吴恩达老师深度学习跟随作业（三）---------多层神经网络以及应用（IMUDGES）

于 2019-05-24 10:03:28 发布
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本文链接：https://blog.youkuaiyun.com/qq_40740411/article/details/90511327
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参考博客：https://blog.youkuaiyun.com/u013733326/article/details/79767169

开始过程还是和之前的一样

提前导入软件包

import numpy as np
import h5py
import matplotlib.pyplot as plt
import testCases
from dnn_utils import sigmoid, sigmoid_backward, relu, relu_backward
import lr_utils

dnn_utils.py部分的代码

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部分的代码

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

testCases.py部分的代码

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

然后主要代码，和之前一样，每个块注释的代码都只对上一部分的测试

import imageio
import numpy as np
import h5py
import matplotlib.pyplot as plt
from scipy import ndimage
from scipy.spatial import transform

import testCases
from dnn_utils import sigmoid, sigmoid_backward, relu, relu_backward
import lr_utils
import scipy
import scipy.ndimage
import scipy.misc
import matplotlib
from PIL import Image

np.random.seed(1)

def initialize_parameters(n_x, n_h, n_y):
    """
    初始化两层网络参数的函数
    :param n_x: 输入层节点数
    :param n_h: 隐藏层节点数
    :param n_y: 输出层节点数
    :return:
        parameters:
        W1:权重矩阵，维度（n_h，n_x）
        b1:偏向量，维度（n_h，1）
        W2:权重矩阵，维度（n_y，n_h）
        b2:谝向量，维度（n_y，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))

    #用断言来确保数据正确
    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
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"]))
"""

def initialize_parameters_deep(layers_dims):
    """
    初始化多层网络参数的函数
    :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：
                     W1 - 权重矩阵，维度为（layers_dims [1]，layers_dims [1-1]）
                     bl - 偏向量，维度为（layers_dims [1]，1）
    """
    np.random.seed(3)
    parameters = {}
    L = len(layers_dims)

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

        #是用断言确保数据正确
        assert (parameters["W" + str(i)].shape == (layers_dims[i], layers_dims[i - 1]))
        assert (parameters["b" + str(i)].shape == (layers_dims[i], 1))

    return parameters

"""
#测试initialize_parameters_deep
layers_dims = [5,4,3]
parameters = initialize_parameters_deep(layers_dims)
print("W1 = " + str(parameters["W1"]))
print("b1 = " + str(parameters["b1"]))
print("W2 = " + str(parameters["W2"]))
print("b2 = " + str(parameters["b2"]))
"""

###前向传播函数
"""
前向传播有以下三个步骤

LINEAR
LINEAR - >ACTIVATION，其中激活函数将会使用ReLU或Sigmoid。
[LINEAR - > RELU] ×（L-1） - > LINEAR - > SIGMOID（整个模型）
线性正向传播模块（向量化所有示例）使用公式(3)进行计算： 
Z[l]=W[l]A[l−1]+b[l]   (3)
"""

#前向传播的线性部分
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（当前涂层的节点数量，前一图层的节点数量）
    :param b: 偏向量，numpy向量，维度为（当前图层节点数量， 1）
    :return: Z:激活功能的输入，也称预激活函数
             cache：一个包含“A”，“W”和“b”的字典，存储这些变量以有效地计算后向传递
    """

    Z = np.dot(W, A) + b
    assert (Z.shape == (W.shape[0], A.shape[1]))
    cache = (A, W ,b)

    return Z, cache

"""
#测试linear_forward
A,W,b = testCases.linear_forward_test_case()
Z,linear_cache = linear_forward(A,W,b)
print("Z = " + str(Z))
"""

#线性激活部分
def linear_activation_forward(A_prev, W, b, activation):
    """
    实现线性激活部分这一层的前向传播
    :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（当前层的节点数量，前一层的大小）
    :param b: 偏移量，numpy阵列，维度为（当前层的节点数量， 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，也称激活后的值
    cache:一个包含“linear_cache”和“activation_cache”的字典，我们需要存储它以有效地计算后向传递
    """

    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_prev.shape[1]))
    cache = (linear_cache, activation_cache)

    return A, cache

"""
#测试linear_activation_forward
A_prev, W,b = testCases.linear_activation_forward_test_case()

A, linear_activation_cache = linear_activation_forward(A_prev, W, b, activation = "sigmoid")
print("sigmoid，A = " + str(A))

