snn_utils.py

import numpy as np
import matplotlib.pyplot as plt
import h5py
import math
import os

def sigmoid(Z):
    """
    Implements the sigmoid activation in numpy
    
    Arguments:
    Z -- numpy array of any shape
    
    Returns:
    A -- output of sigmoid(z), same shape as Z
    cache -- returns Z as well, useful during backpropagation
    """
    
    A = 1/(1+np.exp(-Z))
    cache = Z
    
    return A, cache

def relu(Z):
    """
    Implement the RELU function.

    Arguments:
    Z -- Output of the linear layer, of any shape

    Returns:
    A -- Post-activation parameter, of the same shape as Z
    cache -- a python dictionary containing "A" ; stored for computing the backward pass efficiently
    """
    
    A = np.maximum(0,Z)
    
    assert(A.shape == Z.shape)
    
    cache = Z 
    return A, cache

def softmax(Z):

    exps = np.exp(Z - np.max(Z))

    A = exps / np.sum(exps, axis=0)

    assert(A.shape == Z.shape)

    cache = Z 
    return A, cache

def relu_backward(dA, cache):
    """
    Implement the backward propagation for a single RELU unit.

    Arguments:
    dA -- post-activation gradient, of any shape
    cache -- 'Z' where we store for computing backward propagation efficiently

    Returns:
    dZ -- Gradient of the cost with respect to Z
    """
    
    Z = cache
    dZ = np.array(dA, copy=True) # just converting dz to a correct object.
    
    # When z <= 0, you should set dz to 0 as well. 
    dZ[Z <= 0] = 0
    
    assert (dZ.shape == Z.shape)
    
    return dZ

def sigmoid_backward(dA, cache):
    """
    Implement the backward propagation for a single SIGMOID unit.

    Arguments:
    dA -- post-activation gradient, of any shape
    cache -- 'Z' where we store for computing backward propagation efficiently

    Returns:
    dZ -- Gradient of the cost with respect to Z
    """
    
    Z = cache
    
    s = 1/(1+np.exp(-Z))
    dZ = dA * s * (1-s)
    
    assert (dZ.shape == Z.shape)
    
    return dZ

def softmax_backward(dA, cache, Y_orig = None, AL = None):
    Z = cache

    m = Y_orig.shape[1]

    A, cache2 = softmax(Z)
    A[Y_orig, range(m)] -= 1
    dZ = A/m

    assert (dZ.shape == Z.shape)
    
    return dZ

def load_data(name):
    train_dataset = h5py.File('datasets/train_'+name+'.h5', "r")
    train_set_x_orig = np.array(train_dataset["train_set_x"][:]) # your train set features
    train_set_y_orig = np.array(train_dataset["train_set_y"][:]) # your train set labels

    test_dataset = h5py.File('datasets/test_'+name+'.h5', "r")
    test_set_x_orig = np.array(test_dataset["test_set_x"][:]) # your test set features
    test_set_y_orig = np.array(test_dataset["test_set_y"][:]) # your test set labels

    classes = np.array(test_dataset["list_classes"][:]) # the list of classes
    
    train_set_y_orig = train_set_y_orig.reshape((1, train_set_y_orig.shape[0]))
    test_set_y_orig = test_set_y_orig.reshape((1, test_set_y_orig.shape[0]))
    
    return train_set_x_orig, train_set_y_orig, test_set_x_orig, test_set_y_orig, classes

def initialize_parameters(n_x, n_h, n_y):
    """
    Argument:
    n_x -- size of the input layer
    n_h -- size of the hidden layer
    n_y -- size of the output layer
    
    Returns:
    parameters -- python dictionary containing your parameters:
                    W1 -- weight matrix of shape (n_h, n_x)
                    b1 -- bias vector of shape (n_h, 1)
                    W2 -- weight matrix of shape (n_y, n_h)
                    b2 -- bias vector of shape (n_y, 1)
    """
    
    np.random.seed(1)
    
