java.lang.Object
- pulse.math.LegendrePoly

All Implemented Interfaces:

Serializable
```
public class LegendrePoly
extends Object
implements Serializable
```
A utility class represents the Legendre polynomial of a given order.
May be useful in some applications, particularly, for calculating the ordinate sets in the discrete ordinates method. Allows calculating its coefficients, the value of the polynomial and its derivative at a given point, and the roots of the polynomial (with the help of a LaguerreSolver.

See Also:

LaguerreSolver, Wiki page, Serialized Form

Constructor Summary

Constructors
Constructor Description

LegendrePoly(int n)
Creates a Legendre polynomial of the order n.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`static long`	`binomial(int m, int k)`	Fast calculation of binomial coefficient C_m^k = m!/(k!(m-k)!)
`void`	`coefficients()`	This will generate the coefficients for the Legendre polynomial, arranged in order of significance (from x⁰ to xⁿ).
`double`	`derivative(double x)`	Calculates the derivative of this Legendre polynomial.
`static double`	`generalisedBinomial(double alpha, int k)`	Calculates the generalised binomial coefficient.
`int`	`getOrder()`
`double`	`poly(double x)`	Calculates the value of this Legendre polynomial at `x`
`double[]`	`roots()`	Uses a `LaguerreSolver` to calculate the roots of this polynomial.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - LegendrePoly
```
public LegendrePoly(int n)
```
    Creates a Legendre polynomial of the order n. The coefficients of the polynomial are immediately calculated.
    
    Parameters:
    
    n - the order of the polynomial.
- Method Detail
  - binomial
```
public static long binomial(int m,
                            int k)
```
    Fast calculation of binomial coefficient C_m^k = m!/(k!(m-k)!)
    
    Parameters:
    
    m - integer.
    
    k - integer, k ≤ m.
    
    Returns:
    
    binomial coefficient C_m^k.
  - generalisedBinomial
```
public static double generalisedBinomial(double alpha,
                                         int k)
```
    Calculates the generalised binomial coefficient.
    
    Parameters:
    
    k - integer.
    
    alpha - a double value
    
    Returns:
    
    the generalised binomial coefficient C_α^k.
  - coefficients
```
public void coefficients()
```
    This will generate the coefficients for the Legendre polynomial, arranged in order of significance (from x⁰ to xⁿ). The coeffients will then be stored in a double array for further use.
  - derivative
```
public double derivative(double x)
```
    Calculates the derivative of this Legendre polynomial. The coefficients are assumed to be known.
    
    Parameters:
    
    x - a real value.
    
    Returns:
    
    the derivative at x.
  - getOrder
```
public int getOrder()
```
    Returns:
    
    the order of this polynomial.
  - poly
```
public double poly(double x)
```
    Calculates the value of this Legendre polynomial at x
    
    Parameters:
    
    x - a real value.
    
    Returns:
    
    the value of the Legendre polynomial at x.
  - roots
```
public double[] roots()
```
    Uses a LaguerreSolver to calculate the roots of this polynomial. All coefficients are assumed to be known.
    
    Returns:
    
    the real roots of the Legendre polynomial.

Class LegendrePoly

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

LegendrePoly

Method Detail

binomial

generalisedBinomial

coefficients

derivative

getOrder

poly

roots