Python中的Numpy入门教程
NumPy系统是Python的一种开源的数值计算扩展。这种工具可用来存储和处理大型矩阵，比Python自身的嵌套列表（nested list structure)结构要高效的多（该结构也可以用来表示矩阵（matrix））。据说NumPy将Python相当于变成一种免费的更强大的MatLab系统。
一个用python实现的科学计算包。包括：1、一个强大的N维数组对象Array；2、比较成熟的（广播）函数库；3、用于整合C/C++和Fortran代码的工具包；4、实用的线性代数、傅里叶变换和随机数生成函数。numpy和稀疏矩阵运算包scipy配合使用更加方便。 NumPy（Numeric Python）提供了许多高级的数值编程工具，如：矩阵数据类型、矢量处理，以及精密的运算库。专为进行严格的数字处理而产生。多为很多大型金融公司使用，以及核心的科学计算组织如：Lawrence Livermore，NASA用其处理一些本来使用C++，Fortran或Matlab等所做的任务。
1、Numpy是什么
很简单，Numpy是Python的一个科学计算的库，提供了矩阵运算的功能，其一般与Scipy、matplotlib一起使用。其实，list已经提供了类似于矩阵的表示形式，不过numpy为我们提供了更多的函数。如果接触过matlab、scilab，那么numpy很好入手。 在以下的代码示例中，总是先导入了numpy：
>>> import numpy as np
>>> print np.version.version
1.8.0rc1
2、多维数组 多维数组的类型是：numpy.ndarray。
使用numpy.array方法
以list或tuple变量为参数产生一维数组：
>>> print np.array([1,2,3,4])
[1 2 3 4]
>>> print np.array((1.2,2,3,4))
[ 1.2 2. 3. 4. ]
>>> print type(np.array((1.2,3,4)))
<type 'numpy.ndarray'>
>>> print np.array([[1,2],[3,4]])
[[1 2]
[3 4]]
>>> print np.array((1.2,3,4,2),dtype=np.int32)
[1 3 4 2]
使用numpy.arange方法
>>> print np.arange(15)
[ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14]
>>> print type(np.arange(15))
<type 'numpy.ndarray'>
>>> print np.arange(15).reshape(3,5)
[[ 0 1 2 3 4]
[ 5 6 7 8 9]
[10 11 12 13 14]]
>>> print type(np.arange(15).reshape(3,5))
<type 'numpy.ndarray'>
使用numpy.linspace方法 »> print np.linspace(1,3,9) [ 1. 1.25 1.5 1.75 2. 2.25 2.5 2.75 3. ]
使用numpy.zeros，numpy.ones，numpy.eye等方法可以构造特定的矩阵
>>> print np.zeros((3,4))
[[ 0. 0. 0. 0.]
[ 0. 0. 0. 0.]
[ 0. 0. 0. 0.]]
>>> print np.ones((3,4))
[[ 1. 1. 1. 1.]
[ 1. 1. 1. 1.]
[ 1. 1. 1. 1.]]
>>> print np.eye(3)
[[ 1. 0. 0.]
[ 0. 1. 0.]
[ 0. 0. 1.]]
>>> print np.zeros((2,2,2))
[[[ 0. 0.]
[ 0. 0.]]
[[ 0. 0.]
[ 0. 0.]]]
