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view extra/integration/quad2dggen.m @ 0:6b33357c7561 octave-forge
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author | pkienzle |
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date | Wed, 10 Oct 2001 19:54:49 +0000 |
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function int = quad2dggen(fun,xlow,xhigh,ylow,yhigh,tol) % %usage: int = quad2dggen('Fun','funxlow','funxhigh',ylow,yhigh) %or % int = quad2dggen('Fun','funxlow','funxhigh',ylow,yhigh,tol) % %This function is similar to QUAD or QUAD8 for 2-dimensional integration %over a general 2-dimensional region, but it uses a Gaussian quadrature %integration scheme. %The integral is like: % yhigh funxhigh(y) % int = Int Int Fun(x,y) dx dy % ylow funxlow(y) % % int -- value of the integral % Fun -- Fun(x,y) (function to be integrated) % funxlow -- funxlow(y) % funxhigh-- funxhigh(y) % 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; endif oldint=gquad2dgen(fun,xlow,xhigh,ylow,yhigh,2,2); converge=0; for i=1:7 lim = 2^(i+1); int=gquad2dgen(fun,xlow,xhigh,ylow,yhigh,lim,lim); diff = oldint - int; limit = abs(tol*int); if ( abs(diff) < limit ) converge=1; break; endif oldint=int; endfor if ( converge==0 ) disp('Integral did not converge--singularity likely') endif endfunction