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from dnn_utils_v2 import sigmoid, sigmoid_backward, relu, relu_backward
import numpy as np


# ------------------------------------------
def initialize_parameters_deep(layer_dims):
    """
    Arguments:
    layer_dims -- 包含网络中每一层的维度的Python List
    
    Returns:
    parameters -- Python参数字典 "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(3)
    parameters = {}
    L = len(layer_dims) # 网络层数

    for i in range(1, L):
        parameters["W" + str(i)] = np.random.randn(layer_dims[i], layer_dims[i - 1]) * 0.01
        parameters["b" + str(i)] = np.zeros(layer_dims[i], 1)

        assert(parameters["W" + str(i)].shape == (layer_dims[i], layer_dims[i - 1]))
        assert(parameters["b" + str(i)].shape == (layer_dims[i], 1))

    return parameters

# ------------------------------------------
def linear_forward(A, W, b):
    """
    实现前向传播的线性部分

    Arguments:
    A -- 来自上一层的激活结果 (或者为初始输入数据): (前一层的隐藏单元数, 样本数)
    W -- 权重矩阵: numpy array of shape (当前层的隐藏单元数, 前一层的隐藏单元数)
    b -- 偏置向量, numpy array of shape (当前层的隐藏单元数, 1)

    Returns:
    Z -- 激活函数的输入或称为预激活参数 
    cache -- Python参数字典包含"A", "W" and "b" ; stored for computing the backward pass efficiently
    """

    Z = np.dot(W, 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):
    """
    实现 线性——>激活层 的前向传播

    Arguments:
    A_prev -- 来自上层的激活结果 (或为初始输入数据): (前一层的隐藏单元数, 样本数)
    W -- 权重矩阵: numpy array of shape (当前层的隐藏单元数, 前一层的隐藏单元数)
    b -- 偏置向量, numpy array of shape (当前层的隐藏单元数, 1)
    activation -- 当前隐藏层使用的激活函数: "sigmoid" or "relu"

    Returns:
    A -- 激活函数的输出,也称为激活后值 
    cache -- Python字典包含 "线性缓存" and "激活缓存";
             stored for computing the backward pass efficiently
    """

    if activation == "sigmoid":
        Z, linear_cache = linear_forward(A_prev, W, b)
        A, activation_cache = sigmoid(Z)

    elif activation == "relu":
        Z, linear_cache = linear_forward(A_prev, W, b)
        A, activation_cache = relu(Z)

    assert(A.shape == (W.shape[0], A.shape[1]))
    cache = (linear_cache, activation_cache)

    return A, cache

# ------------------------------------------
# 为了实现L层神经网络更加方便，需要将前L-1层的激活函数设置为ReLU，最后一层输出层激活函数设置为Sigmoid
def L_model_forward(X, parameters):
    """
    实现前向传播： the [LINEAR->RELU]*(L-1)->LINEAR->SIGMOID computation
    
    Arguments:
    X -- 初始数据, numpy array of shape (输入层大小, 样本数量)
    parameters -- 初始化deep网络的参数输出
    
    Returns:
    AL -- 上一层激活后的值
    caches -- cache的列表:
                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
    # 前L-1层为relu激活函数
    for i in range(1, L):
        A_prev = A
        A, cache = linear_activation_forward(A_prev, parameters["W" + str(i)], parameters["b" + str(i)], "relu")
        caches.append(cache)
    # 最后一层为sigmoid激活函数
    AL, cache = linear_activation_forward(A, parameters["W" + str(L)], parameters["b" + str(L)], "sigmoid")
    caches.append(cache)

    assert(AL.shape == (1, X.shape[1]))

    return AL, caches

# ------------------------------------------
def compute_cost(AL, Y):
    """
    计算代价函数 使用Logistic回归中使用的代价函数

    Arguments:
    AL -- 对应于标签的预测概率向量, shape (1, 样本数)
    Y -- 正确的样本 (for example: containing 0 if non-cat, 1 if cat), shape (1, 样本数)