A, linear_activation_cache = linear_activation_forward(A_prev, W, b, activation = "relu")
print("ReLU，A = " + str(A))
"""

#多层模型的前向传播   通过调用上面两个函数实现
def L_model_forward(X, parameters):
    """
    多层网络的前向传播，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（）的每个cache（有L-1个，索引为从0到L-2）
                 linear_sigmoid_forward（）的cache（只有一个，索引为L-1）
    """

    caches = []
    A = X
    L = len(parameters) // 2
    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)

    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 = testCases.L_model_forward_test_case()
AL,caches = L_model_forward(X,parameters)
print("AL = " + str(AL))
print("caches 的长度为 = " + str(len(caches)))
"""

#计算成本
def compute_cost(AL, Y):
    """
    成本函数
    :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，如果是猫则为1），维度（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
Y,AL = testCases.compute_cost_test_case()
print("cost = " + str(compute_cost(AL, Y)))
"""

###反向传播

#后向传播的线性部分
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
dZ, linear_cache = testCases.linear_backward_test_case()

dA_prev, dW, db = linear_backward(dZ, linear_cache)
print ("dA_prev = "+ str(dA_prev))
print ("dW = " + str(dW))
print ("db = " + str(db))
"""

#反向线性激活函数
def linear_activation_backward(dA, cache, activation='relu'):
    """
    实现LINEAR->ACTIVATION层的后向传播
    :param dA: 当前层激活后的梯度值
    :param cache: 存储用于有效计算反向传播的值的元组（值为linear_cache，activation_cache）
    :param activation:使用的激活函数名，字符串类型，【"sigmoid" | "relu"】
    :return:dA_prev :相当于激活（前一层i-1）的成本梯度值，与A_prev维度相同
            dW:相当于W(当前层i)的成本梯度值，与W的维度相同
            db:相当于b(当前层i)的成本梯度值，与b的维度相同
    """

    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

"""
#测试linear_activation_backward
AL, linear_activation_cache = testCases.linear_activation_backward_test_case()

dA_prev, dW, db = linear_activation_backward(AL, linear_activation_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_activation_cache, activation = "relu")
print ("relu:")
print ("dA_prev = "+ str(dA_prev))
print ("dW = " + str(dW))
print ("db = " + str(db))
"""

#多层模型反向传播函数
def L_model_backward(AL, Y, caches):
    """
     对[LINEAR-> RELU] *（L-1） - > LINEAR - > SIGMOID组执行反向传播，就是多层网络的向后传播
    :param AL:概率向量，正向传播的输出（L_model_forward（））
    :param Y:标签向量（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))

    current_cache = caches[L - 1]
    grads["dA" + str(L)], grads["dW" + str(L)], grads["db" + str(L)] = linear_activation_backward(dAL, current_cache, "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, "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

"""
#测试L_model_backward
AL, Y_assess, caches = 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 ("dA1 = "+ str(grads["dA1"]))
"""

#更新参数
"""
更新参数公式
W[l]=W[l]−α * dW[l]

b[l]=b[l]−α * db[l]

α为学习率
"""
def update_parameters(parameters, grads, learning_rate):
    """
    使用梯度下降更新参数
    :param parameters: 包含自己参数的字典
    :param grads: 包含梯度值的字典，是L_model_backward的输出
    :param learming_rate: 学习率
    :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
    for i in range(L):
        parameters["W" + str(i + 1)] = parameters["W" + str(i + 1)] - learning_rate * grads["dW" + str(i + 1)]
        parameters["b" + str(i + 1)] = parameters["b" + str(i + 1)] - learning_rate * grads["db" + str(i + 1)]

    return parameters

"""
#测试update_parameters
parameters, grads = 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"]))
"""

###搭建神经网络

#搭建两层神经网络
def two_layer_model(X, Y, layers_dims, learning_rate = 0.0075, num_iterations = 3000, print_cost = False, isPlot = True):
    """
    实现两层神经网络
    :param X: 输入的数据，维度为（n_x，例子数）
    :param Y: 标签，向量，0不是猫，1是猫，维度为（1，数量）
    :param layers_dims: 层数的向量，维度为（n_y，n_h，n_y）
    :param learning_rate: 学习率
    :param num_iterations: 迭代的次数
    :param print_cost: 是否打印成本值
    :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

