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python中numpy的矩阵、多维数组的用法

2018-02-05 10:33 573 查看

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 np
a = 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:3
a.itemsize #每个元素所占用的字节数目:4
b=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:6
b.itemsize # 每个元素所占用的字节数目:4
c=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:6
c.itemsize # 每个元素所占用的字节数目:2
c.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:16
d.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:12
a1.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 pi
np.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)  # int32
b = np.random.random((2,3))  # float64
b += a # 正确
a += b # 错误
a = np.ones(3,dtype=np.int32)
b = np.linspace(0,pi,3)
c = a + b
d = 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 functions
B = 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)**3
a[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+y
b = 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 newaxis
np.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 = a
b is a # True
b.shape = 3,4
a.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) # 111833936L
id(b) # 111833936L
f(a)  # 111833936L
浅复制
c = a.view()
c is a # False
c.base is a # True
c.flags.owndata # False
c.shape = 2,6
a.shape # (3L,4L)
c[0,4] = 1234
print(a)
输出:
array([[ 0, 1, 2, 3],
[1234, 5, 6, 7],
[ 8, 9, 10, 11]])
s = a[:,1:3]
s[:] = 10
print(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 # False
d.base is a # False
d[0,0] = 9999
print(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

arangearraycopyemptyempty_likeeyefromfilefromfunctionidentitylinspacelogspacemgridogridonesones_like, r, zeros,zeros_like

Conversions

ndarray.astypeatleast_1datleast_2datleast_3dmat

Manipulations

array_splitcolumn_stackconcatenatediagonaldsplitdstackhsplithstackndarray.itemnewaxisravelrepeatreshaperesize,squeezeswapaxestaketransposevsplitvstack

Questionsallanynonzerowhere

Ordering

argmaxargminargsortmaxminptpsearchsortedsort

Operations

choosecompresscumprodcumsuminnerndarray.fillimagprodputputmaskrealsum

Basic Statistics

covmeanstdvar

Basic Linear Algebra

crossdotouterlinalg.svdvdot

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]] = 0
print(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]] += 1
print(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] = 0
print(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,-1,3
a.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.matrix
a1.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 * a2
print(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:
4
a1.min() # 求矩阵元素最小值
输出:
1
np.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脚本之家。

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