tensorlayer3/tensorlayer/cost/tensorflow_cost.py

#! /usr/bin/python
# -*- coding: utf-8 -*-

import numbers

import tensorflow as tf
from tensorflow.python.framework import ops
from tensorflow.python.ops import array_ops, math_ops, nn_ops, standard_ops

from tensorlayer import logging

__all__ = [
    'softmax_cross_entropy_with_logits',
    'sigmoid_cross_entropy',
    'binary_cross_entropy',
    'mean_squared_error',
    'normalized_mean_square_error',
    'absolute_difference_error',
    'dice_coe',
    'dice_hard_coe',
    'iou_coe',
    'cross_entropy_seq',
    'cross_entropy_seq_with_mask',
    'cosine_similarity',
    'li_regularizer',
    'lo_regularizer',
    'maxnorm_regularizer',
    'maxnorm_o_regularizer',
    'maxnorm_i_regularizer',
]


def softmax_cross_entropy_with_logits(output, target, name=None):
    """Softmax cross-entropy operation, returns the TensorFlow expression of cross-entropy for two distributions,
    it implements softmax internally. See ``tf.ops.sparse_softmax_cross_entropy_with_logits``.

    Parameters
    ----------
    output : Tensor
        A batch of distribution with shape: [batch_size, num of classes].
    target : Tensor
        A batch of index with shape: [batch_size, ].
    name : string
        Name of this loss.

    Examples
    --------
    >>> import tensorlayer as tl
    >>> ce = tl.cost.softmax_cross_entropy_with_logits(y_logits, y_target_logits, 'my_loss')

    References
    -----------
    - About cross-entropy: `<https://en.wikipedia.org/wiki/Cross_entropy>`__.
    - The code is borrowed from: `<https://en.wikipedia.org/wiki/Cross_entropy>`__.

    """
    # if name is None:
    #     raise Exception("Please give a unique name to tl.cost.cross_entropy for TF1.0+")
    return tf.reduce_mean(tf.nn.sparse_softmax_cross_entropy_with_logits(labels=target, logits=output), name=name)


def sigmoid_cross_entropy(output, target, name=None):
    """Sigmoid cross-entropy operation, see ``tf.ops.sigmoid_cross_entropy_with_logits``.

    Parameters
    ----------
    output : Tensor
        A batch of distribution with shape: [batch_size, num of classes].
    target : Tensor
        A batch of index with shape: [batch_size, ].
    name : string
        Name of this loss.

    """
    return tf.reduce_mean(tf.nn.sigmoid_cross_entropy_with_logits(labels=target, logits=output), name=name)


def binary_cross_entropy(output, target, epsilon=1e-8, name='bce_loss'):
    """Binary cross entropy operation.

    Parameters
    ----------
    output : Tensor
        Tensor with type of `float32` or `float64`.
    target : Tensor
        The target distribution, format the same with `output`.
    epsilon : float
        A small value to avoid output to be zero.
    name : str
        An optional name to attach to this function.

    References
    -----------
    - `ericjang-DRAW <https://github.com/ericjang/draw/blob/master/draw.py#L73>`__

    """
    #     with ops.op_scope([output, target], name, "bce_loss") as name:
    #         output = ops.convert_to_tensor(output, name="preds")
    #         target = ops.convert_to_tensor(targets, name="target")

    # with tf.name_scope(name):
    return tf.reduce_mean(
        tf.reduce_sum(
            -(target * tf.math.log(output + epsilon) + (1. - target) * tf.math.log(1. - output + epsilon)), axis=1
        ), name=name
    )

    # For brevity, let `x = output`, `z = target`.  The binary cross entropy loss is
    #
    #     loss(x, z) = - sum_i (x[i] * log(z[i]) + (1 - x[i]) * log(1 - z[i]))


def mean_squared_error(output, target, is_mean=False, axis=-1, name="mean_squared_error"):
    """Return the TensorFlow expression of mean-square-error (L2) of two batch of data.

    Parameters
    ----------
    output : Tensor
        2D, 3D or 4D tensor i.e. [batch_size, n_feature], [batch_size, height, width] or [batch_size, height, width, channel].
    target : Tensor
        The target distribution, format the same with `output`.
    is_mean : boolean
        Whether compute the mean or sum for each example.
            - If True, use ``tf.reduce_mean`` to compute the loss between one target and predict data.
            - If False, use ``tf.reduce_sum`` (default).
    axis : int or list of int
        The dimensions to reduce.
    name : str
        An optional name to attach to this function.

