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NumPy (Numerical Python) 是 Python 语言的一个扩展程序库，支持大量的维度数组与矩阵运算。因此，说到 numpy 数值计算模块，我总是忍不住要把他拿来和 MATLAB（ps：作为应用数学专业的学生，我先接触到MATLAB）对比，毕竟矩阵实验室（matrix laboratory）也不是浪得虚名的，但是其下标从1开始的风格很是让人（特别是习惯索引从 0 开始的程序猿）诟病，这也使得它更倾向于是一个进行科学计算的工具而非专门的程序语言，所以，如果可能的话，我会尽量把语法方面的用法和 MATLAB 进行对比。
数组和索引
# Python>>> import numpy as np>>> a = np.array([1, 2, 3])>>> aarray([1, 2, 3])>>> a[0]1-------------------------------------------------------------------------------------------% MATLAB>> a = [1, 2, 3]a = 1 2 3>> a(1)ans = 1>>
矩阵和切片
# Python>>> b = np.array([[1, 2], [3, 4]])>>> barray([[1, 2], [3, 4]])>>> b[0, 1]2>>> b[0][1]2>>> b[1, :]array([3, 4])>>> ----------------------------------------------------------------------------------------% MATLAB>> b = [1, 2; 3, 4]b = 1 2 3 4>> b(1, 2)ans = 2>> b(2,:)ans = 3 4>>
# Python>>> np.e2.718281828459045>>> np.pi3.141592653589793>>> >>> np.eye(5)array([[1., 0., 0., 0., 0.], [0., 1., 0., 0., 0.], [0., 0., 1., 0., 0.], [0., 0., 0., 1., 0.], [0., 0., 0., 0., 1.]])>>> np.eye(5).shape(5, 5)>>> np.zeros((5, 5))array([[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.]])>>> a= np.arange(24)>>> aarray([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23])>>> a.reshape(4,2,3)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]]])>>> np.linspace(0, 10, 11)array([ 0., 1., 2., 3., 4., 5., 6., 7., 8., 9., 10.])>>> np.logspace(2,4,3)array([ 100., 1000., 10000.])----------------------------------------------------------------------------------------% MATLAB>> exp(1)ans = 2.718281828459046>> pians = 3.141592653589793>> eye(5)ans = 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1>> size(eye(5))ans = 5 5>> zeros(5)ans = 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>> aa=0:23aa = Columns 1 through 14 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Columns 15 through 24 14 15 16 17 18 19 20 21 22 23MATLAB是列优先的>> reshape(aa, 2, 3, 4)ans(:,:,1) = 0 2 4 1 3 5ans(:,:,2) = 6 8 10 7 9 11ans(:,:,3) = 12 14 16 13 15 17ans(:,:,4) = 18 20 22 19 21 23>> linspace(0, 10, 11)ans = 0 1 2 3 4 5 6 7 8 9 10>> logspace(2,4,3)ans = 100 1000 10000
子矩阵抽取
# Python>>> np.eye(5)[np.ix_([0,2,4],[1,2])]array([[0., 0.], [0., 1.], [0., 0.]])-------------------------------------------------------------------------------------------% MATLAB>> aa=eye(5)aa = 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1>> aa([1,3,5],[2,3])ans = 0 0 0 1 0 0
数组和矩阵运算
