function int = quad2dg(fun,xlow,xhigh,ylow,yhigh,tol)%usage:  int = quad2dg('Fun',xlow,xhigh,ylow,yhigh)%or%        int = quad2dg('Fun',xlow,xhigh,ylow,yhigh,tol)%%This function is similar to QUAD or QUAD8 for 2-dimensional integration,%but it uses a Gaussian quadrature integration scheme.  % 	int     -- value of the integral%       Fun     -- Fun(x,y) (function to be integrated)%       xlow    -- lower x limit of integration%       xhigh   -- upper x limit of integration%       ylow    -- lower y limit of integration%       yhigh   -- upper y limit of integration%       tol     -- tolerance parameter (optional)%Note that if there are discontinuities the region of integration %should be broken up into separate pieces.  And if there are singularities,%a more appropriate integration quadrature should be used %(such as the Gauss-Chebyshev for a specific type of singularity).%This routine could be optimized.if exist('tol')~=1,  tol=1e-3;elseif tol==[],  tol=1e-3;endn=length(xlow);nquad=2*ones(n,1);[bpx,bpy,wfxy] = grule2d(2,2);int_old=gquad2d(fun,xlow,xhigh,ylow,yhigh,bpx,bpy,wfxy);converge='n';for i=1:7,  [bpx,bpy,wfxy] = grule2d(2^(i+1),2^(i+1));  int=gquad2d(fun,xlow,xhigh,ylow,yhigh,bpx,bpy,wfxy);  if abs(int_old-int) < abs(tol*int),    converge='y';    break;  end  int_old=int;endif converge=='n',  disp('Integral did not converge--singularity likely')end