【深度学习】吴恩达网易公开课练习(class1week4)

# 初始化参数，每一层的权重初始化为随机
# 输入layer_dims是每一层的节点数
# 输出parameters是字典，可以通过parameters['W' + str(l)]，parameters['b' + str(l)]获取每一层的初始参数
parameters = initialize_parameters_deep(layer_dims)   


# 线性前向传播函数
# 根据Z = W*A_prev + b计算当前层的Z， linear_cache=(A_prev, W, b)
Z, linear_cache = linear_forward(A_prev, W, b)


# 线性激活前向传播函数
# 根据A = g(Z) = g(W*A_prev + b)计算前向传播函数, 其中linear_activation_cache=(linear_cache, activation_cache)=((A_prev, W, b), (Z))
A, linear_activation_cache = linear_activation_forward(A_prev, W, b, activation = "sigmoid")


# L层完整的前向传输过程，输出的AL是最终输出，caches是每一层的缓存
AL, caches = L_model_forward(X, parameters)


# 线性反向传播函数
# 通过上述反向传播函数，通过dZ推导出dA_prev, dW, db，其中利用了缓存结果
dA_prev, dW, db = linear_backward(dZ, linear_cache)


# 线性激活函数反向传播
# 通过前面的linear_backward和激活函数导数计算dA_prev, dW, db
dA_prev, dW, db = linear_activation_backward(dA, linear_activation_cache, activation = "sigmoid")


# L层反向传播
# grads是每一层的导数，grads["dA" + str(l)]， grads["dW" + str(l)]， grads["db" + str(l)]格式
grads = L_model_backward(AL, Y, caches)


# 根据学习速率跟新参数
parameters = update_parameters(parameters, grads, 0.1) 


# 整体模型函数，通过迭代次数循环调用上述前向传播和反向传播函数实现
parameters = L_layer_model(train_x, train_y, layers_dims, learning_rate = 0.0075, num_iterations = 2500, print_cost = True)

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


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 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 load_data():
    train_dataset = h5py.File('datasets/train_catvnoncat.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_catvnoncat.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_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
 """
    
    if activation == "sigmoid":
        # Inputs: "A_prev, W, b". Outputs: "A, activation_cache".
        Z, linear_cache = linear_forward(A_prev, W, b)
        A, activation_cache = sigmoid(Z)
    
    elif activation == "relu":
        # Inputs: "A_prev, W, b". Outputs: "A, activation_cache".
        Z, linear_cache = linear_forward(A_prev, W, b)
        A, activation_cache = relu(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)
    
    # 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):
    """
 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]

    # Compute loss from aL and y.
    cost = (1./m) * (-np.dot(Y,np.log(AL).T) - 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 linear_backward(dZ, cache):
    """
 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)
    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):
    """
 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)
        dA_prev, dW, db = linear_backward(dZ, linear_cache)
        
    elif activation == "sigmoid":
        dZ = sigmoid_backward(dA, activation_cache)
        dA_prev, dW, db = linear_backward(dZ, linear_cache)
    
    return dA_prev, dW, db

def L_model_backward(AL, Y, caches):
    """
 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]
    grads["dA" + str(L)], 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 + 2)], current_cache, activation = "relu")
        grads["dA" + str(l + 1)] = 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


# GRADED FUNCTION: L_layer_model

def L_layer_model(X, Y, layers_dims, learning_rate = 0.0075, num_iterations = 3000, print_cost=False):#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.
 """

    np.random.seed(1)
    costs = []                         # keep track of cost
    
    # Parameters initialization.
    ### START CODE HERE ###
    parameters = initialize_parameters_deep(layers_dims)
    ### END CODE HERE ###
    
    # Loop (gradient descent)
    for i in range(0, num_iterations):

        # Forward propagation: [LINEAR -> RELU]*(L-1) -> LINEAR -> SIGMOID.
        ### START CODE HERE ### (≈ 1 line of code)
        AL, caches = L_model_forward(X, parameters)
        ### END CODE HERE ###
        
        # Compute cost.
        ### START CODE HERE ### (≈ 1 line of code)
        cost = compute_cost(AL, Y)
        ### END CODE HERE ###
    
        # Backward propagation.
        ### START CODE HERE ### (≈ 1 line of code)
        grads = L_model_backward(AL, Y, caches)
        ### END CODE HERE ###
 
        # Update parameters.
        ### START CODE HERE ### (≈ 1 line of code)
        parameters = update_parameters(parameters, grads, learning_rate)
        ### END CODE HERE ###
                
        # Print the cost every 100 training example
        if print_cost and i % 100 == 0:
            print ("Cost after iteration %i: %f" %(i, cost))
        if print_cost and i % 100 == 0:
            costs.append(cost)
            
    # plot the cost
    plt.plot(np.squeeze(costs))
    plt.ylabel('cost')
    plt.xlabel('iterations (per tens)')
    plt.title("Learning rate =" + str(learning_rate))
    plt.show()
    
    return parameters


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)

    
    # 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
    
    #print results
    #print ("predictions: " + str(p))
    #print ("true labels: " + str(y))
    print("Accuracy: "  + str(np.sum((p == y)/m)))
        
    return p


train_x_orig, train_y, test_x_orig, test_y, classes = load_data()
# Reshape the training and test examples 
train_x_flatten = train_x_orig.reshape(train_x_orig.shape[0], -1).T   # The "-1" makes reshape flatten the remaining dimensions
test_x_flatten = test_x_orig.reshape(test_x_orig.shape[0], -1).T
# Standardize data to have feature values between 0 and 1.
train_x = train_x_flatten/255.
test_x = test_x_flatten/255.
layers_dims = [12288, 20, 7, 5, 1]

parameters = L_layer_model(train_x, train_y, layers_dims, learning_rate = 0.0075, num_iterations = 2500, print_cost = True)
predictions_train = predict(train_x, train_y, parameters)
pred_test = predict(test_x, test_y, parameters)