# Copyright 2016 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.
# ==============================================================================

import tensorflow as tf

from tensorflow_addons.utils import types


@tf.keras.utils.register_keras_serializable(package="Addons")
def sparsemax(logits: types.TensorLike, axis: int = -1) -> tf.Tensor:
    """Sparsemax activation function [1].

    For each batch `i` and class `j` we have
      $$sparsemax[i, j] = max(logits[i, j] - tau(logits[i, :]), 0)$$

    [1]: https://arxiv.org/abs/1602.02068

    Args:
        logits: Input tensor.
        axis: Integer, axis along which the sparsemax operation is applied.
    Returns:
        Tensor, output of sparsemax transformation. Has the same type and
        shape as `logits`.
    Raises:
        ValueError: In case `dim(logits) == 1`.
    """
    logits = tf.convert_to_tensor(logits, name="logits")

    # We need its original shape for shape inference.
    shape = logits.get_shape()
    rank = shape.rank
    is_last_axis = (axis == -1) or (axis == rank - 1)

    if is_last_axis:
        output = _compute_2d_sparsemax(logits)
        output.set_shape(shape)
        return output

    # If dim is not the last dimension, we have to do a transpose so that we can
    # still perform softmax on its last dimension.

    # Swap logits' dimension of dim and its last dimension.
    rank_op = tf.rank(logits)
    axis_norm = axis % rank
    logits = _swap_axis(logits, axis_norm, tf.math.subtract(rank_op, 1))

    # Do the actual softmax on its last dimension.
    output = _compute_2d_sparsemax(logits)
    output = _swap_axis(output, axis_norm, tf.math.subtract(rank_op, 1))

    # Make shape inference work since transpose may erase its static shape.
    output.set_shape(shape)
    return output


def _swap_axis(logits, dim_index, last_index, **kwargs):
    return tf.transpose(
        logits,
        tf.concat(
            [
                tf.range(dim_index),
                [last_index],
                tf.range(dim_index + 1, last_index),
                [dim_index],
            ],
            0,
        ),
        **kwargs,
    )


def _compute_2d_sparsemax(logits):
    """Performs the sparsemax operation when axis=-1."""
    shape_op = tf.shape(logits)
    obs = tf.math.reduce_prod(shape_op[:-1])
    dims = shape_op[-1]

    # In the paper, they call the logits z.
    # The mean(logits) can be substracted from logits to make the algorithm
    # more numerically stable. the instability in this algorithm comes mostly
    # from the z_cumsum. Substacting the mean will cause z_cumsum to be close
    # to zero. However, in practise the numerical instability issues are very
    # minor and substacting the mean causes extra issues with inf and nan
    # input.
    # Reshape to [obs, dims] as it is almost free and means the remanining
    # code doesn't need to worry about the rank.
    z = tf.reshape(logits, [obs, dims])

    # sort z
    z_sorted, _ = tf.nn.top_k(z, k=dims)

    # calculate k(z)
    z_cumsum = tf.math.cumsum(z_sorted, axis=-1)
    k = tf.range(1, tf.cast(dims, logits.dtype) + 1, dtype=logits.dtype)
    z_check = 1 + k * z_sorted > z_cumsum
    # because the z_check vector is always [1,1,...1,0,0,...0] finding the
    # (index + 1) of the last `1` is the same as just summing the number of 1.
    k_z = tf.math.reduce_sum(tf.cast(z_check, tf.int32), axis=-1)

    # calculate tau(z)
    # If there are inf values or all values are -inf, the k_z will be zero,
    # this is mathematically invalid and will also cause the gather_nd to fail.
    # Prevent this issue for now by setting k_z = 1 if k_z = 0, this is then
    # fixed later (see p_safe) by returning p = nan. This results in the same
    # behavior as softmax.
    k_z_safe = tf.math.maximum(k_z, 1)
    indices = tf.stack([tf.range(0, obs), tf.reshape(k_z_safe, [-1]) - 1], axis=1)
    tau_sum = tf.gather_nd(z_cumsum, indices)
    tau_z = (tau_sum - 1) / tf.cast(k_z, logits.dtype)

    # calculate p
    p = tf.math.maximum(tf.cast(0, logits.dtype), z - tf.expand_dims(tau_z, -1))
    # If k_z = 0 or if z = nan, then the input is invalid
    p_safe = tf.where(
        tf.expand_dims(
            tf.math.logical_or(tf.math.equal(k_z, 0), tf.math.is_nan(z_cumsum[:, -1])),
            axis=-1,
        ),
        tf.fill([obs, dims], tf.cast(float("nan"), logits.dtype)),
        p,
    )

    # Reshape back to original size
    p_safe = tf.reshape(p_safe, shape_op)
    return p_safe