    References
    ------------
    - `Wiki Mean Squared Error <https://en.wikipedia.org/wiki/Mean_squared_error>`__

    """
    # with tf.name_scope(name):
    # if len(output.shape) == 2:  # [batch_size, n_feature]
    #     axis = 1
    # elif len(output.shape) == 3:  # [batch_size, w, h]
    #     axis = [1, 2]
    # elif len(output.shape) == 4:  # [batch_size, w, h, c]
    #     axis = [1, 2, 3]
    # else:
    #     raise Exception("Unknow dimension")

    if is_mean:
        mse = tf.reduce_mean(tf.reduce_mean(tf.math.squared_difference(output, target), axis), name=name)
    else:
        mse = tf.reduce_mean(tf.reduce_sum(tf.math.squared_difference(output, target), axis), name=name)
    return mse


def normalized_mean_square_error(output, target, axis=-1, name="normalized_mean_squared_error_loss"):
    """Return the TensorFlow expression of normalized mean-square-error of two distributions.

    Parameters
    ----------
    output : Tensor
        2D, 3D or 4D tensor i.e. [batch_size, n_feature], [batch_size, height, width] or [batch_size, height, width, channel].
    target : Tensor
        The target distribution, format the same with `output`.
    axis : int or list of int
        The dimensions to reduce.
    name : str
        An optional name to attach to this function.

    """
    with tf.name_scope("normalized_mean_squared_error_loss"):
        # if len(output.shape) == 2:  # [batch_size, n_feature]
        #     axis = 1
        # elif len(output.shape) == 3:  # [batch_size, w, h]
        #     axis = [1, 2]
        # elif len(output.shape) == 4:  # [batch_size, w, h, c]
        #     axis = [1, 2, 3]
        nmse_a = tf.sqrt(tf.reduce_sum(tf.math.squared_difference(output, target), axis=axis))
        nmse_b = tf.sqrt(tf.reduce_sum(tf.square(target), axis=axis))
        nmse = tf.reduce_mean(nmse_a / nmse_b, name=name)
    return nmse


def absolute_difference_error(output, target, is_mean=False, axis=-1, name="absolute_difference_error_loss"):
    """Return the TensorFlow expression of absolute difference error (L1) of two batch of data.

    Parameters
    ----------
    output : Tensor
        2D, 3D or 4D tensor i.e. [batch_size, n_feature], [batch_size, height, width] or [batch_size, height, width, channel].
    target : Tensor
        The target distribution, format the same with `output`.
    is_mean : boolean
        Whether compute the mean or sum for each example.
            - If True, use ``tf.reduce_mean`` to compute the loss between one target and predict data.
            - If False, use ``tf.reduce_sum`` (default).
    axis : int or list of int
        The dimensions to reduce.
    name : str
        An optional name to attach to this function.

    """
    # # with tf.name_scope("absolute_difference_error_loss"):
    # if len(output.shape) == 2:  # [batch_size, n_feature]
    #     axis = 1
    # elif len(output.shape) == 3:  # [batch_size, w, h]
    #     axis = [1, 2]
    # elif len(output.shape) == 4:  # [batch_size, w, h, c]
    #     axis = [1, 2, 3]
    # else:
    #     raise Exception("Unknow dimension")
    if is_mean:
        loss = tf.reduce_mean(tf.reduce_mean(tf.abs(output - target), axis), name=name)
    else:
        loss = tf.reduce_mean(tf.reduce_sum(tf.abs(output - target), axis), name=name)
    return loss


def dice_coe(output, target, loss_type='jaccard', axis=(1, 2, 3), smooth=1e-5):
    """Soft dice (Sørensen or Jaccard) coefficient for comparing the similarity
    of two batch of data, usually be used for binary image segmentation
    i.e. labels are binary. The coefficient between 0 to 1, 1 means totally match.

    Parameters
    -----------
    output : Tensor
        A distribution with shape: [batch_size, ....], (any dimensions).
    target : Tensor
        The target distribution, format the same with `output`.
    loss_type : str
        ``jaccard`` or ``sorensen``, default is ``jaccard``.
    axis : tuple of int
        All dimensions are reduced, default ``[1,2,3]``.
    smooth : float
        This small value will be added to the numerator and denominator.
            - If both output and target are empty, it makes sure dice is 1.
            - If either output or target are empty (all pixels are background), dice = ```smooth/(small_value + smooth)``, then if smooth is very small, dice close to 0 (even the image values lower than the threshold), so in this case, higher smooth can have a higher dice.

