JSci.maths.polynomials
Class RealLagrangeBasis

java.lang.Object
  JSci.maths.polynomials.RealLagrangeBasis

All Implemented Interfaces:

PolynomialBasis

Direct Known Subclasses:

ChebychevBasis

public class RealLagrangeBasis
extends java.lang.Object
implements PolynomialBasis

The Lagrange Basis for real polynomials. For a given set of sampling points {x_1, ..., x_n}, the corresponding Lagrange polynomials are L_k = \kronecker_kj \forall j=1..n. The explicit form is L_k= \prod_{j=0, j\neq k}^n \frac{t-t_j}{t_k-t_j}

Field Summary

protected int	_dim
protected double[]	_samplingsX

Constructor Summary

protected	RealLagrangeBasis()
	RealLagrangeBasis(double[] samplings) Creates a new RealLagrangeBasis object.
	RealLagrangeBasis(Field.Member[] samplings) Creates a new instance of LagrangeBasis for given sampling points

Method Summary

protected void	buildBasis()
int	dimension() The dimension ( # of sampling points)
Polynomial	getBasisVector(int k) The basis vector as described above
Field.Member[]	getSamplingPoints() The sampling points used in constructor
RealPolynomial	superposition(double[] c) Same as above, but type-safe.
Polynomial	superposition(Field.Member[] coeff) Make a superposition of basis-vectors for a given set of coefficients.

Methods inherited from class java.lang.Object

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

Field Detail

_samplingsX

protected double[] _samplingsX

_dim

protected int _dim

Constructor Detail

RealLagrangeBasis

public RealLagrangeBasis(Field.Member[] samplings)

Creates a new instance of LagrangeBasis for given sampling points

RealLagrangeBasis

public RealLagrangeBasis(double[] samplings)

Creates a new RealLagrangeBasis object.

Parameters:

samplings -

RealLagrangeBasis

protected RealLagrangeBasis()

Method Detail

getBasisVector

public Polynomial getBasisVector(int k)

The basis vector as described above

Specified by:

getBasisVector in interface PolynomialBasis

Parameters:

k -

dimension

public int dimension()

The dimension ( # of sampling points)

Specified by:

dimension in interface PolynomialBasis

Returns:

the dimension

getSamplingPoints

public Field.Member[] getSamplingPoints()

The sampling points used in constructor

Specified by:

getSamplingPoints in interface PolynomialBasis

Returns:

the sampling points

superposition

public Polynomial superposition(Field.Member[] coeff)

Make a superposition of basis-vectors for a given set of coefficients. Due to the properties of a lagrange base, the result is the interpolating polynomial with values coeff[k] at sampling point k

Specified by:

superposition in interface PolynomialBasis

Parameters:

coeff - in this case the values of the interpolation problem

Returns:

the interpolating polynomial

superposition

public RealPolynomial superposition(double[] c)

Same as above, but type-safe.

buildBasis

protected void buildBasis()