\

# Standard library
import random

# Third-party libraries
import numpy as np

class Network(object):
    def __init__(self,sizes): #the list sizes contains the number of neurons in the respective layers.
        self.num_layers = len(sizes)  #the number of the layers in Network
        self.sizes = sizes
        self.biases = [np.random.randn(y,1) for y in sizes[1:]]
        self.weights = [np.random.randn(y,x) 
   				for x,y in zip(sizes[:-1],sizes[1:])]
   
    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)		
       	return a
   	
    def SGD(self, training_data, training_labels, epochs, mini_batch_size,eta,
            test_data = None, test_labels=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 output. 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
        process, but slows things down substantially.
        """
        tr_data = []
        for i in range(0,training_data.shape[1]):
            label = np.zeros((2,1))
            label[int(training_labels[i])] = 1
            tr_data.append((training_data[:,i], label))
        training_data = tr_data
        ts_data = []
        for i in range(0,test_data.shape[1]):
            ts_data.append((test_data[:,i], test_labels[i]))
        test_data = ts_data
       # print(test_data)
        print("Reformatted data")
        if test_data: 
            n_test = len(test_data)
            n = len(training_data)
            for j in range(epochs):
                random.shuffle(training_data)        #rearrange the training_data randomly
                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())
       # Note that the variable l in the loop below is used a little
       # differently to the notation in Chapter 2 of the book.  Here,
       # l = 1 means the last layer of neurons, l = 2 is the
       # second-last layer, and so on.  It's a renumbering of the
       # scheme in the book, used here to take advantage of the fact
       # that Python can use negative indices in lists.
    	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]
        print(self.feedforward(test_data[0][0]))
        print(np.argmax(self.feedforward(test_data[0][0])))
        print(test_results[0:10])
        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)
    	
#### Miscellaneous functions
def sigmoid(z):
    """The sigmoid function."""
    return 1.0/(1.0+np.exp(-z))

def sigmoid_prime(z):
    """Derivative of the sigmoid function."""
    return sigmoid(z)*(1-sigmoid(z))