MATLAB: Is there a way to pass an anonymous function with an unknown number of variables to a matlab function and perform operations on it

anonymousanonymous functionanonymous functionsfunctionfunctionsvariablevariables

Basically what I want to do is take in an anonymous function like:
Afunc = @(a,b,c,...) a+b+c+...;   % for any number of variables
and pass it and values for each variable (say in an n-dimensional matrix where n is the number of variables in Afunc) into a matlab function that will evaluate it at all points. So:
Amatrix = AfuncEval(Afunc,vals);
An example using 3 variables:
Afunc = @(a,b,c) a+b+c;
vals = [[1 2 3];[4 5 6];[7 8 9]]; % vals(1,:) are values for variable a, vals(2,:) are b, etc.
Amatrix = AfuncEval(Afunc,vals);
Amatrix(1,1,1) = Afunc(1,4,7);
Amatrix(1,1,2) = Afunc(1,4,8);
And so on. I've looked all over and haven't managed to find a completely general approach to anonymous functions. The closest I've come is using a cell function:
cellfun(Afunc,val{:});
but this only evaluates Afunc at (1,4,7), (2,5,8), and (3,6,9). I could set up val so that it evaluates Afunc at all combinations of the variable values, but that would still require knowing how many variables there are ahead of time. Has anyone tried to do anything like this before?
Thanks very much!

Best Answer

Function for evaluating any anonymous function with any number of value inputs (tested up through 4 dimensions, haven't bothered with higher ones yet.
% function funcEval(func,vals)
% Takes in an anonymous function and an nxm matrix of values and returns an
% n-dimensional matrix filled with the function evaluated at all points
% given in val. That is at all combinations of all the inputs in val.
%
% inputs:
% Afunc - the anonymous function to be normalized
% vals - nxm cell matrix of values corresponding to each variable in Afunc
% as follows:
% Afunc = @(a,b,c) f(a,b,c)
% val = [...
% [1,2,3,4,5,...] % corresponds to a
% [1,2,3,4,5,...] % corresponds to b
% [1,2,3,4,5,...] % corresponds to c
% ...
% ]
%
% output:
% fMatrix - a matrix containing func evaluated at all combinations of
% variable values in val. So for a two variable function with
% three values for each variable:
% fMatrix(1,1) = func(val(1,1),val(2,1));
% fMatrix(1,2) = func(val(1,1),val(2,2));
% fMatrix(1,3) = func(val(1,1),val(2,3));
% fMatrix(2,1) = func(val(1,2),val(2,1));
% fMatrix(2,2) = func(val(1,2),val(2,2));
% fMatrix(2,3) = func(val(1,2),val(2,3));
% fMatrix(3,1) = func(val(1,3),val(2,1));
% fMatrix(3,2) = func(val(1,3),val(2,2));
% fMatrix(3,3) = func(val(1,3),val(2,3));
%
% 3-dimensional example:
% Inputs:
% func = @(a,b,c) a.^b + c;
% vals =
% 2 5 10
% 1 2 3
% .1 .2 .3
%
% Output:
% fMatrix(:,:,1) =
%
% 2.1 4.1 8.1
% 5.1 25.1 125.1
% 10.1 100.1 1000.1
%
%
% fMatrix(:,:,2) =
%
% 2.2 4.2 8.2
% 5.2 25.2 125.2
% 10.2 100.2 1000.2
%
%
% fMatrix(:,:,3) =
%
% 2.3 4.3 8.3
% 5.3 25.3 125.3
% 10.3 100.3 1000.3
%%
function fMatrix = funcEval(func,vals)
    nvars = size(vals,1); % number of variables
    vals_cell = mat2cell(vals, ones(nvars,1), size(vals,2));
    vals_grids = cell(nvars,1);
    [vals_grids{:}] = ndgrid(vals_cell{:});
    vals_2d = cell(nvars,1);
    for i=1:nvars
        vals_2d{i} = vals_grids{i}(:);
    end; % end for i
    % Getting matrix2d - this will be turned into fMatrix which is nvars
    % dimensions rather than two dimensions.
    fSolutions = nan(1,size(vals_2d{1,:},1));
    solution = cell(nvars,1);
    for i=1:size(vals_2d{1,:},1)
        for j=1:size(vals_2d,1)
            solution{j} = vals_2d{j}(i);
        end % end for j
        fSolutions(i) = func(solution{:}); % 2-d version of fMatrix
    end % end for i    
    %filling fMatrix, an nvars dimensional matrix
    sizeM = size(vals_grids{1});
    fMatrix = reshape(fSolutions,sizeM);
end % end funcEval_jfr001
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