MATLAB optimizing fitting function calls

Question

I have a 3D array of dimensions (rows x cols x 8). For each element in the first two dimensions I have 8 values along the third dimension which I must fit to an equation such as exponential, polynomial etc. I have written code for this function, and I'm currently producing my output by looping over the first two dimensions, as follows:

for i=1:rows
    for j=1:cols
        outputArray(i,j) = functionHandle(inputArray(i,j,1:8));
    end
end

Can I somehow use bsxfun, arrayfun, or some other vectorization method to get rid of the for loops, so that I generate my output using something like this?

outputArray = bsxfun(@functionHandle,inputArray)

Adding the functionHandle

function output = functionHandle(xData,yData)
    ft = fittype( 'a*exp(-b*x)+c','independent', 'x','dependent','y' );
    opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
    opts.Algorithm = 'Trust-Region';
    opts.Display = 'Off';
    opts.MaxFunEvals = 100;
    opts.MaxIter = 100;
    opts.Robust = 'LAR';
    opts.Lower = [-Inf 0 -Inf];
    opts.StartPoint = [0.35 0.05 0.90];

    % Fit model to data.
    [FitResult,~] = fit(xData,yData,ft,opts);
    output = FitResult.a;
end

Answer 1

The answer entirely depends on whether your function is vectorized or not. What you should do is write that function so that it allows R × C × 8 input and produces R × C × N output, where N is the number of fit parameters.

That is, vectorization has to be done within the function; it cannot be done outside. From the outside you can only use the function in a loop. Note that arrayfun is similar, and has comparable performance, to a for loop.

Since your function basically uses fit , it seems you cannot vectorize, because fit takes one set of inputs at a time and produces the corresponding output.