diff extra/integration/Contents.m @ 0:6b33357c7561 octave-forge

Initial revision
author pkienzle
date Wed, 10 Oct 2001 19:54:49 +0000
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+% Numerical Integration Toolbox 
+%
+% MATLAB Toolbox for 1-D, 2-D, and n-D Numerical Integration
+%
+% Edited Version for OCTAVE
+% 
+% 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)
+%