pred = activations.sigmoid(y_pred)

    with tf.control_dependencies(deps):
      return metrics_utils.update_confusion_matrix_variables(
          {
              metrics_utils.ConfusionMatrix.TRUE_POSITIVES:
                  self.true_positives,
              metrics_utils.ConfusionMatrix.TRUE_NEGATIVES:
                  self.true_negatives,
              metrics_utils.ConfusionMatrix.FALSE_POSITIVES:
                  self.false_positives,
              metrics_utils.ConfusionMatrix.FALSE_NEGATIVES:
                  self.false_negatives,
          },
          y_true,
          y_pred,
          self._thresholds,
          sample_weight=sample_weight,
          multi_label=self.multi_label,
          label_weights=label_weights)

  def interpolate_pr_auc(self):
    """Interpolation formula inspired by section 4 of Davis & Goadrich 2006.

    https://www.biostat.wisc.edu/~page/rocpr.pdf

    Note here we derive & use a closed formula not present in the paper
    as follows:

      Precision = TP / (TP + FP) = TP / P

    Modeling all of TP (true positive), FP (false positive) and their sum
    P = TP + FP (predicted positive) as varying linearly within each interval
    [A, B] between successive thresholds, we get

      Precision slope = dTP / dP
                      = (TP_B - TP_A) / (P_B - P_A)
                      = (TP - TP_A) / (P - P_A)
      Precision = (TP_A + slope * (P - P_A)) / P

    The area within the interval is (slope / total_pos_weight) times

      int_A^B{Precision.dP} = int_A^B{(TP_A + slope * (P - P_A)) * dP / P}
      int_A^B{Precision.dP} = int_A^B{slope * dP + intercept * dP / P}

    where intercept = TP_A - slope * P_A = TP_B - slope * P_B, resulting in

      int_A^B{Precision.dP} = TP_B - TP_A + intercept * log(P_B / P_A)

    Bringing back the factor (slope / total_pos_weight) we'd put aside, we get

      slope * [dTP + intercept *  log(P_B / P_A)] / total_pos_weight

    where dTP == TP_B - TP_A.

    Note that when P_A == 0 the above calculation simplifies into

      int_A^B{Precision.dTP} = int_A^B{slope * dTP} = slope * (TP_B - TP_A)

    which is really equivalent to imputing constant precision throughout the
    first bucket having >0 true positives.

    Returns:
      pr_auc: an approximation of the area under the P-R curve.
    """
    dtp = self.true_positives[:self.num_thresholds -
                              1] - self.true_positives[1:]
    p = self.true_positives + self.false_positives
    dp = p[:self.num_thresholds - 1] - p[1:]
    prec_slope = tf.math.divide_no_nan(
        dtp, tf.maximum(dp, 0), name='prec_slope')
    intercept = self.true_positives[1:] - tf.multiply(prec_slope, p[1:])

    safe_p_ratio = tf.compat.v1.where(
        tf.logical_and(p[:self.num_thresholds - 1] > 0, p[1:] > 0),
        tf.math.divide_no_nan(
            p[:self.num_thresholds - 1],
            tf.maximum(p[1:], 0),
            name='recall_relative_ratio'),
        tf.compat.v1.ones_like(p[1:]))

    pr_auc_increment = tf.math.divide_no_nan(
        prec_slope * (dtp + intercept * tf.math.log(safe_p_ratio)),
        tf.maximum(self.true_positives[1:] + self.false_negatives[1:], 0),
        name='pr_auc_increment')

    if self.multi_label:
      by_label_auc = tf.reduce_sum(
          pr_auc_increment, name=self.name + '_by_label', axis=0)
      if self.label_weights is None:
        # Evenly weighted average of the label AUCs.
        return tf.reduce_mean(by_label_auc, name=self.name)
      else:
        # Weighted average of the label AUCs.
        return tf.math.divide_no_nan(
            tf.reduce_sum(
                tf.multiply(by_label_auc, self.label_weights)),
            tf.reduce_sum(self.label_weights),
            name=self.name)
    else:
      return tf.reduce_sum(pr_auc_increment, name='interpolate_pr_auc')

  def result(self):
    if (self.curve == metrics_utils.AUCCurve.PR and
        self.summation_method == metrics_utils.AUCSummationMethod.INTERPOLATION
       ):
      # This use case is different and is handled separately.
      return self.interpolate_pr_auc()

