anonymous function with a variable number of input variables

Hi!

I have an anonymous function:

ht = @(A1,A2,A3,....) ...

meaning that I don't know in advance how many variables Ai are included in the definition of ht. Then I need to minimise ht in respect of the variables Ai. For example, for 2 indipendent variables I get a result with:

ht2 = @(A)ht(A(1),A(2));
A0 = [1,1];
[res,fval] = fminunc(ht2,A0)

How can I define ht2 dinamically with a variable number of unknown Ai?

Thanks!

Answer 1

[Ameer Hamza]

See nargin()

f = @(x,y,z) x+y+z;
n = nargin(f)

Output

n =
     3

Edit 2:

To avoid helper functions, you can use the following code.

Create the ht2 with all variables.

ht = @(x1,x2,x3) x1.^2+x2.^2+x3.^2;
ht2 = @(x) ht(struct('x', num2cell(x)).x);
x_sol = fmincon(ht2, rand(1,3))

Result:

x_sol =
   1.0e-08 *
   -0.7647   -0.6963   -0.3199

Create ht2 for single variable

ht = @(x1,x2,x3) x1.^2+x2.^2+x3.^2;
i = 2;
xs = [1 2];
ht2 = @(x) ht(struct('x', num2cell(xs(1:i-1))).x, x, struct('x', num2cell(xs(i:end))).x);
x_sol = fmincon(ht2, rand(1))

Result:

>> x_sol
x_sol =
  -1.1660e-09

Edit 1:

To create ht2 on runtime, you will need to define a helper function like this

function y = helperFun(x, fun_handel)
    x = num2cell(x);
    y = fun_handel(x{:});
end

Then you can use it to create ht2 which is compatible for optimization functions, e.g., fmincon

ht = @(x1,x2,x3) x1.^2+x2.^2+x3.^2;
ht2 = @(x) helperFun(x, ht);
x_sol = fmincon(ht2, rand(1,3))

Result

x_sol =
   1.0e-08 *
   -0.4592   -0.8045    0.0830

If you want to optimize a particular variable (say x2), then you can modify the helper function like this. You will need to specify the value of variables you don't want to optimize

function y = helperFun(x, fun_handel, i, val)
    % x: optimization variable
    % fun_handel: function to optimize 
    % i: variable number to optimize, e.g., i=2 if x2 is optimization
    % variable
    % val: values of variables other then i-th variable
    
    val = num2cell(val);
    y = fun_handel(val{1:i-1}, x, val{i:end});
end

Then run it like this

ht = @(x1,x2,x3) x1.^2+x2.^2+x3.^2;
ht2 = @(x) helperFun(x, ht, 3, [1 2]);
x_sol = fmincon(ht2, rand(1))

Result

x_sol =
  -5.3326e-09

[dario]

Thanks Ameer.

Referring to my example, if nargin(ht) returns 4, how can I define ht2 runtime?

[Ameer Hamza]

To create ht2 on runtime, you will need to define a helper function like this

function y = helperFun(x, fun_handel)
    x = num2cell(x);
    y = fun_handel(x{:});
end

Then you can use it to create ht2 which is compatible for optimization functions, e.g., fmincon

ht = @(x1,x2,x3) x1.^2+x2.^2+x3.^2;
ht2 = @(x) helperFun(x, ht);
x_sol = fmincon(ht2, rand(1,3))

Result

x_sol =
   1.0e-08 *
   -0.4592   -0.8045    0.0830

[Ameer Hamza]

If you want to optimize a particular variable (say x2), then you can modify the helper function like this. You will need to specify the value of variables you don't want to optimize

function y = helperFun(x, fun_handel, i, val)
    % x: optimization variable
    % fun_handel: function to optimize 
    % i: variable number to optimize, e.g., i=2 if x2 is optimization
    % variable
    % val: values of variables other then i-th variable
    
    val = num2cell(val);
    y = fun_handel(val{1:i-1}, x, val{i:end});
end

Then run it like this

ht = @(x1,x2,x3) x1.^2+x2.^2+x3.^2;
ht2 = @(x) helperFun(x, ht, 3, [1 2]);
x_sol = fmincon(ht2, rand(1))

Result

x_sol =
  -5.3326e-09

[dario]

Thanks, it's what I was looking for. Is there any way round to avoid the helper function?

[Ameer Hamza]

It is possible, but it can get a bit messy. Check the code in my updated answer.

[dario]

Thanks Ameer. Very Helpful.

[Ameer Hamza]

I am glad to be of help.

Answer 2

[per isakson]

"anonymous function with a variable number of input variables"

Something like this?

>> ht(1,2,3)
ans =
     6
>> ht(1,2,3,4)
ans =
    10
>> ht(1,2,3,4,5)
ans =
    15
>> 

where

ht = @(varargin) dario( varargin{:} );

and

function    out = dario( varargin )
    out = sum([ varargin{:} ]);
end

[dario]

Thaks.

What if:

ht(A1, A2)

or

ht(A1, A2, A3)

and I need to find the values of Ai that minimise ht?

[per isakson]

I assume that ht shall returns a scalar numerical output. That output could readily be calculated in dario, since all inputs are available. The variables, Ai, what type and size are they?

[dario]

Ai are scalar and yes, ht returns a scalar. I'm calculating Ai as

ht2 = @(A)ht(A(1),A(2));
A0 = [1,1];
[res,fval] = fminunc(ht2,A0)

but I need to know in advance how many Ai are included in the definition of ht2