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## org.apache.commons.math.analysis.polynomials
Class PolynomialsUtils

    java.lang.Object
      org.apache.commons.math.analysis.polynomials.PolynomialsUtils

    public class PolynomialsUtils

extends Object

A collection of static methods that operate on or return polynomials.

Since:
  2.0
Version:
  $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 août 2010) $

Nested Class Summary
`private static interface` | `PolynomialsUtils.RecurrenceCoefficientsGenerator` Interface for recurrence coefficients generation.

Field Summary
`private static ArrayList<BigFraction>` | `CHEBYSHEV_COEFFICIENTS` Coefficients for Chebyshev polynomials.
`private static ArrayList<BigFraction>` | `HERMITE_COEFFICIENTS` Coefficients for Hermite polynomials.
`private static ArrayList<BigFraction>` | `LAGUERRE_COEFFICIENTS` Coefficients for Laguerre polynomials.
`private static ArrayList<BigFraction>` | `LEGENDRE_COEFFICIENTS` Coefficients for Legendre polynomials.

Constructor Summary
`private` | `PolynomialsUtils()` Private constructor, to prevent instantiation.

Method Summary
`private static PolynomialFunction` | `buildPolynomial(int degree, ArrayList<BigFraction> coefficients, PolynomialsUtils.RecurrenceCoefficientsGenerator generator)` Get the coefficients array for a given degree.
`private static void` | `computeUpToDegree(int degree, int maxDegree, PolynomialsUtils.RecurrenceCoefficientsGenerator generator, ArrayList<BigFraction> coefficients)` Compute polynomial coefficients up to a given degree.
`static PolynomialFunction` | `createChebyshevPolynomial(int degree)` Create a Chebyshev polynomial of the first kind.
`static PolynomialFunction` | `createHermitePolynomial(int degree)` Create a Hermite polynomial.
`static PolynomialFunction` | `createLaguerrePolynomial(int degree)` Create a Laguerre polynomial.
`static PolynomialFunction` | `createLegendrePolynomial(int degree)` Create a Legendre polynomial.

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

Field Detail

### CHEBYSHEV_COEFFICIENTS

    private static final ArrayList<BigFraction> CHEBYSHEV_COEFFICIENTS

  Coefficients for Chebyshev polynomials.

### HERMITE_COEFFICIENTS

    private static final ArrayList<BigFraction> HERMITE_COEFFICIENTS

  Coefficients for Hermite polynomials.

### LAGUERRE_COEFFICIENTS

    private static final ArrayList<BigFraction> LAGUERRE_COEFFICIENTS

  Coefficients for Laguerre polynomials.

### LEGENDRE_COEFFICIENTS

    private static final ArrayList<BigFraction> LEGENDRE_COEFFICIENTS

  Coefficients for Legendre polynomials.

Constructor Detail

### PolynomialsUtils

    private PolynomialsUtils()

  Private constructor, to prevent instantiation.

Method Detail

### createChebyshevPolynomial

    public static PolynomialFunction createChebyshevPolynomial(int degree)

  Create a Chebyshev polynomial of the first kind.

  Chebyshev polynomials of the first kind are orthogonal polynomials. They can be defined by the following recurrence relations:

        T0(X)   = 1
        T1(X)   = X
        Tk+1(X) = 2X Tk(X) - Tk-1(X)

  Parameters:
    `degree` - degree of the polynomial
  Returns:
    Chebyshev polynomial of specified degree

### createHermitePolynomial

    public static PolynomialFunction createHermitePolynomial(int degree)

  Create a Hermite polynomial.

  Hermite polynomials are orthogonal polynomials. They can be defined by the following recurrence relations:

        H0(X)   = 1
        H1(X)   = 2X
        Hk+1(X) = 2X Hk(X) - 2k Hk-1(X)

  Parameters:
    `degree` - degree of the polynomial
  Returns:
    Hermite polynomial of specified degree

### createLaguerrePolynomial

    public static PolynomialFunction createLaguerrePolynomial(int degree)

  Create a Laguerre polynomial.

  Laguerre polynomials are orthogonal polynomials. They can be defined by the following recurrence relations:

              L0(X)   = 1
              L1(X)   = 1 - X
        (k+1) Lk+1(X) = (2k + 1 - X) Lk(X) - k Lk-1(X)

  Parameters:
    `degree` - degree of the polynomial
  Returns:
    Laguerre polynomial of specified degree

### createLegendrePolynomial

    public static PolynomialFunction createLegendrePolynomial(int degree)

  Create a Legendre polynomial.

  Legendre polynomials are orthogonal polynomials. They can be defined by the following recurrence relations:

              P0(X)   = 1
              P1(X)   = X
        (k+1) Pk+1(X) = (2k+1) X Pk(X) - k Pk-1(X)

  Parameters:
    `degree` - degree of the polynomial
  Returns:
    Legendre polynomial of specified degree

### buildPolynomial

    private static PolynomialFunction buildPolynomial(int degree,
                                                      ArrayList<BigFraction> coefficients,
                                                      PolynomialsUtils.RecurrenceCoefficientsGenerator generator)

  Get the coefficients array for a given degree.

  Parameters:
    `degree` - degree of the polynomial
    `coefficients` - list where the computed coefficients are stored
    `generator` - recurrence coefficients generator
  Returns:
    coefficients array

### computeUpToDegree

    private static void computeUpToDegree(int degree,
                                          int maxDegree,
                                          PolynomialsUtils.RecurrenceCoefficientsGenerator generator,
                                          ArrayList<BigFraction> coefficients)

  Compute polynomial coefficients up to a given degree.

  Parameters:
    `degree` - maximal degree
    `maxDegree` - current maximal degree
    `generator` - recurrence coefficients generator
    `coefficients` - list where the computed coefficients should be appended

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