# Python>>> a=np.array([1,2,3,4])>>> b = np.array([10,20,30,40])>>> 2*barray([20, 40, 60, 80])>>> a*barray([ 10, 40, 90, 160])>>> a = np.array([[ 0, 0, 0], [10,10,10], [20,20,20], [30,30,30]])>>> b = np.array([1,2,3])>>> a+barray([[ 1, 2, 3], [11, 12, 13], [21, 22, 23], [31, 32, 33]])>>> barray([1, 2, 3])>>> np.tile(b,(5,2)) # 对b进行横向纵向盖瓦片array([[1, 2, 3, 1, 2, 3], [1, 2, 3, 1, 2, 3], [1, 2, 3, 1, 2, 3], [1, 2, 3, 1, 2, 3], [1, 2, 3, 1, 2, 3]])>>> barray([[1, 2], [3, 4]])>>> np.tile(b,(5,2))array([[1, 2, 1, 2], [3, 4, 3, 4], [1, 2, 1, 2], [3, 4, 3, 4], [1, 2, 1, 2], [3, 4, 3, 4], [1, 2, 1, 2], [3, 4, 3, 4], [1, 2, 1, 2], [3, 4, 3, 4]])----------------------------------------------------------------------------------------% MATLAB>> a=[1,2,3,4]a = 1 2 3 4>> b=[10,20,30,40]b = 10 20 30 40>> 2*bans = 20 40 60 80 >> a.*bans = 10 40 90 160>> aa = 0 10 20 30>> bb = 1 2 3>> [x,y]=meshgrid(a,b)x = 0 10 20 30 0 10 20 30 0 10 20 30y = 1 1 1 1 2 2 2 2 3 3 3 3>> (x+y)'ans = 1 2 3 11 12 13 21 22 23 31 32 33
数组和矩阵操作
# Python>>> import numpy as np>>> np.arange(8)array([0, 1, 2, 3, 4, 5, 6, 7])>>> a=np.arange(8)>>> b=a.reshape(4, 2)>>> barray([[0, 1], [2, 3], [4, 5], [6, 7]])>>> a=np.arange(9).reshape(3,3)>>> for element in a.flat: print(element) 012345678>>> aarray([[0, 1, 2], [3, 4, 5], [6, 7, 8]])>>> a.Tarray([[0, 3, 6], [1, 4, 7], [2, 5, 8]])----------------------------------------------------------------------------------------% MATLAB>> a=0:7a = 0 1 2 3 4 5 6 7% MATLAB默认列优先>> reshape(a, 2, 4)'ans = 0 1 2 3 4 5 6 7>> aa = 0 3 6 1 4 7 2 5 8[n, m] = size(a);test.mfor i=1:m for j=1:n disp(a(i,j)) endend>> test 0 3 6 1 4 7 2 5 8>> aa = 0 1 2 3 4 5 6 7 8>> a'ans = 0 3 6 1 4 7 2 5 8
数组和矩阵连接
# Python>>> import numpy as np>>> a = np.array([[1,2],[3,4]])>>> b = np.array([[5,6],[7,8]])>>> np.concatenate((a,b),axis=1)array([[1, 2, 5, 6], [3, 4, 7, 8]])>>> np.concatenate((a,b),axis=0)array([[1, 2], [3, 4], [5, 6], [7, 8]])>>> np.hstack((a,b))array([[1, 2, 5, 6], [3, 4, 7, 8]])>>> np.vstack((a,b))array([[1, 2], [3, 4], [5, 6], [7, 8]])>>> a=np.arange(9)>>> aarray([0, 1, 2, 3, 4, 5, 6, 7, 8])>>> np.split(a, 3)[array([0, 1, 2]), array([3, 4, 5]), array([6, 7, 8])]>>> np.split(a, [4,7])[array([0, 1, 2, 3]), array([4, 5, 6]), array([7, 8])]>>> harr = np.floor(10 * np.random.random((2, 6)))array([[8., 5., 8., 8., 7., 1.], [3., 1., 5., 9., 1., 4.]])>>> np.hsplit(harr,3)[array([[8., 5.], [3., 1.]]), array([[8., 8.], [5., 9.]]), array([[7., 1.], [1., 4.]])]>>> a = np.arange(16).reshape(4,4)>>> aarray([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11], [12, 13, 14, 15]])>>> np.vsplit(a,2)[array([[0, 1, 2, 3], [4, 5, 6, 7]]), array([[ 8, 9, 10, 11], [12, 13, 14, 15]])]>>> a = np.array([[1,2,3],[4,5,6]])>>> aarray([[1, 2, 3], [4, 5, 6]])>>> np.resize(a,(3, 2))array([[1, 2], [3, 4], [5, 6]])>>> np.resize(a,(3, 3))array([[1, 2, 3], [4, 5, 6], [1, 2, 3]])>>> aarray([[1, 2, 3], [4, 5, 6]])>>> np.append(a, [7, 8, 9])array([1, 2, 3, 4, 5, 6, 7, 8, 9])# 当axis为0时，数组是加在下边（列数要相同）。