NumPy

Numpy常用函数总结。

总结参考机器学习算法原理与编程实践

矩阵的初始化

• 导入包

  import numpy as np 
  

• 创建全0和全1矩阵

  myZero = np.zeros([3,5])
  myOnes = np.ones([3,5])
  print myZero, myOnes
  

• 生成随机矩阵

  myRand = np.random.rand(3,4) #3行4列0到1之间的随机数矩阵
  

• 单位阵

  myEye = np.eye(3) #3x3的单位阵
  

矩阵的元素运算

from numpy import *

• 元素相加减

  myOnes = ones([3,3])
  myEye = eye(3)
  print myOnes + myEye
  print myOnes - myEye
  

• 矩阵数乘

$$(cA)_{i,j} = c \cdot A_{i,j}$$

    mymatrix = mat( [[1,2,3],[4,5,6],[7,8,9]])
    print 10*mymatrix

• 矩阵所有元素求和

  sum(mymatrix)
  

• 矩阵各元素的积

  mymatrix2 = ones([3,3])
  print multiply(mymatrix,mymatrix2)
  

• 矩阵各元素的n次幂

  power(mymatrix,2)
  

矩阵的乘法

    mymatrix = mat([[1,2,3],[4,5,6],[7,8,9]])
    mymatrix2 = mat([[1],[2],[3]])
    dot(mymatrix,mymatrix2)
    print mymatrix * mymatrix2

矩阵的转置

    mymatrix.T

矩阵的行列数、切片、复制、比较

    [m,n] = shape(mymatrix)
    myscl1 = mymatrix[0]
    myscl2 = mymatrix.T[0]
    mycpmat = mymatrix.copy()

矩阵的行列式

    A = mat( [[1,2,3],[4,5,6],[7,8,9]])
    linalg.det(A)

矩阵的逆

    linalg.inv(A)

矩阵的秩

    linalg.matrix_rank(A)

可逆矩阵求解

    linalg.solve(A,T(b))

向量范数

    linalg.norm(A)

均值、方差、协方差、相关系数

    A = mat([[88,96,104,111],[12,14,16,18]])
    mean(A[0])
    std(A[0])
    cov(A)
    corrcoef(A)

特征值、特征向量

    A = [[8,1,6],[3,5,7],[4,9,2]]
    evals, evecs = linalg.eig(A)