    Returns:
    cost -- 交叉熵代价
    """ 

    m = Y.shape[1]
    cost = -(np.dot(np.log(AL), Y.T) + np.dot(np.log(1 - AL), (1 - Y).T)) / m

    cost = np.squeeze(cost) # 使得cost的维度是我们想要的（比如将[[17]]变成17）
    assert(cost.shape == ())

    return cost

# ------------------------------------------
def linear_backward(dZ, cache):
    """
    单层实现反向传播的线性部分(l层)

    Arguments:
    dZ -- 代价函数对于线性输出的梯度 (l层)
    cache -- 元组(A_prev, W, b) 来自当前层的前向传播

    Returns:
    dA_prev -- 代价函数对于激活的梯度(l-1层), 和A_prev相同的维度
    dW -- 代价函数对于W的梯度 (l层), 和W相同的维度
    db -- 代价函数对于b的梯度 (l层), 和b相同的维度
    """

    A_prev, W, b = cache
    m = A_prev.shape[1]

    dW = np.dot(dZ, A_prev.T) / m
    db = np.sum(dZ, axis=1, keepdims=True) / m 
    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):
    """
    实现 线性——>激活 过程的反向传播
    
    Arguments:
    dA -- 当前层l激活后的梯度
    cache -- 元组 (linear_cache, activation_cache) 为了有效计算后向传播而存储
    activation -- 当前层的激活函数, stored as a text string: "sigmoid" or "relu"
    
    Returns:
    dA_prev -- 代价函数对于激活的梯度(l-1层), 和A_prev相同的维度,和A_prev相同的维度
    dW -- 代价函数对于W的梯度 (l层), 和W相同的维度
    db -- 代价函数对于b的梯度 (l层), 和b相同的维度
    """

    linear_cache, activation_cache = cache

    if activation == "relu":
        dZ = relu_backward(dA, activation)
        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):
    """
    前L-1层为ReLU激活函数,最后一层为sigmoid函数的后向传播实现
    
    Arguments:
    AL -- 前向传播输出的概率向量 (L_model_forward())
    Y -- 真实值的向量 (containing 0 if non-cat, 1 if cat)
    caches -- 包含cache的列表:
                every cache of linear_activation_forward() with "relu" (it's caches[l], for l in range(L-1) i.e l = 0...L-2)
                the cache of linear_activation_forward() with "sigmoid" (it's caches[L-1])
    
    Returns:
    grads -- 带有渐变值的字典
             grads["dA" + str(l)] = ... 
             grads["dW" + str(l)] = ...
             grads["db" + str(l)] = ... 
    """

    grads = {}
    L = len(caches)
    m = AL.shape[1]
    Y = Y.reshape(AL.shape) # 经过这一行转化，Y的维度和AL维度相同

    dAL = -(np.divide(Y, AL) - np.divide(1 - Y, 1 - AL))

    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 i in reversed(range(L-1)):
        current_cache = caches[i]
        dA_prev_temp, dW_temp, db_temp = linear_activation_backward(grads["dA" + str(i + 2)], current_cache, activation="relu")
        grads["dA" + str(i + 1)] = dA_prev_temp
        grads["dW" + str(i + 1)] = dW_temp
        grads["db" + str(i + 1)] = db_temp

    return grads

# ------------------------------------------
def update_parameters(parameters, grads, learning_rate):
    """
    使用梯度下降更新参数
    
    Arguments:
    parameters -- python dictionary containing your parameters 
    grads -- python dictionary containing your gradients, output of L_model_backward
    
    Returns:
    parameters -- 更新后的参数字典
                  parameters["W" + str(l)] = ... 
                  parameters["b" + str(l)] = ...
    """   