当axis为1时，数组是加在右边（行数要相同）。# axis=0，就代表沿着行坐标变化的方向进行计算，也就是对每一列进行操作。# axis=1，就代表沿着列坐标变化的方向进行计算，也就是对每一行进行操作。>>> np.append(a, [[7, 8, 9]], axis=0)array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])>>> aarray([[1, 2, 3], [4, 5, 6]])>>> np.append(a, [[5,5,5],[7,8,9]],axis = 1)array([[1, 2, 3, 5, 5, 5], [4, 5, 6, 7, 8, 9]])>>> aarray([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]])>>> np.delete(a, 1, axis=1)array([[ 0, 2, 3], [ 4, 6, 7], [ 8, 10, 11]])>>> np.delete(a, 1, axis=0)array([[ 0, 1, 2, 3], [ 8, 9, 10, 11]])----------------------------------------------------------------------------------------% MATLAB>> a=[1,2;3,4];>> b=[5,6;7,8];>> [a(:,:),b(:,:)]ans = 1 2 5 6 3 4 7 8>> [a(:,:);b(:,:)]ans = 1 2 3 4 5 6 7 8>> a=[0,1,2,3;4,5,6,7;8,9,10,11]a = 0 1 2 3 4 5 6 7 8 9 10 11>> a(:,2)=[]a = 0 2 3 4 6 7 8 10 11>> a=[0,1,2,3;4,5,6,7;8,9,10,11]a = 0 1 2 3 4 5 6 7 8 9 10 11>> a(2,:)=[]a = 0 1 2 3 8 9 10 11
位操作
# Python>>> import numpy as np>>> a=13>>> b=17>>> a & b1>>> a | b29>>> a ^ b28>>> np.bitwise_and(a, b)1>>> np.bitwise_or(a, b)29>>> np.bitwise_xor(a,b)28>>> bin(242)'0b11110010'>>> np.left_shift(10, 2)40>>> np.right_shift(40, 2)10>>> bin(10)'0b1010'>>> bin(40)'0b101000'----------------------------------------------------------------------------------------% MATLAB>> bitand(13, 17)ans = 1>> bitor(13, 17)ans = 29>> bitxor(13, 17)ans = 28>> dec2bin(242)ans =11110010>> bitshift(10,2,8)ans = 40>> bitshift(40,-2,8)ans = 10
字符串操作，与Python自带函数对比
# Python>>> import numpy as np>>> "".join(['hello', 'xyz'])'helloxyz'>>> np.char.add(['hello'], ['xyz'])array(['helloxyz'], dtype=' >> [''.join(x) for x in zip(['hello', 'hi'],[' abc', ' xyz'])]['hello abc', 'hi xyz']>>> np.char.add(['hello', 'hi'],[' abc', ' xyz'])array(['hello abc', 'hi xyz'], dtype=' >> 'Runoob '*3'Runoob Runoob Runoob '>>> np.char.multiply('Runoob ',3)array('Runoob Runoob Runoob ', dtype=' >> "Runoob".center(20, '*')'*******Runoob*******'>>> np.char.center('Runoob', 20,fillchar = '*')array('*******Runoob*******', dtype=' >> "runoob".capitalize()'Runoob'>>> np.char.capitalize('runoob')array('Runoob', dtype=' >> 'i like runoob'.title()'I Like Runoob'>>> np.char.title('i like runoob')array('I Like Runoob', dtype=' >> [x.lower() for x in ['RUNOOB','GOOGLE']]['runoob', 'google']>>> np.char.lower(['RUNOOB','GOOGLE'])array(['runoob', 'google'], dtype=' >> "RUNOOB".lower()'runoob'>>> np.char.lower('RUNOOB')array('runoob', dtype=' >> [x.upper() for x in ['runoob','google']]['RUNOOB', 'GOOGLE']>>> np.char.upper(['runoob','google'])array(['RUNOOB', 'GOOGLE'], dtype=' >> 'runoob'.upper()'RUNOOB'>>> np.char.upper('runoob')array('RUNOOB', dtype=' >> 'i like runoob?'