using boolean array for indexing in numpy for 2D arrays

Question

I use boolean indexing to select elements from a numpy array as

x = y[t<tmax]

where t a numpy array with as many elements as y. My question is how can I do the same with 2D numpy arrays? I tried

x = y[t<tmax][t<tmax]

This does not seem to work however since it seems to select first the rows and then complains that the second selection has the wrong dimension.

IndexError: boolean index did not match indexed array along dimension 0; dimension is 50 but corresponding boolean dimension is 200

#

Here is an example

x1D = np.array([1,2,3], np.int32)
x2D = np.array([[1,2,3],[1,2,3],[1,2,3]], np.int32)
print(x1D[x1D<3]) --> [1 2]
print(x2D[x1D<3][x1D<3]) --> error

The second print statement produces an error similar to the error shown above. I use

print(x2D[x1D<3])

I get

[[1 2 3]
 [1 2 3]]

but I want

[[1 2]
 [1 2]]

y[t<tmax] works fine with 2D arrays too. Can you show with a sample what exactly isn't working? — Divakar
– Divakar, Commented Aug 31, 2019 at 20:13
Python processes each indexing operation [] independently. temp[t<tmax] followed by x=temp[t<tmax]. So each step has to make sense by itself. — hpaulj
– hpaulj, Commented Aug 31, 2019 at 20:31

hpaulj · Accepted Answer · 2019-08-31 20:42:38Z

In [28]: x1D = np.array([1,2,3], np.int32) 
    ...: x2D = np.array([[1,2,3],[1,2,3],[1,2,3]], np.int32)

The 1d mask:

In [29]: x1D<3                                                                                               
Out[29]: array([ True,  True, False])

applied to the 1d array (same size):

In [30]: x1D[_]                                                                                              
Out[30]: array([1, 2], dtype=int32)

applied to the 2d it selects 2 rows:

In [31]: x2D[_29]                                                                                            
Out[31]: 
array([[1, 2, 3],
       [1, 2, 3]], dtype=int32)

It can be used again to select columns - but note the : place holder for the row index:

In [32]: _[:, _29]                                                                                           
Out[32]: 
array([[1, 2],
       [1, 2]], dtype=int32)

If we generate an indexing array from that mask, we can do the indexing with one step:

In [37]: idx = np.nonzero(x1D<3)                                                                             
In [38]: idx                                                                                                 
Out[38]: (array([0, 1]),)
In [39]: x2D[idx[0][:,None], idx[0]]                                                                         
Out[39]: 
array([[1, 2],
       [1, 2]], dtype=int32)

An alternate way of writing this '2d' indexing:

In [41]: x2D[ [[0],[1]], [[0,1]] ]                                                                           
Out[41]: 
array([[1, 2],
       [1, 2]], dtype=int32)

ix_ is a convenient tool for tweaking the indexing dimensions:

In [42]: x2D[np.ix_(idx[0], idx[0])]                                                                         
Out[42]: 
array([[1, 2],
       [1, 2]], dtype=int32)

Or passing the boolean mask to ix_:

In [44]: np.ix_(_29, _29)                                                                                    
Out[44]: 
(array([[0],
        [1]]), array([[0, 1]]))
In [45]: x2D[np.ix_(_29, _29)]                                                                               
Out[45]: 
array([[1, 2],
       [1, 2]], dtype=int32)

Writing In[32] so it's close to to your try:

In [46]: x2D[x1D<3][:, x1D<3]                                                                                
Out[46]: 
array([[1, 2],
       [1, 2]], dtype=int32)

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