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）确实也不是浪得虚名，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])
>>> a
array([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]])
>>> b
array([[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.e
2.718281828459045
>>> np.pi
3.141592653589793
>>>
>>> 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)
>>> 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])
>>> 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
>> pi
ans =
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=0:23
aa =
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 23
MATLAB是列优先的
>> reshape(aa, 2, 3, 4)
ans(:,:,1) =
0 2 4
1 3 5
ans(:,:,2) =
6 8 10
7 9 11
ans(:,:,3) =
12 14 16
13 15 17
ans(:,:,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*b
array([20, 40, 60, 80])
>>> a*b
array([ 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+b
array([[ 1, 2, 3],
[11, 12, 13],
[21, 22, 23],
[31, 32, 33]])
>>> b
array([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]])
>>> b
array([[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*b
ans =
20 40 60 80
>> a.*b
ans =
10 40 90 160
>> a
a =
0 10 20 30
>> b
b =
1 2 3
>> [x,y]=meshgrid(a,b)
x =
0 10 20 30
0 10 20 30
0 10 20 30
y =
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)
>>> b
array([[0, 1],
[2, 3],
[4, 5],
[6, 7]])
>>> a=np.arange(9).reshape(3,3)
>>> for element in a.flat:
print(element)
0
1
2
3
4
5
6
7
8
>>> a
array([[0, 1, 2],
[3, 4, 5],
[6, 7, 8]])
>>> a.T
array([[0, 3, 6],
[1, 4, 7],
[2, 5, 8]])
----------------------------------------------------------------------------------------
% MATLAB
>> a=0:7
a =
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
>> a
a =
0 3 6
1 4 7
2 5 8
[n, m] = size(a);
test.m
for i=1:m
for j=1:n
disp(a(i,j))
end
end
>> test
0
3
6
1
4
7
2
5
8
>> a
a =
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)
>>> a
array([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)
>>> a
array([[ 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]])
>>> a
array([[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]])
>>> a
array([[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]])
>>> a
array([[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]])
>>> a
array([[ 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 & b
1
>>> a | b
29
>>> a ^ b
28
>>> 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='<U8')
>>> [''.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='<U9')
>>> 'Runoob '*3
'Runoob Runoob Runoob '
>>> np.char.multiply('Runoob ',3)
array('Runoob Runoob Runoob ', dtype='<U21')
>>> "Runoob".center(20, '*')
'*******Runoob*******'
>>> np.char.center('Runoob', 20,fillchar = '*')
array('*******Runoob*******', dtype='<U20')
>>> "runoob".capitalize()
'Runoob'
>>> np.char.capitalize('runoob')
array('Runoob', dtype='<U6')
>>> 'i like runoob'.title()
'I Like Runoob'
>>> np.char.title('i like runoob')
array('I Like Runoob', dtype='<U13')
>>> [x.lower() for x in ['RUNOOB','GOOGLE']]
['runoob', 'google']
>>> np.char.lower(['RUNOOB','GOOGLE'])
array(['runoob', 'google'], dtype='<U6')
>>> "RUNOOB".lower()
'runoob'
>>> np.char.lower('RUNOOB')
array('runoob', dtype='<U6')
>>> [x.upper() for x in ['runoob','google']]
['RUNOOB', 'GOOGLE']
>>> np.char.upper(['runoob','google'])
array(['RUNOOB', 'GOOGLE'], dtype='<U6')
>>> 'runoob'.upper()
'RUNOOB'
>>> np.char.upper('runoob')
array('RUNOOB', dtype='<U6')
>>> '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='<U14')
>>> [x.strip('a') for x in ['arunooba','admin','java']]
['runoob', 'dmin', 'jav']
>>> np.char.strip(['arunooba','admin','java'],'a')
array(['runoob', 'dmin', 'jav'], dtype='<U8')
>>> ":".join('runoob')
'r:u:n:o:o:b'
>>> np.char.join(':','runoob')
array('r:u:n:o:o:b', dtype='<U11')
>>> [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='<U11')
>>> "i like runoob".replace('oo', 'cc')
'i like runccb'
>>> np.char.replace ('i like runoob', 'oo', 'cc')
array('i like runccb', dtype='<U13')
>>> 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='<U6')
>>>
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)
>>> a
array([[0., 1., 2.],
[3., 4., 5.],
[6., 7., 8.]])
>>> b = np.array([10,10,10])
>>> b
array([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])
>>> a
array([ 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+b
ans =
10 11 12
13 14 15
16 17 18
>> a-b
ans =
-10 -9 -8
-7 -6 -5
-4 -3 -2
>> a.*b
ans =
0 10 20
30 40 50
60 70 80
>> a./b
ans =
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./a
ans =
4.0000 0.7519 1.0000 0.0100
>> a = [10,100,1000]
a =
10 100 1000
>> a.^2
ans =
100 10000 1000000
>> a
a =
10 100 1000
>> b
b =
1 2 3
>> a.^b
ans =
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]])
>>> a
array([[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]])
>>> a
array([[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
>> a
a =
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*b
ans =
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*b
ans =
4 1
2 2
>> a = [1, 2; 3, 4]
a =
1 2
3 4
>> det(a)
ans =
-2
>> a
a =
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)
<class 'numpy.poly1d'>
>>> 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