numpy 数组切片索引

Question

import numpy as np
a=np.array([ [1,2,3],[4,5,6],[7,8,9]])

• How can I get zeroth index column? Expecting output [[1],[2],[3]] a[...,0] gives 1D array. Maybe next question answers this question.

• How to get last 2 columns of a ? a[...,1:2] gives second column only, a[...,2:3] gives last 2 columns, but a[...,3] is invalid dimension. So, how does it work?

By the way, operator ... and : have same meaning? a[...,0] and a[:,0] give same output. Can someone comment here?

Answer 1

numpy indexing is built on python list conventions, but extended to multi-dimensions and multi-element indexing. It is powerful, but complex, but sooner or later you should read a full indexing documentation, one that distinguishes between 'basic' and 'advanced' indexing.

Like range and arange , slice index has a 'open' stop value

In [111]: a = np.arange(1,10).reshape(3,3)                                                       
In [112]: a                                                                                      
Out[112]: 
array([[1, 2, 3],
       [4, 5, 6],
       [7, 8, 9]])

Indexing with a scalar reduces the dimension, regardless of where:

In [113]: a[1,:]                                                                                 
Out[113]: array([4, 5, 6])
In [114]: a[:,1]                                                                                 
Out[114]: array([2, 5, 8])

That also means a[1,1] returns 5 , not np.array([[5]]) .

Indexing with a slice preserves the dimension:

In [115]: a[1:2,:]                                                                               
Out[115]: array([[4, 5, 6]])

so does indexing with a list or array (though this makes a copy , not a view ):

In [116]: a[[1],:]                                                                               
Out[116]: array([[4, 5, 6]])

... is a generalized : - use as many as needed.

In [117]: a[...,[1]]                                                                             
Out[117]: 
array([[2],
       [5],
       [8]])

You can adjust dimensions with newaxis or reshape:

In [118]: a[:,1,np.newaxis]                                                                      
Out[118]: 
array([[2],
       [5],
       [8]])

Note that trailing : are automatic. a[1] is the same as a[1,:] . But leading ones must be explicit.

List indexing also removes a 'dimension/nesting layer'

In [119]: alist = [[1,2,3],[4,5,6]]                                                              
In [120]: alist[0]                                                                               
Out[120]: [1, 2, 3]
In [121]: alist[0][0]                                                                            
Out[121]: 1
In [122]: [l[0] for l in alist]     # a column equivalent                                                                  
Out[122]: [1, 4]

Answer 2

import numpy as np
a=np.array([ [1,2,3],[4,5,6],[7,8,9]])

a[:,0] # first colomn
>>> array([1, 4, 7]) 
a[0,:] # first row
>>> array([1, 2, 3])
a[:,0:2] # first two columns
>>> array([[1, 2],
       [4, 5],
       [7, 8]])
a[0:2,:] # first two rows
>>> array([[1, 2, 3],
       [4, 5, 6]])