LINE_FELIPPA_RULE
Quadrature Rules for a Line Segment in 1D

LINE_FELIPPA_RULE is a C++ library which generates the points and weights of a quadrature rule over the interior of a line segment in 1D.

Licensing:

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

Languages:

LINE_FELIPPA_RULE is available in a C version and a C++ version and a FORTRAN90 version and a FORTRAN77 version and a MATLAB version.

Related Data and Programs:

CCN_RULE, a C++ program which defines a nested Clenshaw Curtis quadrature rule.

CHEBYSHEV1_RULE, a C++ program which computes and prints a Gauss-Chebyshev type 1 quadrature rule.

CHEBYSHEV2_RULE, a C++ program which computes and prints a Gauss-Chebyshev type 2 quadrature rule.

CLENSHAW_CURTIS_RULE, a C++ program which defines a Clenshaw Curtis quadrature rule.

LEGENDRE_RULE, a C++ program which computes a 1D Gauss-Legendre quadrature rule.

LINE_CVT_LLOYD, a C++ library which applies Lloyd's iteration repeatedly to a set of N points, to compute a Centroidal Voronoi Tessellation (CVT) over the interior of a line segment in 1D.

LINE_FEKETE_RULE, a C++ library which estimates the location of N Fekete points, for polynomial interpolation or quadrature, over the interior of a line segment in 1D.

LINE_GRID, a C++ library which computes a grid of points over the interior of a line segment in 1D.

LINE_INTEGRALS, a C++ library which returns the exact value of the integral of any monomial over the length of the unit line in 1D.

LINE_MONTE_CARLO, a C++ library which applies a Monte Carlo method to estimate the integral of a function over the length of the unit line in 1D;

LINE_NCC_RULE, a C++ library which defines a Newton Cotes Closed (NCC) rule using equally spaced points over the interior of a line segment in 1D.

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

PATTERSON_RULE, a C++ 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.

Reference:

1. Carlos Felippa,
   A compendium of FEM integration formulas for symbolic work,
   Engineering Computation,
   Volume 21, Number 8, 2004, pages 867-890.

Source Code:

• line_felippa_rule.cpp, the source code.
• line_felippa_rule.hpp, the include file.
• line_felippa_rule.sh, BASH commands to compile the source code.

Examples and Tests:

• line_felippa_rule_prb.cpp, a sample calling program.
• line_felippa_rule_prb.sh, BASH commands to compile and run the sample program.
• line_felippa_rule_prb_output.txt, the output file.

List of Routines:

• LINE_MONOMIAL: monomial integral over a line segment in 1D.
• LINE_MONOMIAL_TEST tests LINE_MONOMIAL.
• LINE_QUAD_TEST tests the rules for a line segment in 1D.
• LINE_RULE returns a quadrature rule for a line segment in 1D.
• LINE_UNIT_O01 returns a 1 point quadrature rule for the unit line.
• LINE_UNIT_O02 returns a 2 point quadrature rule for the unit line.
• LINE_UNIT_O03 returns a 3 point quadrature rule for the unit line.
• LINE_UNIT_O04 returns a 4 point quadrature rule for the unit line.
• LINE_UNIT_O05 returns a 5 point quadrature rule for the unit line.
• LINE_VOLUME: volume of a line segment in 1D.
• R8VEC_COPY copies an R8VEC.
• R8VEC_DOT_PRODUCT computes the dot product of a pair of R8VEC's.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the C++ source codes.