model_utils.py

import numpy as np
import matplotlib.pyplot as plt

def tanh(x):
    return np.tanh(x)

def relu(x):
    return np.maximum(x, 0)

def sigmoid(x):
    return 1/(1 + np.exp(-x))

def derivative_tanh(x):
    return (1 - np.power(x, 2))

def derivative_relu(x):
    return np.array(x > 0, dtype = np.float32)

def initialize_parameters(layer_dims):

    np.random.seed(3)
    parameters = {}
    L = len(layer_dims)
    
    for l in range(1, L):
        parameters['W' + str(l)] = np.random.randn(layer_dims[l], layer_dims[l-1]) / np.sqrt(layer_dims[l-1])
        parameters['b' + str(l)] = np.zeros((layer_dims[l], 1))
        
        assert(parameters['W' + str(l)].shape == (layer_dims[l], layer_dims[l-1]))
        assert(parameters['b' + str(l)].shape == (layer_dims[l], 1))
        
    return parameters

def forward_propagation(X, parameters):
    W1 = parameters["W1"]
    b1 = parameters["b1"]
    W2 = parameters["W2"]
    b2 = parameters["b2"]
    W3 = parameters["W3"]
    b3 = parameters["b3"]
    
    Z1 = np.dot(W1, X) + b1
    A1 = relu(Z1)
        
    Z2 = np.dot(W2, A1) + b2
    A2 = relu(Z2)
    
    Z3 = np.dot(W3, A2) + b3
    A3 = sigmoid(Z3)
    
    cache = (Z1, A1, W1, b1, Z2, A2, W2, b2, Z3, A3, W3, b3)
    
    return A3, cache


def cost_function(A3, Y):
    m = Y.shape[1]
    
    cost = - 1./m * np.sum(Y*np.log(A3) + (1 - Y)*(np.log(1 - A3)))
    
    return cost


def backward_propagation(X, Y, cache):
    
    m = X.shape[1]
    (Z1, A1, W1, b1, Z2, A2, W2, b2, Z3, A3, W3, b3) = cache
    
    dZ3 = A3 - Y
    dW3 = 1./m * np.dot(dZ3, A2.T)
    db3 = 1./m * np.sum(dZ3, axis=1, keepdims = True)
    
    dA2 = np.dot(W3.T, dZ3)
    dZ2 = np.multiply(dA2, np.int64(A2 > 0))
    dW2 = 1./m * np.dot(dZ2, A1.T)
    db2 = 1./m * np.sum(dZ2, axis=1, keepdims = True)
    
    dA1 = np.dot(W2.T, dZ2)
    dZ1 = np.multiply(dA1, np.int64(A1 > 0))
    dW1 = 1./m * np.dot(dZ1, X.T)
    db1 = 1./m * np.sum(dZ1, axis=1, keepdims = True)
    
    gradients = {"dZ3": dZ3, "dW3": dW3, "db3": db3,
                 "dA2": dA2, "dZ2": dZ2, "dW2": dW2, "db2": db2,
                 "dA1": dA1, "dZ1": dZ1, "dW1": dW1, "db1": db1}
    
    return gradients


def update_parameters(parameters, grads, learning_rate):    
    n = len(parameters) // 2

    for k in range(n):
        parameters["W" + str(k+1)] = parameters["W" + str(k+1)] - learning_rate * grads["dW" + str(k+1)]
        parameters["b" + str(k+1)] = parameters["b" + str(k+1)] - learning_rate * grads["db" + str(k+1)]
        
    return parameters


def accuracy(X, Y, parameters, dataset_type):
    
    A, _ = forward_propagation(X, parameters)

    A = A > 0.5
    
    A = np.array(A, dtype = 'int64')
    
    acc = (1 - np.sum(np.absolute(A - Y))/Y.shape[1])*100
    
    print("Accuracy of the model on " + dataset_type + " dataset is : ", round(acc, 2), "%")
    
    
def predict_dec(parameters, X):
    a3, cache = forward_propagation(X, parameters)
    predictions = (a3>0.5)
    return predictions


def plot_decision_boundary(model, X, y):
    # Set min and max values and give it some padding
    x_min, x_max = X[0, :].min() - 1, X[0, :].max() + 1
    y_min, y_max = X[1, :].min() - 1, X[1, :].max() + 1
    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 grid
    Z = model(np.c_[xx.ravel(), yy.ravel()])
    Z = Z.reshape(xx.shape)
    # Plot the contour and training examples
    
    axes = plt.gca()
    axes.set_xlim([-0.75, 0.40])
    axes.set_ylim([-0.75, 0.65])
    plt.contourf(xx, yy, Z, cmap='twilight')
    plt.ylabel('x2')
    plt.xlabel('x1')
    plt.scatter(X[0, :], X[1, :], c=y, cmap='inferno')
    plt.show()