【吴恩达深度学习编程作业】1.4深层神经网络——搭建多层神经网络及其应用

今天药忘吃喽~ 2022-12-15 11:04 178阅读 0赞

参考文档：[一步步搭建多层神经网络及其应用][Link 1] 码了两天终于码完了，搞不懂的地方CSDN大致是理解了，希望自己可以多回来看看吧。

## 目录结构 ##

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2tlaXZlbl8_size_16_color_FFFFFF_t_70_pic_center]

## main.py ##

import numpy as np
    import matplotlib.pyplot as plt
    import Deep_Learning.test4.testCases
    from Deep_Learning.test4.dnn_utils import sigmoid, sigmoid_backward, relu, relu_backward
    import Deep_Learning.test4.lr_utils
    
    np.random.seed(1)   # 指定随机种子
    
    
    # 初始化参数
    # 对于一个两层的神经网络结构，模型结构是线性->ReLU->线性->sigmoid
    def initialize_parameters(n_x, n_h, n_y):
        """ 此函数是为了初始化两层神经网络参数而使用的函数 :param n_x: -输入层节点数量 :param n_h: -隐藏层节点数量 :param n_y: -输出层节点数量 :return: parameters -包含参数的python字典 W1 -权重矩阵，维度为（n_h, n_x） b1 -偏向量，维度为（n_h, 1） W2 -权重矩阵，维度为（n_y, n_h） b2 -偏向量，维度为（n_y, 1） """
        W1 = np.random.rand(n_h, n_x) * 0.01
        b1 = np.zeros((n_h, 1))
        W2 = np.random.rand(n_y, n_h) * 0.01
        b2 = np.zeros((n_y, 1))
    
        # 使用断言确保数据格式的正确性
        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
    
    # 测试initialize_parameters
    print("=========================测试initialize_parameters======================")
    parameters = initialize_parameters(3, 2, 1)
    print("W1 = " + str(parameters["W1"]))
    print("b1 = " + str(parameters["b1"]))
    print("W2 = " + str(parameters["W2"]))
    print("b2 = " + str(parameters["b2"]))
    """ 运行结果： W1 = [[4.17022005e-03 7.20324493e-03 1.14374817e-06] [3.02332573e-03 1.46755891e-03 9.23385948e-04]] b1 = [[0.] [0.]] W2 = [[0.0018626 0.00345561]] b2 = [[0.]] """
    
    
    # L层的神经网络
    def initialize_parameters_deep(layers_dims):
        """ 初始化多层神经网络参数 :param layers_dims: -包含网络中每个图层的节点数量的列表 :return: parameters -包含参数"W1","b1",...,"WL","bL"的字典 Wl -权重矩阵，维度为（layer_dims[l],layer_dims[l-1]） bl -偏向量，维度为（layer_dims[l],1） """
        np.random.seed(3)
        parameters = { }
        L = len(layers_dims)
    
        for l in range(1, L):
            # 为什么/np.sqrt(layers_dims[l-1]在第二门课程1.11讲到，目的是防止梯度消失或梯度爆炸
            parameters["W" + str(l)] = np.random.randn(layers_dims[l], layers_dims[l - 1]) / np.sqrt(layers_dims[l - 1])
            parameters["b" + str(l)] = np.zeros((layers_dims[l], 1))
    
            # 使用断言确保数据正确性
            assert(parameters["W" + str(l)].shape == (layers_dims[l], layers_dims[l - 1]))
            assert(parameters["b" + str(l)].shape == (layers_dims[l], 1))
    
        return parameters
    
    # 测试initialize_parameters_deep
    print("==================测试initialize_parameters_deep======================")
    layer_dims = [5, 4, 3]
    parameters = initialize_parameters_deep(layer_dims)
    print("W1 = " + str(parameters["W1"]))
    print("b1 = " + str(parameters["b1"]))
    print("W2 = " + str(parameters["W2"]))
    print("b2 = " + str(parameters["b2"]))
    """ 运行结果： W1 = [[ 0.79989897 0.19521314 0.04315498 -0.83337927 -0.12405178] [-0.15865304 -0.03700312 -0.28040323 -0.01959608 -0.21341839] [-0.58757818 0.39561516 0.39413741 0.76454432 0.02237573] [-0.18097724 -0.24389238 -0.69160568 0.43932807 -0.49241241]] b1 = [[0.] [0.] [0.] [0.]] W2 = [[-0.59252326 -0.10282495 0.74307418 0.11835813] [-0.51189257 -0.3564966 0.31262248 -0.08025668] [-0.38441818 -0.11501536 0.37252813 0.98805539]] b2 = [[0.] [0.] [0.]] """
    
    # 前向传播函数
    # 线性部分
    def linear_forward(A, W, b):
        """ 实现前向传播的线性部分 :param A: -来自上一层（或输入数据）的激活，维度为（上一层的节点数量，示例的数量） :param W: -权重矩阵，numpy数组，维度为（当前图层的节点数量，上一图层的节点数量） :param b: -偏向量，numpy向量，维度为（当前图层的节点数量，1） :return: Z -激活功能的输入，也称为预激活参数 cache -一个包含"A"，"W"和"b"字典，存储这些变量方便计算后向传播 """
        Z = np.dot(W, A) + b
        # SyntaxWarning: assertion is always true, perhaps remove parentheses?
        # assert (Z.shape == W.shape[0], A.shape[1])
        cache = (A, W, b)
        return Z, cache
    
