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matlabnumericnumerical-integration

In matlab integrate a function that calls another function

I am numerically evaluating the double integral using integral2 matlab command. My code is as follows:

l1=0; m1=0; 
funn =  @(theta,phi)(Y_hsph_new(l1,m1,theta,phi));
q = integral2(funn,0,pi/2,0,2*pi);

where 'Y_hsph_new' is my own designed MatLab function written as :

function [ YYY ] = Y_hsph_new(l1,m1,theta,phi)
% OUTPUT: (I x (N+1)^2) matrix
I = length(theta);
Y=zeros(I,(l1+1)^2);
for i=1:I
    k=1;
    for n=0:l1
        P=legendre(n,2*cos(theta(i))-1); % (2*x-1) for transformation
        for m=-n:n   % degree
            if m>0
               Y(i,k)=(sqrt(((2*n+1)*factorial(n-abs(m)))/((2*pi)*factorial(n+abs(m)))))*P(abs(m)+1)*sqrt(2)*cos(m*phi(i));
            elseif m == 0
               Y(i,k)=(sqrt(((2*n+1)*factorial(n))/((2*pi)*factorial(n))))*P(1);
            else
               Y(i,k)=(sqrt(((2*n+1)*factorial(n-abs(m)))/((2*pi)*factorial(n+abs(m)))))*P(abs(m)+1)*sqrt(2)*sin(abs(m)*phi(i));
            end
            k=k+1;
         end
     end
 end
 YYY = Y(:,m1+l1+1+(l1)^2);

I have used Y_hsph_new function in my other usual codes and it is working fine. I believe perhaps the function code is fine but something related to its configuration that is going to be used in integration is causing a problem. The error which I am getting while running it is:-

Error using integral2Calc>integral2t/tensor (line 241)
Integrand output size does not match the input size.

Error in integral2Calc>integral2t (line 55)
[Qsub,esub] = tensor(thetaL,thetaR,phiB,phiT);

Error in integral2Calc (line 9)
[q,errbnd] = integral2t(fun,xmin,xmax,ymin,ymax,optionstruct);

Error in integral2 (line 106)
Q = integral2Calc(fun,xmin,xmax,yminfun,ymaxfun,opstruct);

I am seriously pulling my hairs after a lot of trying. It would be really helpful if anyone can help me in this regard.

Solution

  • The way funn is defined is inconsistent with integral2. For example, if I enter an array of theta and phi values to funn I expect the same array size to be the output, but that's not what funn produces. for example:

    [th ph]=meshgrid(linspace(0,pi/2),linspace(0,2*pi))

>> size(th)

ans =

100   100

    whereas:

    >> size(funn(th,ph))

ans =

100     1

    So funn doesn't work properly to be used in integral2. I think the first place to start in your function is I = length(theta); line, as the length of theta is not appropriate if theta is a 2d array.