function int = quadc(fun,xlow,xhigh,tol,trace,p1,p2,p3,p4,p5,p6,p7,p8,p9) %usage: int = quadc('Fun',xlow,xhigh) %or % int = quadc('Fun',xlow,xhigh,tol) %or % int = quadc('Fun',xlow,xhigh,tol,trace,p1,p2,....) % %This function works just like QUAD or QUAD8 but uses a Gaussian-Chebyshev %quadrature integration scheme. % % The Gauss-Chebyshev Quadrature integrates an integral of the form % xhigh % Int ((1/sqrt(1-x^2)) fun(x)) dx % -xhigh %This routine ignores xlow global cb2 global cw2 if exist('tol')~=1, tol=1e-3; elseif tol==[], tol=1e-3; end if exist('trace')~=1, trace=0; elseif trace==[], trace=0; else, trace=1; end xlow=-xhigh; %setup string to call the function exec_string=['y=',fun,'(x']; num_parameters=nargin-5; for i=1:num_parameters, exec_string=[exec_string,',p',int2str(i)]; end exec_string=[exec_string,');'] %setup mapping parameters jacob=(xhigh-xlow)/2; %generate the first two sets of integration points and weights if exist('cb2')~=1, [cb2,cw2]=crule(2); end x=(cb2+1)*jacob+xlow; eval(exec_string); int_old=sum(cw2.*y)*jacob; if trace==1, x_trace=x(:); y_trace=y(:); end converge='n'; for i=1:7, gnum=int2str(2^(i+1)); if exist(['cb',gnum])~=1, eval(['[cb',gnum,',cw',gnum,']=crule(',gnum,');']); eval(['global cb',gnum,',cw',gnum,';']); end eval(['x=(cb',gnum,'+1)*jacob+xlow;']); x=x(:); eval(exec_string); eval(['int=sum(cw',gnum,'.*y)*jacob;']); if trace==1, x_trace=[x_trace;x(:)]; y_trace=[y_trace;y(:)]; end if abs(int_old-int) < abs(tol*int), converge='y'; break; end int_old=int; end if converge=='n', disp('Integral did not converge--singularity likely') end if trace==1, plot(x_trace,y_trace,'+') end