How to write a function equation in matlab?

Hello, I'm having trouble on how to write this function (see insert image) into Matlab. It seems like a basic question, but I'm unsure. Any help would be great.

I have an general idea how to write it in matlab, but I'm not sure if this is correct.

func_l = c*exp(1/pi)*(x - A)^2 * cos*(pi*(x - A)^2);

[James Tursa]

What is d? What is m? Are the xj simply the elements of X?

[Jim]

I would assume the same.

[James Tursa]

You have ranges on both x1 and x2. Does that mean this is supposed to generate a surface plot?

[Jim]

Yes. But I'm not sure how to correctly write the " Given function" into Matlab. Like how to input the written formula into the Matlab language.

Answer 1

[James Tursa]

Here is a function assuming single values for x1 and x2, which would be stored in the vector x:

% Assumes numel(c)==size(A,1) and numel(x)==size(A,2)
function result = fl(A,c,x)
x = reshape(x,1,[]); % make sure x is a row vector
c = c(:); % make sure c is a column vector
y = sum(bsxfun(@minus,x,A).^2,2); % the sum over j part
result = sum(c .* exp((-1/pi)*y) .* cos(pi*y)); % the sum over i part
end

To call it for multiple values of x1 and x2 you could use loops. E.g.,

x1 = 0:.01:10;
x2 = 0:.01:10;
c = [1 2 5 2 3];
A = [3 5;5 2;2 1;1 4;7 9];
z = zeros(numel(x1),numel(x2));
for m=1:numel(x1)
    for n=1:numel(x2)
        z(m,n) = fl(A,c,[x1(m) x2(n)]);
    end
end
surf(x1,x2,z,'LineStyle','none');

There are ways to vectorize the fl function to allow for multiple x1's and x2's per call (speed and convenience), but I did not go that far with my example code.