矩阵运算
论numpy中matrix 和 array的区别：http://blog.csdn.net/vincentlipan/article/details/20717163
matrix 和 array的差别： Numpy matrices必须是2维的,但是 numpy arrays (ndarrays) 可以是多维的（1D，2D，3D····ND）. Matrix是Array的一个小的分支，包含于Array。所以matrix 拥有array的所有特性。
1.基本运算
import numpy as np a = np.array([[-1,2],[2,3]]) b = np.array([[3,4],[4,5]]) print ' a: ',a print ' b: ',b ##转置 print ' a transpose: ',a.T ##共扼矩阵 #print ' a H: ',a.I ##逆矩阵 print ' a inv: ',np.linalg.inv(a) # 求逆 ##转置 print ' a transpose: ',a.T # a + b，矩阵相加 print " a+b: ",a+b # a - b，矩阵相减 print " a-b: ",a-b #2x2 矩阵，矩阵相乘 print " a mul b: ",a.dot(b.T) #2x3矩阵，矩阵点乘 print " a dot b: ",a*b #2x3矩阵，矩阵点除 print " a/b :",a/np.linalg.inv(b) #求迹 print " a trace",np.trace(a) #特征，特征向量 eigval,eigvec = np.linalg.eig(a) #eigval = np.linalg.eigvals(a) #直接求解特征值 print " a eig value: ",eigval, print' a eig vector: ',eigvec
运算结果：
a: [[-1 2] [ 2 3]] b: [[3 4] [4 5]] a transpose: [[-1 2] [ 2 3]] a inv: [[-0.42857143 0.28571429] [ 0.28571429 0.14285714]] a transpose: [[-1 2] [ 2 3]] a+b: [[2 6] [6 8]] a-b: [[-4 -2] [-2 -2]] a mul b: [[ 5 6] [18 23]] a dot b: [[-3 8] [ 8 15]] a/b : [[ 0.2 0.5] [ 0.5 -1. ]] a trace 2 a eig value: [-1.82842712 3.82842712] a eig vector: [[-0.92387953 -0.38268343] [ 0.38268343 -0.92387953]]
2.特殊矩阵
import numpy as np a = np.zeros([4,5]) # all zero print ' all zero ',a a = np.ones([7,6]) # all one print ' all one ',a a = np.eye(4,7) # 4x7 diagonal print ' 4x7 diagonal ',a a = np.diag(range(5)) # 5x5 diagonal print ' 5x5 diagonal ',a a = np.empty((2,3)) print ' empty ',a a = np.arange(10, 30, 5) # array([10, 15, 20, 25]), 1-D print ' array([10, 15, 20, 25]), 1-D ',a a = np.linspace(0, 2, 9) # 9 numbers from 0 to 2 print ' 9 numbers from 0 to 2 ',a a = np.random.random((2,3)) # random matrics print ' random matrics ',a import numpy as np a = np.zeros([4,5]) # all zero print ' all zero ',a a = np.ones([7,6]) # all one print ' all one ',a a = np.eye(4,7) # 4x7 diagonal print ' 4x7 diagonal ',a a = np.diag(range(5)) # 5x5 diagonal print ' 5x5 diagonal ',a a = np.empty((2,3)) print ' empty ',a a = np.arange(10, 30, 5) # array([10, 15, 20, 25]), 1-D print ' array([10, 15, 20, 25]), 1-D ',a a = np.linspace(0, 2, 9) # 9 numbers from 0 to 2 print ' 9 numbers from 0 to 2 ',a a = np.random.random((2,3)) # random matrics print ' random matrics ',a
运算结果：
all zero [[ 0. 0. 0. 0. 0.] [ 0. 0. 0. 0. 0.] [ 0. 0. 0. 0. 0.] [ 0. 0. 0. 0. 0.]] all one [[ 1. 1. 1. 1. 1. 1.] [ 1. 1. 1. 1. 1. 1.] [ 1. 1. 1. 1. 1. 1.] [ 1. 1. 1. 1. 1. 1.] [ 1. 1. 1. 1. 1. 1.] [ 1. 1. 1. 1. 1. 1.] [ 1. 1. 1. 1. 1. 1.]] 4x7 diagonal [[ 1. 0. 0. 0. 0. 0. 0.] [ 0. 1. 0. 0. 0. 0. 0.] [ 0. 0. 1. 0. 0. 0. 0.] [ 0. 0. 0. 1. 0. 0. 0.]] 5x5 diagonal [[0 0 0 0 0] [0 1 0 0 0] [0 0 2 0 0] [0 0 0 3 0] [0 0 0 0 4]] empty [[ 0.06012241 0.30847312 0.20174074] [ 0.37654373 0.71036135 0.15586512]] array([10, 15, 20, 25]), 1-D [10 15 20 25] 9 numbers from 0 to 2 [ 0. 0.25 0.5 0.75 1. 1.25 1.5 1.75 2. ] random matrics [[ 0.44052293 0.42283564 0.44825331] [ 0.66735609 0.32664018 0.17015328]]