    # Set `x` and `y` values for the curves based on `curve` config.
    recall = tf.math.divide_no_nan(self.true_positives,
                                 self.true_positives + self.false_negatives)
    if self.curve == metrics_utils.AUCCurve.ROC:
      fp_rate = tf.math.divide_no_nan(self.false_positives,
                                    self.false_positives + self.true_negatives)
      x = fp_rate
      y = recall
    else:  # curve == 'PR'.
      precision = tf.math.divide_no_nan(
          self.true_positives, self.true_positives + self.false_positives)
      x = recall
      y = precision

    # Find the rectangle heights based on `summation_method`.
    if self.summation_method == metrics_utils.AUCSummationMethod.INTERPOLATION:
      # Note: the case ('PR', 'interpolation') has been handled above.
      heights = (y[:self.num_thresholds - 1] + y[1:]) / 2.
    elif self.summation_method == metrics_utils.AUCSummationMethod.MINORING:
      heights = tf.minimum(y[:self.num_thresholds - 1], y[1:])
    else:  # self.summation_method = metrics_utils.AUCSummationMethod.MAJORING:
      heights = tf.maximum(y[:self.num_thresholds - 1], y[1:])

    # Sum up the areas of all the rectangles.
    if self.multi_label:
      riemann_terms = tf.multiply(x[:self.num_thresholds - 1] - x[1:],
                                        heights)
      by_label_auc = tf.reduce_sum(
          riemann_terms, name=self.name + '_by_label', axis=0)

      if self.label_weights is None:
        # Unweighted average of the label AUCs.
        return tf.reduce_mean(by_label_auc, name=self.name)
      else:
        # Weighted average of the label AUCs.
        return tf.math.divide_no_nan(
            tf.reduce_sum(
                tf.multiply(by_label_auc, self.label_weights)),
            tf.reduce_sum(self.label_weights),
            name=self.name)
    else:
      return tf.reduce_sum(
          tf.multiply(x[:self.num_thresholds - 1] - x[1:], heights),
          name=self.name)

  def reset_states(self):
    if self.multi_label:
      K.batch_set_value([(v, np.zeros((self.num_thresholds, self._num_labels)))
                         for v in self.variables])
    else:
      K.batch_set_value([
          (v, np.zeros((self.num_thresholds,))) for v in self.variables
      ])

  def get_config(self):
    if is_tensor_or_variable(self.label_weights):
      label_weights = K.eval(self.label_weights)
    else:
      label_weights = self.label_weights
    config = {
        'num_thresholds': self.num_thresholds,
        'curve': self.curve.value,
        'summation_method': self.summation_method.value,
        # We remove the endpoint thresholds as an inverse of how the thresholds
        # were initialized. This ensures that a metric initialized from this
        # config has the same thresholds.
        'thresholds': self.thresholds[1:-1],
        'multi_label': self.multi_label,
        'label_weights': label_weights
    }
    base_config = super(AUC, self).get_config()
    return dict(list(base_config.items()) + list(config.items()))


@keras_export('keras.metrics.CosineSimilarity')
class CosineSimilarity(MeanMetricWrapper):
  """Computes the cosine similarity between the labels and predictions.

  `cosine similarity = (a . b) / ||a|| ||b||`

  See: [Cosine Similarity](https://en.wikipedia.org/wiki/Cosine_similarity).

  This metric keeps the average cosine similarity between `predictions` and
  `labels` over a stream of data.

  Args:
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.
    axis: (Optional) Defaults to -1. The dimension along which the cosine
      similarity is computed.

