Combining function handles into one function handle

Is there a convenient way where I can combine N SISO function handles to create one SIMO function handle?

For example of N=2, if I got:

a = @(x) x(1)^2+x(2)^2;
b = @(x) x(3)^2-x(4)^2;

I would like to create a single function handle like:

c = @(x) [x(1)^2+x(2)^2; x(3)^2-x(4)^2];

Thanks in advance!

Answer 1

[Fangjun Jiang]

>> a = @(x) x(1)^2+x(2)^2;
b = @(x) x(3)^2-x(4)^2;
>> a(1:4)
ans =
     5
>> b(1:4)
ans =
    -7
>> c = @(x) [x(1)^2+x(2)^2; x(3)^2-x(4)^2];
>> c(1:4)
ans =
     5
    -7
>> d=@(x) [a(x);b(x)]
d =
  function_handle with value:
    @(x)[a(x);b(x)]
>> d(1:4)
ans =
     5
    -7
>> 

[Kfir Assor]

Hey,

Thank you for the solution, buy I hoped for a more general solution.

If I have N>>1 function handles I can't just solve it like d=@(x) [a1(x);a2(x);a3(x),...,a(n)].

Is there a more general solution? Or maybe an iterative solution I can use with a for loop?

Thanks!

[Steven Lord]

How do you have your many function handles stored? You don't have them stored in numbered variables, do you?

Depending on how they're stored (cell array?) and what they return (scalars or non-scalars, outputs of the same size and type, outputs of different sizes and/or types, etc.) using cellfun may be of use.

[Fangjun Jiang]

In that case, no need to create separate function handles and then combine them, use cell array of function handles, and you can use for-loop easily

f{1}=@(x) x(1)^2+x(2)^2;
f{2}=@(x) x(3)^2-x(4)^2;
f{1}(1:4)
[f{1}(1:4);f{2}(1:4)]

[Kfir Assor]

Let's say I have a loop, where in each iteration I create one more function handle. I want to create a SIMO function handle that looks like that: d=@(x) [a1(x);a2(x);a3(x),...,a(n)].

Fangjun, I'm not interested in the solution of x=1:4, I need the function handle itself. If I could do [f{1};f{2}] that would be great but I can't vertcat nonscalar arrays of function handles.

[Fangjun Jiang]

treat the function handles the same as strings, as in cellstr(). You can't put function handles in a regular array, but you can put them in a cell array.

suppose you have function handles defined in f{1}, f{2}, f{3}, ..., f{n}

then at any iteration k, your SIMO function handle is d=f(1:k). Again, it is a cell array of function handles. If you want to use this function handle cell array d to evaluate without for-loop, Bruno Luong has provided answer below. I can just use a simple example:

%%
f{1}=@(x) x(1)^2+x(2)^2;
f{2}=@(x) x(3)^2-x(4)^2;
f{3}=@(x) x(1)*x(4);

y=1:4;
for k=1:numel(f)
    d=f(1:k);
    out=@(x) cellfun(@(f) f(x), d);
    result=out(y)
end

result =

5

result =

5 -7

result =

5 -7 4

Answer 2

[Bruno Luong]

a = @(x) x(1)^2+x(2)^2;
b = @(x) x(3)^2-x(4)^2;
c = @(x) x(1)*x(4);

% suppose your for-loop puts each function handle in a cell array like this
allfun = {a, b, c};

vecfun = @(x) cellfun(@(f) f(x), allfun(:));

x = rand(1,4);

a(x)
b(x)
c(x)
vecfun(x)