    # 测试linear_forward
    print("=================测试linear_forward================")
    A, W, b = Deep_Learning.test4.testCases.linear_forward_test_case()
    Z, liner_cache = linear_forward(A, W, b)
    print("Z = " + str(Z))
    """ 运行结果： Z = [[ 3.26295337 -1.23429987]] """
    
    # 激活部分
    def linear_activation_forward(A_prev, W, b, activation):
        """ 实现LINEAR -> ACTIVATION这一层的前向传播 :param A_prev: -来自上一层（或输入层）的激活，维度为（上一层的节点数量，示例数） :param W: -权重矩阵，numpy数组，维度为（当前图层的节点数量，上一图层的节点数量） :param b: -偏向量，numpy向量，维度为（当前图层的节点数量，1） :param activation: -选择在此层中使用的激活函数名，字符串类型，【"sigmoid" | "relu"】 :return: A -激活函数的输出，也称为激活后的值 cache -一个包含"linear_cache"和“activation_cache”的字典，储存以便于后向传播使用 """
        if activation == "sigmoid":
            Z, liner_cache = linear_forward(A_prev, W, b)
            A, activation_cache = sigmoid(Z)
        elif activation == "relu":
            Z,liner_cache = linear_forward(A_prev, W, b)
            A,activation_cache = relu(Z)
    
        assert (A.shape == (W.shape[0], A_prev.shape[1]))
        cache = (liner_cache, activation_cache)
    
        return A, cache
    
    # 测试linear_activation_forward
    print("====================测试linear_activation_forward======================")
    A_prev, W, b = Deep_Learning.test4.testCases.linear_activation_forward_test_case()
    A, linear_activaton_cache = linear_activation_forward(A_prev, W, b, activation="sigmoid")
    print("sigmoid, A = " + str(A))
    A, linear_activaton_cache = linear_activation_forward(A_prev, W, b, activation="relu")
    print("ReLU, A = " + str(A))
    """ 运行结果： sigmoid, A = [[0.96890023 0.11013289]] ReLU, A = [[3.43896131 0. ]] """
    
    
    # 多层模型的前向传播计算模型
    def L_model_forward(X, parameters):
        """ 实现[LINEAR -> ReLU] * (L - 1) ->LINEAR -> SIGMOID计算多层神经网络的前向传播，为后面每一层都执行LINEAR和ACTIVATION :param X: -数据，numpy数组，维度为（输入节点数量，示例数） :param parameters: -initialize_parameters_deep()的输出 :return: AL -最后的激活值 caches -包含以下内容的缓存列表： linear_relu_forward()的每一个cache(有L-1个，索引从0到L-2) linear_sigmoid_forward()的cache(只有一个，索引为L-1) """
        caches = []
        A = X
        # // 2是因为 parameters中存储有w_i,b_i两个参数，而L需要的是层数，每层两个参数，所以总参数个数/2就等于层数
        L = len(parameters) // 2
        for l in range(1, L):
            A_prev = A
            A, cache = linear_activation_forward(A_prev, parameters['W' + str(l)], parameters['b' + str(l)], "relu")
            caches.append(cache)
    
        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
    
    # 测试L_model_forward
    print("=====================测试L_model_forward========================")
    X, parameters = Deep_Learning.test4.testCases.L_model_forward_test_case()
    AL, caches = L_model_forward(X, parameters)
    print("AL = " + str(AL))
    print("cache的长度为 = " + str(len(caches)))
    """ 运行结果： AL = [[0.17007265 0.2524272 ]] cache的长度为 = 2 """
    
    
    # 计算成本
    def compute_cost(AL, Y):
        """ :param AL: -与标签预测相对应的概率向量，维度为（1，示例数量） :param Y: -标签向量（例如：如果不是猫则为0，是猫则为1），维度为（1，数量） :return: cost -交叉熵成本 """
        m = Y.shape[1]
        cost = - np.sum(np.multiply(np.log(AL), Y) + np.multiply(np.log(1 - AL), 1 - Y)) / m
    
        cost = np.squeeze(cost)
        assert (cost.shape == ())
    
        return cost
    
    # 测试compute_cost
    print("==========================测试compute_cost====================")
    Y, AL = Deep_Learning.test4.testCases.compute_cost_test_case()
    print("cost = " + str(compute_cost(AL, Y)))
    """ 运行结果： cost = 0.414931599615397 """
    
    # 反向传播
    # 线性部分
    def linear_backward(dZ, cache):
        """ 为单层实现反向传播的线性部分（第L层） :param dZ: -相对于（当前第l层的）线性输出的成本梯度 :param cache: -来自当前层前向传播的值的元组（A_prev, w, b） :return: dA_prev -相对于激活（前一层l-1）的成本梯度，与A_prev维度相同 dW -相对于W（当前层l）的成本梯度，与W的维度相同 db -相对于b（当前层l）的成本梯度，与b维度相同 """
        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
    
