org.jscience.mathematics.analysis.polynomials
Class PolynomialMathUtils

java.lang.Object
  org.jscience.mathematics.analysis.polynomials.PolynomialMathUtils

public final class PolynomialMathUtils
extends java.lang.Object

DOCUMENT ME!

Method Summary

static Complex	evalPolynomial(ComplexPolynomial p, Complex t) Evaluates a polynomial by Horner's scheme.
static double	evalPolynomial(DoublePolynomial p, double t) Evaluates a polynomial by Horner's scheme.
static ExactComplex	evalPolynomial(ExactComplexPolynomial p, ExactComplex t) Evaluates a polynomial by Horner's scheme.
static ExactReal	evalPolynomial(ExactRealPolynomial p, ExactReal t) Evaluates a polynomial by Horner's scheme.
static ComplexPolynomial	interpolateLagrange(Complex[][] samplingPoints) Interpolates a polynomial.
static DoublePolynomial	interpolateLagrange(double[][] samplingPoints) Interpolates a polynomial.
static int	maxDegree(Polynomial p1, Polynomial p2) Get the maximum degree of two polynomials
static int	minDegree(Polynomial p1, Polynomial p2) Get the minimal degree of two polynomials
static ComplexPolynomial	normalize(ComplexPolynomial p) Normalizes a given complex polynomial, i.e. divide by the leading coefficient.
static DoublePolynomial	normalize(DoublePolynomial p) Normalizes a given real polynomial, i.e. divide by the leading coefficient.
static ExactComplexPolynomial	normalize(ExactComplexPolynomial p) Normalize a given complex polynomial, i.e. divide by the leading coefficient.
static ExactRealPolynomial	normalize(ExactRealPolynomial p) Normalizes a given real polynomial, i.e. divide by the leading coefficient.
static AbstractComplexSquareMatrix	toCompanionMatrix(ComplexPolynomial p)
static AbstractDoubleSquareMatrix	toCompanionMatrix(DoublePolynomial p) Returns the companion matrix of a given polynomial.
static RingMatrix	toCompanionMatrix(ExactComplexPolynomial p)
static RingMatrix	toCompanionMatrix(ExactRealPolynomial p) Returns the companion matrix of a given polynomial.
static ComplexPolynomial	toComplex(Polynomial p) Try to cast a Polynomial to a complex polynomial
static ExactComplexPolynomial	toExactComplexPolynomial(Polynomial p) Try to cast a Polynomial to a complex polynomial

Methods inherited from class java.lang.Object

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

Method Detail

toCompanionMatrix

public static AbstractDoubleSquareMatrix toCompanionMatrix(DoublePolynomial p)

Returns the companion matrix of a given polynomial. The eigenvalues of the companion matrix are the roots of the polynomial.

Parameters:

p - the polynomial

Returns:

the companion matrix

toCompanionMatrix

public static RingMatrix toCompanionMatrix(ExactRealPolynomial p)

Returns the companion matrix of a given polynomial. The eigenvalues of the companion matrix are the roots of the polynomial.

Parameters:

p - the polynomial

Returns:

the companion matrix

toCompanionMatrix

public static AbstractComplexSquareMatrix toCompanionMatrix(ComplexPolynomial p)

toCompanionMatrix

public static RingMatrix toCompanionMatrix(ExactComplexPolynomial p)

maxDegree

public static int maxDegree(Polynomial p1,
                            Polynomial p2)

Get the maximum degree of two polynomials

Parameters:

p1 -

p2 -

minDegree

public static int minDegree(Polynomial p1,
                            Polynomial p2)

Get the minimal degree of two polynomials

Parameters:

p1 -

p2 -

evalPolynomial

public static double evalPolynomial(DoublePolynomial p,
                                    double t)

Evaluates a polynomial by Horner's scheme.

Parameters:

p -

t -

evalPolynomial

public static ExactReal evalPolynomial(ExactRealPolynomial p,
                                       ExactReal t)

Evaluates a polynomial by Horner's scheme.

Parameters:

p -

t -

evalPolynomial

public static Complex evalPolynomial(ComplexPolynomial p,
                                     Complex t)

Evaluates a polynomial by Horner's scheme.

Parameters:

p -

t -

evalPolynomial

public static ExactComplex evalPolynomial(ExactComplexPolynomial p,
                                          ExactComplex t)

Evaluates a polynomial by Horner's scheme.

Parameters:

p -

t -

interpolateLagrange

public static DoublePolynomial interpolateLagrange(double[][] samplingPoints)

Interpolates a polynomial. Caveat: this method is brute-force, slow and not very stable. It shouldn't be used for more than approx. 10 points. Remember the strong variations of higher degree polynomials.

Parameters:

samplingPoints - an array[2][n] where array[0] denotes x-values, array[1] y-values

interpolateLagrange

public static ComplexPolynomial interpolateLagrange(Complex[][] samplingPoints)

Interpolates a polynomial. Caveat: this method is brute-force, slow and not very stable. It shouldn't be used for more than approx. 10 points. Remember the strong variations of higher degree polynomials.

Parameters:

samplingPoints - an array[2][n] where array[0] denotes x-values, array[1] y-values

normalize

public static DoublePolynomial normalize(DoublePolynomial p)

Normalizes a given real polynomial, i.e. divide by the leading coefficient.

Parameters:

p -

normalize

public static ExactRealPolynomial normalize(ExactRealPolynomial p)

Normalizes a given real polynomial, i.e. divide by the leading coefficient.

Parameters:

p -

normalize

public static ComplexPolynomial normalize(ComplexPolynomial p)

Normalizes a given complex polynomial, i.e. divide by the leading coefficient.

Parameters:

p -

normalize

public static ExactComplexPolynomial normalize(ExactComplexPolynomial p)

Normalize a given complex polynomial, i.e. divide by the leading coefficient.

Parameters:

p -

Returns:

DOCUMENT ME!

toComplex

public static ComplexPolynomial toComplex(Polynomial p)

Try to cast a Polynomial to a complex polynomial

toExactComplexPolynomial

public static ExactComplexPolynomial toExactComplexPolynomial(Polynomial p)

Try to cast a Polynomial to a complex polynomial

Parameters:

p - DOCUMENT ME!

Returns:

DOCUMENT ME!

Throws:

java.lang.IllegalArgumentException - DOCUMENT ME!