---
name: "sc_LebedevLaikovIntegrator"
section: "3"
platform: "linux"
package: "libsc-doc"
version: "2.3.1-22"
release: "Debian 12 (Bookworm)"
platforms: ["linux"]
url: "https://new.carta.tech/sc_LebedevLaikovIntegrator"
---

# sc\_LebedevLaikovIntegrator(3)

An implementation of a Lebedev angular integrator.

## 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.

### Protected Member Functions

void **init** (int n)\

### Protected Attributes

int **npoint\_**\
 double \* **x\_**\
 double \* **y\_**\
 double \* **z\_**\
 double \* **w\_**\

### Additional Inherited Members

## 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**.

### int sc::LebedevLaikovIntegrator::num\_angular\_points (double r\_value, int ir)` [virtual]`

Implements **sc::AngularIntegrator**.

### int sc::LebedevLaikovIntegrator::nw (void) const` [virtual]`

Implements **sc::AngularIntegrator**.

### void sc::LebedevLaikovIntegrator::print (std::ostream & = ExEnv::out0`()`) const` [virtual]`

Print the object.

Reimplemented from **sc::DescribedClass**.

### void sc::LebedevLaikovIntegrator::save\_data\_state (StateOut &)` [virtual]`

Save the base classes (with save\_data\_state) and the members in the same order that the **StateIn** CTOR initializes them. This must be implemented by the derived class if the class has data.

Reimplemented from **sc::AngularIntegrator**.

## Author

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