LAGUERRE_RULE
GaussLaguerre Quadrature Rules
LAGUERRE_RULE
is a FORTRAN77 program which
generates a specific GaussLaguerre quadrature rule, based on user input.
The rule is written to three files for easy use as input
to other programs.
The GaussLaguerre quadrature rule is used as follows:
Integral ( a <= x < +oo ) exp (  b * ( x  a ) ) f(x) dx
is to be approximated by
Sum ( 1 <= i <= order ) w(i) * f(x(i))
Usage:
laguerre_rule order a b filename
where

order is the number of points in the quadrature rule.

a is the left endpoint. Typically this is 0.

b is the scale factor. Typically this is 1.

filename specifies the output filenames:
filename_w.txt,
filename_x.txt, and filename_r.txt,
containing the weights, abscissas, and interval limits.
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the GNU LGPL license.
Languages:
LAGUERRE_RULE is available in
a C version and
a C++ version and
a FORTRAN77 version and
a FORTRAN90 version and
a MATLAB version.
Related Data and Programs:
CCN_RULE,
a FORTRAN77 program which
defines a nested Clenshaw Curtis quadrature rule.
CLENSHAW_CURTIS_RULE,
a FORTRAN77 program which
defines a Clenshaw Curtis quadrature rule.
HERMITE_RULE,
a FORTRAN77 program which
can compute and print a GaussHermite quadrature rule.
LAGUERRE_EXACTNESS,
a FORTRAN77 program which
checks the polynomial exactness
of a GaussLaguerre quadrature rule.
LAGUERRE_POLYNOMIAL,
a FORTRAN77 library which
evaluates the Laguerre polynomial, the generalized Laguerre polynomials,
and the Laguerre function.
LAGUERRE_TEST_INT,
a FORTRAN77 library which
defines test integrands for integration over [A,+oo).
LEGENDRE_RULE,
a FORTRAN77 program which
computes a GaussLegendre quadrature rule.
LEGENDRE_RULE_FAST,
a FORTRAN77 program which
uses a fast (order N) algorithm to compute a GaussLegendre quadrature
rule of given order.
QUADRULE,
a FORTRAN77 library which
contains 1dimensional quadrature
rules.
Reference:

Milton Abramowitz, Irene Stegun,
Handbook of Mathematical Functions,
National Bureau of Standards, 1964,
ISBN: 0486612724,
LC: QA47.A34.

Philip Davis, Philip Rabinowitz,
Methods of Numerical Integration,
Second Edition,
Dover, 2007,
ISBN: 0486453391,
LC: QA299.3.D28.

Sylvan Elhay, Jaroslav Kautsky,
Algorithm 655:
IQPACK,
FORTRAN Subroutines for the Weights of Interpolatory Quadrature,
ACM Transactions on Mathematical Software,
Volume 13, Number 4, December 1987, pages 399415.

Jaroslav Kautsky, Sylvan Elhay,
Calculation of the Weights of Interpolatory Quadratures,
Numerische Mathematik,
Volume 40, 1982, pages 407422.

Roger Martin, James Wilkinson,
The Implicit QL Algorithm,
Numerische Mathematik,
Volume 12, Number 5, December 1968, pages 377383.

Philip Rabinowitz, George Weiss,
Tables of Abscissas and Weights for Numerical Evaluation of Integrals
of the form $\int_0^{\infty} exp(x) x^n f(x) dx$,
Mathematical Tables and Other Aids to Computation,
Volume 13, Number 68, October 1959, pages 285294.

Arthur Stroud, Don Secrest,
Gaussian Quadrature Formulas,
Prentice Hall, 1966,
LC: QA299.4G3S7.
Source Code:
List of Routines:

MAIN is the main program for LAGUERRE_RULE.

CDGQF computes a Gauss quadrature formula with default A, B and simple knots.

CGQF computes knots and weights of a Gauss quadrature formula.

CH_CAP capitalizes a single character.

CH_EQI is a case insensitive comparison of two characters for equality.

CH_TO_DIGIT returns the integer value of a base 10 digit.

CLASS_MATRIX computes the Jacobi matrix for a quadrature rule.

GET_UNIT returns a free FORTRAN unit number.

IMTQLX diagonalizes a symmetric tridiagonal matrix.

PARCHK checks parameters ALPHA and BETA for classical weight functions.

R8_EPSILON returns the R8 roundoff unit.

R8_GAMMA evaluates Gamma(X) for a real argument.

R8_HUGE returns a very large R8.

R8MAT_WRITE writes an R8MAT file.

RULE_WRITE writes a quadrature rule to a file.

S_TO_I4 reads an I4 from a string.

S_TO_R8 reads an R8 value from a string.

SCQF scales a quadrature formula to a nonstandard interval.

SGQF computes knots and weights of a Gauss Quadrature formula.

TIMESTAMP prints the current YMDHMS date as a time stamp.
You can go up one level to
the FORTRAN77 source codes.
Last revised on 14 May 2014.