吴恩达深度学习：course2 - week1 课后作业（代码解读）

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我是靠谱客的博主自觉路灯，最近开发中收集的这篇文章主要介绍吴恩达深度学习：course2 - week1 课后作业（代码解读），觉得挺不错的，现在分享给大家，希望可以做个参考。

概述

https://blog.csdn.net/u013733326/article/details/79847918
参考该博主完成的代码作业，本文主要针对代码中的一些函数以及为何这样用做一些自己的理解，直接放代码：
main.py

import numpy as np
import matplotlib.pyplot as plt
import sklearn
import sklearn.datasets
import gc_utils
import init_utils
import reg_utils
import initialize_param
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 = init_utils.load_dataset(is_plot=False)
#
# def model(X,Y,learning_rate=0.01,num_iterations=15000,print_cost=True,initialization="he",is_Plot=True):
#
grads = {}
#
costs = []
#
#
m = X.shape[1]
#
layers_dims = [X.shape[0],10,5,1]
#
#
if initialization == "zeros":
#
parameters = initialize_param.initialize_parameters_zeros(layers_dims)
#
#
elif initialization == "random":
#
parameters = initialize_param.initialize_parameters_random(layers_dims)
#
#
elif initialization == "he":
#
parameters = initialize_param.initialize_pwrameters_he(layers_dims)
#
#
else :
#
print("初始化参数错误，程序退出")
#
exit
#
#
for i in range(0,num_iterations):
#
#
a3,cache = init_utils.forward_propagation(X,parameters)
#
#
cost = init_utils.compute_loss(a3,Y)
#
#
grads = init_utils.backward_propagation(X,Y,cache)
#
#
parameters = init_utils.update_parameters(parameters,grads,learning_rate)
#
#
if i % 1000 == 0:
#
costs.append(cost)
#
if print_cost:
#
print("第" + str(i) + "次迭代，成本值为：" + str(cost))
#
#
if is_Plot:
#
plt.plot(costs)
#
plt.ylabel("cost")
#
plt.xlabel("iterations(per thousands)")
#
plt.title("learning_rate = " + str(learning_rate))
#
plt.show()
#
#
return parameters
#初始化为0
# parameters = initialize_param.initialize_parameters_zeros([3,2,1])
# print("W1 = " + str(parameters["W1"]))
# print("b1 = " + str(parameters["b1"]))
# print("W2 = " + str(parameters["W2"]))
# print("b2 = " + str(parameters["b2"]))
#
# parameters = model(train_X, train_Y, initialization = "zeros",is_Plot=True)
# print ("训练集:")
# predictions_train = init_utils.predict(train_X, train_Y, parameters)
# print ("测试集:")
# predictions_test = init_utils.predict(test_X, test_Y, parameters)
#
# print("predictions_train = " + str(predictions_train))
# print("predictions_test = " + str(predictions_test))
#
# plt.title("Model with Zeros initialization")
# axes = plt.gca()
# axes.set_xlim([-1.5, 1.5])
# axes.set_ylim([-1.5, 1.5])
# init_utils.plot_decision_boundary(lambda x: init_utils.predict_dec(parameters, x.T), train_X, train_Y)
#初始化为随机
# parameters = initialize_param.initialize_parameters_random([3, 2, 1])
# print("W1 = " + str(parameters["W1"]))
# print("b1 = " + str(parameters["b1"]))
# print("W2 = " + str(parameters["W2"]))
# print("b2 = " + str(parameters["b2"]))
# parameters = model(train_X, train_Y, initialization = "random",is_Plot=True)
# print("训练集：")
# predictions_train = init_utils.predict(train_X, train_Y, parameters)
# print("测试集：")
# predictions_test = init_utils.predict(test_X, test_Y, parameters)
#
# print(predictions_train)
# print(predictions_test)
# plt.title("Model with large random initialization")
# axes = plt.gca()
# axes.set_xlim([-1.5, 1.5])
# axes.set_ylim([-1.5, 1.5])
# init_utils.plot_decision_boundary(lambda