01.神经网络和深度学习 W2.神经网络基础

// 伪代码 from http://www.ai-start.com/dl2017/html/lesson1-week2.html
J=0; dw1=0; dw2=0; db=0;
for i = 1 to m
    z(i) = wx(i)+b;
    a(i) = sigmoid(z(i));
    J += -[y(i)log(a(i))+(1-y(i))log(1-a(i))];
    dz(i) = a(i)-y(i);
    dw1 += x1(i)dz(i); // 全部样本的梯度累加
    dw2 += x2(i)dz(i);
    db += dz(i);
    
// 求平均值
J /= m;
dw1 /= m;
dw2 /= m;
db /= m;

// 更新参数 w, b
w = w - alpha*dw
b = b - alpha*db

import numpy as np #导入numpy库
a = np.array([1,2,3,4]) #创建一个数据a
print(a)
# [1 2 3 4]
import time #导入时间库
a = np.random.rand(1000000)
b = np.random.rand(1000000) #通过round随机得到两个一百万维度的数组

tic = time.time() #现在测量一下当前时间
#向量化的版本
c = np.dot(a,b)
toc = time.time()
print(c)
print('Vectorized version:' + str(1000*(toc-tic)) +'ms') #打印一下向量化的版本的时间

#继续增加非向量化的版本
c = 0
tic = time.time()
for i in range(1000000):
    c += a[i]*b[i]
toc = time.time()
print(c)
print('For loop:' + str(1000*(toc-tic)) + 'ms')#打印for循环的版本的时间

250241.79388712568
Vectorized version:0.9975433349609375ms
250241.7938871326
For loop:687.734842300415ms

J=0; db=0;
dw = np.zeros((nx,1)) // numpy向量化
for i = 1 to m
    z(i) = wx(i)+b;
    a(i) = sigmoid(z(i));
    J += -[y(i)log(a(i))+(1-y(i))log(1-a(i))];
    dz(i) = a(i)-y(i);
    dw += x(i)dz(i); // 向量化，全部样本的梯度累加
    db += dz(i);
    
// 求平均值
J /= m;
dw /= m;// 向量化
db /= m;

// 更新参数 w, b
w = w - alpha*dw
b = b - alpha*db

import numpy as np

A = np.array([
    [56, 0, 4.4, 68],
    [1.2, 104, 52, 8],
    [1.8, 135, 99, 0.9]
])

cal = A.sum(axis=0)  # 按列求和
print(cal)

percentage = 100 * A / cal.reshape(1, 4)
print(percentage)

[ 59.  239.  155.4  76.9]
[[94.91525424  0.          2.83140283 88.42652796]
 [ 2.03389831 43.51464435 33.46203346 10.40312094]
 [ 3.05084746 56.48535565 63.70656371  1.17035111]]

A = np.array([[1, 2, 3, 4]])
b = 100
print(A+b)

[[101 102 103 104]]

A = np.array([[1, 2, 3],
              [4, 5, 6]])
B = np.array([100, 200, 300])
print(A+B)

[[101 202 303]
 [104 205 306]]

A = np.array([[1, 2, 3],
              [4, 5, 6]])
B = np.array([[100], [200]])
print(A + B)

[[101 102 103]
 [204 205 206]]