NN Optimization.py

'''
Usage of TensorFlow version 1.
Doesnt work with latest verion of TensorFlow 2.
'''



import numpy as np
import matplotlib.pyplot as plt
import h5py
import math
import scipy.io
import sklearn
import sklearn.datasets


figures = []
fig_count = 1


plt.rcParams['figure.figsize'] = (7.0, 4.0) # set default size of plots
plt.rcParams['image.interpolation'] = 'nearest'
plt.rcParams['image.cmap'] = 'gray'

##################################################################################################################################

def sigmoid(x):
    """
    Compute the sigmoid of x

    Arguments:
    x -- A scalar or numpy array of any size.

    Return:
    s -- sigmoid(x)
    """
    s = 1 / (1 + np.exp(-x))
    return s


def relu(x):
    """
    Compute the relu of x

    Arguments:
    x -- A scalar or numpy array of any size.

    Return:
    s -- relu(x)
    """
    s = np.maximum(0, x)

    return s


def load_params_and_grads(seed=1):
    np.random.seed(seed)
    W1 = np.random.randn(2, 3)
    b1 = np.random.randn(2, 1)
    W2 = np.random.randn(3, 3)
    b2 = np.random.randn(3, 1)

    dW1 = np.random.randn(2, 3)
    db1 = np.random.randn(2, 1)
    dW2 = np.random.randn(3, 3)
    db2 = np.random.randn(3, 1)

    return W1, b1, W2, b2, dW1, db1, dW2, db2


def initialize_parameters(layer_dims):
    """
    Arguments:
    layer_dims -- python array (list) containing the dimensions of each layer in our network

    Returns:
    parameters -- python dictionary containing your parameters "W1", "b1", ..., "WL", "bL":
                    W1 -- weight matrix of shape (layer_dims[l], layer_dims[l-1])
                    b1 -- bias vector of shape (layer_dims[l], 1)
                    Wl -- weight matrix of shape (layer_dims[l-1], layer_dims[l])
                    bl -- bias vector of shape (1, layer_dims[l])

    Tips:
    - For example: the layer_dims for the "Planar Data classification model" would have been [2,2,1].
    This means W1's shape was (2,2), b1 was (1,2), W2 was (2,1) and b2 was (1,1). Now you have to generalize it!
    - In the for loop, use parameters['W' + str(l)] to access Wl, where l is the iterative integer.
    """

    np.random.seed(3)
    parameters = {}
    L = len(layer_dims)  # number of layers in the network

    for l in range(1, L):
        parameters['W' + str(l)] = np.random.randn(layer_dims[l], layer_dims[l - 1]) * np.sqrt(2 / layer_dims[l - 1])
        parameters['b' + str(l)] = np.zeros((layer_dims[l], 1))

        assert parameters['W' + str(l)].shape[0] == layer_dims[l], layer_dims[l - 1]
        assert parameters['W' + str(l)].shape[0] == layer_dims[l], 1

    return parameters


def compute_cost(a3, Y):
    """
    Implement the cost function

    Arguments:
    a3 -- post-activation, output of forward propagation
    Y -- "true" labels vector, same shape as a3

    Returns:
    cost - value of the cost function without dividing by number of training examples

    Note:
    This is used with mini-batches,
    so we'll first accumulate costs over an entire epoch
    and then divide by the m training examples
    """

    logprobs = np.multiply(-np.log(a3), Y) + np.multiply(-np.log(1 - a3), 1 - Y)
    cost_total = np.sum(logprobs)

    return cost_total


def forward_propagation(X, parameters):
    """
    Implements the forward propagation (and computes the loss) presented in Figure 2.

    Arguments:
    X -- input dataset, of shape (input size, number of examples)
    parameters -- python dictionary containing your parameters "W1", "b1", "W2", "b2", "W3", "b3":
                    W1 -- weight matrix of shape ()
                    b1 -- bias vector of shape ()
                    W2 -- weight matrix of shape ()
                    b2 -- bias vector of shape ()
                    W3 -- weight matrix of shape ()
                    b3 -- bias vector of shape ()

    Returns:
    loss -- the loss function (vanilla logistic loss)
    """

    # retrieve parameters
    W1 = parameters["W1"]
    b1 = parameters["b1"]
    W2 = parameters["W2"]
    b2 = parameters["b2"]
    W3 = parameters["W3"]
    b3 = parameters["b3"]

    # LINEAR -> RELU -> LINEAR -> RELU -> LINEAR -> SIGMOID
    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 backward_propagation(X, Y, cache):
    """
    Implement the backward propagation presented in figure 2.

