import numpy as np
import random

class Network(object):
  def __init__(self, sizes):
    self.num_layers = len(sizes)
    self.sizes = sizes
    # starts off after the first layer
    # each layer has a single bias per neuron
    self.biases = [np.random.randn(y, 1) for y in sizes[1:]]
    # has y connections for the x number of neurons in each layer
    self.weights = [np.random.randn(y, x) for x, y in zip(sizes[:-1], sizes[1:])] 
    # constructs matrix of weights


  def feedforward(self, a):
    """Return the output of the network if "a" is input."""
    for b, w in zip(self.biases, self.weights):
      a = sigmoid(np.dot(w, a) + b)
    # a bias vector is correlated with a weight matrix at each layer
    return a

  def SGD(self, training_data, epochs, mini_batch_size, eta, test_data=None):
    """Train the neural network using mini-batch stochastic gradient descent. The "training_data" is a list of tuples "(x, y)" representing the training inputs and the desired outputs. The other non-optional parameters are self-explanatory. If "test_data" is provided then the network will be evaluated against the test data after each epoch, and partial progress printed out. This is useful for tracking progress, but slows things down substantially.)"""
    if test_data:
      n_test = len(test_data)
    n = len(training_data)
    for j in range(epochs):
      random.shuffle(training_data)
      mini_batches = [training_data[k:k+mini_batch_size] for k in range(0,n,mini_batch_size)]
      for mini_batch in mini_batches:
        self.update_mini_batch(mini_batch, eta)
    if test_data:
      print("Epoch {0}: {1} / {2}".format(j, self.evaluate(test_data), n_test))
    else:
      print("Epoch {0} complete".format(j))

  def update_mini_batch(self, mini_batch, eta):
    """Update the network's weights and biases by applying gradient descent using backpropagation to a single mini batch. The "mini_batch" is a list of tuples "(x, y)", and "eta" is the learning rate."""
    nabla_b = [np.zeros(b.shape) for b in self.biases]
    nabla_w = [np.zeros(w.shape) for w in self.weights]
    for x, y in mini_batch:
      delta_nabla_b, delta_nabla_w = self.backprop(x, y)
      nabla_b = [nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)]
      nabla_w = [nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)]
    self.weights = [w-(eta/len(mini_batch))*nw for w, nw in zip(self.weights, nabla_w)]
    self.biases = [b-(eta/len(mini_batch))*nb for b, nb in zip(self.biases, nabla_b)]

  def backprop(self, x, y):
    """Return a tuple ''(nabla_b, nabla_w)'' representing the gradient for the cost function C_x. ''nabla_b'' and ''nabla_w'' are layer-by-layer lists of numpy arrays, similar to ''self.biases'' and ''self.weights''."""
    nabla_b = [np.zeros(b.shape) for b in self.biases]
    nabla_w = [np.zeros(w.shape) for w in self.weights]
    # feedforward
    activation = x
    activations = [x] # list to store all the activations, layer by layer
    zs = [] # list to store all the z vectors, layer by layer
    for b, w in zip(self.biases, self.weights):
      z = np.dot(w, activation) + b
      zs.append(z)
      activation = sigmoid(z)
      activations.append(activation)
    # backward pass
    delta = self.cost_derivative(activations[-1], y) * sigmoid_prime(zs[-1])
    nabla_b[-1] = delta
    nabla_w[-1] = np.dot(delta, activations[-2].transpose())
    # l = 1 denotes the last layer, l = 2 denotes second last, etc.
    for l in range(2, self.num_layers):
      z = zs[-l]
      sp = sigmoid_prime(z)
      delta = np.dot(self.weights[-l+1].transpose(), delta) * sp
      nabla_b[-l] = delta
      nabla_w[-l] = np.dot(delta, activations[-l-1].transpose())
    return (nabla_b, nabla_w)


  def evaluate(self, test_data):
    """Return the number of test inputs for which the neural network outputs the correct result. Note that the neural network's output is assumed to be the index of whichever neuron in the final layer has the highest activation.'"""
    test_results = [(np.argmax(self.feedforward(x)), y) for (x, y) in test_data]
    return sum(int(x == y) for (x, y) in test_results)

  def cost_derivative(self, output_activations, y):
    """Return the vector of partial derivatives 'partial C_x / partial a' for the output activations."""
    return (output_activations - y)

def sigmoid(z):
  return 1.0/(1.0+np.exp(-z))

def sigmoid_prime(z):
  return sigmoid(z)*(1-sigmoid(z))


if __name__ == '__main__':
  net = Network([2,3,1])