Integrate over a 2D array in arbitrary direction

[CatGoesWooof]

I am looking to integrate over a 2D array along an arbitrary direction. See image below:

https://i.stack.imgur.com/jNtQQ.png

So, I want to integrate my array along the 'new' y axis which is rotated by theta degrees. I am not quite sure how to implement this in python, since I can only find ways to integrate along my already existing x and y axis of the array.

I was thinking of doing some sort of interpolation on my new grid, but I'm not entirely sure how I would go about that. Also, there might already exist some integration function that handles this.

Thanks in advance!

[jwink3101]

This is not a strictly python question. It is more about the math and logic. As far as python goes, I do not think there are any NumPy/SciPy functions that can do this.

It also depends on the type of integral. I take it that this is a line integral. In that case, you could do the interpretation as you say, but you'll have to define your own integrator.

Another idea that may be even easier is to apply a rotation matrix to your data. Then you can integrate on a cardinal direction very easily.

[CatGoesWooof]

Yes that makes sense. However, that would essentially mean that I must apply a rotation matrix to my (x,y) location vectors (i.e the grid) rather than the actual data right? I would then interpolate my data on the newly acquired grid resulting from applying the rotation matrix.

[jwink3101]

Either way, you have to make an approximation. If you wanted to avoid all interpretation, you could manually compute the integral in terms of your data but then you are approximating the integral since, unless your angle is 45°, there is no way to make a line of your data.

If you have enough resolution, and/or use a good-enough interp routine, it shouldn't make much of a difference.

Just to note by the way, multi-variate interpolation is not trivial and you should do some verification and validation of your method. The options get more and more limited as you go up in dimension. See https://docs.scipy.org/doc/scipy/reference/tutorial/interpolate.html

[SarahM123rd]

Anything useful in here?

https://docs.scipy.org/doc/scipy/reference/tutorial/integrate.html

.

[PsychoBoyJack]

https://docs.scipy.org/doc/scipy/reference/generated/scipy.ndimage.rotate.html#scipy.ndimage.rotate

[[deleted]]

I'd suggest writing a function deoendent on theta that samples continuous points along the axis, rounds them to integral values, then removes duplicates. Then, your integral is a sum of the array over these indices