    Arguments:
    X -- input dataset, of shape (input size, number of examples)
    Y -- true "label" vector (containing 0 if cat, 1 if non-cat)
    cache -- cache output from forward_propagation()

    Returns:
    gradients -- A dictionary with the gradients with respect to each parameter, activation and pre-activation variables
    """
    m = X.shape[1]
    (z1, a1, W1, b1, z2, a2, W2, b2, z3, a3, W3, b3) = cache

    dz3 = 1. / m * (a3 - Y)
    dW3 = np.dot(dz3, a2.T)
    db3 = np.sum(dz3, axis=1, keepdims=True)

    da2 = np.dot(W3.T, dz3)
    dz2 = np.multiply(da2, np.int64(a2 > 0))
    dW2 = np.dot(dz2, a1.T)
    db2 = np.sum(dz2, axis=1, keepdims=True)

    da1 = np.dot(W2.T, dz2)
    dz1 = np.multiply(da1, np.int64(a1 > 0))
    dW1 = np.dot(dz1, X.T)
    db1 = 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 predict(X, y, parameters):
    """
    This function is used to predict the results of a  n-layer neural network.

    Arguments:
    X -- data set of examples you would like to label
    parameters -- parameters of the trained model

    Returns:
    p -- predictions for the given dataset X
    """

    m = X.shape[1]
    p = np.zeros((1, m), dtype=np.int)

    # Forward propagation
    a3, caches = forward_propagation(X, parameters)

    # convert probas to 0/1 predictions
    for i in range(0, a3.shape[1]):
        if a3[0, i] > 0.5:
            p[0, i] = 1
        else:
            p[0, i] = 0

    # print results

    # print ("predictions: " + str(p[0,:]))
    # print ("true labels: " + str(y[0,:]))
    print("Accuracy: " + str(np.mean((p[0, :] == y[0, :]))))

    return p


def load_2D_dataset():
    global figures, fig_count
    data = scipy.io.loadmat('datasets/data.mat')
    train_X = data['X'].T
    train_Y = data['y'].T
    test_X = data['Xval'].T
    test_Y = data['yval'].T

    figures.append(plt.figure(fig_count))
    fig_count += 1

    plt.scatter(train_X[0, :], train_X[1, :], c=train_Y, s=40, cmap=plt.cm.Spectral)

    figures[fig_count - 2].show()

    return train_X, train_Y, test_X, test_Y


def plot_decision_boundary(model, X, y, custom_plot=1):
    global figures, fig_count
    # 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
    if custom_plot == 1:
        figures.append(plt.figure(fig_count))
        fig_count += 1

    plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral)
    plt.ylabel('x2')
    plt.xlabel('x1')
    plt.scatter(X[0, :], X[1, :], c=y, cmap=plt.cm.Spectral)

    figures[fig_count - 2].show()


def predict_dec(parameters, X):
    """
    Used for plotting decision boundary.

    Arguments:
    parameters -- python dictionary containing your parameters
    X -- input data of size (m, K)

    Returns
    predictions -- vector of predictions of our model (red: 0 / blue: 1)
    """

    # Predict using forward propagation and a classification threshold of 0.5
    a3, cache = forward_propagation(X, parameters)
    predictions = (a3 > 0.5)
    return predictions


def load_dataset():
    global figures, fig_count

    np.random.seed(3)
    train_X, train_Y = sklearn.datasets.make_moons(n_samples=300, noise=.2)  # 300 #0.2
    # Visualize the data

    figures.append(plt.figure(fig_count))
    fig_count += 1

    plt.scatter(train_X[:, 0], train_X[:, 1], c=train_Y, s=40, cmap=plt.cm.Spectral)