    Examples
    ---------
    >>> import tensorlayer as tl
    >>> outputs = tl.ops.softmax(outputs)
    >>> dice_loss = 1 - tl.cost.dice_coe(outputs, y_)

    References
    -----------
    - `Wiki-Dice <https://en.wikipedia.org/wiki/Sørensen–Dice_coefficient>`__

    """
    inse = tf.reduce_sum(output * target, axis=axis)
    if loss_type == 'jaccard':
        l = tf.reduce_sum(output * output, axis=axis)
        r = tf.reduce_sum(target * target, axis=axis)
    elif loss_type == 'sorensen':
        l = tf.reduce_sum(output, axis=axis)
        r = tf.reduce_sum(target, axis=axis)
    else:
        raise Exception("Unknow loss_type")
    # old axis=[0,1,2,3]
    # dice = 2 * (inse) / (l + r)
    # epsilon = 1e-5
    # dice = tf.clip_by_value(dice, 0, 1.0-epsilon) # if all empty, dice = 1
    # new haodong
    dice = (2. * inse + smooth) / (l + r + smooth)
    ##
    dice = tf.reduce_mean(dice, name='dice_coe')
    return dice


def dice_hard_coe(output, target, threshold=0.5, axis=(1, 2, 3), smooth=1e-5):
    """Non-differentiable Sørensen–Dice coefficient for comparing the similarity
    of two batch of data, usually be used for binary image segmentation i.e. labels are binary.
    The coefficient between 0 to 1, 1 if totally match.

    Parameters
    -----------
    output : tensor
        A distribution with shape: [batch_size, ....], (any dimensions).
    target : tensor
        The target distribution, format the same with `output`.
    threshold : float
        The threshold value to be true.
    axis : tuple of integer
        All dimensions are reduced, default ``(1,2,3)``.
    smooth : float
        This small value will be added to the numerator and denominator, see ``dice_coe``.

    References
    -----------
    - `Wiki-Dice <https://en.wikipedia.org/wiki/Sørensen–Dice_coefficient>`__

    """
    output = tf.cast(output > threshold, dtype=tf.float32)
    target = tf.cast(target > threshold, dtype=tf.float32)
    inse = tf.reduce_sum(tf.multiply(output, target), axis=axis)
    l = tf.reduce_sum(output, axis=axis)
    r = tf.reduce_sum(target, axis=axis)
    # old axis=[0,1,2,3]
    # hard_dice = 2 * (inse) / (l + r)
    # epsilon = 1e-5
    # hard_dice = tf.clip_by_value(hard_dice, 0, 1.0-epsilon)
    # new haodong
    hard_dice = (2. * inse + smooth) / (l + r + smooth)
    ##
    hard_dice = tf.reduce_mean(hard_dice, name='hard_dice')
    return hard_dice


def iou_coe(output, target, threshold=0.5, axis=(1, 2, 3), smooth=1e-5):
    """Non-differentiable Intersection over Union (IoU) for comparing the
    similarity of two batch of data, usually be used for evaluating binary image segmentation.
    The coefficient between 0 to 1, and 1 means totally match.

    Parameters
    -----------
    output : tensor
        A batch of distribution with shape: [batch_size, ....], (any dimensions).
    target : tensor
        The target distribution, format the same with `output`.
    threshold : float
        The threshold value to be true.
    axis : tuple of integer
        All dimensions are reduced, default ``(1,2,3)``.
    smooth : float
        This small value will be added to the numerator and denominator, see ``dice_coe``.

    Notes
    ------
    - IoU cannot be used as training loss, people usually use dice coefficient for training, IoU and hard-dice for evaluating.