x: init_utils.predict_dec(parameters, x.T), train_X, train_Y)
# #初始化为he
# parameters = initialize_param.initialize_parameters_he([2, 4, 1])
# print("W1 = " + str(parameters["W1"]))
# print("b1 = " + str(parameters["b1"]))
# print("W2 = " + str(parameters["W2"]))
# print("b2 = " + str(parameters["b2"]))
# parameters = model(train_X, train_Y, initialization = "he",is_Plot=True)
# print("训练集:")
# predictions_train = init_utils.predict(train_X, train_Y, parameters)
# print("测试集:")
# init_utils.predictions_test = init_utils.predict(test_X, test_Y, parameters)
# plt.title("Model with He initialization")
# axes = plt.gca()
# axes.set_xlim([-1.5, 1.5])
# axes.set_ylim([-1.5, 1.5])
# init_utils.plot_decision_boundary(lambda x: init_utils.predict_dec(parameters, x.T), train_X, train_Y)
#
# train_X, train_Y, test_X, test_Y = reg_utils.load_2D_dataset(is_plot=True)
def model(X,Y,learning_rate = 0.3,num_iterations = 30000,print_cost = True,is_plot = True,lambd = 0,keep_prob = 1):
"""
正则化模式 - 将lambd输入设置为非零值。 我们使用“lambd”而不是“lambda”，因为“lambda”是Python中的保留关键字。
随机删除节点 - 将keep_prob设置为小于1的值
"""
grads = {}
costs = []
m = X.shape[1]
layders_dims = [X.shape[0],20,3,1]
parameters = reg_utils.initialize_parameters(layders_dims)
for i in range(0,num_iterations):
if keep_prob == 1:
a3,cache = reg_utils.forward_propagation(X,parameters)
elif keep_prob < 1:
a3,cache = forward_propagation_with_dropout(X,parameters,keep_prob)
else:
print("keep_prob参数错误！程序退出。")
exit
if lambd == 0:
cost = reg_utils.compute_cost(a3,Y)
else:
cost = compute_cost_with_regularization(a3,Y,parameters,lambd)
assert (lambd == 0 or keep_prob == 1)
if(lambd == 0 and keep_prob == 1):
grads = reg_utils.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)
parameters = reg_utils.update_parameters(parameters,grads,learning_rate)
if i % 1000 == 0:
## 记录成本
costs.append(cost)
if (print_cost and i % 10000 == 0):
# 打印成本
print("第" + str(i) + "次迭代，成本值为：" + str(cost))
if is_plot:
plt.plot(costs)
plt.ylabel('cost')
plt.xlabel('iterations (x1,000)')
plt.title("Learning rate =" + str(learning_rate))
plt.show()
return parameters
#不使用正则化
# parameters = model(train_X, train_Y,is_plot=True)
# print("训练集:")
# predictions_train = reg_utils.predict(train_X, train_Y, parameters)
# print("测试集:")
# predictions_test = reg_utils.predict(test_X, test_Y, parameters)
# plt.title("Model without regularization")
# axes = plt.gca()
# axes.set_xlim([-0.75,0.40])
# axes.set_ylim([-0.75,0.65])
# reg_utils.plot_decision_boundary(lambda x: reg_utils.predict_dec(parameters, x.T), train_X, train_Y)
#使用正则化
def compute_cost_with_regularization(A3,Y,parameters,lambd):
m = Y.shape[1]
W1 = parameters["W1"]
W2 = parameters["W2"]
W3 = parameters["W3"]
cross_entropy_cost = reg_utils.compute_cost(A3,Y)#entropy:熵
L2_regularization_cost = lambd * (np.sum(np.square(W1)) + np.sum(np.square(W2)) + np.sum(np.square(W3))) / (2*m)
cost = cross_entropy_cost + L2_regularization_cost
return cost
def backward_propagation_with_regularization(X,Y,cache,lambd):
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) + ((lambd * W3)/m)
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) + ((lambd * W2) / m)
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) + ((lambd * W1) / m)