    train_X = train_X.T
    train_Y = train_Y.reshape((1, train_Y.shape[0]))

    figures[fig_count - 2].show()

    return train_X, train_Y


def update_parameters_with_gd_test_case():
    np.random.seed(1)
    learning_rate = 0.01
    W1 = np.random.randn(2, 3)
    b1 = np.random.randn(2, 1)
    W2 = np.random.randn(3, 3)
    b2 = np.random.randn(3, 1)

    dW1 = np.random.randn(2, 3)
    db1 = np.random.randn(2, 1)
    dW2 = np.random.randn(3, 3)
    db2 = np.random.randn(3, 1)

    parameters = {"W1": W1, "b1": b1, "W2": W2, "b2": b2}
    grads = {"dW1": dW1, "db1": db1, "dW2": dW2, "db2": db2}

    return parameters, grads, learning_rate


"""
def update_parameters_with_sgd_checker(function, inputs, outputs):
    if function(inputs) == outputs:
        print("Correct")
    else:
        print("Incorrect")
"""


def random_mini_batches_test_case():
    np.random.seed(1)
    mini_batch_size = 64
    X = np.random.randn(12288, 148)
    Y = np.random.randn(1, 148) < 0.5
    return X, Y, mini_batch_size


def initialize_velocity_test_case():
    np.random.seed(1)
    W1 = np.random.randn(2, 3)
    b1 = np.random.randn(2, 1)
    W2 = np.random.randn(3, 3)
    b2 = np.random.randn(3, 1)
    parameters = {"W1": W1, "b1": b1, "W2": W2, "b2": b2}
    return parameters


def update_parameters_with_momentum_test_case():
    np.random.seed(1)
    W1 = np.random.randn(2, 3)
    b1 = np.random.randn(2, 1)
    W2 = np.random.randn(3, 3)
    b2 = np.random.randn(3, 1)

    dW1 = np.random.randn(2, 3)
    db1 = np.random.randn(2, 1)
    dW2 = np.random.randn(3, 3)
    db2 = np.random.randn(3, 1)
    parameters = {"W1": W1, "b1": b1, "W2": W2, "b2": b2}
    grads = {"dW1": dW1, "db1": db1, "dW2": dW2, "db2": db2}
    v = {'dW1': np.array([[0., 0., 0.],
                          [0., 0., 0.]]), 'dW2': np.array([[0., 0., 0.],
                                                           [0., 0., 0.],
                                                           [0., 0., 0.]]), 'db1': np.array([[0.],
                                                                                            [0.]]),
         'db2': np.array([[0.],
                          [0.],
                          [0.]])}
    return parameters, grads, v


def initialize_adam_test_case():
    np.random.seed(1)
    W1 = np.random.randn(2, 3)
    b1 = np.random.randn(2, 1)
    W2 = np.random.randn(3, 3)
    b2 = np.random.randn(3, 1)
    parameters = {"W1": W1, "b1": b1, "W2": W2, "b2": b2}
    return parameters


def update_parameters_with_adam_test_case():
    np.random.seed(1)
    v, s = ({'dW1': np.array([[0., 0., 0.],
                              [0., 0., 0.]]), 'dW2': np.array([[0., 0., 0.],
                                                               [0., 0., 0.],
                                                               [0., 0., 0.]]), 'db1': np.array([[0.],
                                                                                                [0.]]),
             'db2': np.array([[0.],
                              [0.],
                              [0.]])}, {'dW1': np.array([[0., 0., 0.],
                                                         [0., 0., 0.]]), 'dW2': np.array([[0., 0., 0.],
                                                                                          [0., 0., 0.],
                                                                                          [0., 0., 0.]]),
                                        'db1': np.array([[0.],
                                                         [0.]]), 'db2': np.array([[0.],
                                                                                  [0.],
                                                                                  [0.]])})
    W1 = np.random.randn(2, 3)
    b1 = np.random.randn(2, 1)
    W2 = np.random.randn(3, 3)
    b2 = np.random.randn(3, 1)

    dW1 = np.random.randn(2, 3)
    db1 = np.random.randn(2, 1)
    dW2 = np.random.randn(3, 3)
    db2 = np.random.randn(3, 1)

    parameters = {"W1": W1, "b1": b1, "W2": W2, "b2": b2}
    grads = {"dW1": dW1, "db1": db1, "dW2": dW2, "db2": db2}

    return parameters, grads, v, s


##################################################################################################################################