    """
    pre = tf.cast(output > threshold, dtype=tf.float32)
    truth = tf.cast(target > threshold, dtype=tf.float32)
    inse = tf.reduce_sum(tf.multiply(pre, truth), axis=axis)  # AND
    union = tf.reduce_sum(tf.cast(tf.add(pre, truth) >= 1, dtype=tf.float32), axis=axis)  # OR
    # old axis=[0,1,2,3]
    # epsilon = 1e-5
    # batch_iou = inse / (union + epsilon)
    # new haodong
    batch_iou = (inse + smooth) / (union + smooth)
    iou = tf.reduce_mean(batch_iou, name='iou_coe')
    return iou  # , pre, truth, inse, union


# ## test soft/hard dice and iou
# import numpy as np
# y = np.zeros((1,10,10,1))
# # y[0,0:5,0:5]=1.0
# o = np.zeros((1,10,10,1))
# # o[:,:,:,:] = 0            # what we want: dice=0   iou=0  OK
# # o[0,0:2,0:2]=0.3          # what we want: dice larger iou=0  OK
# # o[0,0:2,0:2]=0.6          # what we want: dice larger  iou small  OK
# # o[0,0:3,0:3]=0.6          # what we want: dice larger iou larger OK
# # o[0,0:3,0:3]=1            # what we want: dice larger iou same OK
# # o[0,0:5,0:5]=1            # what we want: dice=1 iou=1  OK
# # o[0,0:5,0:5]=0.3          # what we want: dice smaller  iou=0  OK
# # o[0,0:5,0:5]=1e-2           # what we want: dice≈0 iou=0  OK
# # o[0,8:10,8:10]=1.0        # what we want: dice=0 iou=0  OK
# # o[0,8:10,8:10]=1e-10        # what we want: dice=0 iou=0  OK
# # y[:,:,:,:] = o[:,:,:,:] = 0 # what we want: dice=1 iou=1  OK
# ## why in u-net, dice=1 hard-dice=1 iou=1 exist?? print bug?
#
# d = dice_coe(o, y, 'jaccard', smooth=1.)
# hd = dice_hard_coe(o, y, smooth=1e-5)
# i = iou_coe(o, y, smooth=1e-5)
# sess = tf.Session(config=tf.ConfigProto(allow_soft_placement=True))
# # sess.run(tf.local_variables_initializer())
# print(sess.run([d,hd,i]))
# # p, t, i, u = sess.run([pre, truth, inse, union])
# # import pprint
# # pprint.pprint(((y>0.5)*(o>0.5)).astype(int).tolist())
# # pprint.pprint(p.tolist())
# # pprint.pprint(t.tolist())
# # pprint.pprint(i)
# # pprint.pprint(u)
# exit()


def sequence_loss_by_example(
    logits, targets, weights, average_across_timesteps=True, softmax_loss_function=None, name=None
):
    """Weighted cross-entropy loss for a sequence of logits (per example). see original tensorflow code :
    <https://github.com/tensorflow/tensorflow/blob/master/tensorflow/contrib/legacy_seq2seq/python/ops/seq2seq.py#L1057>

    Parameters
    ----------
    logits: List
        List of 2D Tensors of shape [batch_size x num_decoder_symbols].
    targets: List
        List of 1D batch-sized int32 Tensors of the same length as logits.
    weights: List
        List of 1D batch-sized float-Tensors of the same length as logits.
    average_across_timesteps: Boolean
        If set, divide the returned cost by the total label weight.
    softmax_loss_function: None or Function
        Function (labels, logits) -> loss-batch to be used instead of the standard softmax (the default if this is None).
        **Note that to avoid confusion, it is required for the function to accept named arguments.**
    name: None or str
        Optional name for this operation, default: "sequence_loss_by_example".

    Returns
    -------
    1D batch-sized float Tensor: The log-perplexity for each sequence.

    Raises
    ------
    ValueError: If len(logits) is different from len(targets) or len(weights).

    """
    if len(targets) != len(logits) or len(weights) != len(logits):
        raise ValueError(
            "Lengths of logits, weights, and targets must be the same "
            "%d, %d, %d." % (len(logits), len(weights), len(targets))
        )
    with ops.name_scope(name, "sequence_loss_by_example", logits + targets + weights):
        log_perp_list = []
        for logit, target, weight in zip(logits, targets, weights):
            if softmax_loss_function is None:
                # TODO(irving,ebrevdo): This reshape is needed because
                # sequence_loss_by_example is called with scalars sometimes, which
                # violates our general scalar strictness policy.
                target = array_ops.reshape(target, [-1])
                crossent = nn_ops.sparse_softmax_cross_entropy_with_logits(labels=target, logits=logit)
            else:
                crossent = softmax_loss_function(labels=target, logits=logit)
            log_perp_list.append(crossent * weight)
    log_perps = math_ops.add_n(log_perp_list)
    if average_across_timesteps:
        total_size = math_ops.add_n(weights)
        total_size += 1e-12  # Just to avoid division by 0 for all-0 weights.
        log_perps /= total_size
    return log_perps


def cross_entropy_seq(logits, target_seqs, batch_size=None):
    """Returns the expression of cross-entropy of two sequences, implement
    softmax internally. Normally be used for fixed length RNN outputs, see `PTB example <https://github.com/tensorlayer/tensorlayer/blob/master/example/tutorial_ptb_lstm.py>`__.