    # 测试linear_backward
    print("====================测试linear_backward===================")
    dZ, liner_cache = Deep_Learning.test4.testCases.linear_backward_test_case()
    dA_prev, dW, db = linear_backward(dZ, liner_cache)
    print("dA_prev = " + str(dA_prev))
    print("dW = " + str(dW))
    print("db = " + str(db))
    """ 运行结果： dA_prev = [[ 0.51822968 -0.19517421] [-0.40506361 0.15255393] [ 2.37496825 -0.89445391]] dW = [[-0.10076895 1.40685096 1.64992505]] db = [[0.50629448]] """
    
    # 线性激活
    def linear_activation_backward(dA, cache, activation="relu"):
        """ 实现LINEAR -> ACTIVATION层的后向传播 :param dA: -当前层l的激活后的梯度值 :param cache: -存储的用于计算反向传播的值的元组（值为linear_cache, activation） :param activation: -要在此层中使用的激活函数名，字符串类型，【"sigmoid" | "relu"】 :return: dA_prev -相对于激活（前一层l-1）的成本梯度下降，与A_prev维度相同 dW -相对于W（当前层l）的成本梯度值，与W维度相同 db -相对于b（当前层l）的成本梯度值，与b维度相同 """
        liner_cache, activation_cache = cache
        if activation == "relu":
            dZ = relu_backward(dA, activation_cache)
            dA_prev, dW, db = linear_backward(dZ, liner_cache)
        elif activation == "sigmoid":
            dZ = sigmoid_backward(dA, activation_cache)
            dA_prev, dW, db = linear_backward(dZ, liner_cache)
    
        return dA_prev, dW, db
    
    # 测试linear_activation_backward
    print("测试=====================linear_activation_backward==============")
    AL, linear_activaton_cache = Deep_Learning.test4.testCases.linear_activation_backward_test_case()
    
    dA_prev, dW, db = linear_activation_backward(AL, linear_activaton_cache, activation="sigmoid")
    print("sigmoid:")
    print("dA_prev: " + str(dA_prev))
    print("dW: " + str(dW))
    print("db: " + str(db) + "\n")
    
    dA_prev, dW, db = linear_activation_backward(AL, linear_activaton_cache, activation="relu")
    print("relu:")
    print("dA_prev: " + str(dA_prev))
    print("dW: " + str(dW))
    print("db: " + str(db))
    """ 运行结果： sigmoid: dA_prev: [[ 0.11017994 0.01105339] [ 0.09466817 0.00949723] [-0.05743092 -0.00576154]] dW: [[ 0.10266786 0.09778551 -0.01968084]] db: [[-0.05729622]] relu: dA_prev: [[ 0.44090989 0. ] [ 0.37883606 0. ] [-0.2298228 0. ]] dW: [[ 0.44513824 0.37371418 -0.10478989]] db: [[-0.20837892]] """
    
    # 多层模型的向后传播函数
    def L_model_backward(AL, Y, caches):
        """ 对[LINEAR -> RELU] * (L-1) -> LINEAR -> SIGMOID组执行反向传播，即多层神经网络的向后传播 :param AL: -概论向量，正向传播的输出(L_model_forward()) :param Y: -便签向量(例如如果不是猫则为0，如果是猫则为1，维度为(1, 数量)) :param caches: -包含以下内容的cache列表： linear_activation_forward("relu")的cache，不包含输出层 linear_activation_forward("sigmoid")的cache :return: grads -具有梯度值的字典 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)
    
        dAL = -(np.divide(Y, AL) - np.divide(1 - Y, 1 - AL))    # 参见笔记2.9：dL(a,y)/a=-y/a+(1-y)/(1-a) 
    
        current_cache = caches[L - 1]   # 存储caches里面的最后一个值
        grads["dA" + str(L - 1)], grads["dW" + str(L)], grads["db" + str(L)] = linear_activation_backward(dAL, current_cache, "sigmoid") # 返回dA[L-1],dW[L],db[L]
    
        for l in reversed(range(L - 1)):    # reversed.range(L-1)表示从倒数第二个元素开始，从后向前到第一个元素结束
            current_cache = caches[l]   # cache[l]表示的是caches[L-2]，即caches[]中存储的倒数第二个cache
            dA_prev_temp, dW_temp, db_temp = linear_activation_backward(grads["dA" + str(l + 1)], current_cache, "relu")    # dA_prev_temp=dA[L-2]
            grads["dA" + str(l)] = dA_prev_temp
            grads["dW" + str(l + 1)] = dW_temp
            grads["db" + str(l + 1)] = db_temp
    
        return grads
    
    # 测试L_model_backward
    print("==================测试L_model_backward==============")
    AL, Y_assess, caches = Deep_Learning.test4.testCases.L_model_backward_test_case()
    grads = L_model_backward(AL, Y_assess, caches)
    print("dW1 = " + str(grads["dW1"]))
    print("db1 = " + str(grads["db1"]))
    print("dA0 = " + str(grads["dA0"]))
    """ 运行结果： dW1 = [[0.41010002 0.07807203 0.13798444 0.10502167] [0. 0. 0. 0. ] [0.05283652 0.01005865 0.01777766 0.0135308 ]] db1 = [[-0.22007063] [ 0. ] [-0.02835349]] dA0 = [[ 0. 0.52257901] [ 0. -0.3269206 ] [ 0. -0.32070404] [ 0. -0.74079187]] """
    