    #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"]

    #开始进行迭代
    for i in range(0, num_iterations):
        #前向传播
        A1, cache1 = linear_activation_forward(X, W1, b1, "relu")
        A2, cache2 = linear_activation_forward(A1, W2, b2, "sigmoid")

        #计算成本
        cost = compute_cost(A2, Y)

        #后向传播
        ##初始化后向传播
        dA2 = - (np.divide(Y, A2) - np.divide(1 - Y, 1 - A2))

        ##后向传播，输入：“dA2，cache2，cache1”。 输出：“dA1，dW2，db2;还有dA0（未使用），dW1，db1”。
        dA1, dW2, db2 = linear_activation_backward(dA2, cache2, "sigmoid")
        dA0, dW1, db1 = linear_activation_backward(dA1, cache1, "relu")

        ##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

        #更新参数
        parameters = update_parameters(parameters, grads, learning_rate)
        W1 = parameters["W1"]
        b1 = parameters["b1"]
        W2 = parameters["W2"]
        b2 = parameters["b2"]

        #打印成本函数，如果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

#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):
    """
    实现一个多层神经网络
    :param X: 输入的数据
    :param Y: 标签，向量，0为非猫，1为猫，维度（1，数量）
    :param layers_dims: 层数的向量，维度（n_y，n_h，…，n_h，n_y）
    :param learning_rate: 学习率
    :param num_iteration: 迭代次数
    :param print_cost: 是否打印成本值，每100次打印一次
    :param isPlot: 是否绘制出误差的图谱
    :return: parameters - 模型学习的参数，然后他们可以用来预测
    """
    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，如果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，根据条件绘制图
    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

#到此为止就可以加载数据集
train_set_x_orig , train_set_y , test_set_x_orig , test_set_y , classes = 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

#正式训练
"""  
#两层--
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)
"""


""" """
#多层--
layers_dims = [12288, 20, 7, 4, 1]
parameters = L_layer_model(train_x, train_set_y, layers_dims , num_iterations = 2500, print_cost=True,isPlot=True)



#预测函数
def predict(X, Y, parameters):
    """
    该函数用于预测L层神经网络的结果，当然也包含两层
    :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
    p = np.zeros((1, m))

    #根据参数前向传播
    probas, caches = L_model_forward(X, parameters)
    for i in range(0, probas.shape[1]):
        if probas[0, i] > 0.5:
            p[0, i] = 1
        else:
            p[0, i] = 0

    print("" + str(float(np.sum((p == Y)) / m)))
    return p

predictions_train = predict(train_x, train_y, parameters)#训练集
predictions_test = predict(test_x, test_y, parameters)#测试集

def print_mislabeled_images(classes, X, y, p):
    """
    绘制预测和实际不同的图像。
        X - 数据集
        y - 实际的标签
        p - 预测
    """
    a = p + y
    mislabeled_indices = np.asarray(np.where(a == 1))
    plt.rcParams['figure.figsize'] = (40, 40)
    num_images = len(mislabeled_indices[0])
    for i in range(num_images):
        index = mislabeled_indices[1][i]

        plt.subplot(2, num_images, i + 1)
        plt.imshow(X[:, index].reshape(64, 64, 3), interpolation='nearest')
        plt.show()
        plt.axis('off')
        plt.title(
            "Prediction: " + classes[int(p[0, index])].decode("utf-8") + " \n Class: " + classes[y[0, index]].decode(
                "utf-8"))


#print_mislabeled_images(classes, test_x, test_y, predictions_test)


## START CODE HERE ##
my_image = "cat.png" # change this to the name of your image file
my_label_y = [1] # the true class of your image (1 -> cat, 0 -> non-cat)
## END CODE HERE ##
num_px = 64
fname = my_image
image = np.array(matplotlib.pyplot.imread(fname))
#my_image = scipy.misc.imresize(image, size=(num_px,num_px))
image =transform.resize(image, (64, 64))
my_image = image.reshape(num_px*num_px*3,1)
my_predicted_image = predict(my_image, my_label_y, parameters)

plt.imshow(image)
plt.show()
print ("y = " + str(np.squeeze(my_predicted_image)) + ", your L-layer model predicts a \"" + classes[int(np.squeeze(my_predicted_image)),].decode("utf-8") +  "\" picture.")

接下来，搭建神经网络

 

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