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<html>
<head>
<title>
INTLIB - 1-dimensional quadrature
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
INTLIB <br> 1-dimensional quadrature
</h1>
<hr>
<p>
<b>INTLIB</b>
is a FORTRAN90 library which
estimates integrals over 1D regions.
</p>
<p>
The integrand may be available as a function F(X), or as data
at equally spaced or unequally spaced points.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/cubpack/cubpack.html">
CUBPACK</a>,
a FORTRAN90 library which
estimates the integral of a function over a collection of N-dimensional
hyperrectangles and simplices.
</p>
<p>
<a href = "../../f_src/nintlib/nintlib.html">
NINTLIB</a>,
a FORTRAN90 library which
estimates integrals over multidimensional regions.
</p>
<p>
<a href = "../../f_src/product_rule/product_rule.html">
PRODUCT_RULE</a>,
a FORTRAN90 program which
constructs a product quadrature rule from 1D factor rules.
</p>
<p>
<a href = "../../datasets/quadrature_rules/quadrature_rules.html">
QUADRATURE_RULES</a>,
a dataset directory which
contains files that define quadrature rules over various 1D intervals
or multidimensional hypercubes.
</p>
<p>
<a href = "../../f_src/quadpack/quadpack.html">
QUADPACK</a>,
a FORTRAN90 library which
numerically estimates integrals.
</p>
<p>
<a href = "../../f_src/quadrule/quadrule.html">
QUADRULE</a>,
a FORTRAN90 library which
defines quadrature rules for 1D domains.
</p>
<p>
<a href = "../../f77_src/simpack/simpack.html">
SIMPACK</a>,
a FORTRAN77 library which
approximates the integral of a function over a multidimensional simplex.
</p>
<p>
<a href = "../../f_src/stroud/stroud.html">
STROUD</a>,
a FORTRAN90 library which
defines quadrature rules for a variety of multidimensional reqions.
</p>
<p>
<a href = "../../f_src/tanh_quad/tanh_quad.html">
TANH_QUAD</a>,
a FORTRAN90 library which
sets up the tanh quadrature rule;
</p>
<p>
<a href = "../../f_src/test_int/test_int.html">
TEST_INT</a>,
a FORTRAN90 library which
defines test integrands for 1D quadrature rules.
</p>
<p>
<a href = "../../f_src/test_int_2d/test_int_2d.html">
TEST_INT_2D</a>,
a FORTRAN90 library which
defines test integrands for 2D quadrature rules.
</p>
<p>
<a href = "../../f77_src/toms351/toms351.html">
TOMS351</a>,
a FORTRAN77 library which
estimates an integral using Romberg integration.
</p>
<p>
<a href = "../../f77_src/toms379/toms379.html">
TOMS379</a>,
a FORTRAN77 library which
estimates an integral.
</p>
<p>
<a href = "../../f77_src/toms418/toms418.html">
TOMS418</a>,
a FORTRAN77 library which
estimates the integral of a function with a sine or cosine factor.
</p>
<p>
<a href = "../../f77_src/toms424/toms424.html">
TOMS424</a>,
a FORTRAN77 library which
estimates the integral of a function using Clenshaw-Curtis quadrature.
</p>
<p>
<a href = "../../f77_src/toms468/toms468.html">
TOMS468</a>,
a FORTRAN77 library which
applies "automatic" integration to a function.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Milton Abramowitz, Irene Stegun,<br>
Handbook of Mathematical Functions,<br>
National Bureau of Standards, 1964,<br>
ISBN: 0-486-61272-4,<br>
LC: QA47.A34.
</li>
<li>
Roland Bulirsch, Josef Stoer,<br>
Fehlerabschaetzungen und Extrapolation mit rationaled Funktionen
bei Verfahren vom Richardson-Typus,<br>
(Error estimates and extrapolation with rational functions
in processes of Richardson type),<br>
Numerische Mathematik,<br>
Volume 6, Number 1, December 1964, pages 413-427.
</li>
<li>
Stephen Chase, Lloyd Fosdick,<br>
An Algorithm for Filon Quadrature,<br>
Communications of the Association for Computing Machinery,<br>
Volume 12, Number 8, August 1969, pages 453-457.
</li>
<li>
Stephen Chase, Lloyd Fosdick,<br>
Algorithm 353:
Filon Quadrature,<br>
Communications of the Association for Computing Machinery,<br>
Volume 12, Number 8, August 1969, pages 457-458.
</li>
<li>
William Cody,<br>
An Overview of Software Development for Special Functions,
in Numerical Analysis Dundee, 1975, <br>
edited by GA Watson,<br>
Lecture Notes in Mathematics, 506, <br>
Springer, 1976.
</li>
<li>
Philip Davis, Philip Rabinowitz,<br>
Methods of Numerical Integration,<br>
Second Edition,<br>
Dover, 2007,<br>
ISBN: 0486453391,<br>
LC: QA299.3.D28.
</li>
<li>
Carl deBoor, John Rice,<br>
CADRE: An algorithm for numerical quadrature,<br>
in Mathematical Software,<br>
edited by John Rice,<br>
Academic Press, 1971,<br>
ISBN: 012587250X,<br>
LC: QA1.M766.
</li>
<li>
Augustin Dubrulle,<br>
A short note on the implicit QL algorithm for symmetric
tridiagonal matrices,<br>
Numerische Mathematik,<br>
Volume 15, Number 5, September 1970, page 450.