    
    # 更新参数
    def update_parameters(parameters, grads, learning_rate):
        """ 使用梯度下降更新参数 :param parameters: -包含参数的字典 :param grads: -包含梯度值的字典，是L_model_backward的输出 :param learning_rate: -学习速率 :return: parameters -包含更新参数的字典 参数["W" + str(l)] = ... 参数["b" + str(l)] = ... """
        L = len(parameters) // 2    # 整除
        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
    
    # 测试update_parameters
    print("=========================测试update_parameters====================")
    parameters, grads = Deep_Learning.test4.testCases.update_parameters_test_case()
    parameters = update_parameters(parameters, grads, 0.1)
    print("W1 = " + str(parameters["W1"]))
    print("b1 = " + str(parameters["b1"]))
    print("W2 = " + str(parameters["W2"]))
    print("b2 = " + str(parameters["b2"]))
    """ 运行结果： W1 = [[-0.59562069 -0.09991781 -2.14584584 1.82662008] [-1.76569676 -0.80627147 0.51115557 -1.18258802] [-1.0535704 -0.86128581 0.68284052 2.20374577]] b1 = [[-0.04659241] [-1.28888275] [ 0.53405496]] W2 = [[-0.55569196 0.0354055 1.32964895]] b2 = [[-0.84610769]] """
    
    
    
    # 正式开始搭建两层的神经网络
    def two_layer_model(X, Y, layers_dims, learning_rate=0.0075, num_iterations=3000, print_cost=False, isPlot=True):
        """ 实现一个两层的神经网络，[LINEAR -> RELU] -> [LINEAR -> SIGMOID] :param X: -输入数据，维度为（n_x, 示例数） :param Y: -标签向量，0为非猫，1为猫，维度为（1, 数量） :param layers_dims: -层数的向量，维度为（n_x,n_h,n_y） :param learning_rate: -学习速率 :param num_iterations: -迭代次数 :param print_cost: -是否打印成本值，每100次打印一次 :param isPlot: -是否绘制出误差值的图谱 :return: parameters -一个包含W1, b1, W2, b2的字典变量 """
        np.random.seed(1)
        grads = { }
        costs = []
        (n_x, n_h, n_y) = layers_dims
    
        # 1.初始化参数
        parameters = initialize_parameters(n_x, n_h, n_y)
    
        W1 = parameters["W1"]
        b1 = parameters["b1"]
        W2 = parameters["W2"]
        b2 = parameters["b2"]
    
        # 2.开始迭代
        for i in range(0, num_iterations):
            # 2.1前向传播
            A1, cache1 = linear_activation_forward(X, W1, b1, "relu")
            A2, cache2 = linear_activation_forward(A1, W2, b2, "sigmoid")
    
            # 2.2计算成本
            cost = compute_cost(A2, Y)
    
            # 2.3后向传播
            # 2.3.1初始化后向传播
            dA2 = -(np.divide(Y, A2) - np.divide(1 - Y, 1 - A2))
            # 2.3.2向后传播，输入“dA2, cache2, cache1”，输出“dA1, dW2, db2, dA0(未使用)， dW1, db1”
            dA1, dW2, db2 = linear_activation_backward(dA2, cache2, "sigmoid")
            dA0, dW1, db1 = linear_activation_backward(dA1, cache1, "relu")
    
            # 2.3.3向后传播完成后的数据保存到grads
            grads["dW1"] = dW1
            grads["db1"] = db1
            grads["dW2"] = dW2
            grads["db2"] = db2
    
            # 2.4更新参数
            parameters = update_parameters(parameters, grads, learning_rate)
            W1 = parameters["W1"]
            b1 = parameters["b1"]
            W2 = parameters["W2"]
            b2 = parameters["b2"]
    
            # 打印成本值，如果print_cost=False则不打印
            if i % 100 == 0:
                # 记录成本
                costs.append(cost)
                # 是否打印成本值
                if print_cost:
                    print("第", i, "次迭代，成本值为：", np.squeeze(cost))
    
        # 3.迭代完成，根据条件绘图
        if isPlot:
            plt.plot(np.squeeze(costs))
            plt.ylabel('cost')
            plt.xlabel('iterations (per tens)')
            plt.title("Learning rate = " + str(learning_rate))
            plt.show()
    
        return parameters
    
    
    # 加载数据集，数据集为第二周作业数据
    """ ????????????????数据集的加载还需要熟悉，不是很懂 """
    train_set_x_orig, train_set_y, test_set_x_orig, test_set_y, classes = Deep_Learning.test4.lr_utils.load_dataset()
    
    train_x_flatten = train_set_x_orig.reshape(train_set_x_orig.shape[0], -1).T
    test_x_flatten = test_set_x_orig.reshape(test_set_x_orig.shape[0], -1).T
    
    train_x = train_x_flatten / 255
    train_y = train_set_y
    test_x = test_x_flatten / 255
    test_y = test_set_y
    
    # 加载数据完成，开始正式训练
    n_x = 12288
    n_h = 7
    n_y = 1
    layers_dims = (n_x, n_h, n_y)
    parameters = two_layer_model(train_x, train_set_y, layers_dims=(n_x, n_h, n_y), num_iterations=2500, print_cost=True, isPlot=True)
    
    # 预测函数
    def predict(X, y, parameters):
        """ 预测L层神经网络的结果 :param X: -测试集 :param y: -标签 :param parameters: -训练模型的参数 :return: p -给定数据集X的预测 """
        m = X.shape[1]
        n = len(parameters) // 2    # 神经网络的层数
        p = np.zeros((1, m))
    
