Double sum and how to make a matrix to plot in 3D? (surface plot)

Question

Edit

To clarify. I have a function f that takes in 5 arguments z,x,y,n,m. The order of events should go as follows:

1. Upon calling the function test, the variable z is assigned, say z = 1.

2. A linear combination is created by adding f with with each of elements of ni inserted and the result is stored in fn, as such (z = 1, so no more z variable):

fn = x + 2.*y + exp(0) - sqrt(m) + x + 2.*y + exp(2) - sqrt(m) + x + 2.*y + exp(4) - sqrt(m) + x + 2.*y + exp(6) - sqrt(m) + x + 2.*y + exp(8) - sqrt(m) + x + 2.*y + exp(10) - sqrt(m) = 6*x + 12*y + 1 + exp(2) + exp(4) + exp(6) + exp(8) + exp(10) - 6*sqrt(m) = 6*x + 12*y + 25473.8 - 6*sqrt(m)

2. A linear combination is created by adding fn with each of elements of mi inserted and the result is stored in fnm. (I don't know how to do 1. and 2. simultaneously. If you do, please let me know):

fnm = 6*x + 12*y + 1 + exp(2) + exp(4) + exp(6) + exp(8) + exp(10) - 6*sqrt(0) + 6*x + 12*y + 1 + exp(2) + exp(4) + exp(6) + exp(8) + exp(10) - 6*sqrt(2) + 6*x + 12*y + 1 + exp(2) + exp(4) + exp(6) + exp(8) + exp(10) - 6*sqrt(4) + 6*x + 12*y + 1 + exp(2) + exp(4) + exp(6) + exp(8) + exp(10) - 6*sqrt(6) + 6*x + 12*y + 1 + exp(2) + exp(4) + exp(6) + exp(8) + exp(10) - 6*sqrt(8) + 6*x + 12*y + 1 + exp(2) + exp(4) + exp(6) + exp(8) + exp(10) - 6*sqrt(10) = 6*x + 12*y + 25453.1

3. A surface is plotted by plugging in x and y from arrays xi and yi into fnm

and of Edit

I'm having trouble with the double summation over the function f. I tried to follow the example in the last answer presented here, but it's not working for some reason. Because my variables x and y are not defined beforehand, I included them into @() in the arrayfun. I was first getting the error Z must be a matrix, not a scalar or vector. , so I changed the function handle fnm to a symbolic function after reading about it here. But now the whole thing exploded ... I don't know what's going on. Why is it saying there aren't enough inputs? fn should only be a function of x, y, m on line 11 since z is already defined to be some number (lets say 1) and n's just got summed over.

    function test(z)

f = @(z,x,y,n,m) z.*x + 2.*y + exp(n) - sqrt(m);

    function s(z)
        ni = 0:2:10;
        mi = 0:2:10;
        xi = -5:5;
        yi = -5:5;
        fn = @(n) arrayfun(@(z, x, y, ni, m) sum(f(z, x, y, ni, m)),n);
        fnm = @(m) arrayfun(@(x, y, mi) sum(fn(x, y, mi)),m);
        zz = sym(fnm);

        [xx,yy] = meshgrid(xi,yi);
        surf(xx,yy,zz)
    end

s
end

so many errors :(

    Error using test2>@(x,y,mi)sum(fn(x,y,mi)) (line 11)
Not enough input arguments.

Error in test2>@(m)arrayfun(@(x,y,mi)sum(fn(x,y,mi)),m) (line 11)
        fnm = @(m) arrayfun(@(x, y, mi) sum(fn(x, y, mi)),m);

Error in sym>funchandle2ref (line 1209)
    S = x(S{:});

Error in sym>tomupad (line 1114)
    x = funchandle2ref(x);

Error in sym (line 151)
                S.s = tomupad(x);

Error in test2/s (line 12)
        zz = sym(fnm);

Error in test2 (line 18)
s

Answer 1

Are you trying to do this?. I am not optimizing anything, for you to understand it clearly....

function test(zi)
syms z x y n m fn fnm;
f0=symfun(z.*x + 2.*y + exp(n) - sqrt(m),[z x y n m]);
z=zi;
ni=0:2:10;
mi=0:2:10;
fn=0;
for i=1:length(ni);
    fn=symfun(fn+f0(z,x,y,ni(i),m),[x y m]);
end
fnm=0;
for i=1:length(mi)
    fnm=symfun(fnm+fn(x,y,mi(i)),[x y]);
end

xi=-5:5;
yi=-5:5;
for i=1:length(xi)
    for j=1:length(yi)
        zz(i,j)=eval(fnm(xi(i),yi(j)));
    end
end

[xx,yy]=meshgrid(xi,yi);
mesh(xx,yy,zz);

So, test(1) produces this:

Beware of the symfun calls, which shall be put there in order every summation keeps onto a "symbolic" framework. The arrayfun could be used, though they are neat, they could be not necesarily efficient... Let that exercise as homework!! XD..