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
# parameters = model(train_X, train_Y, lambd=0.7,is_plot=True)
# print("使用正则化，训练集:")
# predictions_train = reg_utils.predict(train_X, train_Y, parameters)
# print("使用正则化，测试集:")
# predictions_test = reg_utils.predict(test_X, test_Y, parameters)
#
# plt.title("Model with L2-regularization")
# axes = plt.gca()
# axes.set_xlim([-0.75,0.40])
# axes.set_ylim([-0.75,0.65])
# reg_utils.plot_decision_boundary(lambda x: reg_utils.predict_dec(parameters, x.T), train_X, train_Y)
def forward_propagation_with_dropout(X,parameters,keep_prob):
np.random.seed(1)
W1 = parameters["W1"]
b1 = parameters["b1"]
W2 = parameters["W2"]
b2 = parameters["b2"]
W3 = parameters["W3"]
b3 = parameters["b3"]
Z1 = np.dot(W1,X) +b1
A1 = reg_utils.relu(Z1)
D1 = np.random.rand(A1.shape[0],A1.shape[1])
D1 = D1 < keep_prob #这里的意思是如果D1小于keep_prob，就给D1赋值为1，反之为0
A1 = A1 * D1
A1 = A1 / keep_prob
#缩放为舍弃的节点（不为0）的值
Z2 = np.dot(W2,A1) + b2
A2 = reg_utils.relu(Z2)
D2 = np.random.rand(A2.shape[0],A2.shape[1]) # 使用rand来生成D1随机向量
D2 = D2 < keep_prob
A2 = A2 * D2
A2 = A2 / keep_prob
Z3 = np.dot(W3,A2) + b3
A3 = reg_utils.sigmoid(Z3)
cache = (Z1,D1,A1,W1,b1,Z2,D2,A2,W2,b2,Z3,A3,W3,b3)
return A3,cache
def backward_propagation_with_dropout(X,Y,cache,keep_prob):
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)
dA2 = dA2 * D2
#步骤1：使用正向传播期间相同的节点，舍弃那些关闭的节点（因为任何数据乘以0或者False都为0或者False）
dA2 = dA2 / keep_prob #步骤2：缩放未舍弃的节点
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)
dA1 = dA1 * D1
dA1 = dA1 / keep_prob
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
# parameters = model(train_X, train_Y, keep_prob=0.86, learning_rate=0.3,is_plot=True)
#
# print("使用随机删除节点，训练集:")
# predictions_train = reg_utils.predict(train_X, train_Y, parameters)
# print("使用随机删除节点，测试集:")
# reg_utils.predictions_test = reg_utils.predict(test_X, test_Y, parameters)
#
#
# plt.title("Model with dropout")
# axes = plt.gca()
# axes.set_xlim([-0.75, 0.40])
# axes.set_ylim([-0.75, 0.65])
# reg_utils.plot_decision_boundary(lambda x: reg_utils.predict_dec(parameters, x.T), train_X, train_Y)
def forward_propagation(x, theta):
"""
实现图中呈现的线性前向传播（计算J）（J（theta）= theta * x）
参数：
x
- 一个实值输入
theta
- 参数，也是一个实数
返回：
J
- 函数J的值，用公式J（theta）= theta * x计算
"""
J = np.dot(theta, x)
return J
def backward_propagation(x, theta):
"""
计算J相对于θ的导数。
参数：
x
- 一个实值输入
theta
- 参数，也是一个实数
返回：
dtheta
- 相对于θ的成本梯度
"""
dtheta = x
return dtheta
def gradient_check(x,theta,epsilon = 1e-7):
thetaplus = theta + epsilon
thetaminus = theta - epsilon
J_plus = forward_propagation(x,thetaplus)
J_minus = forward_propagation(x,thetaminus)
gradapprox = (J_plus - J_minus) / (2 * epsilon)
grad = backward_propagation(x,theta)
numerator = np.linalg.norm(grad - gradapprox)#np.linalg.norm()是计算范数的函数
denominator = np.linalg.norm(grad) + np.linalg.norm(gradapprox)
difference = numerator / denominator
if difference < 1e-7 :
print("梯度正常")
else:
print("梯度超出阈值")
return difference
#测试gradient_check
print("-----------------测试gradient_check-----------------")
x, theta = 2, 4
difference = gradient_check(x, theta)
print("difference = " + str(difference))

initialize_param.py

import numpy as np
def initialize_parameters_zeros(layers_dims):
parameters = {}
L = len(layers_dims)