        # 根据参数前向传播
        AL, caches = L_model_forward(X, parameters)
    
        for i in range(0, AL.shape[1]):
            if AL[0, i] > 0.5:
                p[0, i] = 1
            else:
                p[0, i] = 0
    
        print("准确度为：" + str(float(np.sum((p == y)) / m)))
    
        return p
    
    # 查看训练集和测试集的准确性
    print("=====================对于两层神经网络而言====================")
    predictions_train = predict(train_x, train_y, parameters)
    predictions_test = predict(test_x, test_y, parameters)
    
    
    
    
    # 正式搭建多层神经网络
    def L_layer_model(X, Y, layers_dims, learning_rate=0.0075, num_iterations=3000, print_cost=False, isPlot=True):
        """ 实现一个L层的神经网络[LINEAR -> RELU] * (L-1) -> LINEAR -> SIGMOID :param X: -输入数据，维度为（n_x, 示例数） :param Y: -标签向量，0为非猫，1为猫，维度为（1，数量） :param layers_dims: -层数的向量，维度为（n_x, n_h, n_y） :param learning_rate: -学习速率 :param num_iterations: -迭代次数 :param print_cost: -是否打印成本，每100次打印一次 :param isPlot: -是否绘制出误差值的图谱 :return: parameters -模型学习的参数，可以用来预测 """
        np.random.seed(1)
        costs = []
    
        parameters = initialize_parameters_deep(layers_dims)
    
        for i in range(0, num_iterations):
            AL, caches = L_model_forward(X, parameters)
    
            cost = compute_cost(AL, Y)
    
            grads = L_model_backward(AL, Y, caches)
    
            parameters = update_parameters(parameters, grads, learning_rate)
    
            # 打印成本值，若print_cost=False则忽略
            if i % 100 == 0:
                # 记录成本
                costs.append(cost)
                # 是否打印成本值
                if print_cost:
                    print("第", i, "次迭代，成本值为：", np.squeeze(cost))
    
        # 迭代完成，根据条件绘图
        if isPlot:
            plt.plot(np.squeeze(costs))
            plt.ylabel('cost')
            plt.xlabel('iterations (per tens)')
            plt.title("Learning rate = " + str(learning_rate))
            plt.show()
    
        return parameters
    
    # 加载数据集
    train_set_x_orig, train_set_y, test_set_x_orig, test_set_y, classes = Deep_Learning.test4.lr_utils.load_dataset()
    
    train_x_flatten = train_set_x_orig.reshape(train_set_x_orig.shape[0], -1).T
    test_x_flatten = test_set_x_orig.reshape(test_set_x_orig.shape[0], -1).T
    
    train_x = train_x_flatten / 255
    train_y = train_set_y
    test_x = test_x_flatten / 255
    test_y = test_set_y
    
    # 数据集加载完成，正式开始训练
    layers_dims = [12288, 20, 7, 5, 1]  # 5-layer model
    parameters = L_layer_model(train_x, train_y, layers_dims, num_iterations=2500, print_cost=True, isPlot=True)
    
    # 查看预测结果的准确性
    print("=========================对于L层神经网络而言=======================")
    pred_train = predict(train_x, train_y, parameters)
    pred_test = predict(test_x, test_y, parameters)
    
    
    
    # 分析：查看在L层被错误标记的图片
    def print_mislabeled_images(classes, X, y, p):
        """ 绘制预测和实际不同的图像 :param classes: -保存的是以bytes类型保存的两个字符串数据，数据位 :param X: -数据集 :param y: -实际的标签 :param p: -预测 :return: """
        a = p + y
        mislabeled_indices = np.asarray(np.where(a == 1))
        plt.rcParams['figure.figsize'] = (40.0, 40.0)   # 设置图片默认大小
        num_images = len(mislabeled_indices[0])
        for i in range(num_images):
            index = mislabeled_indices[1][i]
    
            plt.subplot(2, num_images, i + 1)   # subplot(行，列，索引的位置)，索引从1开始
            plt.imshow(X[:, index].reshape(64, 64, 3), interpolation='nearest')     # 最近邻插值
            plt.axis('off')     # 关闭坐标轴
            plt.title("Prediction:" + classes[int(p[0, index])].decode("utf-8") + "\n Class:"
                                    + classes[y[0, index]].decode("utf-8"))
        plt.show()
    
    print_mislabeled_images(classes, test_x, test_y, pred_test)
    
    
    """ 模型表现欠佳的图像原因包括: 猫身体在一个不同的位置 猫出现相似颜色背景下 不同的猫的颜色和品种 相机角度 图片宽度 比例变化（猫的图像非常大或很小） """
    
    
    # 选做：使用自己的图片，把图片放在特定位置然后识别
    from PIL import Image
    num_px = 64
    my_label_y = [1]     # the true class of your image(1 -> cat, 0 -> non_cat)
    # 读取--转三通道RGB（如果本身是三通道可以移除）--变换像素64*64image = Image.open("img/my_image.jpg")
    my_image = np.array(Image.open('img/my_image.jpg').convert("RGB").resize((num_px, num_px)))
    predict_image = my_image.reshape((num_px * num_px * 3, 1))
    
    print("=======================预测自己准备图片的准确性======================")
    predict_my_image = predict(predict_image, my_label_y, parameters)
    
    plt.imshow(my_image)
    plt.show()
    
    print("y = " + str(np.squeeze(predict_my_image)) + ", your L-layer model predicts a \"" + classes[int(np.squeeze(predict_my_image))].decode("utf-8") + "\" picture.")
    """ 运行结果： y = 1.0, your L-layer model predicts a "cat" picture. """