  Standalone usage:

  >>> # l2_norm(y_true) = [[0., 1.], [1./1.414], 1./1.414]]]
  >>> # l2_norm(y_pred) = [[1., 0.], [1./1.414], 1./1.414]]]
  >>> # l2_norm(y_true) . l2_norm(y_pred) = [[0., 0.], [0.5, 0.5]]
  >>> # result = mean(sum(l2_norm(y_true) . l2_norm(y_pred), axis=1))
  >>> #        = ((0. + 0.) +  (0.5 + 0.5)) / 2
  >>> m = tf.keras.metrics.CosineSimilarity(axis=1)
  >>> m.update_state([[0., 1.], [1., 1.]], [[1., 0.], [1., 1.]])
  >>> m.result().numpy()
  0.49999997

  >>> m.reset_states()
  >>> m.update_state([[0., 1.], [1., 1.]], [[1., 0.], [1., 1.]],
  ...                sample_weight=[0.3, 0.7])
  >>> m.result().numpy()
  0.6999999

  Usage with `compile()` API:

  ```python
  model.compile(
      optimizer='sgd',
      loss='mse',
      metrics=[tf.keras.metrics.CosineSimilarity(axis=1)])
  ```
  """

  def __init__(self, name='cosine_similarity', dtype=None, axis=-1):
    super(CosineSimilarity, self).__init__(
        cosine_similarity, name, dtype=dtype, axis=axis)


@keras_export('keras.metrics.MeanAbsoluteError')
class MeanAbsoluteError(MeanMetricWrapper):
  """Computes the mean absolute error between the labels and predictions.

  Args:
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> m = tf.keras.metrics.MeanAbsoluteError()
  >>> m.update_state([[0, 1], [0, 0]], [[1, 1], [0, 0]])
  >>> m.result().numpy()
  0.25

  >>> m.reset_states()
  >>> m.update_state([[0, 1], [0, 0]], [[1, 1], [0, 0]],
  ...                sample_weight=[1, 0])
  >>> m.result().numpy()
  0.5

  Usage with `compile()` API:

  ```python
  model.compile(
      optimizer='sgd',
      loss='mse',
      metrics=[tf.keras.metrics.MeanAbsoluteError()])
  ```
  """

  def __init__(self, name='mean_absolute_error', dtype=None):
    super(MeanAbsoluteError, self).__init__(
        mean_absolute_error, name, dtype=dtype)


@keras_export('keras.metrics.MeanAbsolutePercentageError')
class MeanAbsolutePercentageError(MeanMetricWrapper):
  """Computes the mean absolute percentage error between `y_true` and `y_pred`.

  Args:
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> m = tf.keras.metrics.MeanAbsolutePercentageError()
  >>> m.update_state([[0, 1], [0, 0]], [[1, 1], [0, 0]])
  >>> m.result().numpy()
  250000000.0

  >>> m.reset_states()
  >>> m.update_state([[0, 1], [0, 0]], [[1, 1], [0, 0]],
  ...                sample_weight=[1, 0])
  >>> m.result().numpy()
  500000000.0

  Usage with `compile()` API:

  ```python
  model.compile(
      optimizer='sgd',
      loss='mse',
      metrics=[tf.keras.metrics.MeanAbsolutePercentageError()])
  ```
  """

  def __init__(self, name='mean_absolute_percentage_error', dtype=None):
    super(MeanAbsolutePercentageError, self).__init__(
        mean_absolute_percentage_error, name, dtype=dtype)


@keras_export('keras.metrics.MeanSquaredError')
class MeanSquaredError(MeanMetricWrapper):
  """Computes the mean squared error between `y_true` and `y_pred`.