for l in range(1,L):
parameters["W" + str(l)] = np.zeros((layers_dims[l],layers_dims[l-1]))#np.zeros()里面只能添加一个参数
parameters["b" + str(l)] = np.zeros((layers_dims[l],1))
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
def initialize_parameters_random(layers_dims):
np.random.seed(3)
parameters = {}
L = len(layers_dims)
for l in range(1,L):
parameters["W" + str(l)] = np.random.randn(layers_dims[l], layers_dims[l - 1])*10#采用十倍缩放，不知为何,解答，如果不采用十倍缩放效果会比较好，这里博主可能是让我们看到随机初始化权重较大会产生什么效果
parameters["b" + str(l)] = np.zeros((layers_dims[l], 1))
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
def initialize_parameters_he(layers_dims):
np.random.seed(3)
# 指定随机种子
parameters = {}
L = len(layers_dims)
# 层数
for l in range(1, L):
parameters['W' + str(l)] = np.random.randn(layers_dims[l], layers_dims[l - 1]) * np.sqrt(2 / layers_dims[l - 1])
parameters['b' + str(l)] = np.zeros((layers_dims[l], 1))
# 使用断言确保我的数据格式是正确的
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

gc_utils.py

在这里插入代码片# -*- coding: utf-8 -*-
import numpy as np
import matplotlib.pyplot as plt
def sigmoid(x):
"""
Compute the sigmoid of x
Arguments:
x -- A scalar or numpy array of any size.
Return:
s -- sigmoid(x)
"""
s = 1/(1+np.exp(-x))
return s
def relu(x):
"""
Compute the relu of x
Arguments:
x -- A scalar or numpy array of any size.
Return:
s -- relu(x)
"""
s = np.maximum(0,x)
return s
def dictionary_to_vector(parameters):
"""
Roll all our parameters dictionary into a single vector satisfying our specific required shape.
"""
keys = []
count = 0
for key in ["W1", "b1", "W2", "b2", "W3", "b3"]:
# flatten parameter
new_vector = np.reshape(parameters[key], (-1,1))
keys = keys + [key]*new_vector.shape[0]#暂不明确什么意思
#把所有的参数都放在一个列向量中，视频中提到过，具体为了什么忘记了？
if count == 0:
theta = new_vector
else:
theta = np.concatenate((theta, new_vector), axis=0)#np.concatenate() 是对array进行拼接的函数，axis参数为指定按照那个维度进行拼接（必须保证其他维度的尺寸是能对应上的，否则会报错）
count = count + 1
return theta, keys
def vector_to_dictionary(theta):
"""
Unroll all our parameters dictionary from a single vector satisfying our specific required shape.unroll：展开 ； satisfying：令人满意的
"""
parameters = {}
parameters["W1"] = theta[:20].reshape((5,4))
parameters["b1"] = theta[20:25].reshape((5,1))
parameters["W2"] = theta[25:40].reshape((3,5))
parameters["b2"] = theta[40:43].reshape((3,1))
parameters["W3"] = theta[43:46].reshape((1,3))
parameters["b3"] = theta[46:47].reshape((1,1))
return parameters
def gradients_to_vector(gradients):
"""
Roll all our gradients dictionary into a single vector satisfying our specific required shape.grads : 梯度
； gradients
: 梯度
"""
count = 0
for key in ["dW1", "db1", "dW2", "db2", "dW3", "db3"]:
# flatten parameter
new_vector = np.reshape(gradients[key], (-1,1))
if count == 0:
theta = new_vector
else:
theta = np.concatenate((theta, new_vector), axis=0)
count = count + 1
return theta

init_utils.py

# -*- coding: utf-8 -*-
import numpy as np
import matplotlib.pyplot as plt
import sklearn
import sklearn.datasets
def sigmoid(x):
"""
Compute the sigmoid of x
Arguments:
x -- A scalar or numpy array of any size.
Return:
s -- sigmoid(x)
"""
s = 1/(1+np.exp(-x))
return s
def relu(x):
"""
Compute the relu of x
Arguments:
x -- A scalar or numpy array of any size.
