ROL
Static Public Member Functions | List of all members
ROL::ROLBurkardtRules Class Reference

Providing integration rules, created by John Burkardt, Scientific Computing, Florida State University, modified and redistributed by D. Kouri. More...

#include <ROL_BurkardtRules.hpp>

Static Public Member Functions

template<class Real >
static void imtqlx (int n, Real d[], Real e[], Real z[])
 
template<class Real >
static Real r8_epsilon (Real one)
 
template<class Real >
static Real r8_sign (Real x)
 
template<class Real >
static void chebyshev1_compute (int order, Real x[], Real w[])
 Gauss-Chebyshev of Type 1; returns points and weights. More...
 
template<class Real >
static void chebyshev1_compute_points (int order, Real x[])
 Gauss-Chebyshev of Type 1; returns points. More...
 
template<class Real >
static void chebyshev1_compute_weights (int order, Real w[])
 Gauss-Chebyshev of Type 1; returns weights. More...
 
template<class Real >
static void chebyshev2_compute (int order, Real x[], Real w[])
 Gauss-Chebyshev of Type 2; returns points and weights. More...
 
template<class Real >
static void chebyshev2_compute_points (int order, Real x[])
 Gauss-Chebyshev of Type 2; returns points. More...
 
template<class Real >
static void chebyshev2_compute_weights (int order, Real w[])
 Gauss-Chebyshev of Type 2; returns weights. More...
 
template<class Real >
static void clenshaw_curtis_compute (int order, Real x[], Real w[])
 Clenshaw-Curtis; returns points and weights. More...
 
template<class Real >
static void clenshaw_curtis_compute_points (int order, Real x[])
 Clenshaw-Curtis; returns points. More...
 
template<class Real >
static void clenshaw_curtis_compute_weights (int order, Real w[])
 Clenshaw-Curtis; returns weights. More...
 
template<class Real >
static void fejer2_compute (int order, Real x[], Real w[])
 Fejer type 2; returns points and weights. More...
 
template<class Real >
static void fejer2_compute_points (int order, Real x[])
 Fejer type 2; returns points. More...
 
template<class Real >
static void fejer2_compute_weights (int order, Real w[])
 Fejer type 2; returns weights. More...
 
template<class Real >
static void hermite_compute (int order, Real x[], Real w[])
 Gauss-Hermite; returns points and weights. More...
 
template<class Real >
static void hermite_compute_points (int order, Real x[])
 Gauss-Hermite; returns points. More...
 
template<class Real >
static void hermite_compute_weights (int order, Real w[])
 Gauss-Hermite; returns weights. More...
 
template<class Real >
static void hermite_lookup (int n, Real x[], Real w[])
 Gauss-Hermite; returns points and weights. More...
 
template<class Real >
static void hermite_lookup_points (int n, Real x[])
 Gauss-Hermite; returns points. More...
 
template<class Real >
static void hermite_lookup_weights (int n, Real w[])
 Gauss-Hermite; returns weights. More...
 
template<class Real >
static void hermite_genz_keister_lookup (int n, Real x[], Real w[])
 Hermite-Genz-Keister; returns points and weights. More...
 
template<class Real >
static void hermite_genz_keister_lookup_points (int n, Real x[])
 Hermite-Genz-Keister; returns points. More...
 
template<class Real >
static void hermite_genz_keister_lookup_weights (int n, Real w[])
 Hermite-Genz-Keister; returns weights. More...
 
template<class Real >
static void laguerre_compute (int n, Real x[], Real w[])
 Gauss-Laguerre; returns points and weights. More...
 
template<class Real >
static void laguerre_compute_points (int order, Real x[])
 Gauss-Laguerre; returns points. More...
 
template<class Real >
static void laguerre_compute_weights (int order, Real w[])
 Gauss-Laguerre; returns weights. More...
 
template<class Real >
static void laguerre_lookup (int n, Real x[], Real w[])
 Gauss-Laguerre; returns points and weights. More...
 
template<class Real >
static void laguerre_lookup_points (int n, Real x[])
 Gauss-Laguerre; returns points. More...
 
template<class Real >
static void laguerre_lookup_weights (int n, Real w[])
 Gauss-Laguerre; returns weights. More...
 
template<class Real >
static void legendre_compute (int n, Real x[], Real w[])
 Gauss-Legendre; returns points and weights. More...
 
template<class Real >
static void legendre_compute_points (int order, Real x[])
 Gauss-Legendre; returns points. More...
 
