/usr/include/trilinos/Intrepid_BurkardtRules.hpp is in libtrilinos-intrepid-dev 12.4.2-2.
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// ************************************************************************
//
// Intrepid Package
// Copyright (2007) Sandia Corporation
//
// Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
// license for use of this work by or on behalf of the U.S. Government.
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//
// 1. Redistributions of source code must retain the above copyright
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// THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
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// Denis Ridzal (dridzal@sandia.gov), or
// Kara Peterson (kjpeter@sandia.gov)
//
// ************************************************************************
// @HEADER
/** \file Intrepid_BurkardtRules.hpp
\brief Header file for integration rules provided by John Burkardt.
<A HREF="http://people.sc.fsu.edu/~jburkardt/cpp_src/sandia_rules/sandia_rules.html">
<\A>
\author Created by D. Kouri and D. Ridzal.
*/
#ifndef INTREPID_BURKARDTRULES_HPP
#define INTREPID_BURKARDTRULES_HPP
#include "Intrepid_ConfigDefs.hpp"
#include "Intrepid_Types.hpp"
#include "Teuchos_Assert.hpp"
//#include <fstream>
//#include <string>
namespace Intrepid {
/** \enum Intrepid::EIntrepidBurkardt
\brief Enumeration of integration rules provided by John Burkardt.
*/
enum EIntrepidBurkardt {
BURK_CHEBYSHEV1 = 0,
BURK_CHEBYSHEV2,
BURK_CLENSHAWCURTIS,
BURK_FEJER2,
BURK_LEGENDRE,
BURK_PATTERSON,
BURK_TRAPEZOIDAL,
BURK_HERMITE,
BURK_GENZKEISTER,
BURK_LAGUERRE
};
inline std::string EIntrepidBurkardtToString(EIntrepidBurkardt rule) {
std::string retString;
switch(rule) {
case BURK_CHEBYSHEV1: retString = "Gauss-Chebyshev Type 1"; break;
case BURK_CHEBYSHEV2: retString = "Gauss-Chebyshev Type 2"; break;
case BURK_CLENSHAWCURTIS: retString = "Clenshaw-Curtis"; break;
case BURK_FEJER2: retString = "Fejer Type 2"; break;
case BURK_LEGENDRE: retString = "Gauss-Legendre"; break;
case BURK_PATTERSON: retString = "Gauss-Patterson"; break;
case BURK_TRAPEZOIDAL: retString = "Trapezoidal Rule"; break;
case BURK_HERMITE: retString = "Gauss-Hermite"; break;
case BURK_GENZKEISTER: retString = "Hermite-Genz-Keister"; break;
case BURK_LAGUERRE: retString = "Gauss-Laguerre"; break;
default: retString = "INVALID EIntrepidBurkardt";
}
return retString;
}
inline EIntrepidBurkardt & operator++(EIntrepidBurkardt &type) {
return type = static_cast<EIntrepidBurkardt>(type+1);
}
inline EIntrepidBurkardt operator++(EIntrepidBurkardt &type, int) {
EIntrepidBurkardt oldval = type;
++type;
return oldval;
}
/** \class Intrepid::IntrepidBurkardtRules
\brief Providing integration rules,
created by John Burkardt, Scientific Computing,
Florida State University,
modified and redistributed by D. Kouri.
See <A HREF="http://people.sc.fsu.edu/~jburkardt/cpp_src/sandia_rules/sandia_rules.html">
<\A>
*/
class IntrepidBurkardtRules {
public:
/* HELPER FUNCTIONS */
template<class Scalar>
static void imtqlx ( int n, Scalar d[], Scalar e[], Scalar z[] );
template<class Scalar> static Scalar r8_epsilon( Scalar one );
template<class Scalar> static Scalar r8_sign( Scalar x );
/* COMPUTE CHEBYSHEV TYPE 1 NODES AND WEIGHTS */
/* Integrates functions on [-1,1] weighted by w(x) = 1/sqrt(1-x^2) */
/** \brief Gauss-Chebyshev of Type 1; returns points and weights.
*/
template<class Scalar>
static void chebyshev1_compute ( int order, Scalar x[], Scalar w[] );
/** \brief Gauss-Chebyshev of Type 1; returns points.
*/
template<class Scalar>
static void chebyshev1_compute_points ( int order, Scalar x[] );
/** \brief Gauss-Chebyshev of Type 1; returns weights.
*/
template<class Scalar>
static void chebyshev1_compute_weights ( int order, Scalar w[] );
/* COMPUTE CHEBYSHEV TYPE 2 NODES AND WEIGHTS */
/* Integrates functions on [-1,1] weighted by w(x) = sqrt(1-x^2) */
/** \brief Gauss-Chebyshev of Type 2; returns points and weights.
*/
template<class Scalar>
static void chebyshev2_compute ( int order, Scalar x[], Scalar w[] );
/** \brief Gauss-Chebyshev of Type 2; returns points.
*/
template<class Scalar>
static void chebyshev2_compute_points ( int order, Scalar x[] );
/** \brief Gauss-Chebyshev of Type 2; returns weights.
*/
template<class Scalar>
static void chebyshev2_compute_weights ( int order, Scalar w[] );
/* COMPUTE CLENSHAW CURTIS NODES AND WEIGHTS */
/* Integrates functions on [-1,1] weighted by w(x) = 1 */
/** \brief Clenshaw-Curtis; returns points and weights.
*/
template<class Scalar>
static void clenshaw_curtis_compute ( int order, Scalar x[], Scalar w[] );
/** \brief Clenshaw-Curtis; returns points.
*/
template<class Scalar>
static void clenshaw_curtis_compute_points ( int order, Scalar x[] );
/** \brief Clenshaw-Curtis; returns weights.
*/
template<class Scalar>
static void clenshaw_curtis_compute_weights ( int order, Scalar w[] );
/* COMPUTE FEJER TYPE 2 NODES AND WEIGHTS */
/* Integrates functions on [-1,1] weighted by w(x) = 1 */
/** \brief Fejer type 2; returns points and weights.
*/
template<class Scalar>
static void fejer2_compute ( int order, Scalar x[], Scalar w[] );
/** \brief Fejer type 2; returns points.
*/
template<class Scalar>
static void fejer2_compute_points ( int order, Scalar x[] );
/** \brief Fejer type 2; returns weights.
*/
template<class Scalar>
static void fejer2_compute_weights ( int order, Scalar w[] );
/* COMPUTE GAUSS HERMITE NODES AND WEIGHTS */
/* Integrates functions on (-oo,oo) weighted by w(x) = exp(-x^2) */
/** \brief Gauss-Hermite; returns points and weights.
*/
template<class Scalar>
static void hermite_compute ( int order, Scalar x[], Scalar w[] );
/** \brief Gauss-Hermite; returns points.
*/
template<class Scalar>
static void hermite_compute_points ( int order, Scalar x[] );
/** \brief Gauss-Hermite; returns weights.
*/
template<class Scalar>
static void hermite_compute_weights ( int order, Scalar w[] );
/** \brief Gauss-Hermite; returns points and weights.
*/
template<class Scalar>
static void hermite_lookup ( int n, Scalar x[], Scalar w[] );
/** \brief Gauss-Hermite; returns points.
*/
template<class Scalar>
static void hermite_lookup_points ( int n, Scalar x[] );
/** \brief Gauss-Hermite; returns weights.
*/
template<class Scalar>
static void hermite_lookup_weights ( int n, Scalar w[] );
/* COMPUTE GENZ KEISTER NODES AND WEIGHTS */
/* Integrates functions on (-oo,oo) weighted by w(x) = exp(-x^2) */
/** \brief Hermite-Genz-Keister; returns points and weights.
*/
template<class Scalar>
static void hermite_genz_keister_lookup ( int n, Scalar x[], Scalar w[] );
/** \brief Hermite-Genz-Keister; returns points.