    W1 = np.random.randn(n_h, n_x)*0.01
    b1 = np.zeros((n_h, 1))
    W2 = np.random.randn(n_y, n_h)*0.01
    b2 = np.zeros((n_y, 1))
    
    assert(W1.shape == (n_h, n_x))
    assert(b1.shape == (n_h, 1))
    assert(W2.shape == (n_y, n_h))
    assert(b2.shape == (n_y, 1))
    
    parameters = {"W1": W1,
                  "b1": b1,
                  "W2": W2,
                  "b2": b2}
    
    return parameters     


def initialize_parameters_deep(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":
                    Wl -- weight matrix of shape (layer_dims[l], layer_dims[l-1])
                    bl -- bias vector of shape (layer_dims[l], 1)
    """
    
    np.random.seed(1)
    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(layer_dims[l-1]) #*0.01
        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 linear_forward(A, W, b):
    """
    Implement the linear part of a layer's forward propagation.

    Arguments:
    A -- activations from previous layer (or input data): (size of previous layer, number of examples)
    W -- weights matrix: numpy array of shape (size of current layer, size of previous layer)
    b -- bias vector, numpy array of shape (size of the current layer, 1)

    Returns:
    Z -- the input of the activation function, also called pre-activation parameter 
    cache -- a python dictionary containing "A", "W" and "b" ; stored for computing the backward pass efficiently
    """
    
    Z = W.dot(A) + b
    
    assert(Z.shape == (W.shape[0], A.shape[1]))
    cache = (A, W, b)
    
    return Z, cache

def linear_activation_forward(A_prev, W, b, activation):
    """
    Implement the forward propagation for the LINEAR->ACTIVATION layer

    Arguments:
    A_prev -- activations from previous layer (or input data): (size of previous layer, number of examples)
    W -- weights matrix: numpy array of shape (size of current layer, size of previous layer)
    b -- bias vector, numpy array of shape (size of the current layer, 1)
    activation -- the activation to be used in this layer, stored as a text string: "sigmoid" or "relu"

    Returns:
    A -- the output of the activation function, also called the post-activation value 
    cache -- a python dictionary containing "linear_cache" and "activation_cache";
             stored for computing the backward pass efficiently
    """
    
    # Inputs: "A_prev, W, b". Outputs: "A, activation_cache".
    Z, linear_cache = linear_forward(A_prev, W, b)

    if activation == "sigmoid":
        A, activation_cache = sigmoid(Z)
    elif activation == "relu":
        A, activation_cache = relu(Z)
    elif activation == "softmax":
        A, activation_cache = softmax(Z)
    
    assert (A.shape == (W.shape[0], A_prev.shape[1]))
    cache = (linear_cache, activation_cache)

    return A, cache

def L_model_forward(X, parameters):
    """
    Implement forward propagation for the [LINEAR->RELU]*(L-1)->LINEAR->SIGMOID computation
    
    Arguments:
    X -- data, numpy array of shape (input size, number of examples)
    parameters -- output of initialize_parameters_deep()
    
    Returns:
    AL -- last post-activation value
    caches -- list of caches containing:
                every cache of linear_relu_forward() (there are L-1 of them, indexed from 0 to L-2)
                the cache of linear_sigmoid_forward() (there is one, indexed L-1)
    """

    caches = []
    A = X
    L = len(parameters) // 2                  # number of layers in the neural network
    
    # Implement [LINEAR -> RELU]*(L-1). Add "cache" to the "caches" list.
    for l in range(1, L):
        A_prev = A 
        A, cache = linear_activation_forward(A_prev, parameters['W' + str(l)], parameters['b' + str(l)], activation = "relu")
        caches.append(cache)

    if parameters['W' + str(L)].shape[0] > 1:
        AL, cache = linear_activation_forward(A, parameters['W' + str(L)], parameters['b' + str(L)], activation = "softmax")
    else:
        # Implement LINEAR -> SIGMOID. Add "cache" to the "caches" list.
        AL, cache = linear_activation_forward(A, parameters['W' + str(L)], parameters['b' + str(L)], activation = "sigmoid")
    caches.append(cache)
    
    assert(AL.shape[1] == X.shape[1])
            
    return AL, caches

def compute_cost(AL, Y, Y_orig):
    """
    Implement the cost function defined by equation (7).