template<class Real >
static void legendre_compute_weights (int order, Real w[])
 Gauss-Legendre; returns weights. More...
 
template<class Real >
static void legendre_lookup (int n, Real x[], Real w[])
 Gauss-Legendre; returns points and weights. More...
 
template<class Real >
static void legendre_lookup_points (int n, Real x[])
 Gauss-Legendre; returns points. More...
 
template<class Real >
static void legendre_lookup_weights (int n, Real w[])
 Gauss-Legendre; returns weights. More...
 
template<class Real >
static void patterson_lookup (int n, Real x[], Real w[])
 Gauss-Patterson; returns points and weights. More...
 
template<class Real >
static void patterson_lookup_points (int n, Real x[])
 Gauss-Patterson; returns points. More...
 
template<class Real >
static void patterson_lookup_weights (int n, Real w[])
 Gauss-Patterson; returns weights. More...
 
template<class Real >
static void trapezoidal_compute (int n, Real x[], Real w[])
 Trapezoidal rule; returns points and weights. More...
 
template<class Real >
static void trapezoidal_compute_points (int order, Real x[])
 Trapezoidal rule; returns points. More...
 
template<class Real >
static void trapezoidal_compute_weights (int order, Real w[])
 Trapezoidal rule; returns weights. More...
 

Detailed Description

Providing integration rules, created by John Burkardt, Scientific Computing, Florida State University, modified and redistributed by D. Kouri.

See <>

Definition at line 116 of file ROL_BurkardtRules.hpp.

Member Function Documentation

template<class Real >
void ROL::ROLBurkardtRules::imtqlx ( int  n,
Real  d[],
Real  e[],
Real  z[] 
)
static

Definition at line 2447 of file ROL_BurkardtRulesDef.hpp.

References r8_epsilon(), and r8_sign().

Referenced by hermite_compute(), laguerre_compute(), and legendre_compute().

template<class Real >
Real ROL::ROLBurkardtRules::r8_epsilon ( Real  one)
static

Definition at line 6390 of file ROL_BurkardtRulesDef.hpp.

Referenced by imtqlx().

template<class Real >
Real ROL::ROLBurkardtRules::r8_sign ( Real  x)
static

Definition at line 6435 of file ROL_BurkardtRulesDef.hpp.

Referenced by imtqlx().

template<class Real >
void ROL::ROLBurkardtRules::chebyshev1_compute ( int  order,
Real  x[],
Real  w[] 
)
static

Gauss-Chebyshev of Type 1; returns points and weights.

Definition at line 67 of file ROL_BurkardtRulesDef.hpp.

template<class Real >
void ROL::ROLBurkardtRules::chebyshev1_compute_points ( int  order,
Real  x[] 
)
static

Gauss-Chebyshev of Type 1; returns points.

Definition at line 137 of file ROL_BurkardtRulesDef.hpp.

template<class Real >
void ROL::ROLBurkardtRules::chebyshev1_compute_weights ( int  order,
Real  w[] 
)
static

Gauss-Chebyshev of Type 1; returns weights.

Definition at line 192 of file ROL_BurkardtRulesDef.hpp.

template<class Real >
void ROL::ROLBurkardtRules::chebyshev2_compute ( int  order,
Real  x[],
Real  w[] 
)
static

Gauss-Chebyshev of Type 2; returns points and weights.

Definition at line 244 of file ROL_BurkardtRulesDef.hpp.

template<class Real >
void ROL::ROLBurkardtRules::chebyshev2_compute_points ( int  order,
Real  x[] 
)
static

Gauss-Chebyshev of Type 2; returns points.

Definition at line 316 of file ROL_BurkardtRulesDef.hpp.

template<class Real >
void ROL::ROLBurkardtRules::chebyshev2_compute_weights ( int  order,
Real  w[] 
)
static

Gauss-Chebyshev of Type 2; returns weights.

Definition at line 375 of file ROL_BurkardtRulesDef.hpp.

template<class Real >
void ROL::ROLBurkardtRules::clenshaw_curtis_compute ( int  order,
Real  x[],
Real  w[] 
)
static

Clenshaw-Curtis; returns points and weights.

Definition at line 430 of file ROL_BurkardtRulesDef.hpp.

template<class Real >
void ROL::ROLBurkardtRules::clenshaw_curtis_compute_points ( int  order,
Real  x[] 
)
static

Clenshaw-Curtis; returns points.

Definition at line 521 of file ROL_BurkardtRulesDef.hpp.

template<class Real >
void ROL::ROLBurkardtRules::clenshaw_curtis_compute_weights ( int  order,
Real  w[] 
)
static

Clenshaw-Curtis; returns weights.