>>> a = np.zeros((2,2,2))
>>> print a.ndim
3
>>> print a.shape
(2, 2, 2)
>>> print a.size
8
>>> print a.dtype
float64
>>> print a.itemsize
8
1.Numpy数组结构
>>> from numpy import *
>>> random.rand(4,4)
array([[ 0.19351968, 0.91315924, 0.17829807, 0.41819051],
[ 0.66942158, 0.16029611, 0.26684278, 0.9305511 ],
[ 0.34128194, 0.2255203 , 0.23691202, 0.99558167],
[ 0.23876372, 0.39216221, 0.03952505, 0.56477796]])
>>> randMat = mat(random.rand(4,4))
>>> randMat.I
matrix([[ 1.16656052, -0.46796672, 0.64398992, -1.28181113],
[-1.52110114, 2.92250587, 1.59543781, -1.55497119],
[-0.49272369, 4.53397506, -1.40982884, -2.29753899],
[ 1.02498117, -4.64379637, -0.16860483, 3.84435249]])
>>> invRandMat = randMat.I
>>> randMat*invRandMat
matrix([[ 1.00000000e+00, 0.00000000e+00, 0.00000000e+00,
2.22044605e-16],
[ -1.11022302e-16, 1.00000000e+00, 0.00000000e+00,
0.00000000e+00],
[ -5.55111512e-17, -4.44089210e-16, 1.00000000e+00,
2.22044605e-16],
[ 0.00000000e+00, -6.66133815e-16, 0.00000000e+00,
1.00000000e+00]])
>>> eye(4)
array([[ 1., 0., 0., 0.],
[ 0., 1., 0., 0.],
[ 0., 0., 1., 0.],
[ 0., 0., 0., 1.]])
>>>
>>> import numpy as np
>>> a = np.array([1,2,3,4])
>>> b = np.array([5,6,7,8])
>>> c = mp.array([[1,2,3,4],[4,5,6,7],[7,8,9,10]])
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
NameError: name 'mp' is not defined
>>> c = np.array([[1,2,3,4],[4,5,6,7],[7,8,9,10]])
>>> b
array([5, 6, 7, 8])
>>> c
array([[ 1, 2, 3, 4],
[ 4, 5, 6, 7],
[ 7, 8, 9, 10]])
>>> c.dtype
dtype('int64')
>>> a.shape
(4,)
>>> c.shape
(3, 4)
>>> c.shape = 4,3
>>> c
array([[ 1, 2, 3],
[ 4, 4, 5],
[ 6, 7, 7],
[ 8, 9, 10]])
>>> c.shape = 2,-1
>>> c
array([[ 1, 2, 3, 4, 4, 5],
[ 6, 7, 7, 8, 9, 10]])
>>> d = a.reshape((2,2))
>>> d
array([[1, 2],
[3, 4]])
>>> a
array([1, 2, 3, 4])
>>> a[1] = 100
>>> d
array([[ 1, 100],
[ 3, 4]])
>>> np.array([[1,2,3,4],[4,5,6,7],[7,8,9,10]],dtype=np.float)
array([[ 1., 2., 3., 4.],
[ 4., 5., 6., 7.],
[ 7., 8., 9., 10.]])
>>> np.array([[1,2,3,4],[4,5,6,7],[7,8,9,10]],dtype=np.complex)
array([[ 1.+0.j, 2.+0.j, 3.+0.j, 4.+0.j],
[ 4.+0.j, 5.+0.j, 6.+0.j, 7.+0.j],
[ 7.+0.j, 8.+0.j, 9.+0.j, 10.+0.j]])
>>> np.arange(0,1,0.1)
array([ 0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9])
>>> np.linspace(0,1,12)
array([ 0. , 0.09090909, 0.18181818, 0.27272727, 0.36363636,
0.45454545, 0.54545455, 0.63636364, 0.72727273, 0.81818182,
0.90909091, 1. ])
>>> np.logspace(0,2,20)
array([ 1. , 1.27427499, 1.62377674, 2.06913808,
2.6366509 , 3.35981829, 4.2813324 , 5.45559478,
6.95192796, 8.8586679 , 11.28837892, 14.38449888,
18.32980711, 23.35721469, 29.76351442, 37.92690191,
48.32930239, 61.58482111, 78.47599704, 100. ])
>>> s = "abcdefgh"
>>> np.fromstring(s,dtype=np.int8)
array([ 97, 98, 99, 100, 101, 102, 103, 104], dtype=int8)
>>> np.fromstring(s,dtype=np.float)
array([ 8.54088322e+194])
>>> def func(i)
File "<stdin>", line 1
def func(i)
^
SyntaxError: invalid syntax
>>> def func(i):
... return i%4+1
File "<stdin>", line 2
return i%4+1
^
IndentationError: expected an indented block
>>> return i%4+1;
File "<stdin>", line 1
SyntaxError: 'return' outside function
>>> return i%4+1;
File "<stdin>", line 1
return i%4+1;
^
IndentationError: unexpected indent
>>> def func(i):
... return i%4+1
...
