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)