.split()['i', 'like', 'runoob?']>>> np.char.split ('i like runoob?')array(list(['i', 'like', 'runoob?']), dtype=object)>>> 'www.runoob.com'.split('.')['www', 'runoob', 'com']>>> np.char.split ('www.runoob.com', sep = '.')array(list(['www', 'runoob', 'com']), dtype=object)>>> 'i\nlike runoob?'.split()['i', 'like', 'runoob?']>>> np.char.splitlines('i\nlike runoob?')array(list(['i', 'like runoob?']), dtype=object)>>> 'ashok arunooba'.strip('a')'shok arunoob'>>> np.char.strip('ashok arunooba','a')array('shok arunoob', dtype=' >> [x.strip('a') for x in ['arunooba','admin','java']]['runoob', 'dmin', 'jav']>>> np.char.strip(['arunooba','admin','java'],'a')array(['runoob', 'dmin', 'jav'], dtype=' >> ":".join('runoob')'r:u:n:o:o:b'>>> np.char.join(':','runoob')array('r:u:n:o:o:b', dtype=' >> [x[0].join(x[1]) for x in zip([':','-'],['runoob','google'])]['r:u:n:o:o:b', 'g-o-o-g-l-e']>>> np.char.join([':','-'],['runoob','google'])array(['r:u:n:o:o:b', 'g-o-o-g-l-e'], dtype=' >> "i like runoob".replace('oo', 'cc')'i like runccb'>>> np.char.replace ('i like runoob', 'oo', 'cc')array('i like runccb', dtype=' >> np.char.encode('runoob', 'cp500')array(b'\x99\xa4\x95\x96\x96\x82', dtype='|S6')>>> np.char.decode(b'\x99\xa4\x95\x96\x96\x82','cp500')array('runoob', dtype=' >>
数学函数
# Python>>> import numpy as np>>> a = np.array([0,30,45,60,90])>>> np.sin(a*np.pi/180)array([0. , 0.5 , 0.70710678, 0.8660254 , 1. ])>>> np.cos(a*np.pi/180)array([1.00000000e+00, 8.66025404e-01, 7.07106781e-01, 5.00000000e-01, 6.12323400e-17])>>> np.tan(a*np.pi/180)array([0.00000000e+00, 5.77350269e-01, 1.00000000e+00, 1.73205081e+00, 1.63312394e+16])>>> a = np.array([0,np.pi/6,np.pi/4,np.pi/3,np.pi/2])>>> np.degrees(a)array([ 0., 30., 45., 60., 90.])>>> a = np.array([1.0,5.55, 123, 0.567, 25.532])>>> np.around(a)array([ 1., 6., 123., 1., 26.])>>> a = np.array([-1.7, 1.5, -0.2, 0.6, 10])>>> np.floor(a)array([-2., 1., -1., 0., 10.])>>> np.ceil(a)array([-1., 2., -0., 1., 10.])----------------------------------------------------------------------------------------% MATLAB>> a=[0, 30, 45, 60, 90]a = 0 30 45 60 90>> sin(pi.*a/180)ans = 0 0.5000 0.7071 0.8660 1.0000>> cos(pi.*a/180)ans = 1.0000 0.8660 0.7071 0.5000 0.0000>> tan(pi.*a/180)ans = 1.0e+16 * 0 0.0000 0.0000 0.0000 1.6331>> a = [1.0,5.55, 123, 0.567, 25.532]a = 1.0000 5.5500 123.0000 0.5670 25.5320>> round(a)ans = 1 6 123 1 26>> a = [-1.7, 1.5, -0.2, 0.6, 10]a = -1.7000 1.5000 -0.2000 0.6000 10.0000>> floor(a)ans = -2 1 -1 0 10>> ceil(a)ans = -1 2 0 1 10
算术函数
