LAGUERRE_RULE
Gauss-Laguerre Quadrature Rules
LAGUERRE_RULE
is a FORTRAN77 program which
generates a specific Gauss-Laguerre quadrature rule, based on user input.
The rule is written to three files for easy use as input
to other programs.
The Gauss-Laguerre 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 Gauss-Hermite quadrature rule.
LAGUERRE_EXACTNESS,
a FORTRAN77 program which
checks the polynomial exactness
of a Gauss-Laguerre 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 Gauss-Legendre quadrature rule.
LEGENDRE_RULE_FAST,
a FORTRAN77 program which
uses a fast (order N) algorithm to compute a Gauss-Legendre quadrature
rule of given order.
QUADRULE,
a FORTRAN77 library which
contains 1-dimensional quadrature
rules.
Reference:
-
Milton Abramowitz, Irene Stegun,
Handbook of Mathematical Functions,
National Bureau of Standards, 1964,
ISBN: 0-486-61272-4,
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 399-415.
-
Jaroslav Kautsky, Sylvan Elhay,
Calculation of the Weights of Interpolatory Quadratures,
Numerische Mathematik,
Volume 40, 1982, pages 407-422.
-
Roger Martin, James Wilkinson,
The Implicit QL Algorithm,
Numerische Mathematik,
Volume 12, Number 5, December 1968, pages 377-383.
-
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 285-294.
-
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.