02. 导数与梯度、矩阵运算性质、科学计算库numpy

一、数学基础

二、numpy

 

 

 

 

一、数学基础

关键字：求导、偏导、梯度、复合函数求导链式法则

             矩阵的转置、矩阵加减、矩阵乘法【矩阵乘法不满足交换律】

 

二、numpy

（1）转置和加、乘

#coding:utf-8

import numpy as np

print np.__version__

 

# 1- create narray

array = np.array([1,2,3],dtype=np.uint8)

print "array:",array

 

# 2- zeros

mat1 = np.zeros((2,3)) #(2,3) tuple

print "mat1:",mat1

 

# 3- 高维矩阵

mat2 = np.zeros((1,2,3,4))

print mat2.shape

print mat2.size

 

# 4- 标准矩阵运算

# (1) 标量与矩阵相乘

scalar = 2

mat = np.ones((2,3))

mat3 = scalar * mat

print "mat3:",mat3

# (2) 矩阵转置 mat.T

mat = np.zeros((2,3))

tmat = mat.T

print mat.shape,tmat.shape

mat4 = np.array((1,2,3))

print "mat4:",mat4

tmat4 = mat4.T

print mat4.shape,tmat4.shape

# (3) 矩阵的加法

print "add--------------------"

mat1 = np.array([[1,2],[3,4]])

mat2 = np.zeros((2,2))

mat3 = mat1 + mat2

print "mat3:",mat3

# (4) 矩阵的乘法

print "multi------------------"

mat1 = np.array([[1,2],[3,4]])

mat2 = np.ones((2,2))

mat3 = mat1.dot(mat2)

print "mat3:",mat3

 

（2）扩展运算

#coding:utf-8

import numpy as np

# 扩展运算

# (1) 对应元素相乘

mat1 = np.array([[1,2],[3,4]])

mat = mat1 * mat1

print "mat:",mat

 

# (2) 标量与矩阵相加

scalar = 2

mat1 = np.array([[1,2],[3,4]])

mat = scalar + mat1

print "mat:",mat

 

# (3) 高位矩阵维度改变

mat1 = np.zeros((1,2,3))

mat = mat1.transpose(0,2,1) # 维度调换

print mat1.shape,mat.shape

 

# (4) broad cast 拓宽操作。先对原来的向量拓宽，再做加法

mat1 = np.ones((3,4))

vec = np.array([[1],[2],[3]])

print mat1+vec

 

 

（2）杂项运算

 

#coding:utf-8

import numpy as np

 

# 杂项操作

# (1) 生成随机数

rannum = np.random.randn(2,3)

print "rannum:",rannum

# 生成一个指定尺寸的矩阵

# 矩阵中的所有数字符合正态分布(normal distribution)

met = [1,2,3]

np.random.shuffle(met)

print "shuffle_met:",met

 

# (2) 对矩阵元素求和

print np.sum(rannum)

 

# (3) numpy axis

print np.sum(rannum,axis = 0) # 列

print np.sum(rannum,axis = 1) # 行

 

# (4) e的指数

print np.exp(rannum)

 

# (5) 求最大下标

a=[3,1,2,3,545,23,23,243]

print np.argmax(a)