How to turn a multivariable function to multidimensional x-function?

So what I want to do is turn an n-dimensional function, for example

f=@(x,y,z)x+y+z+t

to a function which contains only x:s. I'd do this by hand as

f2=@(x)f(x(1),x(2),x(3),x(4))

I'll also have a point at my disposal as a vector, so that will be most likely the easiest way to find the amount of new variables needed. So here's what I've tried:

p=[1 4 6 2]
f=@(x,y,z,t)x+y+z+t

text=[]
for i=1:length(p)-1
     A=['x(',num2str(i),'),']
     text=[text,A]
end
 for i=length(p):length(p)
     A=['x(',num2str(i),')']
     text=[text A]
 end
f2=@(x)f(text)
f2(p)

Of course doing this with "if" would be possible, but i think that's just too heavy way of doing it. So, has anybody an idea, or is it even possible, to make this happen: f2=@(x) x(1)+x(2)+x(3)+x(4)

Answer 1

[Star Strider]

The varargin (link) function is an option:

f = @(varargin) sum(varargin{:});

x = [42 pi];
Out_1 = f(x)

z = 1:5;
Out_2 = f(z)

Out_1 =
       45.142

Out_2 =
    15

Of course, whether this is appropriate depends on what you want to do in your function.

[Star Strider]

nassu100’s ‘Answer’ moved here:

The f2(p) is there only for testing purposes. I'll be using this for a function which calculates gradient in a specific point, and it'll be using a numeric derivative-function, which needs input as x(1),x(2) etc. The function works, if I give it the function as an x-function, but just to refine it, I'd like to be able to give it function with normal variables.

[Star Strider]

The varargin approach will likely do what you want.

Example —

g = @(varargin) varargin{1} .* exp(varargin{2} * varargin{3});
Out_3 = g([1; 2], -0.5, 0:0.1:0.5)

Out_3 =
            1      0.95123      0.90484      0.86071      0.81873       0.7788
            2       1.9025       1.8097       1.7214       1.6375       1.5576

[nassu100]

It doesn't like I hope it to do. There are two parts:

-it has to be n-scaling, depending on the length of the p (or the amount of variables given in, which are the same)

-it has to return a function of an x-variable, which i can import to a function file

I know I can always use Matlab's own gradient-function to calculate the partial derivatives for me, but that's not the case.

[Star Strider]

O.K.

I don’t know what you want to do. This is the best I can do.

Since my Answer doesn’t solve your problem, I’ll delete it in a while.