multi-variable function, sum over one variable

I have a function of three variables N(z,t,n). I'd like to sum over only integers of n such that I am left with N(z,t), where z and t can be arrays of any length.

I've tried:

NN = 1:2000;
sum_function = @(z,t) sum(f(z,t,NN));

where f is a previously defined function of @(z,t,n), but this still requires that z and t have the same size as NN.

How do I evaluate this sum properly?

Answer 1

[Voss]

Maybe something like this

z = 1:3;
t = 1:4;
NN = 1:2000;

% Evaluate f(z,t,n) for each element of NN,
% storing all results in cell array C
C = arrayfun(@(n)f(z,t,n),NN,'uni',0);

% Inspect the first and last elements of C
disp(C{1}); disp(C{end});

     1     2     3     4
     2     4     6     8
     3     6     9    12

        2000        4000        6000        8000
        4000        8000       12000       16000
        6000       12000       18000       24000

% Concatenate all elements of C along the 3rd dimension 
% and then sum that 3d matrix along the 3rd dimension.
% This will work as long as all elements of C are the 
% same size; whether that's true depends on the 
% definition of f.
result = sum(cat(3,C{:}),3)

result = 3×4

2001000 4002000 6003000 8004000 4002000 8004000 12006000 16008000 6003000 12006000 18009000 24012000

function out = f(z,t,n)
% Some function where z and t are vectors, n is a scalar.
% In this case, out is a matrix of size numel(z)-by-numel(t),
% but out can be any size as long as its size only depends on
% the sizes of z and t.
out = z(:).*t(:).'.*n;
end

[Walter Roberson]

I would use a variation on that:

sum_function = @(z,t) sum(arrayfun(@(n)f(z,t,n),NN));

[Voss]

That'll work if f returns a scalar

z = 1:3;
t = 1:4;
NN = 1:2000;
sum_function = @(z,t) sum(arrayfun(@(n)f_scalar(z,t,n),NN));
sum_function(z,t)

ans = 2001000

But not otherwise

sum_function = @(z,t) sum(arrayfun(@(n)f_non_scalar(z,t,n),NN));
sum_function(z,t)

Error using arrayfun
Non-scalar in Uniform output, at index 1, output 1.
Set 'UniformOutput' to false.

Error in solution (line 6)
sum_function = @(z,t) sum(arrayfun(@(n)f_non_scalar(z,t,n),NN));

[Even then, the outputs from f have to be the same size for all n (and if that's not the case then the question doesn't make sense - at least, not to me).]

Of course, without knowing what f is, it's hard to say how general the solution needs to be.

function out = f_scalar(z,t,n)
out = n;
end

function out = f_non_scalar(z,t,n)
out = n*ones(1,10);
end

[Nicolas Couture]

To elaborate, f is the solution of a differential equation I solved analytically with a Fourier series

The issue I am running into is that when I use sum, matlab is summing over z or t instead of n. I'm trying to keep my result as a function handle since I need this function to solve another differential equation, but get an error when trying to plot f(z,t) while keeping one of z/t constant, e.g.

plot(z,f(z,0)) 
% Error: Vectors must be the same length.

which leads me to believe the wrong variable is being summed over.

[Walter Roberson]

The second parameter to sum() can be the dimension to sum over.