  Args:
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> m = tf.keras.metrics.MeanSquaredError()
  >>> m.update_state([[0, 1], [0, 0]], [[1, 1], [0, 0]])
  >>> m.result().numpy()
  0.25

  >>> m.reset_states()
  >>> m.update_state([[0, 1], [0, 0]], [[1, 1], [0, 0]],
  ...                sample_weight=[1, 0])
  >>> m.result().numpy()
  0.5

  Usage with `compile()` API:

  ```python
  model.compile(
      optimizer='sgd',
      loss='mse',
      metrics=[tf.keras.metrics.MeanSquaredError()])
  ```
  """

  def __init__(self, name='mean_squared_error', dtype=None):
    super(MeanSquaredError, self).__init__(
        mean_squared_error, name, dtype=dtype)


@keras_export('keras.metrics.MeanSquaredLogarithmicError')
class MeanSquaredLogarithmicError(MeanMetricWrapper):
  """Computes the mean squared logarithmic error between `y_true` and `y_pred`.

  Args:
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> m = tf.keras.metrics.MeanSquaredLogarithmicError()
  >>> m.update_state([[0, 1], [0, 0]], [[1, 1], [0, 0]])
  >>> m.result().numpy()
  0.12011322

  >>> m.reset_states()
  >>> m.update_state([[0, 1], [0, 0]], [[1, 1], [0, 0]],
  ...                sample_weight=[1, 0])
  >>> m.result().numpy()
  0.24022643

  Usage with `compile()` API:

  ```python
  model.compile(
      optimizer='sgd',
      loss='mse',
      metrics=[tf.keras.metrics.MeanSquaredLogarithmicError()])
  ```
  """

  def __init__(self, name='mean_squared_logarithmic_error', dtype=None):
    super(MeanSquaredLogarithmicError, self).__init__(
        mean_squared_logarithmic_error, name, dtype=dtype)


@keras_export('keras.metrics.Hinge')
class Hinge(MeanMetricWrapper):
  """Computes the hinge metric between `y_true` and `y_pred`.

  `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.

  Args:
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> m = tf.keras.metrics.Hinge()
  >>> m.update_state([[0, 1], [0, 0]], [[0.6, 0.4], [0.4, 0.6]])
  >>> m.result().numpy()
  1.3

  >>> m.reset_states()
  >>> m.update_state([[0, 1], [0, 0]], [[0.6, 0.4], [0.4, 0.6]],
  ...                sample_weight=[1, 0])
  >>> m.result().numpy()
  1.1

  Usage with `compile()` API:

  ```python
  model.compile(optimizer='sgd', loss='mse', metrics=[tf.keras.metrics.Hinge()])
  ```
  """

  def __init__(self, name='hinge', dtype=None):
    super(Hinge, self).__init__(hinge, name, dtype=dtype)


@keras_export('keras.metrics.SquaredHinge')
class SquaredHinge(MeanMetricWrapper):
  """Computes the squared hinge metric between `y_true` and `y_pred`.

  `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.

  Args:
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> m = tf.keras.metrics.SquaredHinge()
  >>> m.update_state([[0, 1], [0, 0]], [[0.6, 0.4], [0.4, 0.6]])
  >>> m.result().numpy()
  1.86

  >>> m.reset_states()
  >>> m.update_state([[0, 1], [0, 0]], [[0.6, 0.4], [0.4, 0.6]],
  ...                sample_weight=[1, 0])
  >>> m.result().numpy()
  1.46

  Usage with `compile()` API:

  ```python
  model.compile(
      optimizer='sgd',
      loss='mse',
      metrics=[tf.keras.metrics.SquaredHinge()])
  ```
  """

  def __init__(self, name='squared_hinge', dtype=None):
    super(SquaredHinge, self).__init__(squared_hinge, name, dtype=dtype)


@keras_export('keras.metrics.CategoricalHinge')
class CategoricalHinge(MeanMetricWrapper):
  """Computes the categorical hinge metric between `y_true` and `y_pred`.

