fr.cnes.sirius.patrius.math.quadrature

Class LebedevRule

java.lang.Object

fr.cnes.sirius.patrius.math.quadrature.LebedevRule

public final class LebedevRule
extends Object

Static class for the generation of Lebedev rule's grid points for a given order, for an approximation to the surface integral of a function over a three-dimensional sphere.
The grid is constructed so to have octahedral rotation and inversion symmetry. The number and location of the grid points together with a corresponding set of integration weights are determined by enforcing the exact integration of polynomials (or equivalently, spherical harmonics) up to a given order, leading to a sequence of increasingly dense grids analogous to the one-dimensional Gauss-Legendre scheme.

Routines adapted from C++. Original routines written by Vyacheslav Ivanovich Lebedev, Dmitri Laikov and John Burkardt under the GNU LGPL license. (see sphere_lebedev_rule.html)

Reference:
Vyacheslav Lebedev, Dmitri Laikov,
A quadrature formula for the sphere of the 131st algebraic order of accuracy,
Russian Academy of Sciences Doklady Mathematics,
Volume 59, Number 3, 1999, pages 477-481.

Author:

GMV

Field Summary

Fields

Modifier and Type	Field and Description
static int	MAX_RULE Max number of defined rules (about half of them are available).

Method Summary

Methods

Modifier and Type	Method and Description
static List<LebedevGridPoint>	createGridByOrder(int order) Returns a Lebedev angular grid given its order. Discussion: Only a certain set of such rules are available through this function, as given by if(isRuleAvailable(rule) > 0) order = getRuleOrder(rule).
static List<LebedevGridPoint>	createGridForRule(int rule) Returns a Lebedev angular grid for given rule.
static int	getRuleOrder(int rule) Returns the order of a Lebedev rule. Original author: John Burkardt (11 September 2010)
static int	getRulePrecision(int rule) Returns the precision of a Lebedev rule. Original author: John Burkardt (11 September 2010)
static int	isRuleAvailable(int rule) Returns the availability of a Lebedev rule. Original author: John Burkardt (12 September 2010)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

MAX_RULE

public static final int MAX_RULE

Max number of defined rules (about half of them are available).

See Also:

Constant Field Values

Method Detail

createGridForRule

public static List<LebedevGridPoint> createGridForRule(int rule)

Returns a Lebedev angular grid for given rule.

Parameters:

rule - the index of the rule, between 1 and 65.

Returns:

the Lebedev grid points, if rule is valid and available (null otherwise)

createGridByOrder

public static List<LebedevGridPoint> createGridByOrder(int order)

Returns a Lebedev angular grid given its order.

Discussion:
Only a certain set of such rules are available through this function, as given by if(isRuleAvailable(rule) > 0) order = getRuleOrder(rule).

Original author:
Dmitri Laikov (13 September 2010)

Available orders are : 6 14 26 38 50 74 86 110 146 170 194 230 266 302 350 434 590 770 974 1202 1454 1730 2030 2354 2702 3074 3470 3890 4334 4802 5294 5810

Parameters:

order - the order of the rule

Returns:

A list of grid points, each containing the coordinates and weight of the point. The number of grid points is the order given as input.

Throws:

IllegalStateException - if not a valid and available order

isRuleAvailable

public static int isRuleAvailable(int rule)

Returns the availability of a Lebedev rule.

Original author:
John Burkardt (12 September 2010)

Parameters:

rule - the index of the rule, between 1 and 65.

Returns:

The availability of the rule:

• -1, there is no such rule;
• 0, there is such a rule, but it is not available in this library.
• 1, the rule is available in this library.

getRuleOrder

public static int getRuleOrder(int rule)

Returns the order of a Lebedev rule.

Original author:
John Burkardt (11 September 2010)

Parameters:

rule - The index of the rule, between 1 and 65.

Returns:

The order of the rule.

getRulePrecision

public static int getRulePrecision(int rule)

Returns the precision of a Lebedev rule.

Original author:
John Burkardt (11 September 2010)

Parameters:

rule - The index of the rule, between 1 and 65.

Returns:

The precision of the rule = (1 + 2*rule).