clenshaw_curtis_rule


clenshaw_curtis_rule, a FORTRAN77 code which generates a Clenshaw Curtis quadrature rule.

The rule is written to three files for easy use as input to other programs.

The standard Clenshaw Curtis quadrature rule is used as follows:

        Integral ( A <= x <= B ) f(x) dx
      
is to be approximated by
        Sum ( 1 <= i <= order ) w(i) * f(x(i))
      

Usage:

clenshaw_curtis_rule order a b filename
where

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

clenshaw_curtis_rule is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

clenshaw_curtis_rule_test

ccn_rule, a FORTRAN77 program which defines one of a set of nested Clenshaw Curtis quadrature rules of any order.

chebyshev1_rule, a FORTRAN90 program which can compute and print a Gauss-Chebyshev type 1 quadrature rule.

CHEBYSHEV2_RULE, a FORTRAN90 program which can compute and print a Gauss-Chebyshev type 2 quadrature rule.

GEGENBAUER_RULE, a FORTRAN90 program which can compute and print a Gauss-Gegenbauer quadrature rule.

GEN_HERMITE_RULE, a FORTRAN90 program which can compute and print a generalized Gauss-Hermite quadrature rule.

GEN_LAGUERRE_RULE, a FORTRAN90 program which can compute and print a generalized Gauss-Laguerre quadrature rule.

HERMITE_RULE, a FORTRAN77 program which can compute and print a Gauss-Hermite quadrature rule.

LAGUERRE_RULE, a FORTRAN77 program which can compute and print a Gauss-Laguerre quadrature rule for estimating the integral of a function with density exp(-x) over the interval [0,+oo).

LEGENDRE_RULE, a FORTRAN77 program which can compute and print a Gauss-Legendre quadrature rule.

LINE_FELIPPA_RULE, a FORTRAN77 library which returns the points and weights of a Felippa quadrature rule over the interior of a line segment in 1D.

LINE_NCC_RULE, a FORTRAN77 library which computes a Newton Cotes Closed (NCC) quadrature rule for the line, that is, for an interval of the form [A,B], using equally spaced points which include the endpoints.

LINE_NCO_RULE, a FORTRAN77 library which computes a Newton Cotes Open (NCO) quadrature rule, using equally spaced points, over the interior of a line segment in 1D.

PATTERSON_RULE, a FORTRAN77 program which returns the points and weights of a 1D Gauss-Patterson quadrature rule of order 1, 3, 7, 15, 31, 63, 127, 255 or 511.

QUADRATURE_RULES_CLENSHAW_CURTIS, a dataset directory which contains quadrature rules for integration on [-1,+1], using a Clenshaw Curtis rule.

QUADRULE, a FORTRAN77 library which defines 1-dimensional quadrature rules.

TRUNCATED_NORMAL_RULE, a FORTRAN77 program which computes a quadrature rule for a normal probability density function (PDF), also called a Gaussian distribution, that has been truncated to [A,+oo), (-oo,B] or [A,B].

Reference:

  1. Milton Abramowitz, Irene Stegun,
    Handbook of Mathematical Functions,
    National Bureau of Standards, 1964,
    ISBN: 0-486-61272-4,
    LC: QA47.A34.
  2. Philip Davis, Philip Rabinowitz,
    Methods of Numerical Integration,
    Second Edition,
    Dover, 2007,
    ISBN: 0486453391,
    LC: QA299.3.D28.
  3. Arthur Stroud, Don Secrest,
    Gaussian Quadrature Formulas,
    Prentice Hall, 1966,
    LC: QA299.4G3S7.

Source Code:


Last revised on 24 September 2023.