fr.cnes.sirius.patrius.math.analysis.polynomials

Class HelmholtzPolynomial

java.lang.Object

fr.cnes.sirius.patrius.math.analysis.polynomials.HelmholtzPolynomial

public final class HelmholtzPolynomial
extends Object

This class represents Helmholtz polynomial.

Since:

3.1.2

Version:

$Id: HelmholtzPolynomial.java 18108 2017-10-04 06:45:27Z bignon $

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and Description
protected void	computeConstantCoefficients() Calculate the constant coefficients of the polynomial as per ph(m,m) = MathLib.sqrt(1 + 1/2m) * ph(m-1,m-1) dpph(m+1,m) = MathLib.sqrt(2m+3) * ph(m,m) alpha(l,m) = MathLib.sqrt( (2l+1)*(2l-1) / (l-m)*(l+m) ) for l >= m + 1 = MathLib.sqrt( (2l+1)*(2l-1) ) for l = m The a(l,m) are represents as a unidimentional tab.
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)        = MathLib.sqrt(1 + 1/2m) * ph(m-1,m-1)
 dpph(m+1,m)    = MathLib.sqrt(2m+3) * ph(m,m)
 alpha(l,m)     = MathLib.sqrt( (2l+1)*(2l-1) / (l-m)*(l+m) )        for l >= m + 1
                = MathLib.sqrt( (2l+1)*(2l-1) )                      for l = m
 

The a(l,m) are represents as a unidimentional tab. The dimension of this tab is:

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

For a pair l,m given, we have:

 a(l, m) = aph(i)
 

with i :

 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)     = MathLib.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