# GRADED FUNCTION: update_parameters_with_gd

def update_parameters_with_gd(parameters, grads, learning_rate):
    """
    Update parameters using one step of gradient descent

    Arguments:
    parameters -- python dictionary containing your parameters to be updated:
                    parameters['W' + str(l)] = Wl
                    parameters['b' + str(l)] = bl
    grads -- python dictionary containing your gradients to update each parameters:
                    grads['dW' + str(l)] = dWl
                    grads['db' + str(l)] = dbl
    learning_rate -- the learning rate, scalar.

    Returns:
    parameters -- python dictionary containing your updated parameters
    """

    L = len(parameters) // 2  # number of layers in the neural networks

    # Update rule for each parameter
    for l in range(L):
        ### START CODE HERE ### (approx. 2 lines)
        parameters["W" + str(l + 1)] = parameters["W" + str(l + 1)] - learning_rate * grads['dW' + str(l +1)]
        parameters["b" + str(l + 1)] = parameters["b" + str(l + 1)] - learning_rate*grads['db' + str(l+1)]
        ### END CODE HERE ###

    return parameters


parameters, grads, learning_rate = update_parameters_with_gd_test_case()

parameters = update_parameters_with_gd(parameters, grads, learning_rate)
print("W1 =\n" + str(parameters["W1"]))
print("b1 =\n" + str(parameters["b1"]))
print("W2 =\n" + str(parameters["W2"]))
print("b2 =\n" + str(parameters["b2"]))


# GRADED FUNCTION: random_mini_batches

def random_mini_batches(X, Y, mini_batch_size=64, seed=0):
    """
    Creates a list of random minibatches from (X, Y)

    Arguments:
    X -- input data, of shape (input size, number of examples)
    Y -- true "label" vector (1 for blue dot / 0 for red dot), of shape (1, number of examples)
    mini_batch_size -- size of the mini-batches, integer

    Returns:
    mini_batches -- list of synchronous (mini_batch_X, mini_batch_Y)
    """

    np.random.seed(seed)  # To make your "random" minibatches the same as ours
    m = X.shape[1]  # number of training examples
    mini_batches = []

    # Step 1: Shuffle (X, Y)
    permutation = list(np.random.permutation(m))
    shuffled_X = X[:, permutation]
    shuffled_Y = Y[:, permutation].reshape((1, m))

    # Step 2: Partition (shuffled_X, shuffled_Y). Minus the end case.
    num_complete_minibatches = math.floor(
        m / mini_batch_size)  # number of mini batches of size mini_batch_size in your partitionning
    for k in range(0, num_complete_minibatches):
        ### START CODE HERE ### (approx. 2 lines)
        mini_batch_X = shuffled_X[:, k * mini_batch_size: (k + 1) * mini_batch_size]
        mini_batch_Y = shuffled_Y[:, k * mini_batch_size: (k + 1) * mini_batch_size]
        ### END CODE HERE ###
        mini_batch = (mini_batch_X, mini_batch_Y)
        mini_batches.append(mini_batch)

    # Handling the end case (last mini-batch < mini_batch_size)
    if m % mini_batch_size != 0:
        ### START CODE HERE ### (approx. 2 lines)
        mini_batch_X = shuffled_X[:, mini_batch_size*num_complete_minibatches: m]
        mini_batch_Y = shuffled_Y[:, mini_batch_size*num_complete_minibatches: m]
        ### END CODE HERE ###
        mini_batch = (mini_batch_X, mini_batch_Y)
        mini_batches.append(mini_batch)

    return mini_batches


X_assess, Y_assess, mini_batch_size = random_mini_batches_test_case()
mini_batches = random_mini_batches(X_assess, Y_assess, mini_batch_size)

print ("shape of the 1st mini_batch_X: " + str(mini_batches[0][0].shape))
print ("shape of the 2nd mini_batch_X: " + str(mini_batches[1][0].shape))
print ("shape of the 3rd mini_batch_X: " + str(mini_batches[2][0].shape))
print ("shape of the 1st mini_batch_Y: " + str(mini_batches[0][1].shape))
print ("shape of the 2nd mini_batch_Y: " + str(mini_batches[1][1].shape))
print ("shape of the 3rd mini_batch_Y: " + str(mini_batches[2][1].shape))
print ("mini batch sanity check: " + str(mini_batches[0][0][0][0:3]))


# GRADED FUNCTION: initialize_velocity

def initialize_velocity(parameters):
    """
    Initializes the velocity as a python dictionary with:
                - keys: "dW1", "db1", ..., "dWL", "dbL"
                - values: numpy arrays of zeros of the same shape as the corresponding gradients/parameters.
    Arguments:
    parameters -- python dictionary containing your parameters.
                    parameters['W' + str(l)] = Wl
                    parameters['b' + str(l)] = bl

    Returns:
    v -- python dictionary containing the current velocity.
                    v['dW' + str(l)] = velocity of dWl
                    v['db' + str(l)] = velocity of dbl
    """

    L = len(parameters) // 2  # number of layers in the neural networks
    v = {}

    # Initialize velocity
    for l in range(L):
        ### START CODE HERE ### (approx. 2 lines)
        v["dW" + str(l + 1)] = np.zeros((parameters["W" + str(l + 1)].shape[0], parameters["W" + str(l + 1)].shape[1]))
        v["db" + str(l + 1)] = np.zeros((parameters["b" + str(l + 1)].shape[0], parameters["b" + str(l + 1)].shape[1]))
        ### END CODE HERE ###

    return v

parameters = initialize_velocity_test_case()

v = initialize_velocity(parameters)
print("v[\"dW1\"] =\n" + str(v["dW1"]))
print("v[\"db1\"] =\n" + str(v["db1"]))
print("v[\"dW2\"] =\n" + str(v["dW2"]))
print("v[\"db2\"] =\n" + str(v["db2"]))


# GRADED FUNCTION: update_parameters_with_momentum

def update_parameters_with_momentum(parameters, grads, v, beta, learning_rate):
    """
    Update parameters using Momentum

    Arguments:
    parameters -- python dictionary containing your parameters:
                    parameters['W' + str(l)] = Wl
                    parameters['b' + str(l)] = bl
    grads -- python dictionary containing your gradients for each parameters:
                    grads['dW' + str(l)] = dWl
                    grads['db' + str(l)] = dbl
    v -- python dictionary containing the current velocity:
                    v['dW' + str(l)] = ...
                    v['db' + str(l)] = ...
    beta -- the momentum hyperparameter, scalar
    learning_rate -- the learning rate, scalar

    Returns:
    parameters -- python dictionary containing your updated parameters
    v -- python dictionary containing your updated velocities
    """

    L = len(parameters) // 2  # number of layers in the neural networks

    # Momentum update for each parameter
    for l in range(L):
        ### START CODE HERE ### (approx. 4 lines)
        # compute velocities
        v["dW" + str(l + 1)] = beta * v["dW" + str(l + 1)] + (1 - beta) * grads['dW' + str(l + 1)]
        v["db" + str(l + 1)] = beta * v["db" + str(l + 1)] + (1 - beta) * grads['db' + str(l + 1)]
        # update parameters
        parameters["W" + str(l + 1)] = parameters["W" + str(l + 1)] - learning_rate * v["dW" + str(l + 1)]
        parameters["b" + str(l + 1)] = parameters["b" + str(l + 1)] - learning_rate * v["db" + str(l + 1)]
        ### END CODE HERE ###

    return parameters, v

parameters, grads, v = update_parameters_with_momentum_test_case()

parameters, v = update_parameters_with_momentum(parameters, grads, v, beta = 0.9, learning_rate = 0.01)
print("W1 = \n" + str(parameters["W1"]))
print("b1 = \n" + str(parameters["b1"]))
print("W2 = \n" + str(parameters["W2"]))
print("b2 = \n" + str(parameters["b2"]))
print("v[\"dW1\"] = \n" + str(v["dW1"]))
print("v[\"db1\"] = \n" + str(v["db1"]))
print("v[\"dW2\"] = \n" + str(v["dW2"]))
print("v[\"db2\"] = v" + str(v["db2"]))


# GRADED FUNCTION: initialize_adam

def initialize_adam(parameters):
    """
    Initializes v and s as two python dictionaries with:
                - keys: "dW1", "db1", ..., "dWL", "dbL"
                - values: numpy arrays of zeros of the same shape as the corresponding gradients/parameters.

