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PURPOSE ^

Numerical Integration Toolbox

SYNOPSIS ^

This is a script file.

DESCRIPTION ^

 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)

CROSS-REFERENCE INFORMATION ^

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