# Python>>> import numpy as np>>> a = np.arange(9, dtype = np.float_).reshape(3,3)>>> aarray([[0., 1., 2.], [3., 4., 5.], [6., 7., 8.]])>>> b = np.array([10,10,10])>>> barray([10, 10, 10])>>> np.add(a, b)array([[10., 11., 12.], [13., 14., 15.], [16., 17., 18.]])>>> np.subtract(a, b)array([[-10., -9., -8.], [ -7., -6., -5.], [ -4., -3., -2.]])>>> np.multiply(a, b)array([[ 0., 10., 20.], [30., 40., 50.], [60., 70., 80.]])>>> np.divide(a, b)array([[0. , 0.1, 0.2], [0.3, 0.4, 0.5], [0.6, 0.7, 0.8]])>>> a = np.array([0.25, 1.33, 1, 100])>>> np.reciprocal(a)array([4. , 0.7518797, 1. , 0.01 ])>>> a = np.array([10,100,1000])>>> np.power(a, 2)array([ 100, 10000, 1000000], dtype=int32)>>> b=np.array([1, 2, 3])>>> aarray([ 10, 100, 1000])>>> np.power(a, b)array([ 10, 10000, 1000000000], dtype=int32)>>> a = np.array([10,20,30])>>> b = np.array([3,5,7])>>> np.mod(a, b)array([1, 0, 2], dtype=int32)>>> np.remainder(a, b)array([1, 0, 2], dtype=int32)>>> ----------------------------------------------------------------------------------------% MATLAB>> a=reshape(0:8, 3, 3)'a = 0 1 2 3 4 5 6 7 8>> b=10*ones(3,3)b = 10 10 10 10 10 10 10 10 10>> a+bans = 10 11 12 13 14 15 16 17 18>> a-bans = -10 -9 -8 -7 -6 -5 -4 -3 -2>> a.*bans = 0 10 20 30 40 50 60 70 80>> a./bans = 0 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000>> a = [0.25, 1.33, 1, 100]a = 0.2500 1.3300 1.0000 100.0000>> 1./aans = 4.0000 0.7519 1.0000 0.0100>> a = [10,100,1000]a = 10 100 1000>> a.^2ans = 100 10000 1000000>> aa = 10 100 1000>> bb = 1 2 3>> a.^bans = 10 10000 1000000000>> a=[10,20,30]a = 10 20 30>> b=[3,5,7]b = 3 5 7>> >> mod(a, b)ans = 1 0 2
统计函数
# Python>>> import numpy as np>>> a = np.array([[3,7,5],[8,4,3],[2,4,9]])>>> aarray([[3, 7, 5], [8, 4, 3], [2, 4, 9]])>>> np.amin(a, 1)array([3, 3, 2])>>> np.amin(a, 0)array([2, 4, 3])>>> np.amax(a, 1)array([7, 8, 9])>>> np.amax(a, 0)array([8, 7, 9])>>> np.ptp(a)7>>> np.ptp(a, 0)array([6, 3, 6])>>> np.ptp(a, 1)array([4, 5, 7])>>> a = np.array([[10, 7, 4], [3, 2, 1]])>>> aarray([[10, 7, 4], [ 3, 2, 1]])>>> np.percentile(a, 50)3.5>>> a = np.array([[30,65,70],[80,95,10],[50,90,60]])>>> np.median(a)65.0>>> a = np.array([[1,2,3],[3,4,5],[4,5,6]])>>> np.mean(a)3.6666666666666665>>> a = np.array([1,2,3,4])>>> np.average(a)2.5>>> np.std([1, 2, 3, 4])1.118033988749895>>> np.var([1, 2, 3, 4])1.25----------------------------------------------------------------------------------------% MATLAB>> aa = 3 7 5 8 4 3 2 4 9>> min(a, [], 2)ans = 3 3 2>> min(a, [], 1)ans = 2 4 3>> max(a, [], 2)ans = 7 