"""Utilities for the neural network modules
"""

# Author: Issam H. Laradji <issam.laradji@gmail.com>
# License: BSD 3 clause

import numpy as np

from scipy.special import expit as logistic_sigmoid
from scipy.special import xlogy


def identity(X):
    """Simply return the input array.

    Parameters
    ----------
    X : {array-like, sparse matrix}, shape (n_samples, n_features)
        Data, where n_samples is the number of samples
        and n_features is the number of features.

    Returns
    -------
    X : {array-like, sparse matrix}, shape (n_samples, n_features)
        Same as the input data.
    """
    return X


def logistic(X):
    """Compute the logistic function inplace.

    Parameters
    ----------
    X : {array-like, sparse matrix}, shape (n_samples, n_features)
        The input data.

    Returns
    -------
    X_new : {array-like, sparse matrix}, shape (n_samples, n_features)
        The transformed data.
    """
    return logistic_sigmoid(X, out=X)


def tanh(X):
    """Compute the hyperbolic tan function inplace.

    Parameters
    ----------
    X : {array-like, sparse matrix}, shape (n_samples, n_features)
        The input data.

    Returns
    -------
    X_new : {array-like, sparse matrix}, shape (n_samples, n_features)
        The transformed data.
    """
    return np.tanh(X, out=X)


def relu(X):
    """Compute the rectified linear unit function inplace.

    Parameters
    ----------
    X : {array-like, sparse matrix}, shape (n_samples, n_features)
        The input data.

    Returns
    -------
    X_new : {array-like, sparse matrix}, shape (n_samples, n_features)
        The transformed data.
    """
    np.clip(X, 0, np.finfo(X.dtype).max, out=X)
    return X


def softmax(X):
    """Compute the K-way softmax function inplace.

    Parameters
    ----------
    X : {array-like, sparse matrix}, shape (n_samples, n_features)
        The input data.

    Returns
    -------
    X_new : {array-like, sparse matrix}, shape (n_samples, n_features)
        The transformed data.
    """
    tmp = X - X.max(axis=1)[:, np.newaxis]
    np.exp(tmp, out=X)
    X /= X.sum(axis=1)[:, np.newaxis]

    return X


ACTIVATIONS = {'identity': identity, 'tanh': tanh, 'logistic': logistic,
               'relu': relu, 'softmax': softmax}


def inplace_identity_derivative(Z, delta):
    """Apply the derivative of the identity function: do nothing.

    Parameters
    ----------
    Z : {array-like, sparse matrix}, shape (n_samples, n_features)
        The data which was output from the identity activation function during
        the forward pass.

    delta : {array-like}, shape (n_samples, n_features)
         The backpropagated error signal to be modified inplace.
    """
    # Nothing to do


def inplace_logistic_derivative(Z, delta):
    """Apply the derivative of the logistic sigmoid function.

    It exploits the fact that the derivative is a simple function of the output
    value from logistic function.

    Parameters
    ----------
    Z : {array-like, sparse matrix}, shape (n_samples, n_features)
        The data which was output from the logistic activation function during
        the forward pass.

    delta : {array-like}, shape (n_samples, n_features)
         The backpropagated error signal to be modified inplace.
    """
    delta *= Z
    delta *= (1 - Z)


def inplace_tanh_derivative(Z, delta):
    """Apply the derivative of the hyperbolic tanh function.

    It exploits the fact that the derivative is a simple function of the output
    value from hyperbolic tangent.

    Parameters
    ----------
    Z : {array-like, sparse matrix}, shape (n_samples, n_features)
        The data which was output from the hyperbolic tangent activation
        function during the forward pass.

    delta : {array-like}, shape (n_samples, n_features)
         The backpropagated error signal to be modified inplace.
    """
    delta *= (1 - Z ** 2)


def inplace_relu_derivative(Z, delta):
    """Apply the derivative of the relu function.

    It exploits the fact that the derivative is a simple function of the output
    value from rectified linear units activation function.

    Parameters
    ----------
    Z : {array-like, sparse matrix}, shape (n_samples, n_features)
        The data which was output from the rectified linear units activation
        function during the forward pass.

    delta : {array-like}, shape (n_samples, n_features)
         The backpropagated error signal to be modified inplace.
    """
    delta[Z == 0] = 0


DERIVATIVES = {'identity': inplace_identity_derivative,
               'tanh': inplace_tanh_derivative,
               'logistic': inplace_logistic_derivative,
               'relu': inplace_relu_derivative}


def squared_loss(y_true, y_pred):
    """Compute the squared loss for regression.

    Parameters
    ----------
    y_true : array-like or label indicator matrix
        Ground truth (correct) values.

    y_pred : array-like or label indicator matrix
        Predicted values, as returned by a regression estimator.

    Returns
    -------
    loss : float
        The degree to which the samples are correctly predicted.
    """
    return ((y_true - y_pred) ** 2).mean() / 2


def log_loss(y_true, y_prob):
    """Compute Logistic loss for classification.

    Parameters
    ----------
    y_true : array-like or label indicator matrix
        Ground truth (correct) labels.

    y_prob : array-like of float, shape = (n_samples, n_classes)
        Predicted probabilities, as returned by a classifier's
        predict_proba method.

    Returns
    -------
    loss : float
        The degree to which the samples are correctly predicted.
    """
    if y_prob.shape[1] == 1:
        y_prob = np.append(1 - y_prob, y_prob, axis=1)

    if y_true.shape[1] == 1:
        y_true = np.append(1 - y_true, y_true, axis=1)

    return - xlogy(y_true, y_prob).sum() / y_prob.shape[0]


def binary_log_loss(y_true, y_prob):
    """Compute binary logistic loss for classification.

    This is identical to log_loss in binary classification case,
    but is kept for its use in multilabel case.

    Parameters
    ----------
    y_true : array-like or label indicator matrix
        Ground truth (correct) labels.

    y_prob : array-like of float, shape = (n_samples, n_classes)
        Predicted probabilities, as returned by a classifier's
        predict_proba method.

    Returns
    -------
    loss : float
        The degree to which the samples are correctly predicted.
    """
    return -(xlogy(y_true, y_prob) +
             xlogy(1 - y_true, 1 - y_prob)).sum() / y_prob.shape[0]


LOSS_FUNCTIONS = {'squared_loss': squared_loss, 'log_loss': log_loss,
                  'binary_log_loss': binary_log_loss}