1. 引言

最近在将一个算法由matlab转成python，初学python，很多地方还不熟悉，总体感觉就是上手容易，实际上很优雅地用python还是蛮难的。目前为止，觉得就算法仿真研究而言，还是matlab用得特别舒服，可能是比较熟悉的缘故吧。matlab直接集成了很多算法工具箱，函数查询、调用、变量查询等非常方便，或许以后用久了python也会感觉很好用。与python相比，最喜欢的莫过于可以直接选中某段代码执行了，操作方便，python也可以实现，就是感觉不是很方便。

言归正传，做算法要用到很多的向量和矩阵运算操作，这些嘛在matlab里面已经很熟悉了，但用python的时候需要用一个查一个，挺烦的，所以在此稍作总结，后续使用过程中会根据使用体验更新。

python的矩阵运算主要依赖numpy包，scipy包以numpy为基础，大大扩展了后者的运算能力。

2. 创建一般的多维数组

import numpy as npa = np.array([1,2,3], dtype=int) # 创建1*3维数组 array([1,2,3])type(a) # numpy.ndarray类型a.shape # 维数信息(3L,)a.dtype.name # 'int32'a.size # 元素个数：3a.itemsize #每个元素所占用的字节数目:4b=np.array([[1,2,3],[4,5,6]],dtype=int) # 创建2*3维数组 array([[1,2,3],[4,5,6]])b.shape # 维数信息（2L,3L）b.size # 元素个数：6b.itemsize # 每个元素所占用的字节数目:4c=np.array([[1,2,3],[4,5,6]],dtype='int16') # 创建2*3维数组 array([[1,2,3],[4,5,6]],dtype=int16)c.shape # 维数信息（2L,3L）c.size # 元素个数：6c.itemsize # 每个元素所占用的字节数目:2c.ndim # 维数 d=np.array([[1,2,3],[4,5,6]],dtype=complex) # 复数二维数组d.itemsize # 每个元素所占用的字节数目：16d.dtype.name # 元素类型：'complex128'

3. 创建特殊类型的多维数组　

a1 = np.zeros((3,4)) # 创建3*4全零二维数组输出：array([[ 0., 0., 0., 0.], [ 0., 0., 0., 0.], [ 0., 0., 0., 0.]])a1.dtype.name # 元素类型：'float64'a1.size # 元素个数：12a1.itemsize # 每个元素所占用的字节个数：8 a2 = np.ones((2,3,4), dtype=np.int16) # 创建2*3*4全1三维数组a2 = np.ones((2,3,4), dtype='int16') # 创建2*3*4全1三维数组输出：array([[[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]], [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]]], dtype=int16) a3 = np.empty((2,3)) # 创建2*3的未初始化二维数组输出：（may vary）array([[ 1., 2., 3.], [ 4., 5., 6.]])a4 = np.arange(10,30,5) # 初始值10，结束值：30（不包含），步长：5输出：array([10, 15, 20, 25])a5 = np.arange(0,2,0.3) # 初始值0，结束值：2（不包含），步长：0.2输出：array([ 0. , 0.3, 0.6, 0.9, 1.2, 1.5, 1.8])from numpy import pinp.linspace(0, 2, 9) # 初始值0，结束值：2（包含），元素个数：9输出：array([ 0. , 0.25, 0.5 , 0.75, 1. , 1.25, 1.5 , 1.75, 2. ])x = np.linspace(0, 2*pi, 9)输出：array([ 0. , 0.78539816, 1.57079633, 2.35619449, 3.14159265, 3.92699082, 4.71238898, 5.49778714, 6.28318531])a = np.arange(6)输出：array([0, 1, 2, 3, 4, 5])b = np.arange(12).reshape(4,3)输出：array([[ 0, 1, 2], [ 3, 4, 5], [ 6, 7, 8], [ 9, 10, 11]])c = np.arange(24).reshape(2,3,4)输出：array([[[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]], [[12, 13, 14, 15], [16, 17, 18, 19], [20, 21, 22, 23]]])　

