% Numerical Integration Toolbox %% MATLAB Toolbox for 1-D, 2-D, and n-D Numerical Integration% % The original 1-D routines were obtained from NETLIB and were % written by%          Howard Wilson%          Department of Engineering Mechanics%          University of Alabama%          Box 870278%          Tuscaloosa, Alabama 35487-0278%          Phone 205 348-1617%          Email address: HWILSON @ UA1VM.UA.EDU% % The rest of the routines were written by%          Bryce Gardner%          Ray W. Herrick Laboratories%          Purdue University%          West Lafayette, IN 47906%          Phone: 317-494-0231%          Fax:  317-494-0787%          Email:  gardner@ecn.purdue.edu%% 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%	   quad2dggen.m	-- 2-D integration over a general region%	   quadndg.m	-- n-D integration over a n-D hyper-rectangular region%          README.nit	-- introductory readme file%% 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%	   quad2dggen.m	-- 2-D integration over a general region%	   quad2dcgen.m	-- 2-D integration over a general region with%			   a 1/sqrt(1-x.^2)/sqrt(1-y.^2) sinqularity%          gquad2dgen.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%          grule2dgen.m -- Calculates the Gauss points and weights for %			   gquad2dgen.m%          crule2d.m	-- Calculates the Gauss-Chebyshev points and weights %			   for gquad2d.m%          crule2dgen.m -- Calculates the Gauss-Chebyshev points and weights %			   for gquad2dgen.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_count.m	-- routine to report the number of function calls and%			   then to reset the counter%% Test scripts:%          run2dtests.m	-- 2-D examples and 1-D Gauss-Chebyshev examples%	   tests2d.log  -- output of run2dtests.m -- Matlab 4.1 on a Sparc 10%	   test_ncrule.m-- m-file to check the Newton-Coates quadrature%	   testsnc.log  -- output of test_ncrule.m -- Matlab 4.1 on a Sparc 10%	   test_quadg.m -- m-file to check the quadg routine%	   testsqg.log  -- output of test_quadg.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)%