I'm pretty new in numpy and I am having a hard time understanding how to extract from a np.array a sub matrix with defined columns and rows:
Y = np.arange(16).reshape(4,4)
If I want to extract columns/rows 0 and 3, I should have:
[[0 3]
[12 15]]
I tried all the reshape functions...but cannot figure out how to do this. Any ideas?
One solution is to index the rows/columns by slicing/striding. Here's an example where you are extracting every third column/row from the first to last columns (i.e. the first and fourth columns)
In [1]: import numpy as np
In [2]: Y = np.arange(16).reshape(4, 4)
In [3]: Y[0:4:3, 0:4:3]
Out[1]: array([[ 0, 3],
[12, 15]])
This gives you the output you were looking for.
For more info, check out this page on indexing in NumPy.
print y[0:4:3,0:4:3]
is the shortest and most appropriate fix .
First of all, your Y only has 4 col and rows, so there is no col4 or row4, at most col3 or row3.
To get 0, 3 cols: Y[[0,3],:]
To get 0, 3 rows: Y[:,[0,3]]
So to get the array you request: Y[[0,3],:][:,[0,3]]
Note that if you just Y[[0,3],[0,3]] it is equivalent to [Y[0,0], Y[3,3]] and the result will be of two elements: array([ 0, 15])
You can also do this using:
Y[[[0],[3]],[0,3]]
which is equivalent to doing this using indexing arrays:
idx = np.array((0,3)).reshape(2,1)
Y[idx,idx.T]
To make the broadcasting work as desired, you need the non-singleton dimension of your indexing array to be aligned with the axis you're indexing into, e.g. for an n x m 2D subarray:
Y[<n x 1 array>,<1 x m array>]
This doesn't create an intermediate array, unlike CT Zhu's answer, which creates the intermediate array Y[(0,3),:], then indexes into it.
This can also be done by slicing: Y[[0,3],:][:,[0,3]]. More elegantly, it is possible to slice arrays (or even reorder them) by given sets of indices for rows, columns, pages, et cetera:
r=np.array([0,3])
c=np.array([0,3])
print(Y[r,:][:,c]) #>>[[ 0 3][12 15]]
for reordering try this:
r=np.array([0,3])
c=np.array([3,0])
print(Y[r,:][:,c])#>>[[ 3 0][15 12]]
Extracting submatrices is possible using two methods, which have already been suggested in the existing answers. Here is a summary using this matrix:
Y: array([[4, 1, 4, 3, 1],
[3, 1, 2, 3, 1],
[4, 3, 2, 2, 4],
[2, 4, 3, 2, 3],
[2, 1, 4, 4, 3]])
Your submatrix is a contiguous rectangular region of the original matrix, then use regular range indexing. E.g to extract the region at intersection of rows 3,4 and cols 2,3:
>>> Y[3:, 2:4]
>>> array([[3, 2],
>>> [4, 4]])
You submatrix is not a contiguous region, some rows and/or columns have been removed within this region, then you must build a mesh of valid cells, and use it as a mask. Fortunately this is the purpose of numpy:ix_, e.g. to extract the intersection of rows 1, 3 and columns 0,3:
>>> np.ix_((1,3), (0,3))
>>> (array([[1],
>>> [3]]),
>>> array([[0, 3]]))
>>>
>>> Y[np.ix_((1,3), (0,3))]
>>> array([[3, 3],
>>> [2, 2]])
Note np.ix_((1,3), (0,3)) is strictly equivalent to [[1],[3]],[0, 3], so you can use it directly instead of calling the meshgrid builder:
>>> Y[[[1],[3]],[0, 3]]
>>> array([[3, 3],
>>> [2, 2]])
