# 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=g-classes-have-attributes
# pylint: disable=g-doc-return-or-yield
"""Built-in metrics."""

import abc
from typing import List, Tuple, Union

from keras import activations
from keras import backend
from keras.dtensor import utils as dtensor_utils
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.metrics import base_metric
from keras.utils import losses_utils
from keras.utils import metrics_utils
from keras.utils.generic_utils import to_list
from keras.utils.tf_utils import is_tensor_or_variable
import numpy as np
import tensorflow.compat.v2 as tf

from tensorflow.python.util.tf_export import keras_export


@keras_export('keras.metrics.MeanRelativeError')
class MeanRelativeError(base_metric.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])])
  ```
  """

  @dtensor_utils.inject_mesh
  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': backend.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()))


@keras_export('keras.metrics.Accuracy')
class Accuracy(base_metric.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_state()
  >>> 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()])
  ```
  """

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


@keras_export('keras.metrics.BinaryAccuracy')
class BinaryAccuracy(base_metric.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_state()
  >>> 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()])
  ```
  """

  @dtensor_utils.inject_mesh
  def __init__(self, name='binary_accuracy', dtype=None, threshold=0.5):
    super(BinaryAccuracy, self).__init__(
        metrics_utils.binary_matches, name, dtype=dtype, threshold=threshold)


@keras_export('keras.metrics.CategoricalAccuracy')
class CategoricalAccuracy(base_metric.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_state()
  >>> 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()])
  ```
  """

  @dtensor_utils.inject_mesh
  def __init__(self, name='categorical_accuracy', dtype=None):
    super(CategoricalAccuracy, self).__init__(
        lambda y_true, y_pred: metrics_utils.sparse_categorical_matches(  # pylint: disable=g-long-lambda
            tf.math.argmax(y_true, axis=-1), y_pred),
        name,
        dtype=dtype)


@keras_export('keras.metrics.SparseCategoricalAccuracy')
class SparseCategoricalAccuracy(base_metric.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_state()
  >>> 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()])
  ```
  """

  @dtensor_utils.inject_mesh
  def __init__(self, name='sparse_categorical_accuracy', dtype=None):
    super(SparseCategoricalAccuracy, self).__init__(
        metrics_utils.sparse_categorical_matches, name, dtype=dtype)


_SPARSE_CATEGORICAL_UPDATE_STATE_DOCSTRING = """Accumulates metric statistics.

For sparse categorical metrics, the shapes of `y_true` and `y_pred` are
different.

Args:
  y_true: Ground truth label values. shape = `[batch_size, d0, .. dN-1]` or
    shape = `[batch_size, d0, .. dN-1, 1]`.
  y_pred: The predicted probability 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.
"""

SparseCategoricalAccuracy.update_state.__doc__ = _SPARSE_CATEGORICAL_UPDATE_STATE_DOCSTRING


@keras_export('keras.metrics.TopKCategoricalAccuracy')
class TopKCategoricalAccuracy(base_metric.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_state()
  >>> 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()])
  ```
  """

  @dtensor_utils.inject_mesh
  def __init__(self, k=5, name='top_k_categorical_accuracy', dtype=None):
    super(TopKCategoricalAccuracy, self).__init__(
        lambda yt, yp, k: metrics_utils.sparse_top_k_categorical_matches(  # pylint: disable=g-long-lambda
            tf.math.argmax(yt, axis=-1), yp, k),
        name,
        dtype=dtype,
        k=k)


@keras_export('keras.metrics.SparseTopKCategoricalAccuracy')
class SparseTopKCategoricalAccuracy(base_metric.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_state()
  >>> 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()])
  ```
  """

  @dtensor_utils.inject_mesh
  def __init__(self, k=5, name='sparse_top_k_categorical_accuracy', dtype=None):
    super(SparseTopKCategoricalAccuracy, self).__init__(
        metrics_utils.sparse_top_k_categorical_matches, name, dtype=dtype, k=k)


SparseTopKCategoricalAccuracy.update_state.__doc__ = _SPARSE_CATEGORICAL_UPDATE_STATE_DOCSTRING


class _ConfusionMatrixConditionCount(base_metric.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._thresholds_distributed_evenly = (
        metrics_utils.is_evenly_distributed_thresholds(self.thresholds))
    self.accumulator = self.add_weight(
        'accumulator',
        shape=(len(self.thresholds),),
        initializer='zeros')

  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,
        thresholds_distributed_evenly=self._thresholds_distributed_evenly,
        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_state(self):
    backend.batch_set_value([
        (v, np.zeros(v.shape.as_list())) 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_state()
  >>> 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()])
  ```
  """

  @dtensor_utils.inject_mesh
  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_state()
  >>> 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()])
  ```
  """

  @dtensor_utils.inject_mesh
  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_state()
  >>> 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()])
  ```
  """

  @dtensor_utils.inject_mesh
  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_state()
  >>> 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()])
  ```
  """

  @dtensor_utils.inject_mesh
  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(base_metric.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_state()
  >>> 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()])
  ```
  """

  @dtensor_utils.inject_mesh
  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._thresholds_distributed_evenly = (
        metrics_utils.is_evenly_distributed_thresholds(self.thresholds))
    self.true_positives = self.add_weight(
        'true_positives',
        shape=(len(self.thresholds),),
        initializer='zeros')
    self.false_positives = self.add_weight(
        'false_positives',
        shape=(len(self.thresholds),),
        initializer='zeros')

  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,
        thresholds_distributed_evenly=self._thresholds_distributed_evenly,
        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,
        tf.math.add(self.true_positives, self.false_positives))
    return result[0] if len(self.thresholds) == 1 else result

  def reset_state(self):
    num_thresholds = len(to_list(self.thresholds))
    backend.batch_set_value([(v, np.zeros((num_thresholds,)))
                             for v in (self.true_positives,
                                       self.false_positives)])

