Intrepid
Static Public Member Functions | List of all members
Intrepid::IntrepidBurkardtRules Class Reference

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

#include <Intrepid_BurkardtRules.hpp>

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

Detailed Description

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

See <\A>

Definition at line 115 of file Intrepid_BurkardtRules.hpp.

Member Function Documentation

◆ chebyshev1_compute()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::chebyshev1_compute ( int  order,
Scalar  x[],
Scalar  w[] 
)
static

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

Definition at line 62 of file Intrepid_BurkardtRulesDef.hpp.

◆ chebyshev1_compute_points()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::chebyshev1_compute_points ( int  order,
Scalar  x[] 
)
static

Gauss-Chebyshev of Type 1; returns points.

Definition at line 132 of file Intrepid_BurkardtRulesDef.hpp.

◆ chebyshev1_compute_weights()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::chebyshev1_compute_weights ( int  order,
Scalar  w[] 
)
static

Gauss-Chebyshev of Type 1; returns weights.

Definition at line 187 of file Intrepid_BurkardtRulesDef.hpp.

◆ chebyshev2_compute()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::chebyshev2_compute ( int  order,
Scalar  x[],
Scalar  w[] 
)
static

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

Definition at line 239 of file Intrepid_BurkardtRulesDef.hpp.

◆ chebyshev2_compute_points()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::chebyshev2_compute_points ( int  order,
Scalar  x[] 
)
static

Gauss-Chebyshev of Type 2; returns points.

Definition at line 311 of file Intrepid_BurkardtRulesDef.hpp.

◆ chebyshev2_compute_weights()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::chebyshev2_compute_weights ( int  order,
Scalar  w[] 
)
static

Gauss-Chebyshev of Type 2; returns weights.

Definition at line 370 of file Intrepid_BurkardtRulesDef.hpp.

◆ clenshaw_curtis_compute()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::clenshaw_curtis_compute ( int  order,
Scalar  x[],
Scalar  w[] 
)
static

Clenshaw-Curtis; returns points and weights.

Definition at line 425 of file Intrepid_BurkardtRulesDef.hpp.

◆ clenshaw_curtis_compute_points()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::clenshaw_curtis_compute_points ( int  order,
Scalar  x[] 
)
static

Clenshaw-Curtis; returns points.

Definition at line 516 of file Intrepid_BurkardtRulesDef.hpp.

◆ clenshaw_curtis_compute_weights()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::clenshaw_curtis_compute_weights ( int  order,
Scalar  w[] 
)
static

Clenshaw-Curtis; returns weights.

Definition at line 574 of file Intrepid_BurkardtRulesDef.hpp.

◆ fejer2_compute()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::fejer2_compute ( int  order,
Scalar  x[],
Scalar  w[] 
)
static

Fejer type 2; returns points and weights.

Definition at line 653 of file Intrepid_BurkardtRulesDef.hpp.

◆ fejer2_compute_points()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::fejer2_compute_points ( int  order,
Scalar  x[] 
)
static

Fejer type 2; returns points.

Definition at line 734 of file Intrepid_BurkardtRulesDef.hpp.

◆ fejer2_compute_weights()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::fejer2_compute_weights ( int  order,
Scalar  w[] 
)
static

Fejer type 2; returns weights.

Definition at line 791 of file Intrepid_BurkardtRulesDef.hpp.

◆ hermite_compute()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::hermite_compute ( int  order,
Scalar  x[],
Scalar  w[] 
)
static

Gauss-Hermite; returns points and weights.

Definition at line 877 of file Intrepid_BurkardtRulesDef.hpp.

Referenced by hermite_compute_points(), and hermite_compute_weights().

◆ hermite_compute_points()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::hermite_compute_points ( int  order,
Scalar  x[] 
)
static

Gauss-Hermite; returns points.

Definition at line 972 of file Intrepid_BurkardtRulesDef.hpp.

References hermite_compute().

