from __future__ import print_function

import numpy as np
import matplotlib.pyplot as plt


class TwoLayerNet(object):
    """
    A two-layer fully-connected neural network. The net has an input dimension
    of N, a hidden layer dimension of H, and performs classification over C 
    classes.
    We train the network with a softmax loss function and L2 regularization on
    the weight matrices. The network uses a ReLU nonlinearity after the first
    fully connected layer.
    In other words, the network has the following architecture:
    input - fully connected layer - ReLU - fully connected layer - softmax
    The outputs of the second fully-connected layer are the scores for each
    class.
    """

    def __init__(self, input_size, hidden_size, output_size, std=1e-4):
        """
        Initialize the model. Weights are initialized to small random values
        and biases are initialized to zero. Weights and biases are stored in
        the variable self.params, which is a dictionary with the following keys
        W1: First layer weights; has shape (D, H)
        b1: First layer biases; has shape (H,)
        W2: Second layer weights; has shape (H, C)
        b2: Second layer biases; has shape (C,)
        Inputs:
        - input_size: The dimension D of the input data.
        - hidden_size: The number of neurons H in the hidden layer.
        - output_size: The number of classes C.
        """
        self.params = {}
        self.params['W1'] = std * np.random.randn(input_size, hidden_size)
        self.params['b1'] = np.zeros(hidden_size)
        self.params['W2'] = std * np.random.randn(hidden_size, output_size)
        self.params['b2'] = np.zeros(output_size)

    def loss(self, X, y=None, reg=0.0):
        """
        Compute the loss and gradients for a two layer fully connected neural
        network.
        Inputs:
        - X: Input data of shape (N, D). Each X[i] is a training sample.
        - y: Vector of training labels. y[i] is the label for X[i], and each
          y[i] is an integer in the range 0 <= y[i] < C. This parameter is
          optional; if it is not passed then we only return scores, and if it
          is passed then we instead return the loss and gradients.
        - reg: Regularization strength.
        Returns:
        If y is None, return a matrix scores of shape (N, C) where scores[i, c]
        is the score for class c on input X[i].
        If y is not None, instead return a tuple of:
        - loss: Loss (data loss and regularization loss) for this batch of
          training samples.
        - grads: Dictionary mapping parameter names to gradients of those
          parameters with respect to the loss function; has the same keys as
          self.params.
        """
        # Unpack variables from the params dictionary
        W1, b1 = self.params['W1'], self.params['b1']
        W2, b2 = self.params['W2'], self.params['b2']
        N, D = X.shape

        # Compute the forward pass
        scores = None
        #######################################################################
        # TODO: Perform the forward pass, computing the class scores for the  #
        # input. Store the result in the scores variable, which should be an  #
        # array of shape (N, C).                                              #
        #######################################################################

        scores1 = X.dot(W1) + b1  # FC1
        X2 = np.maximum(0, scores1)  # ReLU FC1

        scores = X2.dot(W2) + b2  # FC2

        #######################################################################
        #                              END OF YOUR CODE                       #
        #######################################################################

        # If the targets are not given then jump out, we're done
        if y is None:
            return scores

        scores -= np.max(scores)  # Fix Number instability
        scores_exp = 
np.exp(scores)