使用numpy.set_printoptions可以设置numpy变量的打印格式

在ipython环境下，使用help(numpy.set_printoptions)查询使用帮助和示例

4. 多维数组的基本操作

加法和减法操作要求操作双方的维数信息一致，均为M*N为数组方可正确执行操作。

a = np.arange(4)输出：array([0, 1, 2, 3])b = a**2输出：array([0, 1, 4, 9])c = 10*np.sin(a)输出： array([ 0. , 8.41470985, 9.09297427, 1.41120008]) n < 35输出：array([ True, True, True, True], dtype=bool) A = np.array([[1,1],[0,1]])B = np.array([[2,0],[3,4]])C = A * B # 元素点乘输出：array([[2, 0], [0, 4]])D = A.dot(B) # 矩阵乘法输出：array([[5, 4], [3, 4]])E = np.dot(A,B) # 矩阵乘法输出：array([[5, 4], [3, 4]])

多维数组操作过程中的类型转换

When operating with arrays of different types, the type of the resulting array corresponds to the more general or precise one (a behavior known as upcasting)

即操作不同类型的多维数组时，结果自动转换为精度更高类型的数组，即upcasting

a = np.ones((2,3),dtype=int) # int32b = np.random.random((2,3)) # float64b += a # 正确 a += b # 错误 a = np.ones(3,dtype=np.int32)b = np.linspace(0,pi,3)c = a + bd = np.exp(c*1j)输出：array([ 0.54030231+0.84147098j, -0.84147098+0.54030231j, -0.54030231-0.84147098j])d.dtype.name输出： 'complex128'

多维数组的一元操作，如求和、求最小值、最大值等

a = np.random.random((2,3))a.sum()a.min()a.max() b = np.arange(12).reshape(3,4)输出：array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]])b.sum(axis=0) # 按列求和输出：array([12, 15, 18, 21])b.sum(axis=1) # 按行求和输出：array([ 6, 22, 38])b.cumsum(axis=0) # 按列进行元素累加输出：array([[ 0, 1, 2, 3], [ 4, 6, 8, 10], [12, 15, 18, 21]])b.cumsum(axis=1) # 按行进行元素累加输出：array([[ 0, 1, 3, 6], [ 4, 9, 15, 22], [ 8, 17, 27, 38]]) universal functionsB = np.arange(3)np.exp(B)np.sqrt(B)C = np.array([2.,-1.,4.])np.add(B,C)

其他的ufunc函数包括：

all, any, apply_along_axis, argmax, argmin, argsort, average, bincount, ceil, clip, conj, corrcoef, cov, cross, cumprod, cumsum, diff, dot, floor,inner, lexsort, max, maximum, mean, median, min, minimum, nonzero, outer, prod, re, round, sort, std, sum, trace, transpose, var,vdot, vectorize, where

5. 数组索引、切片和迭代

a = np.arange(10)**3a[2]a[2:5]a[::-1] # 逆序输出for i in a: print (i**(1/3.)) def f(x,y): return 10*x+yb = np.fromfunction(f,(5,4),dtype=int)b[2,3]b[0:5,1]b[:,1]b[1:3,:]b[-1] c = np.array([[[0,1,2],[10,11,12]],[[100,101,102],[110,111,112]]])输出：array([[[ 0, 1, 2], [ 10, 11, 12]], [[100, 101, 102], [110, 111, 112]]])c.shape输出：(2L, 2L, 3L)c[0,...]c[0,:,:]输出：array([[ 0, 1, 2], [10, 11, 12]])c[:,:,2]c[...,2]输出：array([[ 2, 12], [102, 112]]) for row in c: print(row) for element in c.flat: print(element) a = np.floor(10*np.random.random((3,4)))输出：array([[ 3., 9., 8., 4.], [ 2., 1., 4., 6.], [ 0., 6., 0., 2.]])a.ravel()输出：array([ 3., 9., 8., ..., 6., 0., 2.])a.reshape(6,2)输出：array([[ 3., 9.], [ 8., 4.], [ 2., 1.], [ 4., 6.], [ 0., 6.], [ 0., 2.]])a.T输出：array([[ 3., 2., 0.], [ 9., 1., 6.], [ 8., 4., 0.], [ 4., 6., 2.]])a.T.shape输出：(4L, 3L)a.resize((2,6))输出：array([[ 3., 9., 8., 4., 2., 1.], [ 4., 6., 0., 6., 0., 2.]])a.shape输出：(2L, 6L)a.reshape(3,-1)输出：array([[ 3., 9., 8., 4.], [ 2., 1., 4., 6.], [ 0., 6., 0., 2.]])