    Parameters
    ----------
    logits : Tensor
        2D tensor with shape of `[batch_size * n_steps, n_classes]`.
    target_seqs : Tensor
        The target sequence, 2D tensor `[batch_size, n_steps]`, if the number of step is dynamic, please use ``tl.cost.cross_entropy_seq_with_mask`` instead.
    batch_size : None or int.
        Whether to divide the cost by batch size.
            - If integer, the return cost will be divided by `batch_size`.
            - If None (default), the return cost will not be divided by anything.

    Examples
    --------
    >>> import tensorlayer as tl
    >>> # see `PTB example <https://github.com/tensorlayer/tensorlayer/blob/master/example/tutorial_ptb_lstm.py>`__.for more details
    >>> # outputs shape : (batch_size * n_steps, n_classes)
    >>> # targets shape : (batch_size, n_steps)
    >>> cost = tl.cost.cross_entropy_seq(outputs, targets)

    """
    sequence_loss_by_example_fn = sequence_loss_by_example

    loss = sequence_loss_by_example_fn(
        [logits], [tf.reshape(target_seqs, [-1])], [tf.ones_like(tf.reshape(target_seqs, [-1]), dtype=tf.float32)]
    )
    # [tf.ones([batch_size * num_steps])])
    cost = tf.reduce_sum(loss)  # / batch_size
    if batch_size is not None:
        cost = cost / batch_size
    return cost


def cross_entropy_seq_with_mask(logits, target_seqs, input_mask, return_details=False, name=None):
    """Returns the expression of cross-entropy of two sequences, implement
    softmax internally. Normally be used for Dynamic RNN with Synced sequence input and output.

    Parameters
    -----------
    logits : Tensor
        2D tensor with shape of [batch_size * ?, n_classes], `?` means dynamic IDs for each example.
        - Can be get from `DynamicRNNLayer` by setting ``return_seq_2d`` to `True`.
    target_seqs : Tensor
        int of tensor, like word ID. [batch_size, ?], `?` means dynamic IDs for each example.
    input_mask : Tensor
        The mask to compute loss, it has the same size with `target_seqs`, normally 0 or 1.
    return_details : boolean
        Whether to return detailed losses.
            - If False (default), only returns the loss.
            - If True, returns the loss, losses, weights and targets (see source code).

    Examples
    --------
    >>> import tensorlayer as tl
    >>> import tensorflow as tf
    >>> import numpy as np
    >>> batch_size = 64
    >>> vocab_size = 10000
    >>> embedding_size = 256
    >>> ni = tl.layers.Input([batch_size, None], dtype=tf.int64)
    >>> net_lits = []
    >>> net_list.append(tl.layers.Embedding(
    ...         vocabulary_size = vocab_size,
    ...         embedding_size = embedding_size,
    ...         name = 'seq_embedding'))
    >>> net_list.append(tl.layers.RNN(
    ...         cell =tf.keras.layers.LSTMCell(units=embedding_size, dropout=0.1),
    ...         return_seq_2d = True,
    ...         name = 'dynamicrnn'))
    >>> net_list.append(tl.layers.Dense(n_units=vocab_size, name="output"))
    >>> model = tl.layers.SequentialLayer(net_list)
    >>> input_seqs = np.random.randint(0, 10, size=(batch_size, 10), dtype=np.int64)
    >>> target_seqs = np.random.randint(0, 10, size=(batch_size, 10), dtype=np.int64)
    >>> input_mask = np.random.randint(0, 2, size=(batch_size, 10), dtype=np.int64)
    >>> outputs = model(input_seqs)
    >>> loss = tl.cost.cross_entropy_seq_with_mask(outputs, target_seqs, input_mask)

    """
    targets = tf.reshape(target_seqs, [-1])  # to one vector
    weights = tf.cast(tf.reshape(input_mask, [-1]), dtype=tf.float32)  # to one vector like targets
    losses = tf.nn.sparse_softmax_cross_entropy_with_logits(logits=logits, labels=targets, name=name) * weights
    # losses = tf.reduce_mean(tf.ops.sparse_softmax_cross_entropy_with_logits(logits=logits, labels=targets, name=name)) # for TF1.0 and others

    loss = tf.divide(
        tf.reduce_sum(losses),  # loss from mask. reduce_sum before element-wise mul with mask !!
        tf.reduce_sum(weights),
        name="seq_loss_with_mask"
    )

    if return_details:
        return loss, losses, weights, targets
    else:
        return loss


def cosine_similarity(v1, v2):
    """Cosine similarity [-1, 1].