Definition at line 579 of file ROL_BurkardtRulesDef.hpp.

template<class Real >
void ROL::ROLBurkardtRules::fejer2_compute ( int  order,
Real  x[],
Real  w[] 
)
static

Fejer type 2; returns points and weights.

Definition at line 658 of file ROL_BurkardtRulesDef.hpp.

template<class Real >
void ROL::ROLBurkardtRules::fejer2_compute_points ( int  order,
Real  x[] 
)
static

Fejer type 2; returns points.

Definition at line 739 of file ROL_BurkardtRulesDef.hpp.

template<class Real >
void ROL::ROLBurkardtRules::fejer2_compute_weights ( int  order,
Real  w[] 
)
static

Fejer type 2; returns weights.

Definition at line 796 of file ROL_BurkardtRulesDef.hpp.

template<class Real >
void ROL::ROLBurkardtRules::hermite_compute ( int  order,
Real  x[],
Real  w[] 
)
static

Gauss-Hermite; returns points and weights.

Definition at line 882 of file ROL_BurkardtRulesDef.hpp.

References imtqlx().

Referenced by hermite_compute_points(), and hermite_compute_weights().

template<class Real >
void ROL::ROLBurkardtRules::hermite_compute_points ( int  order,
Real  x[] 
)
static

Gauss-Hermite; returns points.

Definition at line 977 of file ROL_BurkardtRulesDef.hpp.

References hermite_compute().

template<class Real >
void ROL::ROLBurkardtRules::hermite_compute_weights ( int  order,
Real  w[] 
)
static

Gauss-Hermite; returns weights.

Definition at line 1012 of file ROL_BurkardtRulesDef.hpp.

References hermite_compute().

template<class Real >
void ROL::ROLBurkardtRules::hermite_lookup ( int  n,
Real  x[],
Real  w[] 
)
static

Gauss-Hermite; returns points and weights.

Definition at line 1701 of file ROL_BurkardtRulesDef.hpp.

References hermite_lookup_points(), and hermite_lookup_weights().

template<class Real >
void ROL::ROLBurkardtRules::hermite_lookup_points ( int  n,
Real  x[] 
)
static

Gauss-Hermite; returns points.

Definition at line 1771 of file ROL_BurkardtRulesDef.hpp.

Referenced by hermite_lookup().

template<class Real >
void ROL::ROLBurkardtRules::hermite_lookup_weights ( int  n,
Real  w[] 
)
static

Gauss-Hermite; returns weights.

Definition at line 2109 of file ROL_BurkardtRulesDef.hpp.

Referenced by hermite_lookup().

template<class Real >
void ROL::ROLBurkardtRules::hermite_genz_keister_lookup ( int  n,
Real  x[],
Real  w[] 
)
static

Hermite-Genz-Keister; returns points and weights.

Definition at line 1047 of file ROL_BurkardtRulesDef.hpp.

References hermite_genz_keister_lookup_points(), and hermite_genz_keister_lookup_weights().

template<class Real >
void ROL::ROLBurkardtRules::hermite_genz_keister_lookup_points ( int  n,
Real  x[] 
)
static

Hermite-Genz-Keister; returns points.

Definition at line 1119 of file ROL_BurkardtRulesDef.hpp.

Referenced by hermite_genz_keister_lookup().

template<class Real >
void ROL::ROLBurkardtRules::hermite_genz_keister_lookup_weights ( int  n,
Real  w[] 
)
static

Hermite-Genz-Keister; returns weights.

Definition at line 1410 of file ROL_BurkardtRulesDef.hpp.

Referenced by hermite_genz_keister_lookup().

template<class Real >
void ROL::ROLBurkardtRules::laguerre_compute ( int  n,
Real  x[],
Real  w[] 
)
static

Gauss-Laguerre; returns points and weights.

Definition at line 2610 of file ROL_BurkardtRulesDef.hpp.

References imtqlx().

Referenced by laguerre_compute_points(), and laguerre_compute_weights().

template<class Real >
void ROL::ROLBurkardtRules::laguerre_compute_points ( int  order,
Real  x[] 
)
static

Gauss-Laguerre; returns points.

Definition at line 2688 of file ROL_BurkardtRulesDef.hpp.

References laguerre_compute().

template<class Real >
void ROL::ROLBurkardtRules::laguerre_compute_weights ( int  order,
Real  w[] 
)
static

Gauss-Laguerre; returns weights.