    Arguments:
    parameters -- python dictionary containing your parameters.
                    parameters["W" + str(l)] = Wl
                    parameters["b" + str(l)] = bl

    Returns:
    v -- python dictionary that will contain the exponentially weighted average of the gradient.
                    v["dW" + str(l)] = ...
                    v["db" + str(l)] = ...
    s -- python dictionary that will contain the exponentially weighted average of the squared gradient.
                    s["dW" + str(l)] = ...
                    s["db" + str(l)] = ...

    """

    L = len(parameters) // 2  # number of layers in the neural networks
    v = {}
    s = {}

    # Initialize v, s. Input: "parameters". Outputs: "v, s".
    for l in range(L):
        ### START CODE HERE ### (approx. 4 lines)
        v["dW" + str(l + 1)] = np.zeros((parameters["W" + str(l+1)].shape[0], parameters["W" + str(l+1)].shape[1]))
        v["db" + str(l + 1)] = np.zeros((parameters["b" + str(l+1)].shape[0], parameters["b" + str(l+1)].shape[1]))
        s["dW" + str(l + 1)] = np.zeros((parameters["W" + str(l+1)].shape[0], parameters["W" + str(l+1)].shape[1]))
        s["db" + str(l + 1)] = np.zeros((parameters["b" + str(l+1)].shape[0], parameters["b" + str(l+1)].shape[1]))
    ### END CODE HERE ###

    return v, s

parameters = initialize_adam_test_case()

v, s = initialize_adam(parameters)
print("v[\"dW1\"] = \n" + str(v["dW1"]))
print("v[\"db1\"] = \n" + str(v["db1"]))
print("v[\"dW2\"] = \n" + str(v["dW2"]))
print("v[\"db2\"] = \n" + str(v["db2"]))
print("s[\"dW1\"] = \n" + str(s["dW1"]))
print("s[\"db1\"] = \n" + str(s["db1"]))
print("s[\"dW2\"] = \n" + str(s["dW2"]))
print("s[\"db2\"] = \n" + str(s["db2"]))


# GRADED FUNCTION: update_parameters_with_adam

def update_parameters_with_adam(parameters, grads, v, s, t, learning_rate=0.01,
                                beta1=0.9, beta2=0.999, epsilon=1e-8):
    """
    Update parameters using Adam

    Arguments:
    parameters -- python dictionary containing your parameters:
                    parameters['W' + str(l)] = Wl
                    parameters['b' + str(l)] = bl
    grads -- python dictionary containing your gradients for each parameters:
                    grads['dW' + str(l)] = dWl
                    grads['db' + str(l)] = dbl
    v -- Adam variable, moving average of the first gradient, python dictionary
    s -- Adam variable, moving average of the squared gradient, python dictionary
    learning_rate -- the learning rate, scalar.
    beta1 -- Exponential decay hyperparameter for the first moment estimates
    beta2 -- Exponential decay hyperparameter for the second moment estimates
    epsilon -- hyperparameter preventing division by zero in Adam updates

    Returns:
    parameters -- python dictionary containing your updated parameters
    v -- Adam variable, moving average of the first gradient, python dictionary
    s -- Adam variable, moving average of the squared gradient, python dictionary
    """

    L = len(parameters) // 2  # number of layers in the neural networks
    v_corrected = {}  # Initializing first moment estimate, python dictionary
    s_corrected = {}  # Initializing second moment estimate, python dictionary

    # Perform Adam update on all parameters
    for l in range(L):
        # Moving average of the gradients. Inputs: "v, grads, beta1". Output: "v".
        ### START CODE HERE ### (approx. 2 lines)
        v["dW" + str(l + 1)] = beta1*v["dW" + str(l + 1)]+(1-beta1)*grads['dW' + str(l+1)]
        v["db" + str(l + 1)] = beta1*v["db" + str(l + 1)]+(1-beta1)*grads['db' + str(l+1)]
        ### END CODE HERE ###