## testCases.py ##

import numpy as np
    
    def linear_forward_test_case():
        np.random.seed(1)
        """ X = np.array([[-1.02387576, 1.12397796], [-1.62328545, 0.64667545], [-1.74314104, -0.59664964]]) W = np.array([[ 0.74505627, 1.97611078, -1.24412333]]) b = np.array([[1]]) """
        A = np.random.randn(3,2)
        W = np.random.randn(1,3)
        b = np.random.randn(1,1)
        
        return A, W, b
    
    def linear_activation_forward_test_case():
        """ X = np.array([[-1.02387576, 1.12397796], [-1.62328545, 0.64667545], [-1.74314104, -0.59664964]]) W = np.array([[ 0.74505627, 1.97611078, -1.24412333]]) b = 5 """
        np.random.seed(2)
        A_prev = np.random.randn(3,2)
        W = np.random.randn(1,3)
        b = np.random.randn(1,1)
        return A_prev, W, b
    
    def L_model_forward_test_case():
        """ X = np.array([[-1.02387576, 1.12397796], [-1.62328545, 0.64667545], [-1.74314104, -0.59664964]]) parameters = {'W1': np.array([[ 1.62434536, -0.61175641, -0.52817175], [-1.07296862, 0.86540763, -2.3015387 ]]), 'W2': np.array([[ 1.74481176, -0.7612069 ]]), 'b1': np.array([[ 0.], [ 0.]]), 'b2': np.array([[ 0.]])} """
        np.random.seed(1)
        X = np.random.randn(4,2)
        W1 = np.random.randn(3,4)
        b1 = np.random.randn(3,1)
        W2 = np.random.randn(1,3)
        b2 = np.random.randn(1,1)
        parameters = { "W1": W1,
                      "b1": b1,
                      "W2": W2,
                      "b2": b2}
        
        return X, parameters
    
    def compute_cost_test_case():
        Y = np.asarray([[1, 1, 1]])
        aL = np.array([[.8,.9,0.4]])
        
        return Y, aL
    
    def linear_backward_test_case():
        """ z, linear_cache = (np.array([[-0.8019545 , 3.85763489]]), (np.array([[-1.02387576, 1.12397796], [-1.62328545, 0.64667545], [-1.74314104, -0.59664964]]), np.array([[ 0.74505627, 1.97611078, -1.24412333]]), np.array([[1]])) """
        np.random.seed(1)
        dZ = np.random.randn(1,2)
        A = np.random.randn(3,2)
        W = np.random.randn(1,3)
        b = np.random.randn(1,1)
        linear_cache = (A, W, b)
        return dZ, linear_cache
    
    def linear_activation_backward_test_case():
        """ aL, linear_activation_cache = (np.array([[ 3.1980455 , 7.85763489]]), ((np.array([[-1.02387576, 1.12397796], [-1.62328545, 0.64667545], [-1.74314104, -0.59664964]]), np.array([[ 0.74505627, 1.97611078, -1.24412333]]), 5), np.array([[ 3.1980455 , 7.85763489]]))) """
        np.random.seed(2)
        dA = np.random.randn(1,2)
        A = np.random.randn(3,2)
        W = np.random.randn(1,3)
        b = np.random.randn(1,1)
        Z = np.random.randn(1,2)
        linear_cache = (A, W, b)
        activation_cache = Z
        linear_activation_cache = (linear_cache, activation_cache)
        
        return dA, linear_activation_cache
    
    def L_model_backward_test_case():
        """ X = np.random.rand(3,2) Y = np.array([[1, 1]]) parameters = {'W1': np.array([[ 1.78862847, 0.43650985, 0.09649747]]), 'b1': np.array([[ 0.]])} aL, caches = (np.array([[ 0.60298372, 0.87182628]]), [((np.array([[ 0.20445225, 0.87811744], [ 0.02738759, 0.67046751], [ 0.4173048 , 0.55868983]]), np.array([[ 1.78862847, 0.43650985, 0.09649747]]), np.array([[ 0.]])), np.array([[ 0.41791293, 1.91720367]]))]) """
        np.random.seed(3)
        AL = np.random.randn(1, 2)
        Y = np.array([[1, 0]])
    
        A1 = np.random.randn(4,2)
        W1 = np.random.randn(3,4)
        b1 = np.random.randn(3,1)
        Z1 = np.random.randn(3,2)
        linear_cache_activation_1 = ((A1, W1, b1), Z1)
    