  Args:
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> m = tf.keras.metrics.CategoricalHinge()
  >>> m.update_state([[0, 1], [0, 0]], [[0.6, 0.4], [0.4, 0.6]])
  >>> m.result().numpy()
  1.4000001

  >>> m.reset_states()
  >>> m.update_state([[0, 1], [0, 0]], [[0.6, 0.4], [0.4, 0.6]],
  ...                sample_weight=[1, 0])
  >>> m.result().numpy()
  1.2

  Usage with `compile()` API:

  ```python
  model.compile(
      optimizer='sgd',
      loss='mse',
      metrics=[tf.keras.metrics.CategoricalHinge()])
  ```
  """

  def __init__(self, name='categorical_hinge', dtype=None):
    super(CategoricalHinge, self).__init__(categorical_hinge, name, dtype=dtype)


@keras_export('keras.metrics.RootMeanSquaredError')
class RootMeanSquaredError(Mean):
  """Computes root mean squared error metric between `y_true` and `y_pred`.

  Standalone usage:

  >>> m = tf.keras.metrics.RootMeanSquaredError()
  >>> m.update_state([[0, 1], [0, 0]], [[1, 1], [0, 0]])
  >>> m.result().numpy()
  0.5

  >>> m.reset_states()
  >>> m.update_state([[0, 1], [0, 0]], [[1, 1], [0, 0]],
  ...                sample_weight=[1, 0])
  >>> m.result().numpy()
  0.70710677

  Usage with `compile()` API:

  ```python
  model.compile(
      optimizer='sgd',
      loss='mse',
      metrics=[tf.keras.metrics.RootMeanSquaredError()])
  ```
  """

  def __init__(self, name='root_mean_squared_error', dtype=None):
    super(RootMeanSquaredError, self).__init__(name, dtype=dtype)

  def update_state(self, y_true, y_pred, sample_weight=None):
    """Accumulates root mean squared error statistics.

    Args:
      y_true: The ground truth values.
      y_pred: The predicted values.
      sample_weight: Optional weighting of each example. Defaults to 1. Can be a
        `Tensor` whose rank is either 0, or the same rank as `y_true`, and must
        be broadcastable to `y_true`.

    Returns:
      Update op.
    """
    y_true = tf.cast(y_true, self._dtype)
    y_pred = tf.cast(y_pred, self._dtype)
    y_pred, y_true = losses_utils.squeeze_or_expand_dimensions(
        y_pred, y_true)
    error_sq = tf.math.squared_difference(y_pred, y_true)
    return super(RootMeanSquaredError, self).update_state(
        error_sq, sample_weight=sample_weight)

  def result(self):
    return tf.sqrt(tf.math.divide_no_nan(self.total, self.count))


@keras_export('keras.metrics.LogCoshError')
class LogCoshError(MeanMetricWrapper):
  """Computes the logarithm of the hyperbolic cosine of the prediction error.

  `logcosh = log((exp(x) + exp(-x))/2)`, where x is the error (y_pred - y_true)

  Args:
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> m = tf.keras.metrics.LogCoshError()
  >>> m.update_state([[0, 1], [0, 0]], [[1, 1], [0, 0]])
  >>> m.result().numpy()
  0.10844523

  >>> m.reset_states()
  >>> m.update_state([[0, 1], [0, 0]], [[1, 1], [0, 0]],
  ...                sample_weight=[1, 0])
  >>> m.result().numpy()
  0.21689045

  Usage with `compile()` API:

  ```python
  model.compile(optimizer='sgd',
                loss='mse',
                metrics=[tf.keras.metrics.LogCoshError()])
  ```
  """

  def __init__(self, name='logcosh', dtype=None):
    super(LogCoshError, self).__init__(logcosh, name, dtype=dtype)


@keras_export('keras.metrics.Poisson')
class Poisson(MeanMetricWrapper):
  """Computes the Poisson metric between `y_true` and `y_pred`.

  `metric = y_pred - y_true * log(y_pred)`

  Args:
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> m = tf.keras.metrics.Poisson()
  >>> m.update_state([[0, 1], [0, 0]], [[1, 1], [0, 0]])
  >>> m.result().numpy()
  0.49999997

  >>> m.reset_states()