*/
template<class Scalar>
static void hermite_genz_keister_lookup_points ( int n, Scalar x[] );
/** \brief Hermite-Genz-Keister; returns weights.
*/
template<class Scalar>
static void hermite_genz_keister_lookup_weights ( int n, Scalar w[] );
/* COMPUTE GAUSS LAGUERRE NODES AND WEIGHTS */
/* Integrates functons on [0,oo) weighted by w(x) = exp(-x) */
/** \brief Gauss-Laguerre; returns points and weights.
*/
template<class Scalar>
static void laguerre_compute ( int n, Scalar x[], Scalar w[] );
/** \brief Gauss-Laguerre; returns points.
*/
template<class Scalar>
static void laguerre_compute_points ( int order, Scalar x[] );
/** \brief Gauss-Laguerre; returns weights.
*/
template<class Scalar>
static void laguerre_compute_weights ( int order, Scalar w[] );
/** \brief Gauss-Laguerre; returns points and weights.
*/
template<class Scalar>
static void laguerre_lookup ( int n, Scalar x[], Scalar w[] );
/** \brief Gauss-Laguerre; returns points.
*/
template<class Scalar>
static void laguerre_lookup_points ( int n, Scalar x[] );
/** \brief Gauss-Laguerre; returns weights.
*/
template<class Scalar>
static void laguerre_lookup_weights ( int n, Scalar w[] );
/* COMPUTE GAUSS LEGENDRE NODES AND WEIGHTS */
/* Integrates functions on [-1,1] weighted by w(x) = 1 */
/** \brief Gauss-Legendre; returns points and weights.
*/
template<class Scalar>
static void legendre_compute ( int n, Scalar x[], Scalar w[] );
/** \brief Gauss-Legendre; returns points.
*/
template<class Scalar>
static void legendre_compute_points ( int order, Scalar x[] );
/** \brief Gauss-Legendre; returns weights.
*/
template<class Scalar>
static void legendre_compute_weights ( int order, Scalar w[] );
/** \brief Gauss-Legendre; returns points and weights.
*/
template<class Scalar>
static void legendre_lookup ( int n, Scalar x[], Scalar w[] );
/** \brief Gauss-Legendre; returns points.
*/
template<class Scalar>
static void legendre_lookup_points ( int n, Scalar x[] );
/** \brief Gauss-Legendre; returns weights.
*/
template<class Scalar>
static void legendre_lookup_weights ( int n, Scalar w[] );
/* COMPUTE GAUSS PATTERSON NODES AND WEIGHTS */
/* Integrates functions on [-1,1] weighted by w(x) = 1 */
/** \brief Gauss-Patterson; returns points and weights.
*/
template<class Scalar>
static void patterson_lookup ( int n, Scalar x[], Scalar w[] );
/** \brief Gauss-Patterson; returns points.
*/
template<class Scalar>
static void patterson_lookup_points ( int n, Scalar x[] );
/** \brief Gauss-Patterson; returns weights.
*/
template<class Scalar>
static void patterson_lookup_weights ( int n, Scalar w[] );
/* COMPUTE TRAPEZOIDAL RULE NODES AND WEIGHTS */
/* Integrates functions on [-1,1] weighted by w(x) = 1 */
/** \brief Trapezoidal rule; returns points and weights.
*/
template<class Scalar>
static void trapezoidal_compute ( int n, Scalar x[], Scalar w[] );
/** \brief Trapezoidal rule; returns points.
*/
template<class Scalar>
static void trapezoidal_compute_points ( int order, Scalar x[] );
/** \brief Trapezoidal rule; returns weights.
*/
template<class Scalar>
static void trapezoidal_compute_weights ( int order, Scalar w[] );
}; // class IntrepidBurkardtRules
} // end Intrepid namespace
// include templated definitions
#include "Intrepid_BurkardtRulesDef.hpp"
#endif
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