GPU code to numerically integrate parameterized function

I'm trying to perform an integration in the GPU but haven't managed to figure out how to parse the problem properly. the physics is this (if it's of interest, if not then just skip to code): i have an extended radiance source (blakcbody) that's illuminating a 2D array of pixels. I want to integrate the Planck function over a spectral band that varies from pixel to pixel.

Here's the code, it barfs on the integral.

aoi = 0.9 * ones(nRows,nCols); % dummy values for simplicity

bbTemp = 320;

lambda = [3.000:0.001:5.0]; % filter wavelength grid

transmission = 0.8 * ones(numel(lambda),1)'; % filter transmission

radiance = zeros(nRows, nCols);

radianceGpu = gpuArray(radiance);

spectralRadiance = @CalcPlanck;

lambdaChi = gpuArray(lambda(end) .* aoi);

lambdaClo = gpuArray(lambda(1) .* aoi);

radianceGpu = integral(@(x)spectralRadiance(x,bbTemp), lambdaClo, lambdaChi);

%%%%%%%%

function spectralRadiance = CalcPlanck(lambda, bbTemp )

h = 6.626070e-34;% J-s, Planck's constant

c = 2.997925e14; % um/s, speed of light in vacuum

k = 1.380649e-23; % J/K, Boltzman's constant

c1p=2e8*c; % ph / sec / cm^2 / um / sr

c2=h*c/k; % um K

spectralRadiance = c1p./(lambda.^4)./(exp(c2./(lambda.*bbTemp))-1);

end

Answer 1

[Piotr Balik]

I tried to do it, however arrayfun does not allow to insert custom functions:

radianceGpu = arrayfun( @(lower,upper) integral(@(x)spectralRadiance(x,bbTemp),lower,upper),...
                                                                      lambdaClo,lambdaChi);

Error using gpuArray/arrayfun

Creating anonymous functions is not supported.

For more information see Tips and Restrictions.

So that is one problem. I've tested that you can use your own functions, but only if they are on the list:

mathworks.com/help/matlab/referencelist.html?type=function&capability=gpuarrays

mathworks.com/help/parallel-computing/gpuarray.arrayfun.html

For example:

radianceGpu = arrayfun( @myIntegral,lambdaClo,lambdaChi);
function out=myIntegral(in1,in2)
out = expint(in1)-1+in2^2/in1; % integral formula
end

Works alright, so I think you should find Taylor expansion of your integral or any other method (using these allowed) to compute it's value. That is inconvenience, but keeps only fast functions on your gpu.