Using ufunc.at on matrix

Question

Suppose I have the following numpy array:

>>> a=np.zeros(10)
>>> a
array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.])

I can use numpy.ufunc.at to modify that array in place:

>>> np.add.at(a, [0,3], 2)
>>> a
array([ 2.,  0.,  0.,  2.,  0.,  0.,  0.,  0.,  0.,  0.])

If I now try on a matrix, what I assume to be the method does not work:

>>> m=np.zeros(16).reshape(4,4)
>>> m
array([[ 0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.]])
>>> np.add.at(m, [(0,0),(1,1)], 2)
>>> m
array([[ 0.,  4.,  0.,  0.],
       [ 0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.]])

My expectation based on supplying the list of tuples of [(0,0),(1,1)] would be:

      [[ 2.,  0.,  0.,  0.],
       [ 0.,  2.,  0.,  0.],
       [ 0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.]]

Any suggestions on what I use as a list of indices in numpy.ufunc.at to get that matrix?

Answer 1

If you want to do multidimensional indexing, you don't pass a list of index tuples; you pass a tuple of index lists (or index arrays).

indices = ([0, 1], [0, 1])
np.add.at(m, indices, 2)

indices[0] gives all the first coordinates of the cells you want to modify, and indices[1] gives all the second coordinates. Here's an example:

In [10]: a = numpy.zeros([4, 4])
In [11]: a
Out[11]: 
array([[ 0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.]])
In [12]: indices = ([0, 3], [2, 1])
In [13]: numpy.add.at(a, indices, 2)
In [14]: a
Out[14]: 
array([[ 0.,  0.,  2.,  0.],
       [ 0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.],
       [ 0.,  2.,  0.,  0.]])

I'm not entirely sure why it works this way. I suppose it might be more convenient once you've gotten the hang of it, or it might make the rules more internally consistent somehow, but I don't have enough experience with multidimensional indexing to say one way or another.