    Arguments:
    AL -- probability vector corresponding to your label predictions, shape (1, number of examples)
    Y -- true "label" vector (for example: containing 0 if non-cat, 1 if cat), shape (1, number of examples)

    Returns:
    cost -- cross-entropy cost
    """
    
    m = Y.shape[1]
    
    if Y.shape[0] > 1:
        log_likelihood = -np.log(AL[Y_orig, range(m)])
        cost = np.sum(log_likelihood) / m
    else:
        # Compute loss from aL and y.
        cost = (1./m) * (-np.sum(np.dot(Y,np.log(AL).T)) - np.sum(np.dot(1-Y, np.log(1-AL).T)))

        cost = np.squeeze(cost)      # To make sure your cost's shape is what we expect (e.g. this turns [[17]] into 17).

    assert(cost.shape == ())
    
    return cost

def compute_cost_with_regularization(A3, Y, parameters, lambd, Y_orig):
    """
    Implement the cost function with L2 regularization. See formula (2) above.
    
    Arguments:
    A3 -- post-activation, output of forward propagation, of shape (output size, number of examples)
    Y -- "true" labels vector, of shape (output size, number of examples)
    parameters -- python dictionary containing parameters of the model
    
    Returns:
    cost - value of the regularized loss function (formula (2))
    """
    L = len(parameters) // 2

    m = Y.shape[1]

    cross_entropy_cost = compute_cost(A3, Y, Y_orig) # This gives you the cross-entropy part of the cost
    
    # L2_regularization_cost = lambd * (np.sum(np.square(W1)) + np.sum(np.square(W2)) + np.sum(np.square(W3))) / (2 * m) 
    parameters_sum = 0
    for l in range(1, L):
        parameters_sum += np.sum(np.square(parameters['W' + str(l)]))
    L2_regularization_cost = lambd * parameters_sum / (2 * m)
    
    cost = cross_entropy_cost + L2_regularization_cost
    
    return cost

def linear_backward(dZ, cache, regularization_lambd = 0):
    """
    Implement the linear portion of backward propagation for a single layer (layer l)

    Arguments:
    dZ -- Gradient of the cost with respect to the linear output (of current layer l)
    cache -- tuple of values (A_prev, W, b) coming from the forward propagation in the current layer

    Returns:
    dA_prev -- Gradient of the cost with respect to the activation (of the previous layer l-1), same shape as A_prev
    dW -- Gradient of the cost with respect to W (current layer l), same shape as W
    db -- Gradient of the cost with respect to b (current layer l), same shape as b
    """
    A_prev, W, b = cache
    m = A_prev.shape[1]

    dW = 1./m * np.dot(dZ,A_prev.T)
    if regularization_lambd:
        dW += (regularization_lambd / m) * W
    db = 1./m * np.sum(dZ, axis = 1, keepdims = True)
    dA_prev = np.dot(W.T,dZ)
    
    assert (dA_prev.shape == A_prev.shape)
    assert (dW.shape == W.shape)
    assert (db.shape == b.shape)
    
    return dA_prev, dW, db

def linear_activation_backward(dA, cache, activation, regularization_lambd = 0, Y_orig = None, AL = None):
    """
    Implement the backward propagation for the LINEAR->ACTIVATION layer.
    
    Arguments:
    dA -- post-activation gradient for current layer l 
    cache -- tuple of values (linear_cache, activation_cache) we store for computing backward propagation efficiently
    activation -- the activation to be used in this layer, stored as a text string: "sigmoid" or "relu"
    
    Returns:
    dA_prev -- Gradient of the cost with respect to the activation (of the previous layer l-1), same shape as A_prev
    dW -- Gradient of the cost with respect to W (current layer l), same shape as W
    db -- Gradient of the cost with respect to b (current layer l), same shape as b
    """
    linear_cache, activation_cache = cache
    
    if activation == "relu":
        dZ = relu_backward(dA, activation_cache)
    elif activation == "sigmoid":
        dZ = sigmoid_backward(dA, activation_cache)
    elif activation == "softmax":
        dZ = softmax_backward(dA, activation_cache, Y_orig = Y_orig, AL = AL)

    dA_prev, dW, db = linear_backward(dZ, linear_cache, regularization_lambd)
        
    return dA_prev, dW, db

def L_model_backward(AL, Y, caches, Y_orig = None):
    """
    Implement the backward propagation for the [LINEAR->RELU] * (L-1) -> LINEAR -> SIGMOID group
    
