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view extra/integration/test/run2dtests.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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format long % % x^2+y^2 integrated from -1 to 1 in x and -1 to 1 in y = 8/3 % [bx,by,w]=grule2d(2,2); v=gquad2d('gxy',-1,1,-1,1,bx,by,w) % or v=quad2dg('gxy',-1,1,-1,1) % or v=gquad2d('gxy',-1,1,-1,1,2,2) % or n= gquadnd('hx',[-1;-1],[1;1],[2;2]) % or n=quadndg('hx',[-1;-1],[1;1]) correct_ans=8/3 % % x^2+y^2 integrated from 0 to 2 in x and 0 to 2 in y = 32/3 % [bx,by,w]=grule2d(2,2); vol3=gquad2d('gxy',0,2,0,2,bx,by,w) % or v=quad2dg('gxy',0,2,0,2) % or v=gquad2d('gxy',0,2,0,2,2,2) % or n = gquadnd('hx',[0;0],[2;2],[2;2]) % or n = quadndg('hx',[0;0],[2;2]) correct_ans=32/3 % % x^2+y^2 integrated from 0 to 3 in x and 0 to 3 in y = 54 % [bx,by,w]=grule2d(2,2); v=gquad2d('gxy',0,3,0,3,bx,by,w) % or v=gquad2d('gxy',0,3,0,3,2,2) % or n = gquadnd('hx',[0;0],[3;3],[2;2]) correct_ans=54 % % x^2+y^2 integrated from 0 to 3 in x and 0 to 3 in y = 54 % with the general area of intergration (functional limits in x) % [bx2,wx,by2,wy]=grule2dgen(2,2); v=gquad2dgen('gxy','gliml','glimh',0,3,bx2,wx,by2,wy) % or v=gquad2dgen('gxy','gliml','glimh',0,3,2,2) % or v=quad2dggen('gxy','gliml','glimh',0,3) correct_ans=54 % % x^2+y^2 integrated from 0 to y in x and 0 to 2 in y = 16/3 % v=gquad2dgen('gxy','gliml','glimh2',0,2,bx2,wx,by2,wy) % or v=gquad2dgen('gxy','gliml','glimh2',0,2,2,2) correct_ans=16/3 % % 1 integrated from -sqrt(4-y^2) to sqrt(4-y^2) in x % and -2 to 2 in y = 4*pi -- area of circle with radius 2 or (pi r^2) % v=gquad2dgen('gxy1','lcrcl','lcrcu',-2,2,bx2,wx,by2,wy) % or v=gquad2dgen('gxy1','lcrcl','lcrcu',-2,2,2,2) correct_ans=4*pi % --- same problem better quadratue (more points) % 1 integrated from -sqrt(4-y^2) to sqrt(4-y^2) in x % and -2 to 2 in y = 4*pi -- area of circle with radius 2 or (pi r^2) % [bx3,wx3,by3,wy3]=grule2dgen(5,5); v=gquad2dgen('gxy1','lcrcl','lcrcu',-2,2,bx2,wx,by2,wy) % or v=gquad2dgen('gxy1','lcrcl','lcrcu',-2,2,5,5) correct_ans=4*pi % % sqrt(x^2+y^2) integrated from -sqrt(4-y^2) to sqrt(4-y^2) in x % and -2 to 2 in y = 16*pi/3 % % Need higher order quadrature [bx3,wx3,by3,wy3]=grule2dgen(10,10); v=gquad2dgen('gxy2','lcrcl','lcrcu',-2,2,bx3,wx3,by3,wy3) % or v=gquad2dgen('gxy2','lcrcl','lcrcu',-2,2,10,10) correct_ans=16*pi/3 % % 1/sqrt(1-x^2) integrated from -1 to 1 in x = pi % % Use Gauss-Chebyshev quadrature [bpc,wfc]=crule(2); a=gquad('gxy1',-1,1,1,bpc,wfc) %or a=quadc('gxy1',-1,1) correct_ans=pi % % x^2/sqrt(1-x^2) integrated from -1 to 1 in x = pi/2 % % Use Gauss-Chebyshev quadrature a=gquad('xsquar',-1,1,1,bpc,wfc) a=quadc('xsquar',-1,1) correct_ans=pi/2