8 9>> max(a, [], 1)ans = 8 7 9>> max(max(a)) - min(min(a))ans = 7>> max(a, [], 1) - min(a, [], 1)ans = 6 3 6>> max(a, [], 2) - min(a, [], 2)ans = 4 5 7>> a = [10, 7, 4, 3, 2, 1]a = 10 7 4 3 2 1>> prctile(a,50)ans = 3.5000>> a = [30,65,70,80,95,10,50,90,60]a = 30 65 70 80 95 10 50 90 60>> median(a)ans = 65>> a = [[1,2,3],[3,4,5],[4,5,6]]a = 1 2 3 3 4 5 4 5 6>> mean(a)ans = 3.6667>> std([1, 2, 3, 4], 1)ans = 1.1180>> var([1, 2, 3, 4], 1)ans = 1.2500>> std([1, 2, 3, 4], 0)ans = 1.2910>> var([1, 2, 3, 4], 0)ans = 1.6667
线性代数运算
# Python>>> a = np.array([[1,2],[3,4]])>>> b = np.array([[11,12],[13,14]])>>> np.dot(a, b)array([[37, 40], [85, 92]])>>> np.vdot(a, b)130>>> np.inner(np.array([1,2,3]),np.array([0,1,0]))2>>> a = [[1,0],[0,1]]>>> b = [[4,1],[2,2]]>>> a[[1, 0], [0, 1]]>>> b[[4, 1], [2, 2]]>>> np.matmul(a, b)array([[4, 1], [2, 2]])>>> np.linalg.det(a)-2.0000000000000004>>> x = np.array([[1,2],[3,4]])>>> np.linalg.inv(x)array([[-2. , 1. ], [ 1.5, -0.5]])----------------------------------------------------------------------------------------% MATLAB>> a = [1, 2; 3, 4]a = 1 2 3 4>> b = [11, 12; 13, 14]b = 11 12 13 14>> a*bans = 37 40 85 92>> sum(sum(a.*b))ans = 130>> sum([1, 2, 3].*[0, 1, 0])ans = 2>> a = [1, 0; 0, 1]a = 1 0 0 1>> b = [4, 1; 2, 2]b = 4 1 2 2>> a*bans = 4 1 2 2>> a = [1, 2; 3, 4]a = 1 2 3 4>> det(a)ans = -2>> aa = 1 2 3 4>> inv(a)ans = -2.0000 1.0000 1.5000 -0.5000
多项式计算
# Python>>> import numpy as np>>> np.poly1d([1, 2, 3])* np.poly1d([4, 5, 6])poly1d([ 4, 13, 28, 27, 18])>>> f = np.poly1d(np.array([1,0,-2,1]))>>> type(f) >>> f.deriv()poly1d([ 3, 0, -2])>>> f.integ()poly1d([ 0.25, 0. , -1. , 1. , 0. ])>>> np.roots(f)array([-1.61803399, 1. , 0.61803399])>>> x = np.linspace(-np.pi/2,np.pi/2, 1000)>>> y = np.sin(x)>>> np.polyfit(x, y, 3)array([-1.45021094e-01, 0.00000000e+00, 9.88749145e-01, 3.01152295e-17])>>> np.polyfit(x, y, 4)array([-2.75722813e-17, -1.45021094e-01, 2.03220330e-16, 9.88749145e-01, -3.79170015e-16])>>> np.polyfit(x, y, 5)array([ 7.57279944e-03, -2.75699842e-17, -1.65823793e-01, 3.11560173e-17, 9.99770071e-01, -3.87238941e-18])-------------------------------------------------------------------------------------------% MATLAB>> conv([1, 2, 3], [4, 5, 6])ans = 4 13 28 27 18>> polyder(a)ans = 3 0 -2>> polyint(a)ans = 0.2500 0 -1.0000 1.0000 0>> roots(a)ans = -1.6180 1.0000 0.6180>> x= linspace(-pi/2, pi/2, 1000);>> y=sin(x);>> polyfit(x, y, 3)ans = -0.1450 -0.0000 0.9887 -0.0000>> polyfit(x, y, 4)ans = 0.0000 -0.1450 -0.0000 0.9887 0.0000>> polyfit(x, y, 5)ans = 0.0076 0.0000 -0.1658 -0.0000 0.9998 0.0000
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