    Arguments:
    AL -- probability vector, output of the forward propagation (L_model_forward())
    Y -- true "label" vector (containing 0 if non-cat, 1 if cat)
    caches -- list of caches containing:
                every cache of linear_activation_forward() with "relu" (there are (L-1) or them, indexes from 0 to L-2)
                the cache of linear_activation_forward() with "sigmoid" (there is one, index L-1)
    
    Returns:
    grads -- A dictionary with the gradients
             grads["dA" + str(l)] = ... 
             grads["dW" + str(l)] = ...
             grads["db" + str(l)] = ... 
    """
    grads = {}
    L = len(caches) # the number of layers
    m = AL.shape[1]
    Y = Y.reshape(AL.shape) # after this line, Y is the same shape as AL

    # Initializing the backpropagation
    dAL = - (np.divide(Y, AL) - np.divide(1 - Y, 1 - AL))

    # Lth layer (SIGMOID -> LINEAR) gradients. Inputs: "AL, Y, caches". Outputs: "grads["dAL"], grads["dWL"], grads["dbL"]
    current_cache = caches[L-1]
    if Y.shape[0] > 1:
        grads["dA" + str(L-1)], grads["dW" + str(L)], grads["db" + str(L)] = linear_activation_backward(dAL, current_cache, activation = "softmax", Y_orig = Y_orig, AL = AL)
    else:
        grads["dA" + str(L-1)], grads["dW" + str(L)], grads["db" + str(L)] = linear_activation_backward(dAL, current_cache, activation = "sigmoid")
    
    for l in reversed(range(L-1)):
        # lth layer: (RELU -> LINEAR) gradients.
        current_cache = caches[l]
        dA_prev_temp, dW_temp, db_temp = linear_activation_backward(grads["dA" + str(l + 1)], current_cache, activation = "relu")
        grads["dA" + str(l)] = dA_prev_temp
        grads["dW" + str(l + 1)] = dW_temp
        grads["db" + str(l + 1)] = db_temp

    return grads

def L_model_backward_with_regularization(AL, Y, caches, regularization_lambd, Y_orig = None):
    """
    Implement the backward propagation for the [LINEAR->RELU] * (L-1) -> LINEAR -> SIGMOID group
    
    Arguments:
    AL -- probability vector, output of the forward propagation (L_model_forward())
    Y -- true "label" vector (containing 0 if non-cat, 1 if cat)
    caches -- list of caches containing:
                every cache of linear_activation_forward() with "relu" (there are (L-1) or them, indexes from 0 to L-2)
                the cache of linear_activation_forward() with "sigmoid" (there is one, index L-1)
    
    Returns:
    grads -- A dictionary with the gradients
             grads["dA" + str(l)] = ... 
             grads["dW" + str(l)] = ...
             grads["db" + str(l)] = ... 
    """
    grads = {}
    L = len(caches) # the number of layers
    m = AL.shape[1]
    Y = Y.reshape(AL.shape) # after this line, Y is the same shape as AL
    
    # Initializing the backpropagation
    dAL = - (np.divide(Y, AL) - np.divide(1 - Y, 1 - AL))
    
    # Lth layer (SIGMOID -> LINEAR) gradients. Inputs: "AL, Y, caches". Outputs: "grads["dAL"], grads["dWL"], grads["dbL"]
    current_cache = caches[L-1]
    if Y.shape[0] > 1:
        grads["dA" + str(L-1)], grads["dW" + str(L)], grads["db" + str(L)] = linear_activation_backward(dAL, current_cache, activation = "softmax", regularization_lambd = regularization_lambd, Y_orig = Y_orig)
    else:
        grads["dA" + str(L-1)], grads["dW" + str(L)], grads["db" + str(L)] = linear_activation_backward(dAL, current_cache, activation = "sigmoid", regularization_lambd = regularization_lambd)

    for l in reversed(range(L-1)):
        # lth layer: (RELU -> LINEAR) gradients.
        current_cache = caches[l]
        dA_prev_temp, dW_temp, db_temp = linear_activation_backward(grads["dA" + str(l + 1)], current_cache, activation = "relu", regularization_lambd = regularization_lambd)
        grads["dA" + str(l)] = dA_prev_temp
        grads["dW" + str(l + 1)] = dW_temp
        grads["db" + str(l + 1)] = db_temp

    return grads

def update_parameters(parameters, grads, learning_rate):
    """
    Update parameters using gradient descent
    
