Function handle applied to array in MATLAB

Question

I've searched and there are many answers to this kind of question, suggesting functions like arrayfun, bsxfun, and so on. I haven't been able to resolve the issue due to dimension mismatches (and probably a fundamental misunderstanding as to how MATLAB treats anonymous function handles).

I have a generic function handle of more than one variable:

f = @(x,y) (some function of x, y)

Heuristically, I would like to define a new function handle like

g = @(x) sum(f(x,1:3))

More precisely, the following does exactly what I need, but is tedious to write out for larger arrays (say, 1:10 instead of 1:3):

g = @(x) f(x,1)+f(x,2)+f(x,3)

I tried something like

g = @(x) sum(arrayfun(@(y) f(x,y), 1:3))

but this does not work as soon as the size of x exceeds 1x1.

Thanks in advance.

Is it not an option to vectorize f, so that it also accepts array input for y and not just x? Otherwise what are the allowed dimensions of x? — Andras Deak -- Слава Україні
– Andras Deak -- Слава Україні, Commented Jan 15, 2016 at 19:04
The answer I gave is based on the limited information provided. A better solution may be possible if you provide the implementation of f since it may be possible to vectorize the output in some manner. — TroyHaskin
– TroyHaskin, Commented Jan 15, 2016 at 20:10

TroyHaskin · Accepted Answer · 2016-01-15 19:38:04Z

2

Assuming you cannot change the definition of f to be more vector-friendly, you can use your last solution by specifying a non-uniform output and converting the output cell array to a matrix:

g = @(x) sum(cell2mat(arrayfun(@(y) f(x,y), 1:3,'UniformOutput',false)),2);

This should work well if f(x,y) outputs column vectors and you wish to sum them together. For rows vectors, you can use

g = @(x) sum(cell2mat(arrayfun(@(y) f(x,y), 1:3,'UniformOutput',false).'));

If the arrays are higher in dimension, I actually think a function accumulator would be quicker and easier. For example, consider the (extremely simple) function:

function acc = accumfun(f,y)
    acc = f(y(1));
    for k = 2:numel(y)
        acc = acc + f(y(k));
    end
end

Then, you can make the one-liner

g = @(x) accumfun(@(y) f(x,y),y);

edited Jan 15, 2016 at 19:38

answered Jan 15, 2016 at 19:07

TroyHaskin

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6 Comments

Andras Deak -- Слава Україні Over a year ago

I was just about to write almost the same:) However: does this work for any size of input for x? I was thinking along the lines of C=arrayfun(@(y)f(x,y),1:3,'uniformoutput',false); sum(cat(length(size(x))+1,C{:}),length(size(x))+1) for a general array of x, this should preserve the shape. But putting that into an anon function is messy.

TroyHaskin Over a year ago

@AndrasDeak The shape of x shouldn't matter; only the shape of f(x,y). And since the OP says that f(x,1)+f(x,2)+f(x,3) works, I assume the output array is regular enough that a one-liner could work ... we'll see.

Andras Deak -- Слава Україні Over a year ago

cell2mat will concatenate the cell in 2d, right? While f(x,1)+f(x,2) will work for matrix-valued output. I might be wrong though.

TroyHaskin Over a year ago

@AndrasDeak You're right. cell2mat smashes the arrays together which will not produce a proper sum for general arrays. Rethinking.

Andras Deak -- Слава Україні Over a year ago

Ooh, nice one with the accumulator:)

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