How can I multiply each element of a cell array, defined as an anonymous function handle?

I have a cell array FS which contains a function handle at each cell. I want to multiply the output of each cell with each other (giving each function handle the SAME input). The function handles in each cell are identical except for the i value stored in them.

Define array as:

N = 5;
for i=1:N
FS{i} = @(x) x+i;
end

i can obtain my desired result by a simple loop:

x = 3;
P = FS{1}(x)
for i=2:length(FS)
P = P * FS{i}(x)
end

However, I wish to define this operation as a new function handle, performing the same action:

b = @(x) FS{1}(x) * FS{2}(x) * FS{3}(x) ... * FS{N}(x)

but this should of course be flexible for any number of elements (FS).

Answer 1

[Walter Roberson]

b = @(x) prod(cellfun(@(F) F(x), FS))

This assumes that the output of each handle is scalar even if x is non-scalar.

If you really do mean * as in algebraic matrix multiplication, which assumes that the results of each function handle will be either a scalar or a matrix whose number of columns is the same as the number of rows of output of the next function handle (e.g., square matrices work well) then

b = @(x) fold(@mtimes, cellfun(@(F) F(x), FS), 1);

[Jonas Holfelt]

it does need to be an algebraic matrix multiplication, since my result is not necessarily scalar. I have another more complex configuration where the output of each function handle is actually an object of an abstract class. So it is important that the format would correspond to:

b = @(x) FS{1}(x) * FS{2}(x) * FS{3}(x) ... * FS{N}(x)

Is there a way to avoid using fold? I would prefer to avoid using the symbolic toolbox. But thanks a lot !

[Walter Roberson]

This use of fold comes down to

    F = @mtimes;
    result = v{1};
    for j = 2:numel(v)
        result = F(result, v{j});
    end

In other words, just program your own.

With non-scalar outputs you will need to add 'uniform', 0 to the cellfun() call.

[Jonas Holfelt]

*because I don't have access to this toolbox

[Walter Roberson]

Probably the best thing to do would be to write your own routine that accepted a cell array of function handles and an input array, and implemented the matrix product in a loop.

Using anonymous functions is not always the most efficient route. Indeed, it is seldom the most efficient route: tests show that anonymous functions are distinctly slower than regular functions.

[Jonas Holfelt]

I see. I have tried to figure another way, but the way my script is structured, it seems like the most flexible way. In this case I am trading flexibility over efficiency. Thanks for the reply

[Walter Roberson]

You can still use

b = @(x) MultFuns(FS, x)

assuming you put the work code into function MultFuns .

And other b might be anonymous functions that did the work more in-line.

There is no shame in writing a helper function to implement functionality that Mathworks does not provide in your available toolboxes.

[Jonas Holfelt]

Thanks. I ended up making a function like that, defined as:

function cascadedOut = cascadeCells(fcellArray,F)

cascadedOut = fcellArray{1}(F);
for i=2:length(fcellArray)
    cascadedOut = cascadedOut * fcellArray{i}(F);
end
end

This worked!

[Walter Roberson]

Looks good, and is probably faster than the alternatives.

[Georgios Koutsakis]

Hi, interesting approach.

Could you please share the final working version of the code?

I tried to replicate it from by end, but something doesn't seem quite right.

Thanks