    Arguments:
    parameters -- python dictionary containing your parameters 
    grads -- python dictionary containing your gradients, output of L_model_backward
    
    Returns:
    parameters -- python dictionary containing your updated parameters 
                  parameters["W" + str(l)] = ... 
                  parameters["b" + str(l)] = ...
    """
    
    L = len(parameters) // 2 # number of layers in the neural network

    # Update rule for each parameter. Use a for loop.
    for l in range(L):
        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)]
        
    return parameters

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)
        v["db" + str(l+1)] = np.zeros(parameters["b" + str(l+1)].shape)
        s["dW" + str(l+1)] = v["dW" + str(l+1)]
        s["db" + str(l+1)] = v["db" + str(l+1)]
    ### END CODE HERE ###
    
    return v, s

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 - math.pow(beta1,t))
        v_corrected["db" + str(l+1)] = v["db" + str(l+1)] / (1 - math.pow(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) * pow(grads['dW' + str(l+1)], 2)
        s["db" + str(l+1)] = beta2 * s["db" + str(l+1)] + (1 - beta2) * pow(grads['db' + str(l+1)], 2)
        ### 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 - math.pow(beta2,t))
        s_corrected["db" + str(l+1)] = s["db" + str(l+1)] / (1 - math.pow(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)] -= learning_rate * v_corrected["dW" + str(l+1)] / (np.sqrt(s_corrected["dW" + str(l+1)]) + epsilon) 
        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
    
def predict(X, y, parameters):
    """
    This function is used to predict the results of a  L-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]
    n = len(parameters) // 2 # number of layers in the neural network
    p = np.zeros((1,m))

    # Forward propagation
    probas, caches = L_model_forward(X, parameters)

    if (max(np.squeeze(y)) > 1):
        probas_max_index = np.argmax(probas, axis = 0)
        accuracy = np.sum((probas_max_index == y)/m)
    else:        
        # convert probas to 0/1 predictions
        for i in range(0, probas.shape[1]):
            if probas[0,i] > 0.5:
                p[0,i] = 1
            else:
                p[0,i] = 0
        accuracy = np.sum((p == y)/m)
        
    print("Accuracy: "  + str(accuracy))
        
    return p, accuracy

def predict_minsort(classes, X, y, parameters, shape, figsize = (12.0, 2.0)):
    
    m = X.shape[1]
    n = len(parameters) // 2 # number of layers in the neural network
    p = np.zeros((1,m))
    
    # Forward propagation
    probas, caches = L_model_forward(X, parameters)

    # print(probas.shape)
    tmp_y1pos = np.where(y == 1)[1]
    # print(tmp_y1pos)
    tmp_y1probas = probas[0, tmp_y1pos]
    # print(tmp_y1probas)
    # print('min=%.32f'%tmp_y1probas[21])
    # print('min=%.32f'%tmp_y1probas[26])
    tmp_y1probas_sort_index = np.argsort(tmp_y1probas)
    tmp_y1pos_sort_index = tmp_y1pos[tmp_y1probas_sort_index]
    # print(tmp_y1pos_sort_index)
    # print(tmp_y1probas_sort_index)
    plt.rcParams['figure.figsize'] = figsize # set default size of plots
    num_images = min(len(tmp_y1pos_sort_index), 10)
    for i in range(num_images):
        index = tmp_y1pos_sort_index[i]
        probas_index = tmp_y1probas_sort_index[i]
        
        plt.subplot(1, num_images, i + 1)
        plt.imshow(X[:,index].reshape(*shape), interpolation='nearest')
        plt.axis('off')
        plt.title("Probas: {:.5f}".format(tmp_y1probas[probas_index]), fontsize=8)
    plt.show()

