org.apache.commons.math3.analysis.polynomials
Class HelmholtzPolynomial

java.lang.Object
  org.apache.commons.math3.analysis.polynomials.HelmholtzPolynomial

public final class HelmholtzPolynomial
extends Object

This class represents Helmholtz polynomial.

Since:

3.1.2

Version:

$Id: HelmholtzPolynomial.java 17601 2017-05-18 07:27:52Z bignon $

Constructor Summary

HelmholtzPolynomial(int degree, int order)
Create a Helmholtz polynomial with given degree and order

Method Summary

protected void	computeConstantCoefficients() Calculate the constant coefficients of the polynomial as per
double	computeHelmholtzPolynomial(Vector3D point) Calculate the value of the polynomial in a given point.
double[][]	getDpph() Get the H'lm coefficients
double[][]	getDsph() Get the H''lm coefficients
double[][]	getPh() Get the Hlm coefficients

Methods inherited from class java.lang.Object

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

Constructor Detail

HelmholtzPolynomial

public HelmholtzPolynomial(int degree,
                           int order)

Create a Helmholtz polynomial with given degree and order

Parameters:

degree - max degree

order - max order

Method Detail

computeHelmholtzPolynomial

public double computeHelmholtzPolynomial(Vector3D point)

Calculate the value of the polynomial in a given point.

Parameters:

point - the given point

Returns:

value of polynomial

computeConstantCoefficients

protected void computeConstantCoefficients()

Calculate the constant coefficients of the polynomial as per

 ph(m,m)        = SQRT(1 + 1/2m) * ph(m-1,m-1)
 dpph(m+1,m)    = SQRT(2m+3) * ph(m,m)
 alpha(l,m)     = SQRT( (2l+1)*(2l-1) / (l-m)*(l+m) )        for l >= m + 1
                = SQRT( (2l+1)*(2l-1) )                      for l = m
 

On represente les a(l,m) sous la forme d'un tableau unidimentionnel. La dimension de ce tableau est:

 (lmax * (lmax + 1) - ((lmax + 1) - (mmax + 1)) *
         ((lmax + 1) - (mmax + 1) + 1)) / 2
 

Pour un couple l,m donne, on a:

 a(l, m) = aph(i)
 

avec i valant :

 i = (lmax * (lmax + 1) - ((lmax + 1) - m) *
         ((lmax + 1) - m + 1)) / 2 + (l - m) + 1
 

Initial conditions are :

 ph(0,0)     = 1.0
 ph(1,1)     = SQRT(3)
 

getPh

public double[][] getPh()

Get the Hlm coefficients

Returns:

the Hlm coefficients

getDpph

public double[][] getDpph()

Get the H'lm coefficients

Returns:

the H'lm coefficients

getDsph

public double[][] getDsph()

Get the H''lm coefficients

Returns:

the H''lm coefficients