    Parameters
    ----------
    v1, v2 : Tensor
        Tensor with the same shape [batch_size, n_feature].

    References
    ----------
    - `Wiki <https://en.wikipedia.org/wiki/Cosine_similarity>`__.

    """

    return tf.reduce_sum(tf.multiply(v1, v2), 1) / \
        (tf.sqrt(tf.reduce_sum(tf.multiply(v1, v1), 1)) *
         tf.sqrt(tf.reduce_sum(tf.multiply(v2, v2), 1)))


# Regularization Functions
def li_regularizer(scale, scope=None):
    """Li regularization removes the neurons of previous layer. The `i` represents `inputs`.
    Returns a function that can be used to apply group li regularization to weights.
    The implementation follows `TensorFlow contrib <https://github.com/tensorflow/tensorflow/blob/master/tensorflow/contrib/layers/python/layers/regularizers.py>`__.

    Parameters
    ----------
    scale : float
        A scalar multiplier `Tensor`. 0.0 disables the regularizer.
    scope: str
        An optional scope name for this function.

    Returns
    --------
    A function with signature `li(weights, name=None)` that apply Li regularization.

    Raises
    ------
    ValueError : if scale is outside of the range [0.0, 1.0] or if scale is not a float.

    """
    if isinstance(scale, numbers.Integral):
        raise ValueError('scale cannot be an integer: %s' % scale)
    if isinstance(scale, numbers.Real):
        if scale < 0.:
            raise ValueError('Setting a scale less than 0 on a regularizer: %g' % scale)
        if scale >= 1.:
            raise ValueError('Setting a scale greater than 1 on a regularizer: %g' % scale)
        if scale == 0.:
            logging.info('Scale of 0 disables regularizer.')
            return lambda _, name=None: None

    def li(weights):
        """Applies li regularization to weights."""
        with tf.name_scope('li_regularizer') as scope:
            my_scale = ops.convert_to_tensor(scale, dtype=weights.dtype.base_dtype, name='scale')
            # if tf.__version__ <= '0.12':
            #     standard_ops_fn = standard_ops.mul
            # else:
            standard_ops_fn = standard_ops.multiply
            return standard_ops_fn(
                my_scale, standard_ops.reduce_sum(standard_ops.sqrt(standard_ops.reduce_sum(tf.square(weights), 1))),
                name=scope
            )

    return li


def lo_regularizer(scale):
    """Lo regularization removes the neurons of current layer. The `o` represents `outputs`
    Returns a function that can be used to apply group lo regularization to weights.
    The implementation follows `TensorFlow contrib <https://github.com/tensorflow/tensorflow/blob/master/tensorflow/contrib/layers/python/layers/regularizers.py>`__.

    Parameters
    ----------
    scale : float
        A scalar multiplier `Tensor`. 0.0 disables the regularizer.

    Returns
    -------
    A function with signature `lo(weights, name=None)` that apply Lo regularization.

    Raises
    ------
    ValueError : If scale is outside of the range [0.0, 1.0] or if scale is not a float.

    """
    if isinstance(scale, numbers.Integral):
        raise ValueError('scale cannot be an integer: %s' % scale)

    if isinstance(scale, numbers.Real):
        if scale < 0.:
            raise ValueError('Setting a scale less than 0 on a regularizer: %g' % scale)
        if scale >= 1.:
            raise ValueError('Setting a scale greater than 1 on a regularizer: %g' % scale)
        if scale == 0.:
            logging.info('Scale of 0 disables regularizer.')
            return lambda _, name=None: None

    def lo(weights, name='lo_regularizer'):
        """Applies group column regularization to weights."""
        with tf.name_scope(name) as scope:
            my_scale = ops.convert_to_tensor(scale, dtype=weights.dtype.base_dtype, name='scale')
            # if tf.__version__ <= '0.12':
            #     standard_ops_fn = standard_ops.mul
            # else:
            standard_ops_fn = standard_ops.multiply
            return standard_ops_fn(
                my_scale, standard_ops.reduce_sum(standard_ops.sqrt(standard_ops.reduce_sum(tf.square(weights), 0))),
                name=scope
            )

    return lo


def maxnorm_regularizer(scale=1.0):
    """Max-norm regularization returns a function that can be used to apply max-norm regularization to weights.