def print_mislabeled_images(classes, X, y, p, shape, figsize = (12.0, 2.0)):
    """
    Plots images where predictions and truth were different.
    X -- dataset
    y -- true labels
    p -- predictions
    """
    a = p + y
    mislabeled_indices = np.asarray(np.where(a == 1))
    plt.rcParams['figure.figsize'] = figsize # set default size of plots
    num_images = len(mislabeled_indices[0])
    for i in range(num_images):
        index = mislabeled_indices[1][i]
        
        plt.subplot(1, num_images, i + 1)
        plt.imshow(X[:,index].reshape(*shape), interpolation='nearest')
        plt.axis('off')
        plt.title("Pred: " + classes[int(p[0,index])].decode("utf-8") + " \n Class: " + classes[y[0,index]].decode("utf-8"), fontsize=8)
    plt.show()

def L_layer_model(X, Y, layers_dims, learning_rate = 0.0075, learning_decay_rate = 1, num_iterations = 3000, print_cost = False, regularization_lambd = 0.7, optimization = None, mini_batch_size = 64, Y_orig = None):#lr was 0.009
    """
    Implements a L-layer neural network: [LINEAR->RELU]*(L-1)->LINEAR->SIGMOID.
    
    Arguments:
    X -- data, numpy array of shape (number of examples, num_px * num_px * 3)
    Y -- true "label" vector (containing 0 if cat, 1 if non-cat), of shape (1, number of examples)
    layers_dims -- list containing the input size and each layer size, of length (number of layers + 1).
    learning_rate -- learning rate of the gradient descent update rule
    num_iterations -- number of iterations of the optimization loop
    print_cost -- if True, it prints the cost every 100 steps
    
    Returns:
    parameters -- parameters learnt by the model. They can then be used to predict.
    """
    if print_cost:
        args = locals();
        del args['X']
        del args['Y']
        del args['Y_orig']
        print(args)
    # np.random.seed(1)
    costs = []                         # keep track of cost
    t = 0
    last_cost = 100
    learning_rate_decay = learning_rate
    last_parameters = False

    # Parameters initialization. (\u2248 1 line of code)
    parameters = initialize_parameters_deep(layers_dims)
    # parameters = load('catvnoncat')

    # Initialize the optimizer
    if optimization:
        v, s = initialize_adam(parameters)

    k = 0
    # Loop (gradient descent)
    for i in range(0, num_iterations):

        minibatches = random_mini_batches(X, Y, mini_batch_size, seed = 0, Y_orig = Y_orig)

        learning_rate_decay = learning_rate * (learning_decay_rate ** i)

        for minibatch in minibatches:

            # Select a minibatch
            (minibatch_X, minibatch_Y, minibatch_Y_orig) = minibatch

            # Forward propagation: [LINEAR -> RELU]*(L-1) -> LINEAR -> SIGMOID.
            AL, caches = L_model_forward(minibatch_X, parameters)
            
            # Backward propagation.
            if regularization_lambd == 0:
                grads = L_model_backward(AL, minibatch_Y, caches, minibatch_Y_orig)
            else:
                grads = L_model_backward_with_regularization(AL, minibatch_Y, caches, regularization_lambd, minibatch_Y_orig)

            # Update parameters.
            if optimization:
                t = t + 1 # Adam counter
                parameters, v, s = update_parameters_with_adam(parameters, grads, v, s, t, learning_rate_decay, optimization['beta1'], optimization['beta2'], optimization['epsilon'])
            else:
                parameters = update_parameters(parameters, grads, learning_rate_decay)

            # Compute cost.
            if regularization_lambd == 0:
                cost = compute_cost(AL, minibatch_Y, minibatch_Y_orig)
            else:
                cost = compute_cost_with_regularization(AL, minibatch_Y, parameters, regularization_lambd, minibatch_Y_orig)
        
            # if cost > last_cost:
            #     learning_rate_decay = learning_rate_decay * 0.95
            #     parameters = last_parameters
            #     # print ("Cost %f > %f reset : %.5f i=%f" %(cost, last_cost, learning_rate_decay, i))
            #     break_flag = 1
            #     # break
            # else:
            #     learning_rate_decay = learning_rate_decay / 0.992
            #     last_cost = cost
            #     last_parameters = parameters
            #     break_flag = 0

