Replacing for loops for faster computations involving 3D matrix and sampling

Hi! I'm hoping there's someone out there who would give me an idea on how to increase computation speed for the following code:

for l=1:size(xSample,2) %%anisotropic 3D gaussian distribution of translation
      for m=1:size(ySample,2) %%anisotropic 3D gaussian distribution of translation
          for n=1:size(zSample,2) %%anisotropic 3D gaussian distribution of translation
              shiftedDoseDist=imtranslate(doseDist,[xSample(l),ySample(m),zSample(n)]); %%3D image translation
              shiftedDoseDist=imgaussfilt3(shiftedDoseDist,randomError); %%3D image blurring with Gauss filter
              dose=shiftedDoseDist(index);
              TCP_n(n)=prod(exp(-cellDensity.*vol.*exp(-alpha(q)*numOfFractions*dose- alpha(q)*numOfFractions*dose.^2/AlphaOnBeta+log(2)*T/tPot))); %%function I'm calculating
          end
          TCP_m(m)=1/sum(zWeighting)*dot(zWeighting,TCP_n);
      end
      TCP_l(l)=1/sum(yWeighting)*dot(yWeighting,TCP_m);

So what I'm trying to do is to get a bunch of different combinations of x,y,z from their respective Gaussian distributions for translation of a matrix doseDist (250x250x143), then a Gaussian filter is applied. Then with the resulting distribution, I compute something called TCP where the weighting of the Gaussian distribution is applied to get the expected value.

From the profiler, the bottleneck is in the imtranslate and imgaussfilt3 functions which I don't think they can be further optimised - basically left with getting rid of the nested for loops.

Any help would be appreciated!

[madhan ravi]

what are the sizes of TCP_n,TCP_m &TCP_l??

[Emily Her]

There are 3 samples [1x3] for each x,y,z direction and there is another outer for loop which I didn't include (alpha(q)) which is samples [1x4]

Answer 1

[Bruno Luong]

What are xSample,... zSample and idx?

Not sure you need to translate and filter over and over in the for-loop. It seems awfully wasteful to me.

Rather you could do the filtering once on the big image and extract the information (dose) at appropriate subindexing.