  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(base_metric.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_state()
  >>> 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()])
  ```
  """

  @dtensor_utils.inject_mesh
  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._thresholds_distributed_evenly = (
        metrics_utils.is_evenly_distributed_thresholds(self.thresholds))
    self.true_positives = self.add_weight(
        'true_positives',
        shape=(len(self.thresholds),),
        initializer='zeros')
    self.false_negatives = self.add_weight(
        'false_negatives',
        shape=(len(self.thresholds),),
        initializer='zeros')

  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,
        thresholds_distributed_evenly=self._thresholds_distributed_evenly,
        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,
        tf.math.add(self.true_positives, self.false_negatives))
    return result[0] if len(self.thresholds) == 1 else result

  def reset_state(self):
    num_thresholds = len(to_list(self.thresholds))
    backend.batch_set_value([(v, np.zeros((num_thresholds,)))
                             for v in (self.true_positives,
                                       self.false_negatives)])

  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()))


class SensitivitySpecificityBase(base_metric.Metric, metaclass=abc.ABCMeta):
  """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,
               class_id=None,
               name=None,
               dtype=None):
    super(SensitivitySpecificityBase, self).__init__(name=name, dtype=dtype)
    if num_thresholds <= 0:
      raise ValueError(
          'Argument `num_thresholds` must be an integer > 0. '
          f'Received: num_thresholds={num_thresholds}')
    self.value = value
    self.class_id = class_id
    self.true_positives = self.add_weight(
        'true_positives',
        shape=(num_thresholds,),
        initializer='zeros')
    self.true_negatives = self.add_weight(
        'true_negatives',
        shape=(num_thresholds,),
        initializer='zeros')
    self.false_positives = self.add_weight(
        'false_positives',
        shape=(num_thresholds,),
        initializer='zeros')
    self.false_negatives = self.add_weight(
        'false_negatives',
        shape=(num_thresholds,),
        initializer='zeros')

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

  def reset_state(self):
    num_thresholds = len(self.thresholds)
    confusion_matrix_variables = (self.true_positives, self.true_negatives,
                                  self.false_positives, self.false_negatives)
    backend.batch_set_value([
        (v, np.zeros((num_thresholds,))) for v in confusion_matrix_variables
    ])

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

  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.where(predicate(constrained, self.value))
    feasible_exists = tf.greater(tf.size(feasible), 0)
    max_dependent = tf.reduce_max(tf.gather(dependent, feasible))

    return tf.where(feasible_exists, max_dependent, 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.

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

  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.
    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.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_state()
  >>> 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()])
  ```
  """

  @dtensor_utils.inject_mesh
  def __init__(self,
               specificity,
               num_thresholds=200,
               class_id=None,
               name=None,
               dtype=None):
    if specificity < 0 or specificity > 1:
      raise ValueError(
          'Argument `specificity` must be in the range [0, 1]. '
          f'Received: specificity={specificity}')
    self.specificity = specificity
    self.num_thresholds = num_thresholds
    super(SensitivityAtSpecificity, self).__init__(
        specificity,
        num_thresholds=num_thresholds,
        class_id=class_id,
        name=name,
        dtype=dtype)

  def result(self):
    specificities = tf.math.divide_no_nan(
        self.true_negatives,
        tf.math.add(self.true_negatives, self.false_positives))
    sensitivities = tf.math.divide_no_nan(
        self.true_positives,
        tf.math.add(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.

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

  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.
    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.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_state()
  >>> 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()])
  ```
  """

  @dtensor_utils.inject_mesh
  def __init__(self,
               sensitivity,
               num_thresholds=200,
               class_id=None,
               name=None,
               dtype=None):
    if sensitivity < 0 or sensitivity > 1:
      raise ValueError(
          'Argument `sensitivity` must be in the range [0, 1]. '
          f'Received: sensitivity={sensitivity}')
    self.sensitivity = sensitivity
    self.num_thresholds = num_thresholds
    super(SpecificityAtSensitivity, self).__init__(
        sensitivity,
        num_thresholds=num_thresholds,
        class_id=class_id,
        name=name,
        dtype=dtype)

  def result(self):
    sensitivities = tf.math.divide_no_nan(
        self.true_positives,
        tf.math.add(self.true_positives, self.false_negatives))
    specificities = tf.math.divide_no_nan(
        self.true_negatives,
        tf.math.add(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.

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

  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.
    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.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_state()
  >>> 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)])
  ```
  """

  @dtensor_utils.inject_mesh
  def __init__(self,
               recall,
               num_thresholds=200,
               class_id=None,
               name=None,
               dtype=None):
    if recall < 0 or recall > 1:
      raise ValueError(
          'Argument `recall` must be in the range [0, 1]. '
          f'Received: recall={recall}')
    self.recall = recall
    self.num_thresholds = num_thresholds
    super(PrecisionAtRecall, self).__init__(
        value=recall,
        num_thresholds=num_thresholds,
        class_id=class_id,
        name=name,
        dtype=dtype)

  def result(self):
    recalls = tf.math.divide_no_nan(
        self.true_positives,
        tf.math.add(self.true_positives, self.false_negatives))
    precisions = tf.math.divide_no_nan(
        self.true_positives,
        tf.math.add(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.

