NAME

sc::LebedevLaikovIntegrator - An implementation of a Lebedev angular integrator.

SYNOPSIS

#include <integrator.h>

Inherits sc::AngularIntegrator.

Public Member Functions

LebedevLaikovIntegrator (const Ref< KeyVal > &)
Construct a LebedevLaikovIntegrator using the given KeyVal input. LebedevLaikovIntegrator (StateIn &)
LebedevLaikovIntegrator (int)
void save_data_state (StateOut &)
Save the base classes (with save_data_state) and the members in the same order that the StateIn CTOR initializes them. int nw (void) const
int num_angular_points (double r_value, int ir)
double angular_point_cartesian (int iangular, double r, SCVector3 &integration_point) const
void print (std::ostream &=ExEnv::out0()) const
Print the object.

Public Member Functions inherited from sc::AngularIntegrator
AngularIntegrator (const Ref< KeyVal > &)
AngularIntegrator (StateIn &)
void save_data_state (StateOut &)
Save the base classes (with save_data_state) and the members in the same order that the StateIn CTOR initializes them. virtual int nw (void) const =0
virtual int num_angular_points (double r_value, int ir)=0
virtual double angular_point_cartesian (int iangular, double r, SCVector3 &integration_point) const =0

Public Member Functions inherited from sc::SavableState
SavableState & operator= (const SavableState &)
void save_state (StateOut &)
Save the state of the object as specified by the StateOut object. void save_object_state (StateOut &)
This can be used for saving state when the exact type of the object is known for both the save and the restore. virtual void save_vbase_state (StateOut &)
Save the virtual bases for the object. virtual void save_data_state (StateOut &)
Save the base classes (with save_data_state) and the members in the same order that the StateIn CTOR initializes them.

Public Member Functions inherited from sc::DescribedClass
DescribedClass (const DescribedClass &)
DescribedClass & operator= (const DescribedClass &)
ClassDesc * class_desc () const throw ()
This returns the unique pointer to the ClassDesc corresponding to the given type_info object. const char * class_name () const
Return the name of the object's exact type. int class_version () const
Return the version of the class. virtual void print (std::ostream &=ExEnv::out0()) const
Print the object.

Public Member Functions inherited from sc::RefCount
int lock_ptr () const
Lock this object. int unlock_ptr () const
Unlock this object. void use_locks (bool inVal)
start and stop using locks on this object refcount_t nreference () const
Return the reference count. refcount_t reference ()
Increment the reference count and return the new count. refcount_t dereference ()
Decrement the reference count and return the new count. int managed () const
void unmanage ()
Turn off the reference counting mechanism for this object. int managed () const
Return 1 if the object is managed. Otherwise return 0.

Public Member Functions inherited from sc::Identity
Identifier identifier ()
Return the Identifier for this argument.

Protected Member Functions

void init (int n)

Protected Member Functions inherited from sc::SavableState
SavableState (const SavableState &)
SavableState (StateIn &)
Each derived class StateIn CTOR handles the restore corresponding to calling save_object_state, save_vbase_state, and save_data_state listed above.

Protected Member Functions inherited from sc::RefCount
RefCount (const RefCount &)
RefCount & operator= (const RefCount &)

Protected Attributes

int npoint_
double * x_
double * y_
double * z_
double * w_

Additional Inherited Members

Static Public Member Functions inherited from sc::SavableState
static void save_state (SavableState *s, StateOut &)
static SavableState * restore_state (StateIn &si)
Restores objects saved with save_state. static SavableState * key_restore_state (StateIn &si, const char *keyword)
Like restore_state, but keyword is used to override values while restoring. static SavableState * dir_restore_state (StateIn &si, const char *objectname, const char *keyword=0)

Detailed Description

An implementation of a Lebedev angular integrator.

It uses code written by Dr. Dmitri N. Laikov.

This can generate grids with the following numbers of points: 6, 14, 26, 38, 50, 74, 86, 110, 146, 170, 194, 230, 266, 302, 350, 386, 434, 482, 530, 590, 650, 698, 770, 830, 890, 974, 1046, 1118, 1202, 1274, 1358, 1454, 1538, 1622, 1730, 1814, 1910, 2030, 2126, 2222, 2354, 2450, 2558, 2702, 2810, 2930, 3074, 3182, 3314, 3470, 3590, 3722, 3890, 4010, 4154, 4334, 4466, 4610, 4802, 4934, 5090, 5294, 5438, 5606, and 5810.

V.I. Lebedev, and D.N. Laikov 'A quadrature formula for the sphere of the 131st
algebraic order of accuracy' Doklady Mathematics, Vol. 59, No. 3, 1999, pp. 477-481.

V.I. Lebedev 'A quadrature formula for the sphere of 59th algebraic
order of accuracy' Russian Acad. Sci. Dokl. Math., Vol. 50, 1995, pp. 283-286.

V.I. Lebedev, and A.L. Skorokhodov 'Quadrature formulas of orders 41, 47, and 53 for the sphere' Russian Acad. Sci. Dokl. Math., Vol. 45, 1992, pp. 587-592.

V.I. Lebedev 'Spherical quadrature formulas exact to orders 25-29' Siberian Mathematical Journal, Vol. 18, 1977, pp. 99-107.

V.I. Lebedev 'Quadratures on a sphere' Computational Mathematics and Mathematical Physics, Vol. 16, 1976, pp. 10-24.

V.I. Lebedev 'Values of the nodes and weights of ninth to seventeenth
order Gauss-Markov quadrature formulae invariant under the
octahedron group with inversion' Computational Mathematics and Mathematical Physics, Vol. 15, 1975, pp. 44-51.

Constructor & Destructor Documentation

sc::LebedevLaikovIntegrator::LebedevLaikovIntegrator (const Ref< KeyVal > &)

Construct a LebedevLaikovIntegrator using the given KeyVal input. The n keyword gives the number of angular points. The default is 302.

Member Function Documentation

double sc::LebedevLaikovIntegrator::angular_point_cartesian (int iangular, double r, SCVector3 & integration_point) const [virtual]

Implements sc::AngularIntegrator.

Author

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