    L = len(parameters) // 2 # 神经网络中的层数

    for i in range(1, L + 1):
        parameters["W" + str(i)] -= learning_rate * grads["dW" + str(i)]
        parameters["b" + str(i)] -= learning_rate * grads["db" + str(i)]

    return parameters

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keep_prob = 0.8
def foward(X):
    # 3层neural network的前向传播
    A1 = np.maximum(0, np.dot(W1, X) + b1)  # 计算第一层网络的输出
    D1 = (np.random.rand(*A1.shape) < keep_prob)  # 以keep_prob为标准，判断该层结点哪些可以保留
    Z1 = np.multiply(A1, D1)     #dropout
    Z1 /= keep_prob   # 为了期望的一致，除以keep_prob

    A2 = np.maximum(0, np.dot(W2, Z1) + b2)
    D2 = (np.random.rand(*A2.shape) < keep_prob)
    Z2 = np.multiply(A2, D2) 
    Z2 /= keep_prob

    out = np.dot(W3, Z2) + b3

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import numpy as np
from gc_utils import sigmoid, relu, dictionary_to_vector, vector_to_dictionary, gradients_to_vector

#-------------------------------------------------
def forward_propagation_n(X, Y, parameters):
    """
    Implements the forward propagation (and computes the cost) presented in Figure 3.
    
    Arguments:
    X -- training set for m examples
    Y -- labels for m examples 
    parameters -- python dictionary containing your parameters "W1", "b1", "W2", "b2", "W3", "b3":
                    W1 -- weight matrix of shape (5, 4)
                    b1 -- bias vector of shape (5, 1)
                    W2 -- weight matrix of shape (3, 5)
                    b2 -- bias vector of shape (3, 1)
                    W3 -- weight matrix of shape (1, 3)
                    b3 -- bias vector of shape (1, 1)
    
    Returns:
    cost -- the cost function (logistic cost for one example)
    """
    
    # retrieve parameters
    m = X.shape[1]
    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)

    # Cost
    logprobs = np.multiply(-np.log(A3),Y) + np.multiply(-np.log(1 - A3), 1 - Y)
    cost = 1./m * np.sum(logprobs)
    
    cache = (Z1, A1, W1, b1, Z2, A2, W2, b2, Z3, A3, W3, b3)
    
    return cost, cache
  
#-------------------------------------------------
def backward_propagation_n(X, Y, cache):
    """
    Implement the backward propagation presented in figure 2.
    
    Arguments:
    X -- input datapoint, of shape (input size, 1)
    Y -- true "label"
    cache -- cache output from forward_propagation_n()
    
    Returns:
    gradients -- A dictionary with the gradients of the cost 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 = 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) * 2
    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 = 4./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

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def gradient_check_n(parameters, gradients, X, Y, epsilon = 1e-7):
    """
    Checks if backward_propagation_n computes correctly the gradient of the cost output by forward_propagation_n
    
    Arguments:
    parameters -- python dictionary containing your parameters "W1", "b1", "W2", "b2", "W3", "b3":
    grad -- output of backward_propagation_n, contains gradients of the cost with respect to the parameters. 
    x -- input datapoint, of shape (input size, 1)
    y -- true "label"
    epsilon -- tiny shift to the input to compute approximated gradient with formula(1)
    
    Returns:
    difference -- difference (2) between the approximated gradient and the backward propagation gradient
    """
    
    # Set-up variables
    parameters_values, _ = dictionary_to_vector(parameters)
    grad = gradients_to_vector(gradients)
    num_parameters = parameters_values.shape[0]
    J_plus = np.zeros((num_parameters, 1))
    J_minus = np.zeros((num_parameters, 1))
    gradapprox = np.zeros((num_parameters, 1))
    
    # Compute gradapprox
    for i in range(num_parameters):
        
        # Compute J_plus[i]. Inputs: "parameters_values, epsilon". Output = "J_plus[i]".
        # "_" is used because the function you have to outputs two parameters but we only care about the first one
        ### START CODE HERE ### (approx. 3 lines)
        epsilon = 0.01
        thetaplus = np.copy(parameters_values)                                      # Step 1
        thetaplus[i][0] = thetaplus[i][0] + epsilon                                # Step 2
        J_plus[i], _ = forward_propagation_n(X, Y, vector_to_dictionary(thetaplus))                                   # Step 3
        ### END CODE HERE ###
        