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

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

  >>> m.reset_state()
  >>> 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)])
  ```
  """

  @dtensor_utils.inject_mesh
  def __init__(self,
               precision,
               num_thresholds=200,
               class_id=None,
               name=None,
               dtype=None):
    if precision < 0 or precision > 1:
      raise ValueError(
          'Argument `precision` must be in the range [0, 1]. '
          f'Received: precision={precision}')
    self.precision = precision
    self.num_thresholds = num_thresholds
    super(RecallAtPrecision, self).__init__(
        value=precision,
        num_thresholds=num_thresholds,
        class_id=class_id,
        name=name,
        dtype=dtype)

  def result(self):
    precisions = tf.math.divide_no_nan(
        self.true_positives,
        tf.math.add(self.true_positives, self.false_positives))
    recalls = tf.math.divide_no_nan(
        self.true_positives,
        tf.math.add(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(base_metric.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 class 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]
  >>> # tp_rate = 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_state()
  >>> 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 outputting a probability.
  model.compile(optimizer='sgd',
                loss=tf.keras.losses.BinaryCrossentropy(),
                metrics=[tf.keras.metrics.AUC()])

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

  @dtensor_utils.inject_mesh
  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(
          f'Invalid `curve` argument value "{curve}". '
          f'Expected one of: {list(metrics_utils.AUCCurve)}')
    if isinstance(
        summation_method,
        metrics_utils.AUCSummationMethod) and summation_method not in list(
            metrics_utils.AUCSummationMethod):
      raise ValueError(
          f'Invalid `summation_method` argument value "{summation_method}". '
          f'Expected one of: {list(metrics_utils.AUCSummationMethod)}')

    # Update properties.
    self._init_from_thresholds = thresholds is not None
    if thresholds is not None:
      # If specified, use the supplied thresholds.
      self.num_thresholds = len(thresholds) + 2
      thresholds = sorted(thresholds)
      self._thresholds_distributed_evenly = (
          metrics_utils.is_evenly_distributed_thresholds(
              np.array([0.0] + thresholds + [1.0])))
    else:
      if num_thresholds <= 1:
        raise ValueError('Argument `num_thresholds` must be an integer > 1. '
                         f'Received: num_thresholds={num_thresholds}')

      # 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)]
      self._thresholds_distributed_evenly = True

    # 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 - backend.epsilon()] + thresholds +
                                [1.0 + backend.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)
      tf.debugging.assert_non_negative(
          label_weights,
          message='All values of `label_weights` must be non-negative.')
      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=True`. '
            f'Found rank {shape.ndims}. '
            f'Full shape received for `y_true`: {shape}')
      self._num_labels = shape[1]
      variable_shape = tf.TensorShape([self.num_thresholds, self._num_labels])
    else:
      variable_shape = tf.TensorShape([self.num_thresholds])

    self._build_input_shape = shape
    # Create metric variables
    self.true_positives = self.add_weight(
        'true_positives',
        shape=variable_shape,
        initializer='zeros')
    self.true_negatives = self.add_weight(
        'true_negatives',
        shape=variable_shape,
        initializer='zeros')
    self.false_positives = self.add_weight(
        'false_positives',
        shape=variable_shape,
        initializer='zeros')
    self.false_negatives = self.add_weight(
        'false_negatives',
        shape=variable_shape,
        initializer='zeros')

    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():
          backend._initialize_variables(backend._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.
    """
    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',)))
        tf.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)

    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,
        thresholds_distributed_evenly=self._thresholds_distributed_evenly,
        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 = tf.math.add(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.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.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,
        tf.math.add(self.true_positives, self.false_negatives))
    if self.curve == metrics_utils.AUCCurve.ROC:
      fp_rate = tf.math.divide_no_nan(
          self.false_positives,
          tf.math.add(self.false_positives, self.true_negatives))
      x = fp_rate
      y = recall
    else:  # curve == 'PR'.
      precision = tf.math.divide_no_nan(
          self.true_positives,
          tf.math.add(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_state(self):
    if self._built:
      confusion_matrix_variables = (self.true_positives, self.true_negatives,
                                    self.false_positives, self.false_negatives)
      if self.multi_label:
        backend.batch_set_value(
            [(v, np.zeros((self.num_thresholds, self._num_labels)))
             for v in confusion_matrix_variables])
      else:
        backend.batch_set_value([(v, np.zeros((self.num_thresholds,)))
                                 for v in confusion_matrix_variables])

  def get_config(self):
    if is_tensor_or_variable(self.label_weights):
      label_weights = backend.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,
        'multi_label': self.multi_label,
        'label_weights': label_weights
    }
    # optimization to avoid serializing a large number of generated thresholds
    if self._init_from_thresholds:
      # 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.
      config['thresholds'] = self.thresholds[1:-1]
    base_config = super(AUC, self).get_config()
    return dict(list(base_config.items()) + list(config.items()))


@keras_export('keras.metrics.CosineSimilarity')
class CosineSimilarity(base_metric.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_state()
  >>> 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)])
  ```
  """

  @dtensor_utils.inject_mesh
  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(base_metric.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_state()
  >>> 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()])
  ```
  """

  @dtensor_utils.inject_mesh
  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(base_metric.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_state()
  >>> 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()])
  ```
  """

  @dtensor_utils.inject_mesh
  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(base_metric.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_state()
  >>> 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()])
  ```
  """

  @dtensor_utils.inject_mesh
  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(base_metric.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_state()
  >>> 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()])
  ```
  """

  @dtensor_utils.inject_mesh
  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(base_metric.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_state()
  >>> 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()])
  ```
  """

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


@keras_export('keras.metrics.SquaredHinge')
class SquaredHinge(base_metric.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_state()
  >>> 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()])
  ```
  """

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


@keras_export('keras.metrics.CategoricalHinge')
class CategoricalHinge(base_metric.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_state()
  >>> 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()])
  ```
  """

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


@keras_export('keras.metrics.RootMeanSquaredError')
class RootMeanSquaredError(base_metric.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_state()
  >>> 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()])
  ```
  """

  @dtensor_utils.inject_mesh
  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(base_metric.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_state()
  >>> 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()])
  ```
  """

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


@keras_export('keras.metrics.Poisson')
class Poisson(base_metric.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_state()
  >>> m.update_state([[0, 1], [0, 0]], [[1, 1], [0, 0]],
  ...                sample_weight=[1, 0])
  >>> m.result().numpy()
  0.99999994

  Usage with `compile()` API:

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

  @dtensor_utils.inject_mesh
  def __init__(self, name='poisson', dtype=None):
    super(Poisson, self).__init__(poisson, name, dtype=dtype)


@keras_export('keras.metrics.KLDivergence')
class KLDivergence(base_metric.MeanMetricWrapper):
  """Computes Kullback-Leibler divergence metric between `y_true` and `y_pred`.

  `metric = y_true * log(y_true / 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.KLDivergence()
  >>> m.update_state([[0, 1], [0, 0]], [[0.6, 0.4], [0.4, 0.6]])
  >>> m.result().numpy()
  0.45814306

  >>> m.reset_state()
  >>> m.update_state([[0, 1], [0, 0]], [[0.6, 0.4], [0.4, 0.6]],
  ...                sample_weight=[1, 0])
  >>> m.result().numpy()
  0.9162892

  Usage with `compile()` API:

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

  @dtensor_utils.inject_mesh
  def __init__(self, name='kullback_leibler_divergence', dtype=None):
    super(KLDivergence, self).__init__(
        kullback_leibler_divergence, name, dtype=dtype)


class _IoUBase(base_metric.Metric):
  """Computes the confusion matrix for Intersection-Over-Union metrics.

  Intersection-Over-Union is a common evaluation metric for semantic image
  segmentation.

  For an individual class, the IoU metric is defined as follows:

  ```
  iou = true_positives / (true_positives + false_positives + false_negatives)
  ```

  From IoUs of individual classes, the MeanIoU can be computed as the mean of
  the individual IoUs.

  To compute IoUs, the predictions are accumulated in a confusion matrix,
  weighted by `sample_weight` and the metric is then calculated from it.

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

  Args:
    num_classes: The possible number of labels the prediction task can have.
      This value must be provided, since a confusion matrix of size
      `(num_classes, num_classes)` will be allocated.
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.
  """

  def __init__(self, num_classes, name=None, dtype=None):
    super(_IoUBase, self).__init__(name=name, dtype=dtype)
    self.num_classes = num_classes

    # Variable to accumulate the predictions in the confusion matrix.
    self.total_cm = self.add_weight(
        'total_confusion_matrix',
        shape=(num_classes, num_classes),
        initializer='zeros')

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

    y_true = tf.cast(y_true, self._dtype)
    y_pred = tf.cast(y_pred, self._dtype)

    # Flatten the input if its rank > 1.
    if y_pred.shape.ndims > 1:
      y_pred = tf.reshape(y_pred, [-1])

    if y_true.shape.ndims > 1:
      y_true = tf.reshape(y_true, [-1])

    if sample_weight is not None:
      sample_weight = tf.cast(sample_weight, self._dtype)
      if sample_weight.shape.ndims > 1:
        sample_weight = tf.reshape(sample_weight, [-1])

    # Accumulate the prediction to current confusion matrix.
    current_cm = tf.math.confusion_matrix(
        y_true,
        y_pred,
        self.num_classes,
        weights=sample_weight,
        dtype=self._dtype)
    return self.total_cm.assign_add(current_cm)

  def reset_state(self):
    backend.set_value(
        self.total_cm, np.zeros((self.num_classes, self.num_classes)))


@keras_export('keras.metrics.IoU')
class IoU(_IoUBase):
  """Computes the Intersection-Over-Union metric for specific target classes.

  General definition and computation:

  Intersection-Over-Union is a common evaluation metric for semantic image
  segmentation.

  For an individual class, the IoU metric is defined as follows:

  ```
  iou = true_positives / (true_positives + false_positives + false_negatives)
  ```

  To compute IoUs, the predictions are accumulated in a confusion matrix,
  weighted by `sample_weight` and the metric is then calculated from it.

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

  Note, this class first computes IoUs for all individual classes, then returns
  the mean of IoUs for the classes that are specified by `target_class_ids`. If
  `target_class_ids` has only one id value, the IoU of that specific class is
  returned.

  Args:
    num_classes: The possible number of labels the prediction task can have.
      A confusion matrix of dimension = [num_classes, num_classes] will be
      allocated to accumulate predictions from which the metric is calculated.
    target_class_ids: A tuple or list of target class ids for which the metric
      is returned. To compute IoU for a specific class, a list (or tuple) of a
      single id value should be provided.
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> # cm = [[1, 1],
  >>> #        [1, 1]]
  >>> # sum_row = [2, 2], sum_col = [2, 2], true_positives = [1, 1]
  >>> # iou = true_positives / (sum_row + sum_col - true_positives))
  >>> # iou = [0.33, 0.33]
  >>> m = tf.keras.metrics.IoU(num_classes=2, target_class_ids=[0])
  >>> m.update_state([0, 0, 1, 1], [0, 1, 0, 1])
  >>> m.result().numpy()
  0.33333334

  >>> m.reset_state()
  >>> m.update_state([0, 0, 1, 1], [0, 1, 0, 1],
  ...                sample_weight=[0.3, 0.3, 0.3, 0.1])
  >>> # cm = [[0.3, 0.3],
  >>> #        [0.3, 0.1]]
  >>> # sum_row = [0.6, 0.4], sum_col = [0.6, 0.4], true_positives = [0.3, 0.1]
  >>> # iou = [0.33, 0.14]
  >>> m.result().numpy()
  0.33333334

  Usage with `compile()` API:

  ```python
  model.compile(
    optimizer='sgd',
    loss='mse',
    metrics=[tf.keras.metrics.IoU(num_classes=2, target_class_ids=[0])])
  ```
  """

  @dtensor_utils.inject_mesh
  def __init__(
      self,
      num_classes: int,
      target_class_ids: Union[List[int], Tuple[int, ...]],
      name=None,
      dtype=None,
  ):
    super(IoU, self).__init__(
        name=name,
        num_classes=num_classes,
        dtype=dtype,
    )
    if max(target_class_ids) >= num_classes:
      raise ValueError(
          f'Target class id {max(target_class_ids)} is out of range, which is '
          f'[{0}, {num_classes}).')
    self.target_class_ids = list(target_class_ids)

  def result(self):
    """Compute the intersection-over-union via the confusion matrix."""
    sum_over_row = tf.cast(
        tf.reduce_sum(self.total_cm, axis=0), dtype=self._dtype)
    sum_over_col = tf.cast(
        tf.reduce_sum(self.total_cm, axis=1), dtype=self._dtype)
    true_positives = tf.cast(
        tf.linalg.tensor_diag_part(self.total_cm), dtype=self._dtype)

    # sum_over_row + sum_over_col =
    #     2 * true_positives + false_positives + false_negatives.
    denominator = sum_over_row + sum_over_col - true_positives

    # Only keep the target classes
    true_positives = tf.gather(true_positives, self.target_class_ids)
    denominator = tf.gather(denominator, self.target_class_ids)

    # If the denominator is 0, we need to ignore the class.
    num_valid_entries = tf.reduce_sum(
        tf.cast(tf.not_equal(denominator, 0), dtype=self._dtype))

    iou = tf.math.divide_no_nan(true_positives, denominator)

    return tf.math.divide_no_nan(
        tf.reduce_sum(iou, name='mean_iou'), num_valid_entries)

  def get_config(self):
    config = {
        'num_classes': self.num_classes,
        'target_class_ids': self.target_class_ids,
    }
    base_config = super(IoU, self).get_config()
    return dict(list(base_config.items()) + list(config.items()))


@keras_export('keras.metrics.BinaryIoU')
class BinaryIoU(IoU):
  """Computes the Intersection-Over-Union metric for class 0 and/or 1.

  General definition and computation:

  Intersection-Over-Union is a common evaluation metric for semantic image
  segmentation.

  For an individual class, the IoU metric is defined as follows:

  ```
  iou = true_positives / (true_positives + false_positives + false_negatives)
  ```

  To compute IoUs, the predictions are accumulated in a confusion matrix,
  weighted by `sample_weight` and the metric is then calculated from it.

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

  This class can be used to compute IoUs for a binary classification task where
  the predictions are provided as logits. First a `threshold` is applied to the
  predicted values such that those that are below the `threshold` are converted
  to class 0 and those that are above the `threshold` are converted to class 1.

  IoUs for classes 0 and 1 are then computed, the mean of IoUs for the classes
  that are specified by `target_class_ids` is returned.

  Note: with `threshold=0`, this metric has the same behavior as `IoU`.

  Args:
    target_class_ids: A tuple or list of target class ids for which the metric
      is returned. Options are `[0]`, `[1]`, or `[0, 1]`. With `[0]` (or `[1]`),
      the IoU metric for class 0 (or class 1, respectively) is returned. With
      `[0, 1]`, the mean of IoUs for the two classes is returned.
    threshold: A threshold that applies to the prediction logits to convert them
      to either predicted class 0 if the logit is below `threshold` or predicted
      class 1 if the logit is above `threshold`.
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> m = tf.keras.metrics.BinaryIoU(target_class_ids=[0, 1], threshold=0.3)
  >>> m.update_state([0, 1, 0, 1], [0.1, 0.2, 0.4, 0.7])
  >>> m.result().numpy()
  0.33333334

  >>> m.reset_state()
  >>> m.update_state([0, 1, 0, 1], [0.1, 0.2, 0.4, 0.7],
  ...                sample_weight=[0.2, 0.3, 0.4, 0.1])
  >>> # cm = [[0.2, 0.4],
  >>> #        [0.3, 0.1]]
  >>> # sum_row = [0.6, 0.4], sum_col = [0.5, 0.5], true_positives = [0.2, 0.1]
  >>> # iou = [0.222, 0.125]
  >>> m.result().numpy()
  0.17361112

  Usage with `compile()` API:

  ```python
  model.compile(
    optimizer='sgd',
    loss='mse',
    metrics=[tf.keras.metrics.BinaryIoU(target_class_ids=[0], threshold=0.5)])
  ```
  """

  @dtensor_utils.inject_mesh
  def __init__(
      self,
      target_class_ids: Union[List[int], Tuple[int, ...]] = (0, 1),
      threshold=0.5,
      name=None,
      dtype=None,
  ):

    super(BinaryIoU, self).__init__(
        num_classes=2,
        target_class_ids=target_class_ids,
        name=name,
        dtype=dtype,
    )
    self.threshold = threshold

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

    Before the confusion matrix is updated, the predicted values are thresholded
    to be:
      0 for values that are smaller than the `threshold`
      1 for values that are larger or equal to the `threshold`

    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_pred = tf.cast(y_pred, self._dtype)
    y_pred = tf.cast(y_pred >= self.threshold, self._dtype)
    return super().update_state(y_true, y_pred, sample_weight)

  def get_config(self):
    return {
        'target_class_ids': self.target_class_ids,
        'threshold': self.threshold,
        'name': self.name,
        'dtype': self._dtype,
    }


@keras_export('keras.metrics.MeanIoU')
class MeanIoU(IoU):
  """Computes the mean Intersection-Over-Union metric.

  General definition and computation:

  Intersection-Over-Union is a common evaluation metric for semantic image
  segmentation.

  For an individual class, the IoU metric is defined as follows:

  ```
  iou = true_positives / (true_positives + false_positives + false_negatives)
  ```

  To compute IoUs, the predictions are accumulated in a confusion matrix,
  weighted by `sample_weight` and the metric is then calculated from it.

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

  Note that this class first computes IoUs for all individual classes, then
  returns the mean of these values.

  Args:
    num_classes: The possible number of labels the prediction task can have.
      This value must be provided, since a confusion matrix of dimension =
      [num_classes, num_classes] will be allocated.
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> # cm = [[1, 1],
  >>> #        [1, 1]]
  >>> # sum_row = [2, 2], sum_col = [2, 2], true_positives = [1, 1]
  >>> # iou = true_positives / (sum_row + sum_col - true_positives))
  >>> # result = (1 / (2 + 2 - 1) + 1 / (2 + 2 - 1)) / 2 = 0.33
  >>> m = tf.keras.metrics.MeanIoU(num_classes=2)
  >>> m.update_state([0, 0, 1, 1], [0, 1, 0, 1])
  >>> m.result().numpy()
  0.33333334

  >>> m.reset_state()
  >>> m.update_state([0, 0, 1, 1], [0, 1, 0, 1],
  ...                sample_weight=[0.3, 0.3, 0.3, 0.1])
  >>> m.result().numpy()
  0.23809525

  Usage with `compile()` API:

  ```python
  model.compile(
    optimizer='sgd',
    loss='mse',
    metrics=[tf.keras.metrics.MeanIoU(num_classes=2)])
  ```
  """

  @dtensor_utils.inject_mesh
  def __init__(self, num_classes, name=None, dtype=None):
    target_class_ids = list(range(num_classes))
    super(MeanIoU, self).__init__(
        name=name,
        num_classes=num_classes,
        target_class_ids=target_class_ids,
        dtype=dtype,
    )

  def get_config(self):
    return {
        'num_classes': self.num_classes,
        'name': self.name,
        'dtype': self._dtype,
    }


@keras_export('keras.metrics.OneHotIoU')
class OneHotIoU(IoU):
  """Computes the Intersection-Over-Union metric for one-hot encoded labels.

  General definition and computation:

  Intersection-Over-Union is a common evaluation metric for semantic image
  segmentation.

  For an individual class, the IoU metric is defined as follows:

  ```
  iou = true_positives / (true_positives + false_positives + false_negatives)
  ```

  To compute IoUs, the predictions are accumulated in a confusion matrix,
  weighted by `sample_weight` and the metric is then calculated from it.

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

  This class can be used to compute IoU for multi-class classification tasks
  where the labels are one-hot encoded (the last axis should have one dimension
  per class). Note that the predictions should also have the same shape. To
  compute the IoU, first the labels and predictions are converted back into
  integer format by taking the argmax over the class axis. Then the same
  computation steps as for the base `IoU` class apply.

  Note, if there is only one channel in the labels and predictions, this class
  is the same as class `IoU`. In this case, use `IoU` instead.

  Also, make sure that `num_classes` is equal to the number of classes in the
  data, to avoid a "labels out of bound" error when the confusion matrix is
  computed.

  Args:
    num_classes: The possible number of labels the prediction task can have.
      A confusion matrix of shape `(num_classes, num_classes)` will be
      allocated to accumulate predictions from which the metric is calculated.
    target_class_ids: A tuple or list of target class ids for which the metric
      is returned. To compute IoU for a specific class, a list (or tuple) of a
      single id value should be provided.
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> y_true = tf.constant([[0, 0, 1], [1, 0, 0], [0, 1, 0], [1, 0, 0]])
  >>> y_pred = tf.constant([[0.2, 0.3, 0.5], [0.1, 0.2, 0.7], [0.5, 0.3, 0.1],
  ...                       [0.1, 0.4, 0.5]])
  >>> sample_weight = [0.1, 0.2, 0.3, 0.4]
  >>> m = tf.keras.metrics.OneHotIoU(num_classes=3, target_class_ids=[0, 2])
  >>> m.update_state(y_true=y_true, y_pred=y_pred, sample_weight=sample_weight)
  >>> # cm = [[0, 0, 0.2+0.4],
  >>> #       [0.3, 0, 0],
  >>> #       [0, 0, 0.1]]
  >>> # sum_row = [0.3, 0, 0.7], sum_col = [0.6, 0.3, 0.1]
  >>> # true_positives = [0, 0, 0.1]
  >>> # single_iou = true_positives / (sum_row + sum_col - true_positives))
  >>> # mean_iou = (0 / (0.3 + 0.6 - 0) + 0.1 / (0.7 + 0.1 - 0.1)) / 2
  >>> m.result().numpy()
  0.071

  Usage with `compile()` API:

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

  @dtensor_utils.inject_mesh
  def __init__(
      self,
      num_classes: int,
      target_class_ids: Union[List[int], Tuple[int, ...]],
      name=None,
      dtype=None,
  ):
    super(OneHotIoU, self).__init__(
        num_classes=num_classes,
        target_class_ids=target_class_ids,
        name=name,
        dtype=dtype,
    )

  def update_state(self, y_true, y_pred, sample_weight=None):
    """Accumulates the 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.
    """
    # Select max hot-encoding channels to convert into all-class format
    y_true = tf.argmax(y_true, axis=-1, output_type=tf.int32)
    y_pred = tf.argmax(y_pred, axis=-1, output_type=tf.int32)

    return super().update_state(y_true, y_pred, sample_weight)


@keras_export('keras.metrics.OneHotMeanIoU')
class OneHotMeanIoU(MeanIoU):
  """Computes mean Intersection-Over-Union metric for one-hot encoded labels.

  General definition and computation:

  Intersection-Over-Union is a common evaluation metric for semantic image
  segmentation.

  For an individual class, the IoU metric is defined as follows:

  ```
  iou = true_positives / (true_positives + false_positives + false_negatives)
  ```

  To compute IoUs, the predictions are accumulated in a confusion matrix,
  weighted by `sample_weight` and the metric is then calculated from it.

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

  This class can be used to compute the mean IoU for multi-class classification
  tasks where the labels are one-hot encoded (the last axis should have one
  dimension per class). Note that the predictions should also have the same
  shape. To compute the mean IoU, first the labels and predictions are converted
  back into integer format by taking the argmax over the class axis. Then the
  same computation steps as for the base `MeanIoU` class apply.

  Note, if there is only one channel in the labels and predictions, this class
  is the same as class `MeanIoU`. In this case, use `MeanIoU` instead.

  Also, make sure that `num_classes` is equal to the number of classes in the
  data, to avoid a "labels out of bound" error when the confusion matrix is
  computed.

  Args:
    num_classes: The possible number of labels the prediction task can have.
      A confusion matrix of shape `(num_classes, num_classes)` will be
      allocated to accumulate predictions from which the metric is calculated.
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.

  Standalone usage:

  >>> y_true = tf.constant([[0, 0, 1], [1, 0, 0], [0, 1, 0], [1, 0, 0]])
  >>> y_pred = tf.constant([[0.2, 0.3, 0.5], [0.1, 0.2, 0.7], [0.5, 0.3, 0.1],
  ...                       [0.1, 0.4, 0.5]])
  >>> sample_weight = [0.1, 0.2, 0.3, 0.4]
  >>> m = tf.keras.metrics.OneHotMeanIoU(num_classes=3)
  >>> m.update_state(y_true=y_true, y_pred=y_pred, sample_weight=sample_weight)
  >>> # cm = [[0, 0, 0.2+0.4],
  >>> #       [0.3, 0, 0],
  >>> #       [0, 0, 0.1]]
  >>> # sum_row = [0.3, 0, 0.7], sum_col = [0.6, 0.3, 0.1]
  >>> # true_positives = [0, 0, 0.1]
  >>> # single_iou = true_positives / (sum_row + sum_col - true_positives))
  >>> # mean_iou = (0 + 0 + 0.1 / (0.7 + 0.1 - 0.1)) / 3
  >>> m.result().numpy()
  0.048

  Usage with `compile()` API:

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

  @dtensor_utils.inject_mesh
  def __init__(
      self,
      num_classes: int,
      name=None,
      dtype=None,
  ):
    super(OneHotMeanIoU, self).__init__(
        num_classes=num_classes,
        name=name,
        dtype=dtype,
    )

  def update_state(self, y_true, y_pred, sample_weight=None):
    """Accumulates the 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.
    """
    # Select max hot-encoding channels to convert into all-class format
    y_true = tf.argmax(y_true, axis=-1, output_type=tf.int32)
    y_pred = tf.argmax(y_pred, axis=-1, output_type=tf.int32)

    return super().update_state(y_true, y_pred, sample_weight)


@keras_export('keras.metrics.BinaryCrossentropy')
class BinaryCrossentropy(base_metric.MeanMetricWrapper):
  """Computes the crossentropy metric between the labels and predictions.

  This is the crossentropy metric class to be used when there are only two
  label classes (0 and 1).

  Args:
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.
    from_logits: (Optional )Whether output is expected to be a logits tensor.
      By default, we consider that output encodes a probability distribution.
    label_smoothing: (Optional) Float in [0, 1]. When > 0, label values are
      smoothed, meaning the confidence on label values are relaxed.
      e.g. `label_smoothing=0.2` means that we will use a value of `0.1` for
      label `0` and `0.9` for label `1`".

  Standalone usage:

  >>> m = tf.keras.metrics.BinaryCrossentropy()
  >>> m.update_state([[0, 1], [0, 0]], [[0.6, 0.4], [0.4, 0.6]])
  >>> m.result().numpy()
  0.81492424

  >>> m.reset_state()
  >>> m.update_state([[0, 1], [0, 0]], [[0.6, 0.4], [0.4, 0.6]],
  ...                sample_weight=[1, 0])
  >>> m.result().numpy()
  0.9162905

  Usage with `compile()` API:

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

  @dtensor_utils.inject_mesh
  def __init__(self,
               name='binary_crossentropy',
               dtype=None,
               from_logits=False,
               label_smoothing=0):
    super(BinaryCrossentropy, self).__init__(
        binary_crossentropy,
        name,
        dtype=dtype,
        from_logits=from_logits,
        label_smoothing=label_smoothing)


@keras_export('keras.metrics.CategoricalCrossentropy')
class CategoricalCrossentropy(base_metric.MeanMetricWrapper):
  """Computes the crossentropy metric between the labels and predictions.

  This is the crossentropy metric class to be used when there are multiple
  label classes (2 or more). Here we assume that labels are given as a `one_hot`
  representation. eg., When labels values are [2, 0, 1],
   `y_true` = [[0, 0, 1], [1, 0, 0], [0, 1, 0]].

  Args:
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.
    from_logits: (Optional) Whether output is expected to be a logits tensor.
      By default, we consider that output encodes a probability distribution.
    label_smoothing: (Optional) Float in [0, 1]. When > 0, label values are
      smoothed, meaning the confidence on label values are relaxed. e.g.
      `label_smoothing=0.2` means that we will use a value of `0.1` for label
      `0` and `0.9` for label `1`"

  Standalone usage:

  >>> # EPSILON = 1e-7, y = y_true, y` = y_pred
  >>> # y` = clip_ops.clip_by_value(output, EPSILON, 1. - EPSILON)
  >>> # y` = [[0.05, 0.95, EPSILON], [0.1, 0.8, 0.1]]
  >>> # xent = -sum(y * log(y'), axis = -1)
  >>> #      = -((log 0.95), (log 0.1))
  >>> #      = [0.051, 2.302]
  >>> # Reduced xent = (0.051 + 2.302) / 2
  >>> m = tf.keras.metrics.CategoricalCrossentropy()
  >>> m.update_state([[0, 1, 0], [0, 0, 1]],
  ...                [[0.05, 0.95, 0], [0.1, 0.8, 0.1]])
  >>> m.result().numpy()
  1.1769392

  >>> m.reset_state()
  >>> m.update_state([[0, 1, 0], [0, 0, 1]],
  ...                [[0.05, 0.95, 0], [0.1, 0.8, 0.1]],
  ...                sample_weight=tf.constant([0.3, 0.7]))
  >>> m.result().numpy()
  1.6271976

  Usage with `compile()` API:

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

  @dtensor_utils.inject_mesh
  def __init__(self,
               name='categorical_crossentropy',
               dtype=None,
               from_logits=False,
               label_smoothing=0):
    super(CategoricalCrossentropy, self).__init__(
        categorical_crossentropy,
        name,
        dtype=dtype,
        from_logits=from_logits,
        label_smoothing=label_smoothing)


@keras_export('keras.metrics.SparseCategoricalCrossentropy')
class SparseCategoricalCrossentropy(base_metric.MeanMetricWrapper):
  """Computes the crossentropy metric between the labels and predictions.

  Use this crossentropy metric when there are two or more label classes.
  We expect labels to be provided as integers. If you want to provide labels
  using `one-hot` representation, please use `CategoricalCrossentropy` metric.
  There should be `# classes` floating point values per feature for `y_pred`
  and a single floating point value per feature for `y_true`.

  In the snippet below, there is a single floating point value per example for
  `y_true` and `# classes` floating pointing values per example for `y_pred`.
  The shape of `y_true` is `[batch_size]` and the shape of `y_pred` is
  `[batch_size, num_classes]`.

  Args:
    name: (Optional) string name of the metric instance.
    dtype: (Optional) data type of the metric result.
    from_logits: (Optional) Whether output is expected to be a logits tensor.
      By default, we consider that output encodes a probability distribution.
    axis: (Optional) Defaults to -1. The dimension along which the metric is
