Double integration problem (can not use symbolic math tool box)

I have a function of two variable to double integrate but i can not use symbolic integration as i want to compile this to .exe file.

clc;

 sig=0.5;      

 L=4;            

 k=1.0472;

 k_sig=k*sig;

 kls=k*ls;

   er=3.5;

   theta=(0:10:70)';       

   g=length(theta);

   Q=zeros(g,1);

for i=1:g;

   cs=cosd(theta(i)); s=sind(theta(i)); s2=s.*s; cs2=cs.*cs;

   ks=k.*sig; kL=k.*L; ks2=ks.*ks; kL2=kL.*kL;

   %(*Integration variables*)

   r2=@(r)(r.*r); sf=@(phi)sin(phi); csf=@(phi)cos(phi); 

   rx=@(r,phi)(r.*csf(phi)); ry=@(r,phi)(r.*sf(phi));

Wmh=0; Wnh=0.0;

for n=1:4;

    for m=1:4;

      wn=@(r,phi)(n.*kL2./(n.*n + kL2.*((rx(r,phi) - s).^2...

 + ry(r,phi).^2))^1.5);     

      wm=@(r,phi)(m.*kL2./(m.*m + kL2.*((rx(r,phi) + s).^2...

 + ry(r,phi).^2))^1.5);     

      vhmn=((ks2.*cs2).^(n+m))./(factorial(m).*factorial(n));

      Wm=@(r,phi)(vhmn.*wn(r,phi).*wm(r,phi));

      Wmh=@(r,phi)(Wmh(r,phi)+Wm(r,phi));

    end

end

 Wnh=@(r,phi)(Wnh(r,phi)+Wmh(r,phi));

 VH=@(r,phi)(Wnh(r,phi).*r);

%% Double Integration

 Q(i)=quad2d(VH,0,1,0,pi/4);

end

 HV=10*log10(Q);

 table=[theta HV]

This is giving Error:

Error:

 Subscript indices must either be real positive integers or logicals.

 Error in @(r,phi)(Wnh(r,phi)+Wmh(r,phi))

 Error in @(r,phi)(Wnh(r,phi).*r)

 Error in quad2d/tensor (line 344)

        Z = FUN(X,Y);  NFE = NFE + 1;

 Error in quad2d (line 168)

[Qsub,esub] = tensor(thetaL,thetaR,phiB,phiT);

 Error in Untitled1 (line 32)

 Q(i)=quad2d(VH,0,1,0,pi/4);

>>

Answer 1

[Matt Fig]

You have a couple of errors. One is you didn't define the base recursion functions to be functions but doubles - this is where your error comes from. Second you didn't use .^ everywhere instead of ^.

clc;

   sig=0.5;      

   L=4;            

   k=1.0472;

   k_sig=k*sig;

   kls=k*ls;

     er=3.5;

     theta=(0:10:70)';       

     g=length(theta);

     Q=zeros(g,1);

for i=1:g;

     cs=cosd(theta(i)); s=sind(theta(i)); s2=s.*s; cs2=cs.*cs;

     ks=k.*sig; kL=k.*L; ks2=ks.*ks; kL2=kL.*kL;

     %(*Integration variables*)

     r2=@(r)(r.*r); sf=@(phi)sin(phi); csf=@(phi)cos(phi); 

     rx=@(r,phi)(r.*csf(phi)); ry=@(r,phi)(r.*sf(phi));

Wmh=@(x,y) 0; Wnh=@(x,y) 0*x;

for n=1:4;

      for m=1:4;

        wn=@(r,phi)(n.*kL2./(n.*n + kL2.*((rx(r,phi) - s).^2  ...
                    + ry(r,phi).^2)).^1.5);     

        wm=@(r,phi)(m.*kL2./(m.*m + kL2.*((rx(r,phi) + s).^2 ...
             + ry(r,phi).^2)).^1.5);     

        vhmn=((ks2.*cs2).^(n+m))./(factorial(m).*factorial(n));

        Wm=@(r,phi)(vhmn.*wn(r,phi).*wm(r,phi));

        Wmh=@(r,phi)(Wmh(r,phi)+Wm(r,phi));

      end

end

   Wnh=@(r,phi)(Wnh(r,phi)+Wmh(r,phi));

   VH=@(r,phi)(Wnh(r,phi).*r);

%%Double Integration

   Q(i)=quad2d(VH,0,1,0,pi/4);

end

[Dharmendra]

Thanks you so much Mr. Matt Fig for solving my problem. Now it is working.

Answer 2

[Jan]

Initially you defined:

Wnh = 0.0;

Later you replace this by:

Wnh = @(r,phi)(Wnh(r,phi)+Wmh(r,phi));

Now in the first call of "Wnh(r,phi)" the term "Wnh" is a scalar array and "r,phi" is interpreted as index. And indices must be positive integers.

Are you sure you want to define the function handle Wnh recursively?!