        # Compute J_minus[i]. Inputs: "parameters_values, epsilon". Output = "J_minus[i]".
        ### START CODE HERE ### (approx. 3 lines)
        thetaminus = np.copy(parameters_values)                                     # Step 1
        thetaminus[i][0] = thetaminus[i][0] - epsilon                               # Step 2        
        J_minus[i], _ = forward_propagation_n(X, Y, vector_to_dictionary(thetaminus))                                  # Step 3
        ### END CODE HERE ###
        
        # Compute gradapprox[i]
        ### START CODE HERE ### (approx. 1 line)
        gradapprox[i] = (J_plus[i] - J_minus[i]) / (2*epsilon)
        ### END CODE HERE ###
    
    # Compare gradapprox to backward propagation gradients by computing difference.
    ### START CODE HERE ### (approx. 1 line)
    # np.linalg.norm()的作用是求二范数
    numerator = np.linalg.norm(grad)                                           # Step 1'
    denominator = np.linalg.norm(gradapprox)                                         # Step 2'
    difference = np.linalg.norm(grad - gradapprox) / (numerator + denominator)                                          # Step 3'
    ### END CODE HERE ###

    if difference > 1e-7:
        print ("\033[93m" + "There is a mistake in the backward propagation! difference = " + str(difference) + "\033[0m")
    else:
        print ("\033[92m" + "Your backward propagation works perfectly fine! difference = " + str(difference) + "\033[0m")
    
    return difference

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import numpy as np
import matplotlib.pyplot as plt
import sklearn
import sklearn.datasets
from init_utils import sigmoid, relu, compute_loss, forward_propagation, backward_propagation
from init_utils import update_parameters, predict, load_dataset, plot_decision_boundary, predict_dec

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

# load image dataset: blue/red dots in circles
train_X, train_Y, test_X, test_Y = load_dataset()

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def model(X, Y, learning_rate = 0.01, num_iterations = 15000, print_cost = True, initialization = "he"):
    """
    Implements a three-layer neural network: LINEAR->RELU->LINEAR->RELU->LINEAR->SIGMOID.
    
    Arguments:
    X -- input data, of shape (2, number of examples)
    Y -- true "label" vector (containing 0 for red dots; 1 for blue dots), of shape (1, number of examples)
    learning_rate -- learning rate for gradient descent 
    num_iterations -- number of iterations to run gradient descent
    print_cost -- if True, print the cost every 1000 iterations
    initialization -- flag to choose which initialization to use ("zeros","random" or "he")
    
    Returns:
    parameters -- parameters learnt by the model
    """
        
    grads = {}
    costs = [] # to keep track of the loss
    m = X.shape[1] # number of examples
    layers_dims = [X.shape[0], 10, 5, 1]
    
    # Initialize parameters dictionary.
    if initialization == "zeros":
        parameters = initialize_parameters_zeros(layers_dims)
    elif initialization == "random":
        parameters = initialize_parameters_random(layers_dims)
    elif initialization == "he":
        parameters = initialize_parameters_he(layers_dims)

    # Loop (gradient descent)

    for i in range(0, num_iterations):

        # Forward propagation: LINEAR -> RELU -> LINEAR -> RELU -> LINEAR -> SIGMOID.
        a3, cache = forward_propagation(X, parameters)
        
        # Loss
        cost = compute_loss(a3, Y)

        # Backward propagation.
        grads = backward_propagation(X, Y, cache)
        
        # Update parameters.
        parameters = update_parameters(parameters, grads, learning_rate)
        
        # Print the loss every 1000 iterations
        if print_cost and i % 1000 == 0:
            print("Cost after iteration {}: {}".format(i, cost))
            costs.append(cost)
            
    # plot the loss
    plt.plot(costs)
    plt.ylabel('cost')
    plt.xlabel('iterations (per hundreds)')
    plt.title("Learning rate =" + str(learning_rate))
    plt.show()
    
    return parameters

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def initialize_parameters_zeros(layers_dims):
    """
    Arguments:
    layer_dims -- python array (list) containing the size of each layer.
    
