Multiplying a numpy array with another numpy array at a specific index

Question

For ease of explanation I will be using 2-dimensional numpy arrays (I am using 3-dimensional arrays in my problem).

I have 2 arrays, one records the odds of something occuring at those specific coordinates. The other array is a pre-generated matrix that is used to lower the values of the first array around a central point in a pre-determined radius.

I want to automatically select points in the first matrix (henceforth A), and prevent the program to select another point that sits too close to previously selected points. So I want to multiply the values around the selected point related to the distance from said point.

E.G.:

Matrix A:

[[0, 0, 0, 0, 0, 0],
 [0, 1, 2, 2, 1, 0],
 [0, 2, 4, 4, 2, 0],
 [0, 2, 4, 4, 2, 0],
 [0, 1, 2, 2, 1, 0],
 [0, 0, 0, 0, 0, 0]]

Matrix B:

[[ 1, 0.5, 1 ],
 [0.5, 0, 0.5],
 [ 1, 0.5, 1 ]]

Now say that index [2, 1] is selected as a point of interest. B is multiplied with A, but only with the values in a 3*3 around [2, 1]

Result:

[[0,  0,  0, 0, 0, 0],
 [0, 0.5, 0, 1, 1, 0],
 [0,  2,  2, 4, 2, 0],
 [0,  2,  4, 4, 2, 0],
 [0,  1,  2, 2, 1, 0],
 [0,  0,  0, 0, 0, 0]]

This should result in the points around [2, 1] not being valuable enough to be selected as points of interest, unless the conditions are high enough to be selected anyway, hence the multiplication.

Now, I can't seem to figure out a way to perform this specific multiplication. numpy.multiply() would repeat B so that it gets applied over the entire matrix A while I only want to apply it on a small part of A.

Another option would be looping over the affected section of Matrix A, but this requires an insane amount of time (especially in 3-dimensional matrices)

In other words, I want to apply a convolution filter without summing up the multiplication results at the end, but apply them to the underlying values of the convolved matrix (A)

Any insights on this issue are appreciated.

@ElMaravilla Yes, the issue with numpy.multiply(), as I added in my edit, is that it will repeat B so that it will fit inside A, thus applying B over the entirity of A, instead of the small part I want to apply it to. — Czorio
– Czorio, Commented Feb 19, 2018 at 21:12
Looks like a convolution problem. stackoverflow.com/questions/48871285/proper-numpy-vectorization — hpaulj
– hpaulj, Commented Feb 19, 2018 at 21:13
@hpaulj Convolutions only change one value per operation though, right? If I were to use a convolve with B on A at [2,1] I would just change [2,1] to the value (1 * 0) + (0.5 * 0) + (1 * 0) + (0.5 * 1) + (0 * 2) + (0.5 * 2) + (1 * 2) + (0.5 * 4) + (1 * 4) == 9.5, right? Instead I want to change each value under the "convolution filter" to what they multiply to be, and not sum them up after. — Czorio
– Czorio, Commented Feb 19, 2018 at 21:32
2 solutions: (1) Create a matrix with all zeros and a 1 at the selected point, then convolve with your 3x3 matrix. The result you can apply in a point-wise multiplication with the input matrix. (2) slice the input matrix around the selected point, apply a point-wise multiplication, and write back to the same slice. — Cris Luengo
– Cris Luengo, Commented Feb 19, 2018 at 21:40

Cris Luengo · Accepted Answer · 2018-02-19 23:48:27Z

2

The easiest solution uses slicing:

A[5:8, 8:11] = np.multiply(A[5:8,8:11], B)

What this does is extract from A the 3x3 area around the selected point (here [6,9]), multiply it (element-wise) by B, and write it back at the same location.

Since you talked about convolution, if you want to use that the approach would be to create a matrix M of the same shape as A, but that is zero everywhere except at the selected point. This matrix you can convolve with B, and then multiply with A:

M = np.zeros(A.shape)
M[6,9] = 1
M = scipy.ndimage.filters.convolve(M, B)
A = np.multiply(A, M)

(or something to that extent, I did not test this variant).

answered Feb 19, 2018 at 23:48

Cris Luengo

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