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<html>
<head>
<title>
LINE_FELIPPA_RULE - Quadrature Rules for a Line Segment in 1D
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
LINE_FELIPPA_RULE <br> Quadrature Rules for a Line Segment in 1D
</h1>
<hr>
<p>
<b>LINE_FELIPPA_RULE</b>
is a C++ library which
generates the points and weights of a quadrature rule
over the interior of a line segment in 1D.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>LINE_FELIPPA_RULE</b> is available in
<a href = "../../c_src/line_felippa_rule/line_felippa_rule.html">a C version</a> and
<a href = "../../cpp_src/line_felippa_rule/line_felippa_rule.html">a C++ version</a> and
<a href = "../../f_src/line_felippa_rule/line_felippa_rule.html">a FORTRAN90 version</a> and
<a href = "../../f77_src/line_felippa_rule/line_felippa_rule.html">a FORTRAN77 version</a> and
<a href = "../../m_src/line_felippa_rule/line_felippa_rule.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/ccn_rule/ccn_rule.html">
CCN_RULE</a>,
a C++ program which
defines a nested Clenshaw Curtis quadrature rule.
</p>
<p>
<a href = "../../cpp_src/chebyshev1_rule/chebyshev1_rule.html">
CHEBYSHEV1_RULE</a>,
a C++ program which
computes and prints a Gauss-Chebyshev type 1 quadrature rule.
</p>
<p>
<a href = "../../cpp_src/chebyshev2_rule/chebyshev2_rule.html">
CHEBYSHEV2_RULE</a>,
a C++ program which
computes and prints a Gauss-Chebyshev type 2 quadrature rule.
</p>
<p>
<a href = "../../cpp_src/clenshaw_curtis_rule/clenshaw_curtis_rule.html">
CLENSHAW_CURTIS_RULE</a>,
a C++ program which
defines a Clenshaw Curtis quadrature rule.
</p>
<p>
<a href = "../../cpp_src/legendre_rule/legendre_rule.html">
LEGENDRE_RULE</a>,
a C++ program which
computes a 1D Gauss-Legendre quadrature rule.
</p>
<p>
<a href = "../../cpp_src/line_cvt_lloyd/line_cvt_lloyd.html">
LINE_CVT_LLOYD</a>,
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.
</p>
<p>
<a href = "../../cpp_src/line_fekete_rule/line_fekete_rule.html">
LINE_FEKETE_RULE</a>,
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.
</p>
<p>
<a href = "../../cpp_src/line_grid/line_grid.html">
LINE_GRID</a>,
a C++ library which
computes a grid of points
over the interior of a line segment in 1D.
</p>
<p>
<a href = "../../cpp_src/line_integrals/line_integrals.html">
LINE_INTEGRALS</a>,
a C++ library which
returns the exact value of the integral of any monomial
over the length of the unit line in 1D.
</p>
<p>
<a href = "../../cpp_src/line_monte_carlo/line_monte_carlo.html">
LINE_MONTE_CARLO</a>,
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;
</p>
<p>
<a href = "../../cpp_src/line_ncc_rule/line_ncc_rule.html">
LINE_NCC_RULE</a>,
a C++ library which
defines a Newton Cotes Closed (NCC) rule using equally spaced points
over the interior of a line segment in 1D.
</p>
<p>
<a href = "../../cpp_src/line_nco_rule/line_nco_rule.html">
LINE_NCO_RULE</a>,
a C++ library which
defines a Newton Cotes Open (NCO) rule using equally spaced points
over the interior of a line segment in 1D.
</p>
<p>
<a href = "../../cpp_src/patterson_rule/patterson_rule.html">
PATTERSON_RULE</a>,
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.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Carlos Felippa,<br>
A compendium of FEM integration formulas for symbolic work,<br>
Engineering Computation,<br>
Volume 21, Number 8, 2004, pages 867-890.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "line_felippa_rule.cpp">line_felippa_rule.cpp</a>, the source code.
</li>
<li>
<a href = "line_felippa_rule.hpp">line_felippa_rule.hpp</a>, the include file.
</li>
<li>
<a href = "line_felippa_rule.sh">line_felippa_rule.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "line_felippa_rule_prb.cpp">line_felippa_rule_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "line_felippa_rule_prb.sh">line_felippa_rule_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "line_felippa_rule_prb_output.txt">line_felippa_rule_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>LINE_MONOMIAL:</b> monomial integral over a line segment in 1D.
</li>
<li>
<b>LINE_MONOMIAL_TEST</b> tests LINE_MONOMIAL.
</li>
<li>
<b>LINE_QUAD_TEST</b> tests the rules for a line segment in 1D.
</li>
<li>
<b>LINE_RULE</b> returns a quadrature rule for a line segment in 1D.
</li>
<li>
<b>LINE_UNIT_O01</b> returns a 1 point quadrature rule for the unit line.
</li>
<li>
<b>LINE_UNIT_O02</b> returns a 2 point quadrature rule for the unit line.
</li>
<li>
<b>LINE_UNIT_O03</b> returns a 3 point quadrature rule for the unit line.
</li>
<li>
<b>LINE_UNIT_O04</b> returns a 4 point quadrature rule for the unit line.
</li>
<li>
<b>LINE_UNIT_O05</b> returns a 5 point quadrature rule for the unit line.
</li>
<li>
<b>LINE_VOLUME:</b> volume of a line segment in 1D.
</li>
<li>
<b>R8VEC_COPY</b> copies an R8VEC.
</li>
<li>
<b>R8VEC_DOT_PRODUCT</b> computes the dot product of a pair of R8VEC's.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 07 September 2014.
</i>
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