    Returns:
    parameters -- python dictionary containing your parameters "W1", "b1", ..., "WL", "bL":
                    W1 -- weight matrix of shape (layers_dims[1], layers_dims[0])
                    b1 -- bias vector of shape (layers_dims[1], 1)
                    ...
                    WL -- weight matrix of shape (layers_dims[L], layers_dims[L-1])
                    bL -- bias vector of shape (layers_dims[L], 1)
    """
    
    parameters = {}
    L = len(layers_dims)            # number of layers in the network
    
    for i in range(1, L):
        ### START CODE HERE ### (≈ 2 lines of code)
        parameters['W' + str(i)] = np.zeros((layers_dims[i], layers_dims[i - 1]))
        parameters['b' + str(i)] = np.zeros((layers_dims[i], 1))
        ### END CODE HERE ###
    return parameters
  
#---------------------------------------------
parameters = initialize_parameters_zeros([3,2,1])
parameters = model(train_X, train_Y, initialization = "zeros")
print ("On the train set:")
predictions_train = predict(train_X, train_Y, parameters)
print ("On the test set:")
predictions_test = predict(test_X, test_Y, parameters)

#---------------------------------------------
# 画图
def plot_decision_boundary(model, X, y):
    #import pdb;pdb.set_trace()
    # 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
    plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral)
    plt.ylabel('x2')
    plt.xlabel('x1')
    y = y.reshape(X[0,:].shape)#must reshape,otherwise confliction with dimensions
    plt.scatter(X[0, :], X[1, :], c=y, cmap=plt.cm.Spectral)
    plt.show()

#---------------------------------------------
plt.title("Model with Zeros initialization")
axes = plt.gca()
axes.set_xlim([-1.5,1.5])
axes.set_ylim([-1.5,1.5])
plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)

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def initialize_parameters_random(layers_dims):
    """
    Arguments:
    layer_dims -- python array (list) containing the size of each layer.
    
    Returns:
    parameters -- python dictionary containing your parameters "W1", "b1", ..., "WL", "bL":
                    W1 -- weight matrix of shape (layers_dims[1], layers_dims[0])
                    b1 -- bias vector of shape (layers_dims[1], 1)
                    ...
                    WL -- weight matrix of shape (layers_dims[L], layers_dims[L-1])
                    bL -- bias vector of shape (layers_dims[L], 1)
    """
    
    np.random.seed(3)               # This seed makes sure your "random" numbers will be the as ours
    parameters = {}
    L = len(layers_dims)            # integer representing the number of layers
    
    for i in range(1, L):
        ### START CODE HERE ### (≈ 2 lines of code)
        parameters['W' + str(i)] = np.random.randn(layers_dims[i], layers_dims[i - 1]) * 10
        parameters['b' + str(i)] = np.zeros((layers_dims[i], 1))
        ### END CODE HERE ###

    return parameters
  
#---------------------------------------------
parameters = initialize_parameters_random([3, 2, 1])
parameters = model(train_X, train_Y, initialization = "random")
print ("On the train set:")
predictions_train = predict(train_X, train_Y, parameters)
print ("On the test set:")
predictions_test = predict(test_X, test_Y, parameters)

#---------------------------------------------
# 画图
plt.title("Model with large random initialization")
axes = plt.gca()
axes.set_xlim([-1.5,1.5])
axes.set_ylim([-1.5,1.5])
plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)

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def initialize_parameters_he(layers_dims):
    """
    Arguments:
    layer_dims -- python array (list) containing the size of each layer.
    
    Returns:
    parameters -- python dictionary containing your parameters "W1", "b1", ..., "WL", "bL":
                    W1 -- weight matrix of shape (layers_dims[1], layers_dims[0])
                    b1 -- bias vector of shape (layers_dims[1], 1)
                    ...
                    WL -- weight matrix of shape (layers_dims[L], layers_dims[L-1])
                    bL -- bias vector of shape (layers_dims[L], 1)
    """
    
    np.random.seed(3)
    parameters = {}
    L = len(layers_dims) - 1 # integer representing the number of layers
     
    for i in range(1, L + 1):
        ### START CODE HERE ### (≈ 2 lines of code)
        parameters['W' + str(i)] = np.random.randn(layers_dims[i],layers_dims[i - 1]) * np.sqrt(2.0 / layers_dims[i - 1])
        parameters['b' + str(i)] = np.zeros((layers_dims[i], 1))
        ### END CODE HERE ###
        
    return parameters
  
#---------------------------------------------
parameters = initialize_parameters_he([2, 4, 1])
parameters = model(train_X, train_Y, initialization = "he")
print ("On the train set:")
predictions_train = predict(train_X, train_Y, parameters)
print ("On the test set:")
predictions_test = predict(test_X, test_Y, parameters)

#---------------------------------------------
# 画图
plt.title("Model with He initialization")
axes = plt.gca()
axes.set_xlim([-1.5,1.5])
axes.set_ylim([-1.5,1.5])
plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)

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import numpy as np
import matplotlib.pyplot as plt
from reg_utils import sigmoid, relu, plot_decision_boundary, initialize_parameters, load_2D_dataset, predict_dec
from reg_utils import compute_cost, predict, forward_propagation, backward_propagation, update_parameters
import sklearn
import sklearn.datasets
import scipy.io
from testCases import *

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

train_X, train_Y, test_X, test_Y = load_2D_dataset()

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# 这里其实已经包含了L2正则化和dropout正则化的情况，只默认情况下的参数不使用正则化
def model(X, Y, learning_rate = 0.3, num_iterations = 30000, print_cost = True, lambd = 0, keep_prob = 1):
    """
    Implements a three-layer neural network: LINEAR->RELU->LINEAR->RELU->LINEAR->SIGMOID.
    
    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 (output size, number of examples)
    learning_rate -- learning rate of the optimization
    num_iterations -- number of iterations of the optimization loop
    print_cost -- If True, print the cost every 10000 iterations
    lambd -- regularization hyperparameter, scalar
    keep_prob - probability of keeping a neuron active during drop-out, scalar.
    
    Returns:
    parameters -- parameters learned by the model. They can then be used to predict.
    """
        
    grads = {}
    costs = []                            # to keep track of the cost
    m = X.shape[1]                        # number of examples
    layers_dims = [X.shape[0], 20, 3, 1]  # 网络结构为三层网络结构，分别有20，3，1个节点 
    
    # Initialize parameters dictionary.
    parameters = initialize_parameters(layers_dims)

    # Loop (gradient descent)

    for i in range(0, num_iterations):

        # Forward propagation: LINEAR -> RELU -> LINEAR -> RELU -> LINEAR -> SIGMOID.
        if keep_prob == 1:
            a3, cache = forward_propagation(X, parameters)
        elif keep_prob < 1:
            a3, cache = forward_propagation_with_dropout(X, parameters, keep_prob)
        
        # Cost function
        if lambd == 0:
            cost = compute_cost(a3, Y)
        else:
            cost = compute_cost_with_regularization(a3, Y, parameters, lambd)
            
        # Backward propagation.
        assert(lambd==0 or keep_prob==1)    # it is possible to use both L2 regularization and dropout, 
                                            # but this assignment will only explore one at a time
        if lambd == 0 and keep_prob == 1:
            grads = backward_propagation(X, Y, cache)
        elif lambd != 0:
            grads = backward_propagation_with_regularization(X, Y, cache, lambd)
        elif keep_prob < 1:
            grads = backward_propagation_with_dropout(X, Y, cache, keep_prob)
        
        # Update parameters.
        parameters = update_parameters(parameters, grads, learning_rate)
        
        # Print the loss every 10000 iterations
        if print_cost and i % 10000 == 0:
            print("Cost after iteration {}: {}".format(i, cost))
        if print_cost and i % 1000 == 0:
            costs.append(cost)
    
    # plot the cost
    plt.plot(costs)
    plt.ylabel('cost')
    plt.xlabel('iterations (x1,000)')
    plt.title("Learning rate =" + str(learning_rate))
    plt.show()
    
    return parameters
  
  
#----------------------------------------------------
parameters = model(train_X, train_Y)
print ("On the training set:")
predictions_train = predict(train_X, train_Y, parameters)
print ("On the test set:")
predictions_test = predict(test_X, test_Y, parameters)
# 画图
plt.title("Model without regularization")
axes = plt.gca()
axes.set_xlim([-0.75,0.40])
axes.set_ylim([-0.75,0.65])
plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)

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# 前向传播
def compute_cost_with_regularization(A3, Y, parameters, lambd):
    """
    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))
    """
    m = Y.shape[1]
    W1 = parameters["W1"]
    W2 = parameters["W2"]
    W3 = parameters["W3"]
    
    cross_entropy_cost = compute_cost(A3, Y) # This gives you the cross-entropy part of the cost
    
    ### START CODE HERE ### (approx. 1 line)
    L2_regularization_cost = lambd * (np.sum(np.square(W1)) + np.sum(np.square(W2)) + np.sum(np.square(W3))) / (2*m)
    ### END CODER HERE ###
    
    cost = cross_entropy_cost + L2_regularization_cost
    
    return cost
  
#----------------------------------------------------
# 后向传播
def backward_propagation_with_regularization(X, Y, cache, lambd):
    """
    Implements the backward propagation of our baseline model to which we added an L2 regularization.
    
    Arguments:
    X -- input dataset, of shape (input size, number of examples)
    Y -- "true" labels vector, of shape (output size, number of examples)
    cache -- cache output from forward_propagation()
    lambd -- regularization hyperparameter, scalar
    
    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 = A3 - Y
    
    ### START CODE HERE ### (approx. 1 line)
    dW3 = 1./m * np.dot(dZ3, A2.T) + lambd * W3 / m
    ### END CODE HERE ###
    db3 = 1./m * np.sum(dZ3, axis=1, keepdims = True)
    
    dA2 = np.dot(W3.T, dZ3)
    dZ2 = np.multiply(dA2, np.int64(A2 > 0))
    ### START CODE HERE ### (approx. 1 line)
    dW2 = 1./m * np.dot(dZ2, A1.T) + lambd * W2 / m
    ### END CODE HERE ###
    db2 = 1./m * np.sum(dZ2, axis=1, keepdims = True)
    
    dA1 = np.dot(W2.T, dZ2)
    dZ1 = np.multiply(dA1, np.int64(A1 > 0))
    ### START CODE HERE ### (approx. 1 line)
    dW1 = 1./m * np.dot(dZ1, X.T) + lambd * W1 / m
    ### END CODE HERE ###
    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
  
#----------------------------------------------------
# 使用L2正则化进行梯度下降
parameters = model(train_X, train_Y, lambd = 0.7)
print ("On the train set:")
predictions_train = predict(train_X, train_Y, parameters)
print ("On the test set:")
predictions_test = predict(test_X, test_Y, parameters)
# 画图
plt.title("Model with L2-regularization")
axes = plt.gca()
axes.set_xlim([-0.75,0.40])
axes.set_ylim([-0.75,0.65])
plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)

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# 前向传播
def forward_propagation_with_dropout(X, parameters, keep_prob = 0.5):
    """
    Implements the forward propagation: LINEAR -> RELU + DROPOUT -> LINEAR -> RELU + DROPOUT -> LINEAR -> SIGMOID.
    
    Arguments:
    X -- input dataset, of shape (2, number of examples)
    parameters -- python dictionary containing your parameters "W1", "b1", "W2", "b2", "W3", "b3":
                    W1 -- weight matrix of shape (20, 2)
                    b1 -- bias vector of shape (20, 1)
                    W2 -- weight matrix of shape (3, 20)
                    b2 -- bias vector of shape (3, 1)
                    W3 -- weight matrix of shape (1, 3)
                    b3 -- bias vector of shape (1, 1)
    keep_prob - probability of keeping a neuron active during drop-out, scalar
    
    Returns:
    A3 -- last activation value, output of the forward propagation, of shape (1,1)
    cache -- tuple, information stored for computing the backward propagation
    """
    
    np.random.seed(1)
    
    # 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)
    ### START CODE HERE ### (approx. 4 lines)         # Steps 1-4 below correspond to the Steps 1-4 described above. 
    D1 = np.random.rand(*A1.shape)                    # Step 1: initialize matrix D1 = np.random.rand(..., ...)
    D1 = D1 < keep_prob                               # Step 2: convert entries of D1 to 0 or 1 (using keep_prob as the threshold)
    A1 = np.multiply(A1, D1)                          # Step 3: shut down some neurons of A1
    A1 = A1 / keep_prob                               # Step 4: scale the value of neurons that haven't been shut down
    ### END CODE HERE ###
    Z2 = np.dot(W2, A1) + b2
    A2 = relu(Z2)
    ### START CODE HERE ### (approx. 4 lines)
    D2 = np.random.rand(*A2.shape)                    # Step 1: initialize matrix D2 = np.random.rand(..., ...)
    D2 = D2 < keep_prob                               # Step 2: convert entries of D2 to 0 or 1 (using keep_prob as the threshold)
    A2 = np.multiply(A2, D2)                          # Step 3: shut down some neurons of A2
    A2 = A2 / keep_prob                               # Step 4: scale the value of neurons that haven't been shut down
    ### END CODE HERE ###
    Z3 = np.dot(W3, A2) + b3
    A3 = sigmoid(Z3)
    
    cache = (Z1, D1, A1, W1, b1, Z2, D2, A2, W2, b2, Z3, A3, W3, b3)
    
    return A3, cache
  
  
#----------------------------------------------
# 后向传播
def backward_propagation_with_dropout(X, Y, cache, keep_prob):
    """
    Implements the backward propagation of our baseline model to which we added dropout.
    
    Arguments:
    X -- input dataset, of shape (2, number of examples)
    Y -- "true" labels vector, of shape (output size, number of examples)
    cache -- cache output from forward_propagation_with_dropout()
    keep_prob - probability of keeping a neuron active during drop-out, scalar
    
    Returns:
    gradients -- A dictionary with the gradients with respect to each parameter, activation and pre-activation variables
    """
    
    m = X.shape[1]
    (Z1, D1, A1, W1, b1, Z2, D2, 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)
    ### START CODE HERE ### (≈ 2 lines of code)
    dA2 = dA2 * D2              # Step 1: Apply mask D2 to shut down the same neurons as during the forward propagation
    dA2 = dA2 / keep_prob       # Step 2: Scale the value of neurons that haven't been shut down
    ### END CODE HERE ###
    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)
    ### START CODE HERE ### (≈ 2 lines of code)
    dA1 = dA1 * D1              # Step 1: Apply mask D1 to shut down the same neurons as during the forward propagation
    dA1 = dA1 / keep_prob       # Step 2: Scale the value of neurons that haven't been shut down
    ### END CODE HERE ###
    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
  
#-------------------------------------------------------------------
# 使用dropout正则化来梯度下降
parameters = model(train_X, train_Y, keep_prob = 0.86, learning_rate = 0.3)

print ("On the train set:")
predictions_train = predict(train_X, train_Y, parameters)
print ("On the test set:")
predictions_test = predict(test_X, test_Y, parameters)
# 画图
plt.title("Model with dropout")
axes = plt.gca()
axes.set_xlim([-0.75,0.40])
axes.set_ylim([-0.75,0.65])
plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)