import matplotlib.pyplot as plt
import numpy as np
import sklearn
import sklearn.datasets
import sklearn.linear_model
import matplotlib

def plot_decision_boundary(pred_func):
	# Set min and max values and give it some padding
	x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5
	y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5
	h = 0.01
	# Generate a grid of points with distance h between them
	xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
	# Predict the function value for the whole gid
	Z = pred_func(np.c_[xx.ravel(), yy.ravel()])
	Z = Z.reshape(xx.shape)
	# Plot the contour and training examples
	plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral)
	plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Spectral)

# Helper function to evaluate the total loss on the dataset
def calculate_loss(model):
	W1, b1, W2, b2 = model['W1'], model['b1'], model['W2'], model['b2']
	# Forward propagation to calculate our predictions
	z1 = X.dot(W1) + b1
	a1 = np.tanh(z1)
	z2 = a1.dot(W2) + b2
	exp_scores = np.exp(z2)
	probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)
	# Calculating the loss
	corect_logprobs = -np.log(probs[range(num_examples), y])
	data_loss = np.sum(corect_logprobs)
	# Add regulatization term to loss (optional)
	data_loss += reg_lambda/2 * (np.sum(np.square(W1)) + np.sum(np.square(W2)))
	return 1./num_examples * data_loss

def predict(model, x):
	W1, b1, W2, b2 = model['W1'], model['b1'], model['W2'], model['b2']
	# Forward propagation
	z1 = x.dot(W1) + b1
	a1 = np.tanh(z1)
	z2 = a1.dot(W2) + b2
	exp_scores = np.exp(z2)
	probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)
	return np.argmax(probs, axis=1)

def build_model(nn_hdim, num_passes=20000, print_loss=False):
	# Initialize the parameters to random values. We need to learn these.
	np.random.seed(0)
	W1 = np.random.randn(nn_input_dim, nn_hdim) / np.sqrt(nn_input_dim)
	b1 = np.zeros((1, nn_hdim))
	W2 = np.random.randn(nn_hdim, nn_output_dim) / np.sqrt(nn_hdim)
	b2 = np.zeros((1, nn_output_dim))

	# This is what we return at the end
	model = {}

	# Gradient descent. For each batch...
	for i in xrange(0, num_passes):
		# Forward propagation
		z1 = X.dot(W1) + b1
		a1 = np.tanh(z1)
		z2 = a1.dot(W2) + b2
		exp_scores = np.exp(z2)
		probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)
		# Backpropagation
		delta3 = probs
		delta3[range(num_examples), y] -= 1
		dW2 = (a1.T).dot(delta3)
		db2 = np.sum(delta3, axis=0, keepdims=True)
		delta2 = delta3.dot(W2.T) * (1 - np.power(a1, 2))
		dW1 = np.dot(X.T, delta2)
		db1 = np.sum(delta2, axis=0)
		# Add regularization terms (b1 and b2 don't have regularization terms)
		dW2 += reg_lambda * W2
		dW1 += reg_lambda * W1
		# Gradient descent parameter update
		W1 += -epsilon * dW1
		b1 += -epsilon * db1
		W2 += -epsilon * dW2
		b2 += -epsilon * db2
		# Assign new parameters to the model
		model = { 'W1': W1, 'b1': b1, 'W2': W2, 'b2': b2}
		# Optionally print the loss.
		# This is expensive because it uses the whole dataset, so we don't want to do it too often.
		if print_loss and i % 1000 == 0:
			print "Loss after iteration %i: %f" %(i, calculate_loss(model))
	return model

np.random.seed(0)
X, y = sklearn.datasets.make_moons(200, noise=0.20)
plt.scatter(X[:,0], X[:,1], s=40, c=y, cmap=plt.cm.Spectral)

clf = sklearn.linear_model.LogisticRegressionCV()
clf.fit(X, y)

num_examples = len(X) # training set size
nn_input_dim = 2 # input layer dimensionality
nn_output_dim = 2 # output layer dimensionality

# Gradient descent parameters (I picked these by hand)
epsilon = 0.01 # learning rate for gradient descent
reg_lambda = 0.01 # regularization strength

# Build a model with a 3-dimensional hidden layer
model = build_model(3, print_loss=True)

# Plot the decision boundary
plot_decision_boundary(lambda X: predict(model, X))
plt.title("Decision Boundary for hidden layer size 3")
plt.figure(figsize=(16, 32))
hidden_layer_dimensions = [1, 2, 3, 4, 5, 20, 50]
for i, nn_hdim in enumerate(hidden_layer_dimensions):
	plt.subplot(5, 2, i+1)
	plt.title('Hidden Layer size %d' % nn_hdim)
	model = build_model(nn_hdim)
	plot_decision_boundary(lambda X: predict(model, X))
plt.show()