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

double integration problem

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);
>>

Best Answer

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
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