        # Compute bias-corrected first moment estimate. Inputs: "v, beta1, t". Output: "v_corrected".
        ### START CODE HERE ### (approx. 2 lines)
        v_corrected["dW" + str(l + 1)] = v["dW" + str(l + 1)] /(1-beta1**t)
        v_corrected["db" + str(l + 1)] = v["db" + str(l + 1)]  / (1-beta1**t)
        ### END CODE HERE ###

        # Moving average of the squared gradients. Inputs: "s, grads, beta2". Output: "s".
        ### START CODE HERE ### (approx. 2 lines)
        s["dW" + str(l + 1)] = beta2*s["dW" + str(l + 1)]+(1-beta2)*(grads['dW' + str(l+1)]*grads['dW' + str(l+1)])
        s["db" + str(l + 1)] = beta2*s["db" + str(l + 1)]+(1-beta2)*(grads['db' + str(l+1)]*grads['db' + str(l+1)])
        ### END CODE HERE ###

        # Compute bias-corrected second raw moment estimate. Inputs: "s, beta2, t". Output: "s_corrected".
        ### START CODE HERE ### (approx. 2 lines)
        s_corrected["dW" + str(l + 1)] = s["dW" + str(l + 1)]/(1-beta2**t)
        s_corrected["db" + str(l + 1)] = s["db" + str(l + 1)]/(1-beta2**t)
        ### END CODE HERE ###

        # Update parameters. Inputs: "parameters, learning_rate, v_corrected, s_corrected, epsilon". Output: "parameters".
        ### START CODE HERE ### (approx. 2 lines)
        parameters["W" + str(l + 1)] = parameters["W" + str(l + 1)] - learning_rate*(v_corrected["dW" + str(l + 1)]/(np.sqrt(s_corrected["dW" + str(l + 1)])+epsilon))
        parameters["b" + str(l + 1)] = parameters["b" + str(l + 1)] - learning_rate*(v_corrected["db" + str(l + 1)]/(np.sqrt(s_corrected["db" + str(l + 1)])+epsilon))
        ### END CODE HERE ###

    return parameters, v, s


parameters, grads, v, s = update_parameters_with_adam_test_case()
parameters, v, s  = update_parameters_with_adam(parameters, grads, v, s, t = 2)

print("W1 = \n" + str(parameters["W1"]))
print("b1 = \n" + str(parameters["b1"]))
print("W2 = \n" + str(parameters["W2"]))
print("b2 = \n" + str(parameters["b2"]))
print("v[\"dW1\"] = \n" + str(v["dW1"]))
print("v[\"db1\"] = \n" + str(v["db1"]))
print("v[\"dW2\"] = \n" + str(v["dW2"]))
print("v[\"db2\"] = \n" + str(v["db2"]))
print("s[\"dW1\"] = \n" + str(s["dW1"]))
print("s[\"db1\"] = \n" + str(s["db1"]))
print("s[\"dW2\"] = \n" + str(s["dW2"]))
print("s[\"db2\"] = \n" + str(s["db2"]))

train_X, train_Y = load_dataset()


def model(X, Y, layers_dims, optimizer, learning_rate=0.0007, mini_batch_size=64, beta=0.9,
          beta1=0.9, beta2=0.999, epsilon=1e-8, num_epochs=10000, print_cost=True):

    global figures, fig_count
    """
    3-layer neural network model which can be run in different optimizer modes.

