标签：tin oid ica 乘法 ast turn res 矩阵 计算
1. print大法
test = Hello World
print ("test:" + test)
2. math和numpy的区别：math只对单个元素，numpy会broadcasting。
import math import numpy as np x = [1, 2, 3] s = 1/(1+math.exp(-x) #这条语句会报错 s = 1/(1+np.exp(-x)) #这条语句没问题。
3. 定义函数
def sigmoid_derivative(x):
s = 1/(1+np.exp(-x)
ds = s*(1-s)
return ds
x = np.array([1, 2, 3])
print ("sigmoid_derivative(x) = " + str(sigmoid_derivative(x))
4. Shape和Reshape
image = np.array([[[ 0.67826139, 0.29380381],
[ 0.90714982, 0.52835647],
[ 0.4215251 , 0.45017551]],
[[ 0.92814219, 0.96677647],
[ 0.85304703, 0.52351845],
[ 0.19981397, 0.27417313]],
[[ 0.60659855, 0.00533165],
[ 0.10820313, 0.49978937],
[ 0.34144279, 0.94630077]],
[[ 0.85304703, 0.52835647],
[ 0.10820313, 0.45017551],
[ 0.34144279, 0.90714982]]])
print ("image[3][2][1]: " + str(image[3][2][1])) # image[2][3][1]: 0.90714982
print ("image.shape = " + str(image.shape)) # image.shape = (4, 3, 2)
vector = image.reshape(image.shape[0]*image.shape[1]*image.shape[2], 1)
print ("vector.shape = " + str(vector.shape)) # vector.shape = (24, 1)
5. Normalize： x_norm = np.linalg.norm(x, ord = 2, axis = 1, keepdims = True)，其中ord=2是默认值可以不写，axis=1是对横向量归一化，对于一维向量，axis只可以为0，keepdims=True是保持array的shape，防止出现(2, )这种shape，以防万一尽量都写上keepdims=True。
x = np.array([[0,3,4],[2,6,4]])
x_norm = np.linalg.norm(x, ord=2, axis =1, keepdims=True)
x_new = x/x_norm
print ("x: " + str(x))
print ("x_norm: "+str(x_norm))
print ("x_new: "+str(x_new))
输出：
x: [[0 3 4]
[2 6 4]]
x_norm: [[ 5. ]
[ 7.48331477]]
x_new: [[ 0. 0.6 0.8 ]
[ 0.26726124 0.80178373 0.53452248]]
6. 求和：x_sum = np.sum(x, axis = 1, keepdims = True)，其中axis=1是对横向量求和。
x = np.array([[0,3,4],[2,6,4]])
x_sum = np.sum(x, axis = 1, keepdims = True)
print ("x_sum: "+str(x_sum))
输出：
x_sum: [[ 7]
[12]]
7. 不同的乘法：
np.dot(x1, x2)对于矩阵是正常的矩阵乘法，对于一维向量是对应元素相乘再求和；
np.multiply(x1, x2)是一维向量对应元素相乘，得到一个一维向量。
这里time是计时的方法。
import time
x1 = [9, 2, 5, 0, 0, 7, 5, 0, 0, 0, 9, 2, 5, 0, 0]
x2 = [9, 2, 2, 9, 0, 9, 2, 5, 0, 0, 9, 2, 5, 0, 0]
### 向量点乘，对应元素相乘再求和 ###
tic = time.process_time()
dot = np.dot(x1,x2)
toc = time.process_time()
print ("dot = " + str(dot) + "\n ----- Computation time = " + str(1000*(toc - tic)) + "ms")
### x1和x2的转置做矩阵乘法，n*1的矩阵乘以1*n的矩阵 ###
tic = time.process_time()
outer = np.outer(x1,x2)
toc = time.process_time()
print ("outer = " + str(outer) + "\n ----- Computation time = " + str(1000*(toc - tic)) + "ms")
### 对应元素相乘得到1*n的向量 ###
tic = time.process_time()
mul = np.multiply(x1,x2)
toc = time.process_time()
print ("elementwise multiplication = " + str(mul) + "\n ----- Computation time = " + str(1000*(toc - tic)) + "ms")
### 正常的矩阵乘法 ###
W = np.random.rand(3,len(x1)) # Random 3*len(x1) numpy array
tic = time.process_time()
dot = np.dot(W,x1)
toc = time.process_time()
print ("gdot = " + str(dot) + "\n ----- Computation time = " + str(1000*(toc - tic)) + "ms")
输出：
dot = 278
----- Computation time = 0.0ms
outer = [[81 18 18 81 0 81 18 45 0 0 81 18 45 0 0]
[18 4 4 18 0 18 4 10 0 0 18 4 10 0 0]
[45 10 10 45 0 45 10 25 0 0 45 10 25 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[63 14 14 63 0 63 14 35 0 0 63 14 35 0 0]
[45 10 10 45 0 45 10 25 0 0 45 10 25 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[81 18 18 81 0 81 18 45 0 0 81 18 45 0 0]
[18 4 4 18 0 18 4 10 0 0 18 4 10 0 0]
[45 10 10 45 0 45 10 25 0 0 45 10 25 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]]
----- Computation time = 0.0ms
elementwise multiplication = [81 4 10 0 0 63 10 0 0 0 81 4 25 0 0]
----- Computation time = 0.0ms
gdot = [ 14.98632469 18.30746169 17.30396991]
----- Computation time = 0.0ms
8. Broadcasting：loss = np.sum((yhat - y)**2, keepdims = True)，这种**的运算，也是对每个元素计算平方。
标签：tin oid ica 乘法 ast turn res 矩阵 计算
原文地址：http://www.cnblogs.com/zonghaochen/p/7739899.html
