Numpy loop using an index - numpy

Question

I'm a newbie and was trying something in python 2.7.2 with Numpy which wasn't working as expected so wanted to check if there was something basic I was misunderstanding.
I was calculating a value for a triangle (trinormals) and then updating a value per point of the triangle (vertnormals) using an array of triangle indexes (trivertexidx). As a loop I was calculating:
for itri in range(ntriangles) :
vertnormals[(trivertidx[itri,0]),:] += trinormals[itri,:]
vertnormals[(trivertidx[itri,1]),:] += trinormals[itri,:]
vertnormals[(trivertidx[itri,2]),:] += trinormals[itri,:]
As this was a little slow I thought it could be modified to :
vertnormals[(trivertidx[:,0]),:] += trinormals[:,:]
vertnormals[(trivertidx[:,1]),:] += trinormals[:,:]
vertnormals[(trivertidx[:,2]),:] += trinormals[:,:]
However this doesn't give the same results. Is there another simpler way to write the loop? Any pointers appreciated. Note the intent here was to get a single value for each entry in vertnormals and then normalise the result.

Answer 1

Numpy has a function bincount that can be very helpful in situations like this. The two lines bellow are the the same when the elements of index are unique, but different when index has repeated values:
A[index] += W
A += np.bincount(index, W, minlenght=len(A))
I believe you want the behavior of the second, but you're code is a little more complex because A, index, and W are not 1d. You can try something like this,
import numpy as np
N = len(vertnormals)
for j in range(vertnormals.shape[-1]):
vertnormals[:, j] += np.bincount(trivertidx[:, 0], trinormals[:, j], minlength=N)
vertnormals[:, j] += np.bincount(trivertidx[:, 1], trinormals[:, j], minlength=N)
vertnormals[:, j] += np.bincount(trivertidx[:, 2], trinormals[:, j], minlength=N)
Hope that helps.

Answer 2

If I am understanding your question well, you have m points from which you have formed n triangles, and trivertidx is an array of shape (n, 3) holding values in the range [0, m), where trivertidx[j] is the list of the 3 points making up the j-th triangle.
trinormals then is an array of shape (n,) holding a value assigned to each triangle, and you want vertnormals to be an array of shape (m,) holding, for each point, the sum of the values assigned to each triangle that point is a vertex of.
If the above is right, the following example should show why your second code is not working properly:
>>> a = np.arange(5)
>>> a
array([0, 1, 2, 3, 4])
>>> a[[1,2,0,2]] += 1
>>> a
array([1, 2, 3, 3, 4])
Even though the element in position 2 shows up twice in the left hand side, what happens is that two copies of the same value have 1 added, and then the incremented value is copied twice to the same position.
To vectorize this summation you would need an array of shape (n, m) where the value at position [j, k] is True if vertex k is part of triangle j, False if not. You could build that array like this:
trivert = np.zeros((n, m), dtype='bool')
trivert[np.arange(n).reshape(n, 1), trivertidx] = 1
Once you have this array, you can get your sums for each vertex as
vertnormals = np.sum(trivert * trinormals.reshape(-1, 1), axis=0)