NIT工具箱 MATLAB

% Numerical Integration Toolbox % Version 2.0 24-Mar-1998 % % MATLAB Toolbox for 1-D, 2-D, and n-D Numerical Integration % % Written by Howard Wilson, Bryce Gardner. % Modified by MathTools Ltd. (see readme.nit for more information). % % Easy to use routines: (these routines iteratively integrate with % higher order quadratures until the integral has % converged--use these routine unless you want to % specify the order of integration quadrature that % is to be used) % % quadg.m -- High accuracy replacement for QUAD and QUAD8 (1-D) % quad2dg.m -- 2-D integration over a rectangular region % quad2dgg.m -- 2-D integration over a general region % quadndg.m -- n-D integration over a n-D hyper-rectangular region % The 1-D routines: % % README -- The original readme file by Howard Wilson % gquad.m -- Integrates a 1-D function with input Gauss % points and weights (modified by Bryce Gardner to % handle an optional parameter in the function to be % integrated and also to calculate the Gauss points % and weights on the fly) % gquad6.m -- Integrates a 1-D function with a 6-point quadrature % grule.m -- Calculates the Gauss points and weights % run.log -- File with examples % % New 1-D routines: % quadg.m -- High accuracy replacement for QUAD and QUAD8 % quadc.m -- 1-D Gauss-Chebyshev integration routine % crule.m -- Calculates the Gauss-Chebyshev points and weights % ncrule.m -- Calculates the Newton-Coates points and weights % % The 2-D routines: % quad2dg.m -- 2-D integration over a rectangular region % quad2dc.m -- 2-D integration over a rectangular region with % a 1/sqrt(1-x.^2)/sqrt(1-y.^2) sinqularity % gquad2d.m -- Integrates a 2-D function over a square region % gquad2d6.m -- Integrates a 2-D function over a square region with % a 6-point quadrature % quad2dgg.m -- 2-D integration over a general region % quad2dcg.m -- 2-D integration over a general region with % a 1/sqrt(1-x.^2)/sqrt(1-y.^2) sinqularity % gquad2dg.m -- Integrates a 2-D function over a variable region % (That is the limits on the inner integration are % defined by a function of the variable of integration % of the outer integral.) % grule2d.m -- Calculates the Gauss points and weights for gquad2d.m % grule2dg.m -- Calculates the Gauss points and weights for % gquad2dg.m % crule2d.m -- Calculates the Gauss-Chebyshev points and weights % for gquad2d.m % crule2dg.m -- Calculates the Gauss-Chebyshev points and weights % for gquad2dg.m % % The n-D routines: % quadndg.m -- n-D integration over an n-D hyper-rectangular region % gquadnd.m -- Integrates a n-D function over % an n-D hyper-rectangular % region using a Gauss quadrature % cquadnd.m -- Integrates a n-D function over % an n-D hyper-rectangular % region using a Gauss-Chebyshev quadrature % innerfun.m -- used internally to gquadnd.m and cquadnd.m % % Utility routines: % count.m -- routine to count the number of function calls % zero_cnt.m -- routine to report the number of function calls and % then to reset the counter % % Test scripts: % tests_2d.m -- 2-D examples and 1-D Gauss-Chebyshev examples % tests2d.log -- output of tests_2d.m -- Matlab 4.1 on a Sparc 10 % test_nc.m -- m-file to check the Newton-Coates quadrature % testsnc.log -- output of test_nc.m -- Matlab 4.1 on a Sparc 10 % test_qg.m -- m-file to check the quadg routine % testsqg.log -- output of test_qg.m -- Matlab 4.1 on a Sparc 10 % % Test functions: % xsquar.m -- xsquar(x)=x.^2 % xcubed.m -- xcubed(x)=x.^3 % x25.m -- x25(x)=x.^25 % fxpow.m -- fxpow(x,y)=x.^y % hx.m -- hx(x)=sum(x.^2) % gxy.m -- gxy(x,y)=x.^2+y.^2 % gxy1.m -- gxy1(x,y)=ones(size(x)) % gxy2.m -- gxy2(x,y)=sqrt(x.^2+y.^2) % glimh.m -- glimh(y)=3 % glimh2.m -- glimh(y)=y % gliml.m -- gliml(y)=0 % lcrcl.m -- lcrcl(y)=-sqrt(4-y.^2) % lcrcu.m -- lcrcu(y)=sqrt(4-y.^2) %