◆ hermite_compute_weights()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::hermite_compute_weights ( int  order,
Scalar  w[] 
)
static

Gauss-Hermite; returns weights.

Definition at line 1007 of file Intrepid_BurkardtRulesDef.hpp.

References hermite_compute().

◆ hermite_genz_keister_lookup()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::hermite_genz_keister_lookup ( int  n,
Scalar  x[],
Scalar  w[] 
)
static

Hermite-Genz-Keister; returns points and weights.

Definition at line 1042 of file Intrepid_BurkardtRulesDef.hpp.

References hermite_genz_keister_lookup_points(), and hermite_genz_keister_lookup_weights().

◆ hermite_genz_keister_lookup_points()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::hermite_genz_keister_lookup_points ( int  n,
Scalar  x[] 
)
static

Hermite-Genz-Keister; returns points.

Definition at line 1114 of file Intrepid_BurkardtRulesDef.hpp.

Referenced by hermite_genz_keister_lookup().

◆ hermite_genz_keister_lookup_weights()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::hermite_genz_keister_lookup_weights ( int  n,
Scalar  w[] 
)
static

Hermite-Genz-Keister; returns weights.

Definition at line 1405 of file Intrepid_BurkardtRulesDef.hpp.

Referenced by hermite_genz_keister_lookup().

◆ hermite_lookup()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::hermite_lookup ( int  n,
Scalar  x[],
Scalar  w[] 
)
static

Gauss-Hermite; returns points and weights.

Definition at line 1696 of file Intrepid_BurkardtRulesDef.hpp.

References hermite_lookup_points(), and hermite_lookup_weights().

◆ hermite_lookup_points()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::hermite_lookup_points ( int  n,
Scalar  x[] 
)
static

Gauss-Hermite; returns points.

Definition at line 1766 of file Intrepid_BurkardtRulesDef.hpp.

Referenced by hermite_lookup().

◆ hermite_lookup_weights()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::hermite_lookup_weights ( int  n,
Scalar  w[] 
)
static

Gauss-Hermite; returns weights.

Definition at line 2104 of file Intrepid_BurkardtRulesDef.hpp.

Referenced by hermite_lookup().

◆ imtqlx()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::imtqlx ( int  n,
Scalar  d[],
Scalar  e[],
Scalar  z[] 
)
static

Definition at line 2442 of file Intrepid_BurkardtRulesDef.hpp.

◆ laguerre_compute()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::laguerre_compute ( int  n,
Scalar  x[],
Scalar  w[] 
)
static

Gauss-Laguerre; returns points and weights.

Definition at line 2605 of file Intrepid_BurkardtRulesDef.hpp.

Referenced by laguerre_compute_points(), and laguerre_compute_weights().

◆ laguerre_compute_points()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::laguerre_compute_points ( int  order,
Scalar  x[] 
)
static

Gauss-Laguerre; returns points.

Definition at line 2683 of file Intrepid_BurkardtRulesDef.hpp.

References laguerre_compute().

◆ laguerre_compute_weights()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::laguerre_compute_weights ( int  order,
Scalar  w[] 
)
static

Gauss-Laguerre; returns weights.

Definition at line 2718 of file Intrepid_BurkardtRulesDef.hpp.

References laguerre_compute().

◆ laguerre_lookup()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::laguerre_lookup ( int  n,
Scalar  x[],
Scalar  w[] 
)
static

Gauss-Laguerre; returns points and weights.

Definition at line 2753 of file Intrepid_BurkardtRulesDef.hpp.

References laguerre_lookup_points(), and laguerre_lookup_weights().

◆ laguerre_lookup_points()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::laguerre_lookup_points ( int  n,
Scalar  x[] 
)
static

Gauss-Laguerre; returns points.

Definition at line 2847 of file Intrepid_BurkardtRulesDef.hpp.

Referenced by laguerre_lookup().

◆ laguerre_lookup_weights()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::laguerre_lookup_weights ( int  n,
Scalar  w[] 
)
static

Gauss-Laguerre; returns weights.