详查以下函数：

ndarray.shape, reshape, resize, ravel

6. 组合不同的多维数组

a = np.floor(10*np.random.random((2,2)))输出：array([[ 5., 2.], [ 6., 2.]])b = np.floor(10*np.random.random((2,2)))输出：array([[ 0., 2.], [ 4., 1.]])np.vstack((a,b))输出：array([[ 5., 2.], [ 6., 2.], [ 0., 2.], [ 4., 1.]])np.hstack((a,b))输出：array([[ 5., 2., 0., 2.], [ 6., 2., 4., 1.]]) from numpy import newaxisnp.column_stack((a,b))输出：array([[ 5., 2., 0., 2.], [ 6., 2., 4., 1.]]) a = np.array([4.,2.])b = np.array([2.,8.])a[:,newaxis]输出：array([[ 4.], [ 2.]])b[:,newaxis]输出：array([[ 2.], [ 8.]])np.column_stack((a[:,newaxis],b[:,newaxis]))输出：array([[ 4., 2.], [ 2., 8.]])np.vstack((a[:,newaxis],b[:,newaxis]))输出：array([[ 4.], [ 2.], [ 2.], [ 8.]])np.r_[1:4,0,4]输出：array([1, 2, 3, 0, 4])np.c_[np.array([[1,2,3]]),0,0,0,np.array([[4,5,6]])]输出：array([[1, 2, 3, 0, 0, 0, 4, 5, 6]])

详细使用请查询以下函数：

hstack, vstack, column_stack, concatenate, c_, r_

7. 将较大的多维数组分割成较小的多维数组

a = np.floor(10*np.random.random((2,12)))输出：array([[ 9., 7., 9., ..., 3., 2., 4.], [ 5., 3., 3., ..., 9., 7., 7.]])np.hsplit(a,3)输出：[array([[ 9., 7., 9., 6.], [ 5., 3., 3., 1.]]), array([[ 7., 2., 1., 6.], [ 7., 5., 0., 2.]]), array([[ 9., 3., 2., 4.], [ 3., 9., 7., 7.]])]np.hsplit(a,(3,4))输出：[array([[ 9., 7., 9.], [ 5., 3., 3.]]), array([[ 6.], [ 1.]]), array([[ 7., 2., 1., ..., 3., 2., 4.], [ 7., 5., 0., ..., 9., 7., 7.]])]

实现类似功能的函数包括：

hsplit,vsplit,array_split

8. 多维数组的复制操作

a = np.arange(12)输出：array([ 0, 1, 2, ..., 9, 10, 11]) not copy at all b = ab is a # Trueb.shape = 3,4a.shape # (3L,4L) def f(x) # Python passes mutable objects as references, so function calls make no copy. print(id(x)) # id是python对象的唯一标识符 id(a) # 111833936Lid(b) # 111833936Lf(a) # 111833936L 浅复制c = a.view()c is a # Falsec.base is a # Truec.flags.owndata # Falsec.shape = 2,6a.shape # (3L,4L)c[0,4] = 1234print(a)输出：array([[ 0, 1, 2, 3], [1234, 5, 6, 7], [ 8, 9, 10, 11]])s = a[:,1:3]s[:] = 10print(a)输出：array([[ 0, 10, 10, 3], [1234, 10, 10, 7], [ 8, 10, 10, 11]]) 深复制d = a.copy()d is a # Falsed.base is a # Falsed[0,0] = 9999print(a)输出：array([[ 0, 10, 10, 3], [1234, 10, 10, 7], [ 8, 10, 10, 11]])

numpy基本函数和方法一览

arange,array,copy,empty,empty_like,eye,fromfile,fromfunction,identity,linspace,logspace,mgrid,ogrid,ones,ones_like,r,zeros,zeros_like

Conversions

ndarray.astype,atleast_1d,atleast_2d,atleast_3d,mat

Manipulations

array_split,column_stack,concatenate,diagonal,dsplit,dstack,hsplit,hstack,ndarray.item,newaxis,ravel,repeat,reshape,resize,squeeze,swapaxes,take,transpose,vsplit,vstack