    Arguments:
    X -- input data, of shape (2, number of examples)
    Y -- true "label" vector (1 for blue dot / 0 for red dot), of shape (1, number of examples)
    layers_dims -- python list, containing the size of each layer
    learning_rate -- the learning rate, scalar.
    mini_batch_size -- the size of a mini batch
    beta -- Momentum hyperparameter
    beta1 -- Exponential decay hyperparameter for the past gradients estimates
    beta2 -- Exponential decay hyperparameter for the past squared gradients estimates
    epsilon -- hyperparameter preventing division by zero in Adam updates
    num_epochs -- number of epochs
    print_cost -- True to print the cost every 1000 epochs

    Returns:
    parameters -- python dictionary containing your updated parameters
    """

    L = len(layers_dims)  # number of layers in the neural networks
    costs = []  # to keep track of the cost
    t = 0  # initializing the counter required for Adam update
    seed = 10  # For grading purposes, so that your "random" minibatches are the same as ours
    m = X.shape[1]  # number of training examples

    # Initialize parameters
    parameters = initialize_parameters(layers_dims)

    # Initialize the optimizer
    if optimizer == "gd":
        pass  # no initialization required for gradient descent
    elif optimizer == "momentum":
        v = initialize_velocity(parameters)
    elif optimizer == "adam":
        v, s = initialize_adam(parameters)

    # Optimization loop
    for i in range(num_epochs):

        # Define the random minibatches. We increment the seed to reshuffle differently the dataset after each epoch
        seed = seed + 1
        minibatches = random_mini_batches(X, Y, mini_batch_size, seed)
        cost_total = 0

        for minibatch in minibatches:

            # Select a minibatch
            (minibatch_X, minibatch_Y) = minibatch

            # Forward propagation
            a3, caches = forward_propagation(minibatch_X, parameters)

            # Compute cost and add to the cost total
            cost_total += compute_cost(a3, minibatch_Y)

            # Backward propagation
            grads = backward_propagation(minibatch_X, minibatch_Y, caches)

            # Update parameters
            if optimizer == "gd":
                parameters = update_parameters_with_gd(parameters, grads, learning_rate)
            elif optimizer == "momentum":
                parameters, v = update_parameters_with_momentum(parameters, grads, v, beta, learning_rate)
            elif optimizer == "adam":
                t = t + 1  # Adam counter
                parameters, v, s = update_parameters_with_adam(parameters, grads, v, s,
                                                               t, learning_rate, beta1, beta2, epsilon)
        cost_avg = cost_total / m

        # Print the cost every 1000 epoch
        if print_cost and i % 1000 == 0:
            print("Cost after epoch %i: %f" % (i, cost_avg))
        if print_cost and i % 100 == 0:
            costs.append(cost_avg)

    # plot the cost
    figures.append(plt.figure(fig_count))
    fig_count += 1
    plt.plot(costs)
    plt.ylabel('cost')
    plt.xlabel('epochs (per 100)')
    plt.title("Learning rate = " + str(learning_rate))
    figures[fig_count - 2].show()

    return parameters


# train 3-layer model
layers_dims = [train_X.shape[0], 5, 2, 1]
parameters = model(train_X, train_Y, layers_dims, optimizer = "gd")

# Predict
predictions = predict(train_X, train_Y, parameters)

# Plot decision boundary
figures.append(plt.figure(fig_count))
fig_count += 1
plt.title("Model with Gradient Descent optimization")
axes = plt.gca()
axes.set_xlim([-1.5,2.5])
axes.set_ylim([-1,1.5])
plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y, 0)
figures[fig_count - 2].show()


# train 3-layer model
layers_dims = [train_X.shape[0], 5, 2, 1]
parameters = model(train_X, train_Y, layers_dims, beta = 0.9, optimizer = "momentum")

# Predict
predictions = predict(train_X, train_Y, parameters)

# Plot decision boundary
figures.append(plt.figure(fig_count))
fig_count += 1
plt.title("Model with Momentum optimization")
axes = plt.gca()
axes.set_xlim([-1.5,2.5])
axes.set_ylim([-1,1.5])
plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y,0)
figures[fig_count - 2].show()


# train 3-layer model
layers_dims = [train_X.shape[0], 5, 2, 1]
parameters = model(train_X, train_Y, layers_dims, optimizer = "adam")

# Predict
predictions = predict(train_X, train_Y, parameters)

# Plot decision boundary
figures.append(plt.figure(fig_count))
fig_count += 1
plt.title("Model with Adam optimization")
axes = plt.gca()
axes.set_xlim([-1.5,2.5])
axes.set_ylim([-1,1.5])
plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y,0)
figures[fig_count - 2].show()





plt.show()