Definition at line 2723 of file ROL_BurkardtRulesDef.hpp.

References laguerre_compute().

template<class Real >
void ROL::ROLBurkardtRules::laguerre_lookup ( int  n,
Real  x[],
Real  w[] 
)
static

Gauss-Laguerre; returns points and weights.

Definition at line 2758 of file ROL_BurkardtRulesDef.hpp.

References laguerre_lookup_points(), and laguerre_lookup_weights().

template<class Real >
void ROL::ROLBurkardtRules::laguerre_lookup_points ( int  n,
Real  x[] 
)
static

Gauss-Laguerre; returns points.

Definition at line 2852 of file ROL_BurkardtRulesDef.hpp.

Referenced by laguerre_lookup().

template<class Real >
void ROL::ROLBurkardtRules::laguerre_lookup_weights ( int  n,
Real  w[] 
)
static

Gauss-Laguerre; returns weights.

Definition at line 3174 of file ROL_BurkardtRulesDef.hpp.

Referenced by laguerre_lookup().

template<class Real >
void ROL::ROLBurkardtRules::legendre_compute ( int  n,
Real  x[],
Real  w[] 
)
static

Gauss-Legendre; returns points and weights.

Definition at line 3496 of file ROL_BurkardtRulesDef.hpp.

References imtqlx().

Referenced by legendre_compute_points(), and legendre_compute_weights().

template<class Real >
void ROL::ROLBurkardtRules::legendre_compute_points ( int  order,
Real  x[] 
)
static

Gauss-Legendre; returns points.

Definition at line 3581 of file ROL_BurkardtRulesDef.hpp.

References legendre_compute().

template<class Real >
void ROL::ROLBurkardtRules::legendre_compute_weights ( int  order,
Real  w[] 
)
static

Gauss-Legendre; returns weights.

Definition at line 3616 of file ROL_BurkardtRulesDef.hpp.

References legendre_compute().

template<class Real >
void ROL::ROLBurkardtRules::legendre_lookup ( int  n,
Real  x[],
Real  w[] 
)
static

Gauss-Legendre; returns points and weights.

Definition at line 3651 of file ROL_BurkardtRulesDef.hpp.

References legendre_lookup_points(), and legendre_lookup_weights().

template<class Real >
void ROL::ROLBurkardtRules::legendre_lookup_points ( int  n,
Real  x[] 
)
static

Gauss-Legendre; returns points.

Definition at line 3721 of file ROL_BurkardtRulesDef.hpp.

Referenced by legendre_lookup().

template<class Real >
void ROL::ROLBurkardtRules::legendre_lookup_weights ( int  n,
Real  w[] 
)
static

Gauss-Legendre; returns weights.

Definition at line 4420 of file ROL_BurkardtRulesDef.hpp.

Referenced by legendre_lookup().

template<class Real >
void ROL::ROLBurkardtRules::patterson_lookup ( int  n,
Real  x[],
Real  w[] 
)
static

Gauss-Patterson; returns points and weights.

Definition at line 5119 of file ROL_BurkardtRulesDef.hpp.

References patterson_lookup_points(), and patterson_lookup_weights().

template<class Real >
void ROL::ROLBurkardtRules::patterson_lookup_points ( int  n,
Real  x[] 
)
static

Gauss-Patterson; returns points.

Definition at line 5175 of file ROL_BurkardtRulesDef.hpp.

Referenced by patterson_lookup().

template<class Real >
void ROL::ROLBurkardtRules::patterson_lookup_weights ( int  n,
Real  w[] 
)
static

Gauss-Patterson; returns weights.

Definition at line 5750 of file ROL_BurkardtRulesDef.hpp.

Referenced by patterson_lookup().

template<class Real >
void ROL::ROLBurkardtRules::trapezoidal_compute ( int  n,
Real  x[],
Real  w[] 
)
static

Trapezoidal rule; returns points and weights.

Definition at line 6327 of file ROL_BurkardtRulesDef.hpp.

template<class Real >
void ROL::ROLBurkardtRules::trapezoidal_compute_points ( int  order,
Real  x[] 
)
static

Trapezoidal rule; returns points.

Definition at line 6351 of file ROL_BurkardtRulesDef.hpp.

template<class Real >
void ROL::ROLBurkardtRules::trapezoidal_compute_weights ( int  order,
Real  w[] 
)
static

Trapezoidal rule; returns weights.

Definition at line 6368 of file ROL_BurkardtRulesDef.hpp.


The documentation for this class was generated from the following files: