MATLAB: Creating arrayfun with two variables

arraycell array

Hello.
I'd like to create cell array with results of a function S for variables q and k, which is defined in a code below.
function z=comparison_sum_integral_trapz
tic
format long
tt=-0.000689609;t=0.242731; muu=0.365908;
[m,NN]=meshgrid(0:100,-500:1:500);
    y1= @(N,q,k) t*q./k.*log((-k.^2+2*k.*q-q.^2+muu+1i*(2*pi*N.*t-(2*m(1,:)+1)*pi*t))./(-k.^2-2*k.*q-...
        q.^2+muu+1i*(2*pi*N.*t-(2*m(1,:)+1)*pi*t)))./(tt*pi+integral(@(a)a.*tanh((a.^2-muu)./(2*t)).*log((2*a.^2+2*a.*q+...
        q.^2-2*muu-1i*2*pi*N*t)./(2*a.^2-2*a.*q+q.^2-2*muu-1i*2*pi*N*t))./q-2,0,10000,'AbsTol',1e-6,'RelTol',1e-3,'ArrayValued',true));
    
      R1=@(q,k) integral(@(N)y1(N,q,k),500,10^6,'AbsTol',1e-6,'RelTol',1e-3,'ArrayValued',true);
      R11=@(q,k) integral(@(N)y1(N,q,k),-10^6,-500,'AbsTol',1e-6,'RelTol',1e-3,'ArrayValued',true);
    
    y2=@(q,k) t*q./k.*log((-k.^2+2*k.*q-q.^2+muu+1i*(2*pi*NN(:,1).*t-(2*m(1,:)+1)*pi*t))./(-k.^2-2*k.*q-...
        q.^2+muu+1i*(2*pi*NN(:,1).*t-(2*m(1,:)+1)*pi*t)))./(tt*pi+integral(@(a)a.*tanh((a.^2-muu)./(2*t)).*log((2*a.^2+2*a.*q+...
        q.^2-2*muu-1i*2*pi*NN(:,1).*t)./(2*a.^2-2*a.*q+q.^2-2*muu-1i*2*pi*NN(:,1).*t))./q-2,0,10000,'AbsTol',1e-6,'RelTol',1e-3,'ArrayValued',true));
    
    R2=@(q,k) sum(y2(q,k));
    
    S=@(q,k) R2(q,k)+R11(q,k)+R1(q,k)-4*sqrt(2)/pi*(1/1000)/(pi^(3/2)*sqrt(t))*q.^2;
q=0.001:1:7;
k=0.001:1:7;
out=arrayfun(S,k,q,'UniformOutput',false)
end
My problem is that I expected to get a cell array 7×7 but instead of I obtained 1×7. 
out =
  1×7 cell array
  Columns 1 through 5
    [1×101 double]    [1×101 double]    [1×101 double]    [1×101 double]    [1×101 double]
  Columns 6 through 7
    [1×101 double]    [1×101 double]
Elapsed time is 3.165576 seconds.
I'd like to avoid an expoitation of 
meshgrid
due to long time calculations (on the next step I will calculate the cell array out for larger arrays of q and k ).
What I did it wrong?
I will apreciate for any suggestions.

Best Answer

You seem to be expecting implicit expansion out of arrayfun (the way bsxfun works). arrayfun doesn't do that (and bsxfun can't create cell arrays, so you can't use that either. I'm afraid that you don't have any other choice than using meshgrid or ndgrid:
[k, q] = ndgrid(0.001:7);
out = arrayfun(S, k, q, 'UniformOutput', false)
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