Return:
s -- relu(x)
"""
s = np.maximum(0,x)
return s
def compute_loss(a3, Y):
"""
Implement the loss function
Arguments:
a3 -- post-activation, output of forward propagation
Y -- "true" labels vector, same shape as a3
Returns:
loss - value of the loss function
"""
m = Y.shape[1]
logprobs = np.multiply(-np.log(a3),Y) + np.multiply(-np.log(1 - a3), 1 - Y)
loss = 1./m * np.nansum(logprobs)#np.nansum(): nan代表一个“不是数字”的值，如果有这种值就会报错，用nansum会在求和，取均值的时候忽略nan（取均值：mean）
return loss
def forward_propagation(X, parameters):
"""
Implements the forward propagation (and computes the loss) presented in Figure 2.
Arguments:
X -- input dataset, of shape (input size, number of examples)
Y -- true "label" vector (containing 0 if cat, 1 if non-cat)
parameters -- python dictionary containing your parameters "W1", "b1", "W2", "b2", "W3", "b3":
W1 -- weight matrix of shape ()
b1 -- bias vector of shape ()
W2 -- weight matrix of shape ()
b2 -- bias vector of shape ()
W3 -- weight matrix of shape ()
b3 -- bias vector of shape ()
Returns:
loss -- the loss function (vanilla logistic loss)
"""
# 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)
z2 = np.dot(W2, a1) + b2
a2 = relu(z2)
z3 = np.dot(W3, a2) + b3
a3 = sigmoid(z3)
cache = (z1, a1, W1, b1, z2, a2, W2, b2, z3, a3, W3, b3)
return a3, cache
def backward_propagation(X, Y, cache):
"""
Implement the backward propagation presented in figure 2.
Arguments:
X -- input dataset, of shape (input size, number of examples)
Y -- true "label" vector (containing 0 if cat, 1 if non-cat)
cache -- cache output from forward_propagation()
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 = 1./m * (a3 - Y)
dW3 = np.dot(dz3, a2.T)
db3 = np.sum(dz3, axis=1, keepdims = True)
da2 = np.dot(W3.T, dz3)
dz2 = np.multiply(da2, np.int64(a2 > 0))
dW2 = np.dot(dz2, a1.T)
db2 = np.sum(dz2, axis=1, keepdims = True)
da1 = np.dot(W2.T, dz2)
dz1 = np.multiply(da1, np.int64(a1 > 0))
dW1 = np.dot(dz1, X.T)
db1 = 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
def update_parameters(parameters, grads, learning_rate):
"""
Update parameters using gradient descent
Arguments:
parameters -- python dictionary containing your parameters
grads -- python dictionary containing your gradients, output of n_model_backward
Returns:
parameters -- python dictionary containing your updated parameters
parameters['W' + str(i)] = ...
parameters['b' + str(i)] = ...
"""
L = len(parameters) // 2 # number of layers in the neural networks
# Update rule for each parameter
for k in range(L):
parameters["W" + str(k+1)] = parameters["W" + str(k+1)] - learning_rate * grads["dW" + str(k+1)]
parameters["b" + str(k+1)] = parameters["b" + str(k+1)] - learning_rate * grads["db" + str(k+1)]
return parameters
def predict(X, y, parameters):
"""
This function is used to predict the results of a
n-layer neural network.