Questionsall,any,nonzero,where

Ordering

argmax,argmin,argsort,max,min,ptp,searchsorted,sort

Operations

choose,compress,cumprod,cumsum,inner,ndarray.fill,imag,prod,put,putmask,real,sum

Basic Statistics

cov,mean,std,var

Basic Linear Algebra

cross,dot,outer,linalg.svd,vdot

完整的函数和方法一览表链接：

https://docs.scipy.org/doc/numpy-dev/reference/routines.html#routines

9. 特殊的索引技巧

a = np.arange(12)**2输出：array([ 0, 1, 4, ..., 81, 100, 121])i = np.array([1,1,3,8,5])a[i]输出：array([ 1, 1, 9, 64, 25])j = np.array([[3,4],[9,7]])a[j]输出：array([[ 9, 16], [81, 49]])palette = np.array([[0,0,0],[255,0,0],[0,255,0],[0,0,255],[255,255,255]])image = np.array([[0,1,2,0],[0,3,4,0]])palette[image]输出：array([[[ 0, 0, 0], [255, 0, 0], [ 0, 255, 0], [ 0, 0, 0]], [[ 0, 0, 0], [ 0, 0, 255], [255, 255, 255], [ 0, 0, 0]]])i = np.array([[0,1],[1,2]])j = np.array([[2,1],[3,3]])a[i,j]输出：array([[ 2, 5], [ 7, 11]])l = [i,j]a[l]输出：array([[ 2, 5], [ 7, 11]])a[i,2]输出：array([[ 2, 6], [ 6, 10]])a[:,j]输出：array([[[ 2, 1], [ 3, 3]], [[ 6, 5], [ 7, 7]], [[10, 9], [11, 11]]])s = np.array([i,j])print(s)array([[[0, 1], [1, 2]], [[2, 1], [3, 3]]])a[tuple(s)]输出：array([[ 2, 5], [ 7, 11]])print(tupe(s))输出：(array([[0, 1], [1, 2]]), array([[2, 1], [3, 3]]))

10. 寻找最大值/最小值及其对应索引值

time = np.linspace(20, 145, 5)输出： array([ 20. , 51.25, 82.5 , 113.75, 145. ])data = np.sin(np.arange(20)).reshape(5,4)输出：array([[ 0. , 0.84147098, 0.90929743, 0.14112001], [-0.7568025 , -0.95892427, -0.2794155 , 0.6569866 ], [ 0.98935825, 0.41211849, -0.54402111, -0.99999021], [-0.53657292, 0.42016704, 0.99060736, 0.65028784], [-0.28790332, -0.96139749, -0.75098725, 0.14987721]])ind = data.argmax(axis=0)输出：array([2, 0, 3, 1], dtype=int64)time_max = time[ind]输出：array([ 82.5 , 20. , 113.75, 51.25])data_max = data[ind, xrange(data.shape[1])]输出：array([ 0.98935825, 0.84147098, 0.99060736, 0.6569866 ])np.all(data_max == data.max(axis=0))输出：True a = np.arange(5)a[[1,3,4]] = 0print(a)输出：array([0, 0, 2, 0, 0])a = np.arange(5)a[[0,0,2]] = [1,2,3]print(a)输出：array([2, 1, 3, 3, 4])a = np.arange(5)a[[0,0,2]] += 1print(a)输出：array([1, 1, 3, 3, 4])a = np.arange(12).reshape(3,4) b = a > 4输出：array([[False, False, False, False], [False, True, True, True], [ True, True, True, True]], dtype=bool)a[b]输出：array([ 5, 6, 7, 8, 9, 10, 11])a[b] = 0print(a)输出：array([[0, 1, 2, 3], [4, 0, 0, 0], [0, 0, 0, 0]])a = np.arange(12).reshape(3,4)b1 = np.array([False,True,True])b2 = n.array([True,False,True,False])a[b1,:]输出：array([[ 4, 5, 6, 7], [ 8, 9, 10, 11]])a[b1]输出：array([[ 4, 5, 6, 7], [ 8, 9, 10, 11]])a[:,b2]输出：array([[ 0, 2], [ 4, 6], [ 8, 10]])a[b1,b2]输出：array([ 4, 10])