>>> np.fromfunction(func,(10,))
array([ 1., 2., 3., 4., 1., 2., 3., 4., 1., 2.])
>>> def func2(i,j):
... return (i+1)*(j+1)
...
>>> a = np.fromfunction(func2,(9,9))
>>> a
array([[ 1., 2., 3., 4., 5., 6., 7., 8., 9.],
[ 2., 4., 6., 8., 10., 12., 14., 16., 18.],
[ 3., 6., 9., 12., 15., 18., 21., 24., 27.],
[ 4., 8., 12., 16., 20., 24., 28., 32., 36.],
[ 5., 10., 15., 20., 25., 30., 35., 40., 45.],
[ 6., 12., 18., 24., 30., 36., 42., 48., 54.],
[ 7., 14., 21., 28., 35., 42., 49., 56., 63.],
[ 8., 16., 24., 32., 40., 48., 56., 64., 72.],
[ 9., 18., 27., 36., 45., 54., 63., 72., 81.]])
>>>
2.数据基本操作
>>> a = np.arange(10)
>>> a[5]
5
>>> a[3:5]
array([3, 4])
>>> a[:5]
array([0, 1, 2, 3, 4])
>>> a[:-1]
array([0, 1, 2, 3, 4, 5, 6, 7, 8])
>>> a[2,4] = 100,101
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
IndexError: too many indices
>>> a[2:4] = 100,101
>>> a
array([ 0, 1, 100, 101, 4, 5, 6, 7, 8, 9])
>>> a[1:-1:2]
array([ 1, 101, 5, 7])
>>> a[::-1]
array([ 9, 8, 7, 6, 5, 4, 101, 100, 1, 0])
>>> a[5:1:-2]
array([ 5, 101])
>>> b = a[3;7]
File "<stdin>", line 1
b = a[3;7]
^
SyntaxError: invalid syntax
>>> b = a[3:7]
>>> b
array([101, 4, 5, 6])
>>> b[2] = -10
>>> b
array([101, 4, -10, 6])
>>> a
array([ 0, 1, 100, 101, 4, -10, 6, 7, 8, 9])
>>> x = np.arange(10,1,-1)
>>> x
array([10, 9, 8, 7, 6, 5, 4, 3, 2])
>>> x[[3,3,1,8]]
array([7, 7, 9, 2])
>>> b = x[np.array([3,3,-3,8])]
>>> b[2]=100
>>> b
array([ 7, 7, 100, 2])
>>> x
array([10, 9, 8, 7, 6, 5, 4, 3, 2])
>>> x[[3,5,1]] = -1,-2,-3
>>> x
array([10, -3, 8, -1, 6, -2, 4, 3, 2])
>>> x = np.arange(5,0,-1)
>>> x
array([5, 4, 3, 2, 1])
>>> x[np.array[True,False,True,False,False,False]]
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
TypeError: 'builtin_function_or_method' object has no attribute '__getitem__'
>>> x[np.array([True,False,True,False,False,False])]
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
ValueError: too many boolean indices
>>> x[np.array([True,False,True,False,False])]
array([5, 3])
>>> x[[True,False,True,False,False]]
array([4, 5, 4, 5, 5])
>>> x[np.array([True,False,True,True])]
array([5, 3, 2])
>>> x[np.array([True,False,True,True])] = -1,-2,-3
>>> x
array([-1, 4, -2, -3, 1])
>>> x = np.random.rand(10)
>>> x
array([ 0.08780116, 0.67866796, 0.55219757, 0.56943565, 0.83619672,
0.18465457, 0.71232327, 0.02118506, 0.96978577, 0.39900369])
>>> x>0.5
array([False, True, True, True, True, False, True, False, True, False], dtype=bool)