        # if break_flag == 1:
        #     continue

        # Print the cost every 100 training example
        if print_cost and i % (num_iterations/10) == 0:
            print ("Cost after iteration %i: %f" %(i, cost))
            print('learning_rate: %.5f' % learning_rate_decay)
        # if print_cost and i % (num_iterations/25) == 0:
        costs.append(cost)
        k += 1
    print ("Cost after iteration %i: %f" %(i, cost))
    print('learning_rate: %.5f' % learning_rate_decay)
    print(k)
    
    return parameters, costs

# GRADED FUNCTION: random_mini_batches
def random_mini_batches(X, Y, mini_batch_size = 64, seed = 0, Y_orig = None):
    """
    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((Y.shape[0],m))
    if Y_orig.any():
        shuffled_Y_orig = Y_orig[:, permutation].reshape((Y_orig.shape[0],m))

    # Step 2: Partition (shuffled_X, shuffled_Y). Minus the end case.
    if mini_batch_size > m or mini_batch_size == 0:
        mini_batch_size = m
    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):

        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]
        if Y_orig.any():
            mini_batch_Y_orig = shuffled_Y_orig[:, k * mini_batch_size : (k+1) * mini_batch_size]
        else:
            mini_batch_Y_orig = mini_batch_Y

        mini_batch = (mini_batch_X, mini_batch_Y, mini_batch_Y_orig)
        mini_batches.append(mini_batch)
    
    # Handling the end case (last mini-batch < mini_batch_size)
    if m % mini_batch_size != 0:

        mini_batch_X = shuffled_X[:, mini_batch_size * num_complete_minibatches : m]
        mini_batch_Y = shuffled_Y[:, mini_batch_size * num_complete_minibatches : m]
        if Y_orig.any():
            mini_batch_Y_orig = shuffled_Y_orig[:, mini_batch_size * num_complete_minibatches : m]
        else:
            mini_batch_Y_orig = mini_batch_Y

        mini_batch = (mini_batch_X, mini_batch_Y, mini_batch_Y_orig)
        mini_batches.append(mini_batch)
    
    return mini_batches
    
def convert_to_one_hot(Y, C = None):
    if C == 1:
        return Y
    Y = np.eye(C)[Y.reshape(-1)].T
    # Y = np.eye(3)[[0,1,2]].T
    return Y

def save(file_name, value):
    with h5py.File('datasets/'+file_name+'.h5', "w") as dataset:
        for i in value.keys():
            dataset[i] = value[i]
    return dataset

def load(file_name):
    with h5py.File('datasets/'+file_name+'.h5', "r") as dataset_orig:
        dataset = {}
        for i in dataset_orig.keys():
            dataset[i] = np.array(dataset_orig[i])
    return dataset

def save_list(file_name, value):
    print(value)
    with h5py.File('datasets/'+file_name+'.h5', "w") as dataset:
        dataset['data'] = value
    return dataset

def load_list(file_name):
    with h5py.File('datasets/'+file_name+'.h5', "r") as dataset_orig:
        dataset = dataset_orig['data']
    return dataset

# def log_cost(cost, learning_rate, learning_decay_rate, tran_accuracy, test_accuracy):
#     if os.path.isfile('datasets/costs_log.h5') == False:
#         save_list('costs_log', [{
#             'cost': cost,
#             'learning_rate': learning_rate,
#             'learning_decay_rate': learning_decay_rate,
#             'tran_accuracy': tran_accuracy,
#             'test_accuracy': test_accuracy
#         }])
#         return True
#     log = load_list('costs_log')
#     data = {
#         'cost': cost,
#         'learning_rate': learning_rate,
#         'learning_decay_rate': learning_decay_rate,
#         'tran_accuracy': tran_accuracy,
#         'test_accuracy': test_accuracy
#     }
#     if log.shape[0] > 5:
#         log = np.delete(log, 0, 0)
#     np.append(log, [data], axis = 0)
#     save_list('costs_log', log)

# def get_cost():
#     data = load('costs_log')
#     data.costs = 
#     if os.path.isfile('costs_log.npy') == False:
#         np.save('costs_log', np.array([cost]))
#         return True
#     costs=np.load('costs_log.npy')
#     if costs.shape[0] > 5:
#         costs = np.delete(costs, 0, 0)
#     costs = np.append(costs, [cost], axis = 0)
#     np.save('costs_log', costs)