text: # Copyright 2018 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.
  # ==============================================================================
  """Numpy-related utilities."""
  from __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  
  import numpy as np
  from tensorflow.python.util.tf_export import keras_export
  
  
  @keras_export('keras.utils.to_categorical')
  def to_categorical(y, num_classes=None, dtype='float32'):
    """Converts a class vector (integers) to binary class matrix.
  
    E.g. for use with categorical_crossentropy.
  
    Args:
        y: class vector to be converted into a matrix
            (integers from 0 to num_classes).
        num_classes: total number of classes. If `None`, this would be inferred
          as the (largest number in `y`) + 1.
        dtype: The data type expected by the input. Default: `'float32'`.
  
    Returns:
        A binary matrix representation of the input. The classes axis is placed
        last.
  
    Example:
  
    >>> a = tf.keras.utils.to_categorical([0, 1, 2, 3], num_classes=4)
    >>> a = tf.constant(a, shape=[4, 4])
    >>> print(a)
    tf.Tensor(
      [[1. 0. 0. 0.]
       [0. 1. 0. 0.]
       [0. 0. 1. 0.]
       [0. 0. 0. 1.]], shape=(4, 4), dtype=float32)
  
    >>> b = tf.constant([.9, .04, .03, .03,
    ...                  .3, .45, .15, .13,
    ...                  .04, .01, .94, .05,
    ...                  .12, .21, .5, .17],
    ...                 shape=[4, 4])
    >>> loss = tf.keras.backend.categorical_crossentropy(a, b)
    >>> print(np.around(loss, 5))
    [0.10536 0.82807 0.1011  1.77196]
  
    >>> loss = tf.keras.backend.categorical_crossentropy(a, a)
    >>> print(np.around(loss, 5))
    [0. 0. 0. 0.]
  
    Raises:
        Value Error: If input contains string value
  
    """
    y = np.array(y, dtype='int')
    input_shape = y.shape
    if input_shape and input_shape[-1] == 1 and len(input_shape) > 1:
      input_shape = tuple(input_shape[:-1])
    y = y.ravel()
    if not num_classes:
      num_classes = np.max(y) + 1
    n = y.shape[0]
    categorical = np.zeros((n, num_classes), dtype=dtype)
    categorical[np.arange(n), y] = 1
    output_shape = input_shape + (num_classes,)
    categorical = np.reshape(categorical, output_shape)
    return categorical
  
  
  @keras_export('keras.utils.normalize')
  def normalize(x, axis=-1, order=2):
    """Normalizes a Numpy array.
  
    Args:
        x: Numpy array to normalize.
        axis: axis along which to normalize.
        order: Normalization order (e.g. `order=2` for L2 norm).
  
    Returns:
        A normalized copy of the array.
    """
    l2 = np.atleast_1d(np.linalg.norm(x, order, axis))
    l2[l2 == 0] = 1
    return x / np.expand_dims(l2, axis)
  