>>> x[x>0.5]
array([ 0.67866796, 0.55219757, 0.56943565, 0.83619672, 0.71232327,
0.96978577])
>>> np.arange(0,60,10).reshape(-1,1) + np.arange(0,6)
array([[ 0, 1, 2, 3, 4, 5],
[10, 11, 12, 13, 14, 15],
[20, 21, 22, 23, 24, 25],
[30, 31, 32, 33, 34, 35],
[40, 41, 42, 43, 44, 45],
[50, 51, 52, 53, 54, 55]])
>>> a[(0,1,2,3,4),(1,2,3,4,5)]
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
IndexError: too many indices for array
>>> a = np.arange(0,60,10).reshape(-1,1) + np.arange(0,6)
>>> a[(0,1,2,3,4),(1,2,3,4,5)]
array([ 1, 12, 23, 34, 45])
>>> a[3:,[0,2,5]]
array([[30, 32, 35],
[40, 42, 45],
[50, 52, 55]])
>>>
3.矩阵操作
>>> a = np.matrix([[1,2,3],[5,5,6],[7,9,9]])
>>> a*a**-1
matrix([[ 1.00000000e+00, 0.00000000e+00, 0.00000000e+00],
[ 4.44089210e-16, 1.00000000e+00, 4.44089210e-16],
[ 0.00000000e+00, -4.44089210e-16, 1.00000000e+00]])
>>> a = array([1,2,3])
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
NameError: name 'array' is not defined
>>> a = aarray([1,2,3])
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
NameError: name 'aarray' is not defined
>>> a = array([1,2,3])
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
NameError: name 'array' is not defined
>>> a = np.array([1,2,3])
>>> a.reshape((-1,1))
array([[1],
[2],
[3]])
>>> a.reshape((1,-1))
array([[1, 2, 3]])
>>> m = np.mat([1,2,3])
>>> m
matrix([[1, 2, 3]])
>>> m[0]
matrix([[1, 2, 3]])
>>> m[0,1]
2
>>> list = [1,2,3]
>>> np.mat(list)
matrix([[1, 2, 3]])
>>> m1 = np.mat([1,2,3])
>>> m2 = np.mat([4,5,6])
>>> m1*m2.T
matrix([[32]])
>>> np.multiply(m1,m2)
matrix([[ 4, 10, 18]])
>>> m = np.mat([[2,5,1],[4,6,2]])
>>> m
matrix([[2, 5, 1],
[4, 6, 2]])
>>> m.sort()
>>> m
matrix([[1, 2, 5],
[2, 4, 6]])
>>> m.shape()
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
TypeError: 'tuple' object is not callable
>>> m.shape
(2, 3)
>>> m.shape[0]
2
>>> m.shape[1]
3
>>> m[1:]
matrix([[2, 4, 6]])
>>> m{1,0:1}
File "<stdin>", line 1
m{1,0:1}
^
SyntaxError: invalid syntax
>>> m(1,0:1)
File "<stdin>", line 1
m(1,0:1)
^
SyntaxError: invalid syntax
>>> m[1,0:1]
matrix([[2]])
>>> m[1,0:3]
matrix([[2, 4, 6]])
>>> m[1,0:2]
matrix([[2, 4]])
>>> x = np.mat([0,0,0])
>>> x
matrix([[0, 0, 0]])
>>> tile(x,(3,1))
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
NameError: name 'tile' is not defined
>>> np.tile(x,(3,1))
matrix([[0, 0, 0],
[0, 0, 0],
[0, 0, 0]])
>>> np.tile(x,(2,2))
matrix([[0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0]])
>>>