        A2 = np.random.randn(3,2)
        W2 = np.random.randn(1,3)
        b2 = np.random.randn(1,1)
        Z2 = np.random.randn(1,2)
        linear_cache_activation_2 = ( (A2, W2, b2), Z2)
    
        caches = (linear_cache_activation_1, linear_cache_activation_2)
    
        return AL, Y, caches
    
    def update_parameters_test_case():
        """ parameters = {'W1': np.array([[ 1.78862847, 0.43650985, 0.09649747], [-1.8634927 , -0.2773882 , -0.35475898], [-0.08274148, -0.62700068, -0.04381817], [-0.47721803, -1.31386475, 0.88462238]]), 'W2': np.array([[ 0.88131804, 1.70957306, 0.05003364, -0.40467741], [-0.54535995, -1.54647732, 0.98236743, -1.10106763], [-1.18504653, -0.2056499 , 1.48614836, 0.23671627]]), 'W3': np.array([[-1.02378514, -0.7129932 , 0.62524497], [-0.16051336, -0.76883635, -0.23003072]]), 'b1': np.array([[ 0.], [ 0.], [ 0.], [ 0.]]), 'b2': np.array([[ 0.], [ 0.], [ 0.]]), 'b3': np.array([[ 0.], [ 0.]])} grads = {'dW1': np.array([[ 0.63070583, 0.66482653, 0.18308507], [ 0. , 0. , 0. ], [ 0. , 0. , 0. ], [ 0. , 0. , 0. ]]), 'dW2': np.array([[ 1.62934255, 0. , 0. , 0. ], [ 0. , 0. , 0. , 0. ], [ 0. , 0. , 0. , 0. ]]), 'dW3': np.array([[-1.40260776, 0. , 0. ]]), 'da1': np.array([[ 0.70760786, 0.65063504], [ 0.17268975, 0.15878569], [ 0.03817582, 0.03510211]]), 'da2': np.array([[ 0.39561478, 0.36376198], [ 0.7674101 , 0.70562233], [ 0.0224596 , 0.02065127], [-0.18165561, -0.16702967]]), 'da3': np.array([[ 0.44888991, 0.41274769], [ 0.31261975, 0.28744927], [-0.27414557, -0.25207283]]), 'db1': 0.75937676204411464, 'db2': 0.86163759922811056, 'db3': -0.84161956022334572} """
        np.random.seed(2)
        W1 = np.random.randn(3,4)
        b1 = np.random.randn(3,1)
        W2 = np.random.randn(1,3)
        b2 = np.random.randn(1,1)
        parameters = { "W1": W1,
                      "b1": b1,
                      "W2": W2,
                      "b2": b2}
        np.random.seed(3)
        dW1 = np.random.randn(3,4)
        db1 = np.random.randn(3,1)
        dW2 = np.random.randn(1,3)
        db2 = np.random.randn(1,1)
        grads = { "dW1": dW1,
                 "db1": db1,
                 "dW2": dW2,
                 "db2": db2}
        
        return parameters, grads

## dnn\_utils.py ##

import numpy as np
    
    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 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 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

## lr\_utils.py ##

import numpy as np
    import h5py
        
        
    def load_dataset():
        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

## 运行结果 ##

=========================测试initialize_parameters======================
    W1 = [[4.17022005e-03 7.20324493e-03 1.14374817e-06]
     [3.02332573e-03 1.46755891e-03 9.23385948e-04]]
    b1 = [[0.]
     [0.]]
    W2 = [[0.0018626  0.00345561]]
    b2 = [[0.]]
    ==================测试initialize_parameters_deep======================
    W1 = [[ 0.79989897  0.19521314  0.04315498 -0.83337927 -0.12405178]
     [-0.15865304 -0.03700312 -0.28040323 -0.01959608 -0.21341839]
     [-0.58757818  0.39561516  0.39413741  0.76454432  0.02237573]
     [-0.18097724 -0.24389238 -0.69160568  0.43932807 -0.49241241]]
    b1 = [[0.]
     [0.]
     [0.]
     [0.]]
    W2 = [[-0.59252326 -0.10282495  0.74307418  0.11835813]
     [-0.51189257 -0.3564966   0.31262248 -0.08025668]
     [-0.38441818 -0.11501536  0.37252813  0.98805539]]
    b2 = [[0.]
     [0.]
     [0.]]
    =================测试linear_forward================
    Z = [[ 3.26295337 -1.23429987]]
    ====================测试linear_activation_forward======================
    sigmoid, A = [[0.96890023 0.11013289]]
    ReLU, A = [[3.43896131 0.        ]]
    =====================测试L_model_forward========================
    AL = [[0.17007265 0.2524272 ]]
    cache的长度为 = 2
    ==========================测试compute_cost====================
    cost = 0.414931599615397
    ====================测试linear_backward===================
    dA_prev = [[ 0.51822968 -0.19517421]
     [-0.40506361  0.15255393]
     [ 2.37496825 -0.89445391]]
    dW = [[-0.10076895  1.40685096  1.64992505]]
    db = [[0.50629448]]
    测试=====================linear_activation_backward==============
    sigmoid:
    dA_prev: [[ 0.11017994  0.01105339]
     [ 0.09466817  0.00949723]
     [-0.05743092 -0.00576154]]
    dW: [[ 0.10266786  0.09778551 -0.01968084]]
    db: [[-0.05729622]]
    