Definition at line 3169 of file Intrepid_BurkardtRulesDef.hpp.

Referenced by laguerre_lookup().

◆ legendre_compute()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::legendre_compute ( int  n,
Scalar  x[],
Scalar  w[] 
)
static

Gauss-Legendre; returns points and weights.

Definition at line 3491 of file Intrepid_BurkardtRulesDef.hpp.

Referenced by legendre_compute_points(), and legendre_compute_weights().

◆ legendre_compute_points()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::legendre_compute_points ( int  order,
Scalar  x[] 
)
static

Gauss-Legendre; returns points.

Definition at line 3576 of file Intrepid_BurkardtRulesDef.hpp.

References legendre_compute().

◆ legendre_compute_weights()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::legendre_compute_weights ( int  order,
Scalar  w[] 
)
static

Gauss-Legendre; returns weights.

Definition at line 3611 of file Intrepid_BurkardtRulesDef.hpp.

References legendre_compute().

◆ legendre_lookup()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::legendre_lookup ( int  n,
Scalar  x[],
Scalar  w[] 
)
static

Gauss-Legendre; returns points and weights.

Definition at line 3646 of file Intrepid_BurkardtRulesDef.hpp.

References legendre_lookup_points(), and legendre_lookup_weights().

◆ legendre_lookup_points()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::legendre_lookup_points ( int  n,
Scalar  x[] 
)
static

Gauss-Legendre; returns points.

Definition at line 3716 of file Intrepid_BurkardtRulesDef.hpp.

Referenced by legendre_lookup().

◆ legendre_lookup_weights()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::legendre_lookup_weights ( int  n,
Scalar  w[] 
)
static

Gauss-Legendre; returns weights.

Definition at line 4415 of file Intrepid_BurkardtRulesDef.hpp.

Referenced by legendre_lookup().

◆ patterson_lookup()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::patterson_lookup ( int  n,
Scalar  x[],
Scalar  w[] 
)
static

Gauss-Patterson; returns points and weights.

Definition at line 5114 of file Intrepid_BurkardtRulesDef.hpp.

References patterson_lookup_points(), and patterson_lookup_weights().

◆ patterson_lookup_points()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::patterson_lookup_points ( int  n,
Scalar  x[] 
)
static

Gauss-Patterson; returns points.

Definition at line 5170 of file Intrepid_BurkardtRulesDef.hpp.

Referenced by patterson_lookup().

◆ patterson_lookup_weights()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::patterson_lookup_weights ( int  n,
Scalar  w[] 
)
static

Gauss-Patterson; returns weights.

Definition at line 5745 of file Intrepid_BurkardtRulesDef.hpp.

Referenced by patterson_lookup().

◆ r8_epsilon()

template<class Scalar >
Scalar Intrepid::IntrepidBurkardtRules::r8_epsilon ( Scalar  one)
static

Definition at line 6385 of file Intrepid_BurkardtRulesDef.hpp.

◆ r8_sign()

template<class Scalar >
Scalar Intrepid::IntrepidBurkardtRules::r8_sign ( Scalar  x)
static

Definition at line 6430 of file Intrepid_BurkardtRulesDef.hpp.

◆ trapezoidal_compute()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::trapezoidal_compute ( int  n,
Scalar  x[],
Scalar  w[] 
)
static

Trapezoidal rule; returns points and weights.

Definition at line 6322 of file Intrepid_BurkardtRulesDef.hpp.

◆ trapezoidal_compute_points()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::trapezoidal_compute_points ( int  order,
Scalar  x[] 
)
static

Trapezoidal rule; returns points.

Definition at line 6346 of file Intrepid_BurkardtRulesDef.hpp.

◆ trapezoidal_compute_weights()

template<class Scalar >
void Intrepid::IntrepidBurkardtRules::trapezoidal_compute_weights ( int  order,
Scalar  w[] 
)
static

Trapezoidal rule; returns weights.

Definition at line 6363 of file Intrepid_BurkardtRulesDef.hpp.


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