Arguments:
X -- data set of examples you would like to label
parameters -- parameters of the trained model
Returns:
p -- predictions for the given dataset X
"""
m = X.shape[1]
p = np.zeros((1,m), dtype = np.int)
# Forward propagation
a3, caches = forward_propagation(X, parameters)
# convert probas to 0/1 predictions
for i in range(0, a3.shape[1]):
if a3[0,i] > 0.5:
p[0,i] = 1
else:
p[0,i] = 0
# print results
print("Accuracy: "
+ str(np.mean((p[0,:] == y[0,:]))))
return p
def load_dataset(is_plot=True):
np.random.seed(1)
train_X, train_Y = sklearn.datasets.make_circles(n_samples=300, noise=.05)
np.random.seed(2)
test_X, test_Y = sklearn.datasets.make_circles(n_samples=100, noise=.05)
# Visualize the data
if is_plot:
plt.scatter(train_X[:, 0], train_X[:, 1], c=train_Y, s=40, cmap=plt.cm.Spectral)
plt.show()
train_X = train_X.T
train_Y = train_Y.reshape((1, train_Y.shape[0]))
test_X = test_X.T
test_Y = test_Y.reshape((1, test_Y.shape[0]))
return train_X, train_Y, test_X, test_Y
def plot_decision_boundary(model, X, y):
# 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))#X, Y = np.meshgrid(x, y) 代表的是将x中每一个数据和y中每一个数据组合生成很多点,然后将这些点的x坐标放入到X中,y坐标放入Y中,并且相应位置是对应的
#np.arange()函数返回一个有终点和起点的固定步长的排列，如[1,2,3,4,5]，起点是1，终点是6，步长为1
# Predict the function value for the whole grid
Z = model(np.c_[xx.ravel(), yy.ravel()])#np.c 中的c 是 column(列)的缩写，就是按列叠加两个矩阵，就是把两个矩阵左右组合，要求行数相等。
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')
plt.scatter(X[0, :], X[1, :], c=y, cmap=plt.cm.Spectral)
plt.show()
def predict_dec(parameters, X):
"""
Used for plotting decision boundary.
Arguments:
parameters -- python dictionary containing your parameters
X -- input data of size (m, K)
Returns
predictions -- vector of predictions of our model (red: 0 / blue: 1)
"""
# Predict using forward propagation and a classification threshold of 0.5
a3, cache = forward_propagation(X, parameters)
predictions = (a3>0.5)
return predictions

reg_utils.py

# -*- coding: utf-8 -*-
import numpy as np
import matplotlib.pyplot as plt
import scipy.io as sio#基于numpy的数学计算库，主要包含了统计学、最优化、线性代数、积分、傅里叶变换、信号处理和图像处理以及常微分方程的求解以及其他科学工程中所用到的计算
#io ： 输入和输出
def sigmoid(x):
"""
Compute the sigmoid of x
Arguments:
x -- A scalar or numpy array of any size.
Return:
s -- sigmoid(x)
"""
s = 1/(1+np.exp(-x))
return s
def relu(x):
"""
Compute the relu of x
Arguments:
x -- A scalar or numpy array of any size.
Return:
s -- relu(x)
"""
s = np.maximum(0,x)
return s
def initialize_parameters(layer_dims):
"""
Arguments:
layer_dims -- python array (list) containing the dimensions of each layer in our network
Returns:
parameters -- python dictionary containing your parameters "W1", "b1", ..., "WL", "bL":
W1 -- weight matrix of shape (layer_dims[l], layer_dims[l-1])
b1 -- bias vector of shape (layer_dims[l], 1)
Wl -- weight matrix of shape (layer_dims[l-1], layer_dims[l])
bl -- bias vector of shape (1, layer_dims[l])
Tips:
- For example: the layer_dims for the "Planar Data classification model" would have been [2,2,1].
This means W1's shape was (2,2), b1 was (1,2), W2 was (2,1) and b2 was (1,1). Now you have to generalize it!
- In the for loop, use parameters['W' + str(l)] to access Wl, where l is the iterative integer.
"""
np.random.seed(3)
parameters = {}
L = len(layer_dims) # number of layers in the network
for l in range(1, L):
parameters['W' + str(l)] = np.random.randn(layer_dims[l], layer_dims[l-1]) / np.sqrt(layer_dims[l-1])
parameters['b' + str(l)] = np.zeros((layer_dims[l], 1))
assert(parameters['W' + str(l)].shape == (layer_dims[l], layer_dims[l-1]))
assert(parameters['b' + str(l)].shape == (layer_dims[l], 1))
return parameters
def forward_propagation(X, parameters):
"""
Implements the forward propagation (and computes the loss) presented in Figure 2.
Arguments:
X -- input dataset, of shape (input size, number of examples)
Y -- true "label" vector (containing 0 if cat, 1 if non-cat)
parameters -- python dictionary containing your parameters "W1", "b1", "W2", "b2", "W3", "b3":
W1 -- weight matrix of shape ()
b1 -- bias vector of shape ()
W2 -- weight matrix of shape ()
b2 -- bias vector of shape ()
W3 -- weight matrix of shape ()
b3 -- bias vector of shape ()
Returns:
loss -- the loss function (vanilla logistic loss)
"""
# 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)
z2 = np.dot(W2, a1) + b2
a2 = relu(z2)
z3 = np.dot(W3, a2) + b3
a3 = sigmoid(z3)
cache = (z1, a1, W1, b1, z2, a2, W2, b2, z3, a3, W3, b3)
return a3, cache
def compute_cost(a3, Y):
"""
Implement the cost function
Arguments:
a3 -- post-activation, output of forward propagation
Y -- "true" labels vector, same shape as a3
Returns:
cost - value of the cost function
"""
m = Y.shape[1]
logprobs = np.multiply(-np.log(a3),Y) + np.multiply(-np.log(1 - a3), 1 - Y)
cost = 1./m * np.nansum(logprobs)
return cost
def backward_propagation(X, Y, cache):
"""
Implement the backward propagation presented in figure 2.
Arguments:
X -- input dataset, of shape (input size, number of examples)
Y -- true "label" vector (containing 0 if cat, 1 if non-cat)
cache -- cache output from forward_propagation()
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 = 1./m * (a3 - Y)
dW3 = np.dot(dz3, a2.T)
db3 = np.sum(dz3, axis=1, keepdims = True)
da2 = np.dot(W3.T, dz3)
dz2 = np.multiply(da2, np.int64(a2 > 0))
dW2 = np.dot(dz2, a1.T)
db2 = np.sum(dz2, axis=1, keepdims = True)
da1 = np.dot(W2.T, dz2)
dz1 = np.multiply(da1, np.int64(a1 > 0))
dW1 = np.dot(dz1, X.T)
db1 = 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
def update_parameters(parameters, grads, learning_rate):
"""
Update parameters using gradient descent
Arguments:
parameters -- python dictionary containing your parameters
grads -- python dictionary containing your gradients, output of n_model_backward
Returns:
parameters -- python dictionary containing your updated parameters
parameters['W' + str(i)] = ...
parameters['b' + str(i)] = ...
"""
L = len(parameters) // 2 # number of layers in the neural networks
# Update rule for each parameter
for k in range(L):
parameters["W" + str(k+1)] = parameters["W" + str(k+1)] - learning_rate * grads["dW" + str(k+1)]
parameters["b" + str(k+1)] = parameters["b" + str(k+1)] - learning_rate * grads["db" + str(k+1)]
return parameters
def load_2D_dataset(is_plot=True):
data = sio.loadmat('datasets/data.mat')#scipy.io.losdmat()
： 读取.mat文件并获取数据
train_X = data['X'].T
train_Y = data['y'].T
test_X = data['Xval'].T
test_Y = data['yval'].T
if is_plot:
plt.scatter(train_X[0, :], train_X[1, :], c=train_Y, s=40, cmap=plt.cm.Spectral)
plt.show()
return train_X, train_Y, test_X, test_Y
def predict(X, y, parameters):
"""
This function is used to predict the results of a
n-layer neural network.
Arguments:
X -- data set of examples you would like to label
parameters -- parameters of the trained model
Returns:
p -- predictions for the given dataset X
"""
m = X.shape[1]
p = np.zeros((1,m), dtype = np.int)
# Forward propagation
a3, caches = forward_propagation(X, parameters)
# convert probas to 0/1 predictions
for i in range(0, a3.shape[1]):
if a3[0,i] > 0.5:
p[0,i] = 1
else:
p[0,i] = 0
# print results
print("Accuracy: "
+ str(np.mean((p[0,:] == y[0,:]))))
return p
def plot_decision_boundary(model, X, y):
# 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')
plt.scatter(X[0, :], X[1, :], c=y, cmap=plt.cm.Spectral)
plt.show()
def predict_dec(parameters, X):
"""
Used for plotting decision boundary.
Arguments:
parameters -- python dictionary containing your parameters
X -- input data of size (m, K)
Returns
predictions -- vector of predictions of our model (red: 0 / blue: 1)
"""
# Predict using forward propagation and a classification threshold of 0.5
a3, cache = forward_propagation(X, parameters)
predictions = (a3>0.5)
return predictions