    relu:
    dA_prev: [[ 0.44090989  0.        ]
     [ 0.37883606  0.        ]
     [-0.2298228   0.        ]]
    dW: [[ 0.44513824  0.37371418 -0.10478989]]
    db: [[-0.20837892]]
    ==================测试L_model_backward==============
    dW1 = [[0.41010002 0.07807203 0.13798444 0.10502167]
     [0.         0.         0.         0.        ]
     [0.05283652 0.01005865 0.01777766 0.0135308 ]]
    db1 = [[-0.22007063]
     [ 0.        ]
     [-0.02835349]]
    dA0 = [[ 0.          0.52257901]
     [ 0.         -0.3269206 ]
     [ 0.         -0.32070404]
     [ 0.         -0.74079187]]
    =========================测试update_parameters====================
    W1 = [[-0.59562069 -0.09991781 -2.14584584  1.82662008]
     [-1.76569676 -0.80627147  0.51115557 -1.18258802]
     [-1.0535704  -0.86128581  0.68284052  2.20374577]]
    b1 = [[-0.04659241]
     [-1.28888275]
     [ 0.53405496]]
    W2 = [[-0.55569196  0.0354055   1.32964895]]
    b2 = [[-0.84610769]]
    第 0 次迭代，成本值为： 0.829942437000611
    第 100 次迭代，成本值为： 0.7818573247017775
    第 200 次迭代，成本值为： 0.6539324137759398
    第 300 次迭代，成本值为： 0.6514620469500948
    第 400 次迭代，成本值为： 0.6479215647343921
    第 500 次迭代，成本值为： 0.6370394959826985
    第 600 次迭代，成本值为： 0.6232298722708977
    第 700 次迭代，成本值为： 0.5898122359183274
    第 800 次迭代，成本值为： 0.5494888383394619
    第 900 次迭代，成本值为： 0.5081456895132139
    第 1000 次迭代，成本值为： 0.4684114873896508
    第 1100 次迭代，成本值为： 0.43101822373691157
    第 1200 次迭代，成本值为： 0.39592674052199744
    第 1300 次迭代，成本值为： 0.36297399801937474
    第 1400 次迭代，成本值为： 0.3322907935221445
    第 1500 次迭代，成本值为： 0.3016329118998794
    第 1600 次迭代，成本值为： 0.27214637093651933
    第 1700 次迭代，成本值为： 0.24269206419611508
    第 1800 次迭代，成本值为： 0.19083073982532248
    第 1900 次迭代，成本值为： 0.11637694704551979
    第 2000 次迭代，成本值为： 0.09759870407998461
    第 2100 次迭代，成本值为： 0.08281830207274377
    第 2200 次迭代，成本值为： 0.07098612498105607
    第 2300 次迭代，成本值为： 0.06142718125431676
    第 2400 次迭代，成本值为： 0.053635364487233765
    =====================对于两层神经网络而言====================
    准确度为：0.9952153110047847
    准确度为：0.68
    第 0 次迭代，成本值为： 0.715731513413713
    第 100 次迭代，成本值为： 0.6747377593469114
    第 200 次迭代，成本值为： 0.6603365433622127
    第 300 次迭代，成本值为： 0.6462887802148751
    第 400 次迭代，成本值为： 0.6298131216927773
    第 500 次迭代，成本值为： 0.606005622926534
    第 600 次迭代，成本值为： 0.5690041263975134
    第 700 次迭代，成本值为： 0.519796535043806
    第 800 次迭代，成本值为： 0.46415716786282285
    第 900 次迭代，成本值为： 0.40842030048298916
    第 1000 次迭代，成本值为： 0.37315499216069026
    第 1100 次迭代，成本值为： 0.30572374573047106
    第 1200 次迭代，成本值为： 0.26810152847740837
    第 1300 次迭代，成本值为： 0.23872474827672654
    第 1400 次迭代，成本值为： 0.20632263257914718
    第 1500 次迭代，成本值为： 0.17943886927493605
    第 1600 次迭代，成本值为： 0.1579873581880163
    第 1700 次迭代，成本值为： 0.14240413012274492
    第 1800 次迭代，成本值为： 0.12865165997888675
    第 1900 次迭代，成本值为： 0.1124431499816437
    第 2000 次迭代，成本值为： 0.08505631034982422
    第 2100 次迭代，成本值为： 0.05758391198616691
    第 2200 次迭代，成本值为： 0.044567534546991264
    第 2300 次迭代，成本值为： 0.03808275166600256
    第 2400 次迭代，成本值为： 0.034410749018419895
    =========================对于L层神经网络而言=======================
    准确度为：0.9952153110047847
    准确度为：0.78
    =======================预测自己准备图片的准确性======================
    准确度为：1.0
    y = 1.0, your L-layer model predicts a "cat" picture.

## 依次显示的图片 ##

**两层神经网络的代价函数图像**  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2tlaXZlbl8_size_16_color_FFFFFF_t_70_pic_center 1]

**L层神经网络的代价函数**  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2tlaXZlbl8_size_16_color_FFFFFF_t_70_pic_center 2]  
**预测错误的图片**  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2tlaXZlbl8_size_16_color_FFFFFF_t_70_pic_center 3]

**经过处理后的自己准备的猫的图片**  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2tlaXZlbl8_size_16_color_FFFFFF_t_70_pic_center 4]

[Link 1]: https://blog.csdn.net/u013733326/article/details/79767169
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[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2tlaXZlbl8_size_16_color_FFFFFF_t_70_pic_center 1]: /images/20221123/03d99d4dad8e4cc9bf26b0a453df00a3.png
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