title: Double Numerical Integration Error
body: <p>In the script below, in the for loop for calculating the double integrations, I keep receiving an error, and I'm unsure why:</p>
  
  <pre><code>Error using  * 
  Inner matrix dimensions must agree.
  
  Error in @(t,p)-sin(t)*(G(:,1)*cos(p)+H(:,1)*sin(p))
  
  
  Error in @(t,p)B{k}(t,p).*A{k}(t,p).*(V(t)-Veq).*sin(t)
  
  
  Error in integral2Calc&gt;integral2t/tensor (line 228)
          Z = FUN(X,Y);  NFE = NFE + 1;
  
  Error in integral2Calc&gt;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);
  </code></pre>
  
  <p>This script was formed from another which only had to deal with one variable t, so I'm assuming that I've done something wrong in adapting it to two variable functions.</p>
  
  <p>Thanks!</p>
  
  <pre><code>%%Calculation of dH/dt for mode m=1 for the entire sphere, NH and SH
  clear all
  %%Radius of photosphere
  r = 6.957*(10^5); %In km
  R = 1/r; %This will come in handy later
  
  %%Call in spherical harmonic coefficients, change the 535 figure as more
  %%data is added to the spreadsheets
  G(:,1) = xlsread('G Coefficients.xls', 'D3:D535');
  G(:,2) = xlsread('G Coefficients.xls', 'F3:F535');
  G(:,3) = xlsread('G Coefficients.xls', 'I3:I535');
  G(:,4) = xlsread('G Coefficients.xls', 'M3:M535');
  G(:,5) = xlsread('G Coefficients.xls', 'R3:R535');
  G(:,6) = xlsread('G Coefficients.xls', 'X3:X535');
  G(:,7) = xlsread('G Coefficients.xls', 'AE3:AE535');
  G(:,8) = xlsread('G Coefficients.xls', 'AM3:AM535');
  G(:,9) = xlsread('G Coefficients.xls', 'AV3:AV535');
  
  H(:,1) = xlsread('H Coefficients.xls', 'D3:D535');
  H(:,2) = xlsread('H Coefficients.xls', 'F3:F535');
  H(:,3) = xlsread('H Coefficients.xls', 'I3:I535');
  H(:,4) = xlsread('H Coefficients.xls', 'M3:M535');
  H(:,5) = xlsread('H Coefficients.xls', 'R3:R535');
  H(:,6) = xlsread('H Coefficients.xls', 'X3:X535');
  H(:,7) = xlsread('H Coefficients.xls', 'AE3:AE535');
  H(:,8) = xlsread('H Coefficients.xls', 'AM3:AM535');
  H(:,9) = xlsread('H Coefficients.xls', 'AV3:AV535');
  
  %%Set function v which always remains the same
  nhztoradperday = 2*pi*86400*(10^(-9));
  a = 460.7*nhztoradperday;
  b = -62.69*nhztoradperday;
  c = -67.13*nhztoradperday;
  
  B{1} = @(t,p) -sin(t)*(G(:,1)*cos(p) + H(:,1)*sin(p));
  
  B{2} = @(t,p) -3*sin(t)*cos(t)*(G(:,2)*cos(p) + H(:,2)*sin(p));
  
  B{3} = @(t,p) -1.5*(5*(cos(t)^2)-1)*sin(t)*(G(:,3)*cos(p) + H(:,3)*sin(p));
  
  B{4} = @(t,p) -2.5*(7*(cos(t)^3)-3*cos(t))*sin(t)*(G(:,4)*cos(p) + H(:,4)*sin(p));
  
  B{5} = @(t,p) -1.875*sin(t)*(21*(cos(t)^4)-14*(cos(t)^2)+1)*(G(:,5)*cos(p) + H(:,5)*sin(p));
  
  B{6} = @(t,p) -2.625*cos(t)*sin(t)*(33*(cos(t)^4)-30*(cos(t)^2)+5)*(G(:,6)*cos(p) + H(:,6)*sin(p));
  
  B{7} = @(t,p) -0.4375*sin(t)*(429*(cos(t)^6)-495*(cos(t)^4)+135*(cos(t)^2)-5)*(G(:,7)*cos(p) + H(:,7)*sin(p));
  
  B{8} = @(t,p) -0.5625*cos(t)*sin(t)*(715*(cos(t)^6)-1001*(cos(t)^4)+385*(cos(t)^2)-35)*(G(:,8)*cos(p) + H(:,8)*sin(p));
  
  
  
  A{1} = @(t,p) 0.5*R*cos(t)*(G(:,1)*cos(p) + H(:,1)*sin(p));
  
  A{2} = @(t,p) 0.5*R*cos(2*t)*(G(:,2)*cos(p) + H(:,2)*sin(p));
  
  A{3} = @(t,p) 0.125*R*cos(t)*(15*(cos(t)^2)-11)*(G(:,3)*cos(p) + H(:,3)*sin(p));
  
  A{4} = @(t,p) 0.125*R*(-3*cos(2*t)+7*(cos(t)^4-3*sin(t)^2*cos(t)^2))*(G(:,4)*cos(p) + H(:,4)*sin(p));
  
  A{5} = @(t,p) 0.0625*R*(21*(cos(t)^5)-(cos(t)^3)*(14+84*(sin(t)^2))+cos(t)*(1+28*(sin(t)^2)))*(G(:,5)*cos(p) + H(:,5)*sin(p));
  
  A{6} = @(t,p) 0.0625*R*(33*(cos(t)^6)-(cos(t)^4)*(165*(sin(t)^2)+30)+90*(sin(t)^2)*(cos(t)^2)+5*cos(2*t))*(G(:,6)*cos(p) + H(:,6)*sin(p));
  
  A{7} = @(t,p) 1/128*R*(429*(cos(t)^7)-(cos(t)^5)*(495+2574*(sin(t)^2))+(cos(t)^3)*(135+1980*(sin(t)^2))-cos(t)*(5+270*(sin(t)^2)))*(G(:,7)*cos(p) + H(:,7)*sin(p));
  
  A{8} = @(t,p) 1/128*R*(715*(cos(t)^8)-1001*(cos(t)^6)+385*(cos(t)^4)-35*(cos(t)^2)+(sin(t)^2)*(-5005*(cos(t)^6)+5005*(cos(t)^4)-1155*(cos(t)^2)+35))*(G(:,8)*cos(p) + H(:,8)*sin(p));
  
  V = @(t) a + (b*cos(t)^2) + (c*cos(t)^4);
  Veq = V(0);
  
  intNH = zeros(length(G),9);
  intSH = zeros(length(G),9);
  intSun = zeros(length(G),9);
  for k=1:8
     fun{k} = @(t,p) B{k}(t,p).*A{k}(t,p).*(V(t)-Veq).*sin(t);
     intNH(:,k) = integral2(fun{k},0,pi/2,0,2*pi);
     intSH(:,k) = integral2(fun{k},pi/2,pi,0,2*pi);
     intSun(:,k) = integral2(fun{k},0,pi,0,2*pi);
  end
  
  for i=1:length(G)
     NH(i) = sum(intNH(i,:));
     SH(i) = sum(intSH(i,:));
     Sun(i) = sum(intSun(i,:));
  end
  </code></pre>