    More about max-norm, see `wiki-max norm <https://en.wikipedia.org/wiki/Matrix_norm#Max_norm>`_.
    The implementation follows `TensorFlow contrib <https://github.com/tensorflow/tensorflow/blob/master/tensorflow/contrib/layers/python/layers/regularizers.py>`__.

    Parameters
    ----------
    scale : float
        A scalar multiplier `Tensor`. 0.0 disables the regularizer.

    Returns
    ---------
    A function with signature `mn(weights, name=None)` that apply Lo regularization.

    Raises
    --------
    ValueError : If scale is outside of the range [0.0, 1.0] or if scale is not a float.

    """
    if isinstance(scale, numbers.Integral):
        raise ValueError('scale cannot be an integer: %s' % scale)

    if isinstance(scale, numbers.Real):
        if scale < 0.:
            raise ValueError('Setting a scale less than 0 on a regularizer: %g' % scale)
        # if scale >= 1.:
        #   raise ValueError('Setting a scale greater than 1 on a regularizer: %g' %
        #                    scale)
        if scale == 0.:
            logging.info('Scale of 0 disables regularizer.')
            return lambda _, name=None: None

    def mn(weights, name='max_regularizer'):
        """Applies max-norm regularization to weights."""
        with tf.name_scope(name) as scope:
            my_scale = ops.convert_to_tensor(scale, dtype=weights.dtype.base_dtype, name='scale')
            #   if tf.__version__ <= '0.12':
            #       standard_ops_fn = standard_ops.mul
            #   else:
            standard_ops_fn = standard_ops.multiply
            return standard_ops_fn(my_scale, standard_ops.reduce_max(standard_ops.abs(weights)), name=scope)

    return mn


def maxnorm_o_regularizer(scale):
    """Max-norm output regularization removes the neurons of current layer.
    Returns a function that can be used to apply max-norm regularization to each column of weight matrix.
    The implementation follows `TensorFlow contrib <https://github.com/tensorflow/tensorflow/blob/master/tensorflow/contrib/layers/python/layers/regularizers.py>`__.

    Parameters
    ----------
    scale : float
        A scalar multiplier `Tensor`. 0.0 disables the regularizer.

    Returns
    ---------
    A function with signature `mn_o(weights, name=None)` that apply Lo regularization.

    Raises
    ---------
    ValueError : If scale is outside of the range [0.0, 1.0] or if scale is not a float.

    """
    if isinstance(scale, numbers.Integral):
        raise ValueError('scale cannot be an integer: %s' % scale)

    if isinstance(scale, numbers.Real):
        if scale < 0.:
            raise ValueError('Setting a scale less than 0 on a regularizer: %g' % scale)
        # if scale >= 1.:
        #   raise ValueError('Setting a scale greater than 1 on a regularizer: %g' %
        #                    scale)
        if scale == 0.:
            logging.info('Scale of 0 disables regularizer.')
            return lambda _, name=None: None

    def mn_o(weights, name='maxnorm_o_regularizer'):
        """Applies max-norm regularization to weights."""
        with tf.name_scope(name) as scope:
            my_scale = ops.convert_to_tensor(scale, dtype=weights.dtype.base_dtype, name='scale')
            if tf.__version__ <= '0.12':
                standard_ops_fn = standard_ops.mul
            else:
                standard_ops_fn = standard_ops.multiply
            return standard_ops_fn(
                my_scale, standard_ops.reduce_sum(standard_ops.reduce_max(standard_ops.abs(weights), 0)), name=scope
            )

    return mn_o


def maxnorm_i_regularizer(scale):
    """Max-norm input regularization removes the neurons of previous layer.
    Returns a function that can be used to apply max-norm regularization to each row of weight matrix.
    The implementation follows `TensorFlow contrib <https://github.com/tensorflow/tensorflow/blob/master/tensorflow/contrib/layers/python/layers/regularizers.py>`__.