</li>
<li>
Philip Gill, GF Miller,<br>
An algorithm for the integration of unequally spaced data,<br>
The Computer Journal, <br>
Number 15, Number 1, 1972, pages 80-83.
</li>
<li>
Gene Golub,<br>
Some Modified Matrix Eigenvalue Problems,<br>
SIAM Review,<br>
Volume 15, Number 2, Part 1, April 1973, pages 318-334.
</li>
<li>
Gene Golub, John Welsch,<br>
Calculation of Gaussian Quadrature Rules,<br>
Mathematics of Computation,<br>
Volume 23, Number 106, April 1969, pages 221-230.
</li>
<li>
John Hart, Ward Cheney, Charles Lawson, Hans Maehly,
Charles Mesztenyi, John Rice, Henry Thatcher,
Christoph Witzgall,<br>
Computer Approximations,<br>
Wiley, 1968.
</li>
<li>
Tore Havie,<br>
On a Modification of the Clenshaw Curtis Quadrature Rule,<br>
BIT,<br>
Volume 9, Number 4, December 1969, pages 338-350.
</li>
<li>
Paul Hennion,<br>
Algorithm 77:
Interpolation, Differentiation and Integration,<br>
Communications of the ACM,<br>
Volume 5, 1962, page 96.
</li>
<li>
Robert Kubik,<br>
Algorithm 257:
Havie Integrator,<br>
Communications of the ACM,<br>
Volume 8, Number 6, June 1965, page 381.
</li>
<li>
James Lyness,<br>
Algorithm 379:
SQUANK (Simpson Quadrature Used Adaptively
- Noise Killed),<br>
Communications of the ACM,<br>
Volume 13, Number 4, April 1970, pages 260-263.
</li>
<li>
Roger Martin, James Wilkinson,<br>
The Implicit QL Algorithm,<br>
Numerische Mathematik,<br>
Volume 12, Number 5, December 1968, pages 377-383.
</li>
<li>
William McKeeman, Lawrence Tesler,<br>
Algorithm 182:
Nonrecursive adaptive integration,<br>
Communications of the ACM,<br>
Volume 6, 1963, page 315.
</li>
<li>
Arthur Stroud, Don Secrest,<br>
Gaussian Quadrature Formulas,<br>
Prentice Hall, 1966,<br>
LC: QA299.4G3S7.
</li>
<li>
James Wilkinson, Christian Reinsch,<br>
Handbook for Automatic Computation,<br>
Volume II, Linear Algebra, Part 2,<br>
Springer, 1971,<br>
ISBN: 0387054146.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "intlib.f90">intlib.f90</a>, the source code.
</li>
<li>
<a href = "intlib.sh">intlib.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "intlib_prb.f90">intlib_prb.f90</a>, a sample problem.
</li>
<li>
<a href = "intlib_prb.sh">intlib_prb.sh</a>,
commands to compile, link and run the sample problem.
</li>
<li>
<a href = "intlib_prb_output.txt">intlib_prb_output.txt</a>, the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>AVINT</b> estimates the integral of unevenly spaced data.
</li>
<li>
<b>CADRE</b> estimates the integral of F(X) from A to B.
</li>
<li>
<b>CHINSP</b> estimates an integral using a modified Clenshaw-Curtis scheme.
</li>
<li>
<b>CLASS</b> sets recurrence coeeficients for various orthogonal polynomials.
</li>
<li>
<b>CSPINT</b> estimates the integral of a tabulated function.
</li>
<li>
<b>CUBINT</b> approximates an integral using cubic interpolation of data.
</li>
<li>
<b>FILON_COS</b> uses Filon's method on integrals with a cosine factor.
</li>
<li>
<b>FILON_SIN</b> uses Filon's method on integrals with a sine factor.
</li>
<li>
<b>GAMMA</b> calculates the Gamma function for a real argument X.
</li>
<li>
<b>GAUS8</b> estimates the integral of a function.
</li>
<li>
<b>GAUSQ2</b> finds the eigenvalues of a symmetric tridiagonal matrix.
</li>
<li>
<b>GAUSSQ</b> computes a Gauss quadrature rule.
</li>
<li>
<b>HIORDQ</b> approximates the integral of a function using equally spaced data.
</li>
<li>
<b>IRATEX</b> estimates the integral of a function.
</li>
<li>
<b>MONTE_CARLO</b> estimates the integral of a function by Monte Carlo.
</li>
<li>
<b>PLINT</b> approximates the integral of unequally spaced data.
</li>
<li>
<b>QNC79</b> approximates the integral of F(X) using Newton-Cotes quadrature.
</li>
<li>
<b>QUAD</b> approximates the integral of F(X) by Romberg integration.
</li>
<li>
<b>R8VEC_EVEN</b> returns N values, evenly spaced between ALO and AHI.
</li>
<li>
<b>RMINSP</b> approximates the integral of a function using Romberg integration.
</li>
<li>
<b>SIMP</b> approximates the integral of a function by an adaptive Simpson's rule.
</li>
<li>
<b>SIMPNE</b> approximates the integral of unevenly spaced data.
</li>
<li>
<b>SIMPSN</b> approximates the integral of evenly spaced data.
</li>
<li>
<b>SOLVE</b> solves a special linear system.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>WEDINT</b> uses Weddle's rule to integrate data at equally spaced points.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 02 December 2005.
</i>
<!-- John Burkardt -->
</body>
</html>