      computed.

  Standalone usage:

  >>> # y_true = one_hot(y_true) = [[0, 1, 0], [0, 0, 1]]
  >>> # logits = log(y_pred)
  >>> # softmax = exp(logits) / sum(exp(logits), axis=-1)
  >>> # softmax = [[0.05, 0.95, EPSILON], [0.1, 0.8, 0.1]]
  >>> # xent = -sum(y * log(softmax), 1)
  >>> # log(softmax) = [[-2.9957, -0.0513, -16.1181],
  >>> #                [-2.3026, -0.2231, -2.3026]]
  >>> # y_true * log(softmax) = [[0, -0.0513, 0], [0, 0, -2.3026]]
  >>> # xent = [0.0513, 2.3026]
  >>> # Reduced xent = (0.0513 + 2.3026) / 2
  >>> m = tf.keras.metrics.SparseCategoricalCrossentropy()
  >>> m.update_state([1, 2],
  ...                [[0.05, 0.95, 0], [0.1, 0.8, 0.1]])
  >>> m.result().numpy()
  1.1769392

  >>> m.reset_state()
  >>> m.update_state([1, 2],
  ...                [[0.05, 0.95, 0], [0.1, 0.8, 0.1]],
  ...                sample_weight=tf.constant([0.3, 0.7]))
  >>> m.result().numpy()
  1.6271976

  Usage with `compile()` API:

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

  @dtensor_utils.inject_mesh
  def __init__(self,
               name='sparse_categorical_crossentropy',
               dtype=None,
               from_logits=False,
               axis=-1):
    super(SparseCategoricalCrossentropy, self).__init__(
        sparse_categorical_crossentropy,
        name,
        dtype=dtype,
        from_logits=from_logits,
        axis=axis)


SparseCategoricalCrossentropy.update_state.__doc__ = _SPARSE_CATEGORICAL_UPDATE_STATE_DOCSTRING


def accuracy(y_true, y_pred):
  [y_pred, y_true], _ = \
      metrics_utils.ragged_assert_compatible_and_get_flat_values(
          [y_pred, y_true])
  y_true.shape.assert_is_compatible_with(y_pred.shape)
  if y_true.dtype != y_pred.dtype:
    y_pred = tf.cast(y_pred, y_true.dtype)
  return tf.cast(tf.equal(y_true, y_pred), backend.floatx())


@keras_export('keras.metrics.binary_accuracy')
@tf.__internal__.dispatch.add_dispatch_support
def binary_accuracy(y_true, y_pred, threshold=0.5):
  """Calculates how often predictions match binary labels.

  Standalone usage:
  >>> y_true = [[1], [1], [0], [0]]
  >>> y_pred = [[1], [1], [0], [0]]
  >>> m = tf.keras.metrics.binary_accuracy(y_true, y_pred)
  >>> assert m.shape == (4,)
  >>> m.numpy()
  array([1., 1., 1., 1.], dtype=float32)

  Args:
    y_true: Ground truth values. shape = `[batch_size, d0, .. dN]`.
    y_pred: The predicted values. shape = `[batch_size, d0, .. dN]`.
    threshold: (Optional) Float representing the threshold for deciding whether
      prediction values are 1 or 0.

  Returns:
    Binary accuracy values. shape = `[batch_size, d0, .. dN-1]`
  """
  # Note: calls metrics_utils.binary_matches with mean reduction. This maintains
  # public facing binary_accuracy behavior and seperates it from the vital
  # behavior of the binary_matches method needed in backend dependencies.

  return tf.reduce_mean(
      metrics_utils.binary_matches(y_true, y_pred, threshold), axis=-1)


@keras_export('keras.metrics.categorical_accuracy')
@tf.__internal__.dispatch.add_dispatch_support
def categorical_accuracy(y_true, y_pred):
  """Calculates how often predictions match one-hot labels.

  Standalone usage:
  >>> y_true = [[0, 0, 1], [0, 1, 0]]
  >>> y_pred = [[0.1, 0.9, 0.8], [0.05, 0.95, 0]]
  >>> m = tf.keras.metrics.categorical_accuracy(y_true, y_pred)
  >>> assert m.shape == (2,)
  >>> m.numpy()
  array([0., 1.], dtype=float32)

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

  Args:
    y_true: One-hot ground truth values.
    y_pred: The prediction values.

  Returns:
    Categorical accuracy values.
  """
  # Note: wraps metrics_utils.categorical_matches. This seperates public facing
  # categorical_accuracy behavior from the vital behavior of the
  # categorical_matches method needed in backend dependencies.

  return metrics_utils.sparse_categorical_matches(
      tf.math.argmax(y_true, axis=-1), y_pred)


@keras_export('keras.metrics.sparse_categorical_accuracy')
@tf.__internal__.dispatch.add_dispatch_support
def sparse_categorical_accuracy(y_true, y_pred):
  """Calculates how often predictions match integer labels.

  Standalone usage:
  >>> y_true = [2, 1]
  >>> y_pred = [[0.1, 0.9, 0.8], [0.05, 0.95, 0]]
  >>> m = tf.keras.metrics.sparse_categorical_accuracy(y_true, y_pred)
  >>> assert m.shape == (2,)
  >>> m.numpy()
  array([0., 1.], dtype=float32)

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

  Args:
    y_true: Integer ground truth values.
    y_pred: The prediction values.

  Returns:
    Sparse categorical accuracy values.
  """
  # Note: wraps metrics_utils.sparse_categorical_matches method and checks for
  # squeezing to align with expected public facing behavior. This seperates
  # public facing sparse_categorical_accuracy behavior from the vital behavior
  # of the sparse_categorical_matches method needed in backend dependencies.

  matches = metrics_utils.sparse_categorical_matches(y_true, y_pred)

  # if shape is (num_samples, 1) squeeze
  if matches.shape.ndims > 1 and matches.shape[-1] == 1:
    matches = tf.squeeze(matches, [-1])

  return matches


@keras_export('keras.metrics.top_k_categorical_accuracy')
@tf.__internal__.dispatch.add_dispatch_support
def top_k_categorical_accuracy(y_true, y_pred, k=5):
  """Computes how often targets are in the top `K` predictions.

  Standalone usage:
  >>> y_true = [[0, 0, 1], [0, 1, 0]]
  >>> y_pred = [[0.1, 0.9, 0.8], [0.05, 0.95, 0]]
  >>> m = tf.keras.metrics.top_k_categorical_accuracy(y_true, y_pred, k=3)
  >>> assert m.shape == (2,)
  >>> m.numpy()
  array([1., 1.], dtype=float32)

  Args:
    y_true: The ground truth values.
    y_pred: The prediction values.
    k: (Optional) Number of top elements to look at for computing accuracy.
      Defaults to 5.

  Returns:
    Top K categorical accuracy value.
  """
  # Note: wraps metrics_utils.top_k_categorical_matches. This seperates
  # public facing top_k_categorical_accuracy behavior from the vital behavior
  # of the top_k_categorical_matches method needed in backend dependencies.

  return metrics_utils.sparse_top_k_categorical_matches(
      tf.math.argmax(y_true, axis=-1), y_pred, k)


@keras_export('keras.metrics.sparse_top_k_categorical_accuracy')
@tf.__internal__.dispatch.add_dispatch_support
def sparse_top_k_categorical_accuracy(y_true, y_pred, k=5):
  """Computes how often integer targets are in the top `K` predictions.

  Standalone usage:
  >>> y_true = [2, 1]
  >>> y_pred = [[0.1, 0.9, 0.8], [0.05, 0.95, 0]]
  >>> m = tf.keras.metrics.sparse_top_k_categorical_accuracy(
  ...     y_true, y_pred, k=3)
  >>> assert m.shape == (2,)
  >>> m.numpy()
  array([1., 1.], dtype=float32)

  Args:
    y_true: tensor of true targets.
    y_pred: tensor of predicted targets.
    k: (Optional) Number of top elements to look at for computing accuracy.
      Defaults to 5.

  Returns:
    Sparse top K categorical accuracy value.
  """
  # Note: wraps metrics_utils.sparse_top_k_categorical_matches. This seperates
  # public facing sparse_top_k_categorical_accuracy behavior from the vital
  # behavior of the sparse_top_k_categorical_matches method needed in backend
  # dependencies.

  return metrics_utils.sparse_top_k_categorical_matches(y_true, y_pred, k)


def cosine_similarity(y_true, y_pred, axis=-1):
  """Computes the cosine similarity between labels and predictions.

  Args:
    y_true: The ground truth values.
    y_pred: The prediction values.
    axis: (Optional) Defaults to -1. The dimension along which the cosine
      similarity is computed.

  Returns:
    Cosine similarity value.
  """
  y_true = tf.linalg.l2_normalize(y_true, axis=axis)
  y_pred = tf.linalg.l2_normalize(y_pred, axis=axis)
  return tf.reduce_sum(y_true * y_pred, axis=axis)