    Parameters
    ----------
    scale : float
        A scalar multiplier `Tensor`. 0.0 disables the regularizer.

    Returns
    ---------
    A function with signature `mn_i(weights, name=None)` that apply Lo regularization.

    Raises
    ---------
    ValueError : If scale is outside of the range [0.0, 1.0] or if scale is not a float.

    """
    if isinstance(scale, numbers.Integral):
        raise ValueError('scale cannot be an integer: %s' % scale)

    if isinstance(scale, numbers.Real):
        if scale < 0.:
            raise ValueError('Setting a scale less than 0 on a regularizer: %g' % scale)
        # if scale >= 1.:
        #   raise ValueError('Setting a scale greater than 1 on a regularizer: %g' %
        #                    scale)
        if scale == 0.:
            logging.info('Scale of 0 disables regularizer.')
            return lambda _, name=None: None

    def mn_i(weights, name='maxnorm_i_regularizer'):
        """Applies max-norm regularization to weights."""
        with tf.name_scope(name) as scope:
            my_scale = ops.convert_to_tensor(scale, dtype=weights.dtype.base_dtype, name='scale')
            if tf.__version__ <= '0.12':
                standard_ops_fn = standard_ops.mul
            else:
                standard_ops_fn = standard_ops.multiply
            return standard_ops_fn(
                my_scale, standard_ops.reduce_sum(standard_ops.reduce_max(standard_ops.abs(weights), 1)), name=scope
            )

    return mn_i


def huber_loss(
    output, target, is_mean=True, delta=1.0, dynamichuber=False, reverse=False, axis=-1, epsilon=0.00001, name=None
):
    """Huber Loss operation, see ``https://en.wikipedia.org/wiki/Huber_loss`` .
    Reverse Huber Loss operation, see  ''https://statweb.stanford.edu/~owen/reports/hhu.pdf''.
    Dynamic Reverse Huber Loss operation, see  ''https://arxiv.org/pdf/1606.00373.pdf''.

    Parameters
    ----------
    output : Tensor
        A distribution with shape: [batch_size, ....], (any dimensions).
    target : Tensor
        The target distribution, format the same with `output`.
    is_mean : boolean
        Whether compute the mean or sum for each example.
        - If True, use ``tf.reduce_mean`` to compute the loss between one target and predict data (default).
        - If False, use ``tf.reduce_sum``.
    delta: float
        The point where the huber loss function changes from a quadratic to linear.
    dynamichuber: boolean
        Whether compute the coefficient c for each batch.
        - If True, c is 20% of the maximal per-batch error.
        - If False, c is delta.
    reverse: boolean
        Whether compute the reverse huber loss.
    axis : int or list of int
        The dimensions to reduce.
    epsilon:
        Eplison.
    name : string
        Name of this loss.

    """
    if reverse:
        if dynamichuber:
            huber_c = 0.2 * tf.reduce_max(tf.abs(output - target))
        else:
            huber_c = delta
        if is_mean:
            loss = tf.reduce_mean(
                tf.where(
                    tf.less_equal(tf.abs(output - target), huber_c), tf.abs(output - target),
                    tf.multiply(
                        tf.pow(output - target, 2.0) + tf.pow(huber_c, 2.0),
                        tf.math.divide_no_nan(.5, huber_c + epsilon)
                    )
                ), name=name
            )
        else:
            loss = tf.reduce_mean(
                tf.reduce_sum(
                    tf.where(
                        tf.less_equal(tf.abs(output - target), huber_c), tf.abs(output - target),
                        tf.multiply(
                            tf.pow(output - target, 2.0) + tf.pow(huber_c, 2.0),
                            tf.math.divide_no_nan(.5, huber_c + epsilon)
                        )
                    ), axis
                ), name=name
            )
    elif is_mean:
        loss = tf.reduce_mean(
            tf.where(
                tf.less_equal(tf.abs(output - target), delta), 0.5 * tf.pow(output - target, 2),
                delta * (tf.abs(output - target) - 0.5 * delta)
            ), name=name
        )
    else:
        loss = tf.reduce_mean(
            tf.reduce_sum(
                tf.where(
                    tf.less_equal(tf.abs(output - target), delta), 0.5 * tf.pow(output - target, 2),
                    delta * (tf.abs(output - target) - 0.5 * delta)
                ), axis
            ), name=name
        )
    return loss