11. ix_() function

a = np.array([2,3,4,5])b = np.array([8,5,4])c = np.array([5,4,6,8,3])ax,bx,cx = np.ix_(a,b,c)print(ax) # (4L, 1L, 1L)输出：array([[[2]], [[3]], [[4]], [[5]]])print(bx) # (1L, 3L, 1L)输出：array([[[8], [5], [4]]])print(cx) # (1L, 1L, 5L)输出：array([[[5, 4, 6, 8, 3]]])result = ax + bx*cx输出：array([[[42, 34, 50, 66, 26], [27, 22, 32, 42, 17], [22, 18, 26, 34, 14]], [[43, 35, 51, 67, 27], [28, 23, 33, 43, 18], [23, 19, 27, 35, 15]], [[44, 36, 52, 68, 28], [29, 24, 34, 44, 19], [24, 20, 28, 36, 16]], [[45, 37, 53, 69, 29], [30, 25, 35, 45, 20], [25, 21, 29, 37, 17]]])result[3,2,4]输出：17

12. 线性代数运算

a = np.array([[1.,2.],[3.,4.]])a.transpose() # 转置np.linalg.inv(a) # 求逆u = np.eye(2) # 产生单位矩阵np.dot(a,a) # 矩阵乘积np.trace(a) # 求矩阵的迹y = np.array([5.],[7.]])np.linalg.solve(a,y) # 求解线性方程组np.linalg.eig(a) # 特征分解

“Automatic” Reshaping

a = np.arange(30)a.shape = 2,-1,3a.shape # (2L, 5L, 3L)print(a)array([[[ 0, 1, 2], [ 3, 4, 5], [ 6, 7, 8], [ 9, 10, 11], [12, 13, 14]], [[15, 16, 17], [18, 19, 20], [21, 22, 23], [24, 25, 26], [27, 28, 29]]])x = np.arange(0,10,2)y = np.arange(5)m = np.vstack([x,y])输出：array([[0, 2, 4, 6, 8], [0, 1, 2, 3, 4]])n = np.hstack([x,y])输出：array([0, 2, 4, 6, 8, 0, 1, 2, 3, 4])

13. 矩阵的创建

a = np.array([1,2,3])a1 = np.mat(a)输出：matrix([[1, 2, 3]])type(a1)输出：numpy.matrixlib.defmatrix.matrixa1.shape输出：(1L, 3L)a.shape输出：(3L,)b=np.matrix([1,2,3])输出：matrix([[1, 2, 3]])from numpy import *data1 = mat(zeros((3,3)))data2 = mat(ones((2,4)))data3 = mat(random.rand(2,2))data4 = mat(random.randint(2,8,size=(2,5)))data5 = mat(eye(2,2,dtype=int))

14. 常见的矩阵运算

a1 = mat([1,2])a2 = mat([[1],[2]])a3 = a1 * a2print(a3)输出：matrix([[5]])print(a1*2)输出：matrix([[2, 4]])a1 = mat(eye(2,2)*0.5)print(a1.I)输出：matrix([[ 2., 0.], [ 0., 2.]])a1 = mat([[1,2],[2,3],[4,2]])a1.sum(axis=0)输出：matrix([[7, 7]])a1.sum(axis=1)输出：matrix([[3], [5], [6]])a1.max() # 求矩阵元素最大值输出：4a1.min() # 求矩阵元素最小值输出：1np.max(a1,0) # 求矩阵每列元素最大值输出：matrix([[4, 3]])np.max(a1,1) # 求矩阵每行元素最大值输出：matrix([[2], [3], [4]])a = mat(ones((2,2)))b = mat(eye((2)))c = hstack((a,b))输出：matrix([[ 1., 1., 1., 0.], [ 1., 1., 0., 1.]])d = vstack((a,b))输出：matrix([[ 1., 1.], [ 1., 1.], [ 1., 0.], [ 0., 1.]])

15. 矩阵、数组、列表之间的互相转换

aa = [[1,2],[3,4],[5,6]]bb = array(aa)cc = mat(bb)cc.getA() # 矩阵转换为数组cc.tolist() # 矩阵转换为列表bb.tolist() # 数组转换为列表# 当列表为一维时，情况有点特殊aa = [1,2,3,4]bb = array(aa)输出：array([1, 2, 3, 4])cc = mat(bb)输出：matrix([[1, 2, 3, 4]])cc.tolist()输出：[[1, 2, 3, 4]]bb.tolist()输出：[1, 2, 3, 4]cc.tolist()[0]输出：[1, 2, 3, 4]

内容整理参考链接如下：

https://docs.scipy.org/doc/numpy-dev/user/quickstart.html

http://python.usyiyi.cn/translate/NumPy_v111/reference/arrays.scalars.html#arrays-scalars-built-in

以上就是本文的全部内容，希望对大家的学习有所帮助，也希望大家多多支持。