function vol = gquad2d(fun,xlow,xhigh,ylow,yhigh,b1,b2,w1) % %usage: vol = gquad2d(fun,xlow,xhigh,ylow,yhigh,bpx,bpy,wfxy) % or % vol = gquad2d(fun,xlow,xhigh,ylow,yhigh,nquadx,nquady) % This function evaluates the integral of an externally % defined function fun(x,y) between limits xlow and xhigh % and ylow and yhigh. The numerical integration is performed % using a Gauss integration rule. The integration % is done with an nquadx by nquady Gauss formula which involves base % point matrices bpx and bpy and weight factor matrix wfxy. The normalized % interval of integration for the bpx, bpy and wfxy constants is -1 to +1 % (in x) and -1 to +1 (in y). The algorithm is described by the % summation relation % x=b j=nx k=ny % integral( f(x)*dx ) = J*sum sum( wfxy(j,k)*fun( x(j), y(k) ) ) % x=a j=1 k=1 % where wfxy are weight factors, % nx = nquadx = number of Gauss points in the x-direction, % ny = nquady = number of Gauss points in the y-direction, % x = (xhigh-xlow)/2 * bpx + (xhigh+xlow)/2 = mapping function in x, % y = (yhigh-ylow)/2 * bpy + (yhigh+ylow)/2 = mapping function in y, % and J = (xhigh-xlow)*(yhigh-ylow)/4 = Jacobian of the mapping. % The base points and weight factors must first be generated % by a call to grule of the form [bpx,bpy,wfxy] = grule2d(nquadx,nquady) % % The first form of gquad2d is faster when used several times, because % the points and weights are only calculated once. % % The second form of gquad2d is usefull if it is only called once (or a % few times). % by Bryce Gardner, Purdue University, Spring 1993 % extending Howard Wilson's (U. of Alabama, Spring 1990) % set of 1-D Gauss quadrature routines. if ( nargin == 7 ) nquadx=b1; nquady=b2; [bpx,bpy,wfxy]=grule2d(nquadx,nquady); elseif ( nargin == 8 ) bpx = b1; bpy = b2; wfxy = w1; else disp('Wrong Number of Input Arguments') return endif %Map to x qx=(xhigh-xlow)/2; px=(xhigh+xlow)/2; x=qx*bpx+px; %Map to y qy=(yhigh-ylow)/2; py=(yhigh+ylow)/2; y=qy*bpy+py; fv = feval(fun,x,y); vol = sum(sum(wfxy.*fv))*qx*qy; endfunction

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