fr.cnes.sirius.patrius.math.analysis.interpolation

Class HermiteInterpolator

java.lang.Object

fr.cnes.sirius.patrius.math.analysis.interpolation.HermiteInterpolator

All Implemented Interfaces:

UnivariateDifferentiableVectorFunction, UnivariateVectorFunction, Serializable

public class HermiteInterpolator
extends Object
implements UnivariateDifferentiableVectorFunction, Serializable

Polynomial interpolator using both sample values and sample derivatives.

WARNING: this class is not expected to remain in Orekit. It is provided by version 3.1 of Apache Commons Math. However, since as of writing (June 2012) this version is not released yet, Orekit depends on the latest official version 3.0 which does not provides this class. So despite it is implemented as a public class in Orekit so it can be used in from any package, it does not belong to Orekit public API and should not be used at application level. Once version 3.1 of Apache Commons Math is released, this class will be removed from Orekit.

The interpolation polynomials match all sample points, including both values and provided derivatives. There is one polynomial for each component of the values vector. All polynomial have the same degree. The degree of the polynomials depends on the number of points and number of derivatives at each point. For example the interpolation polynomials for n sample points without any derivatives all have degree n-1. The interpolation polynomials for n sample points with the two extreme points having value and first derivative and the remaining points having value only all have degree n+1. The interpolation polynomial for n sample points with value, first and second derivative for all points all have degree 3n-1.

Author:

Luc Maisonobe

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
HermiteInterpolator() Create an empty interpolator.

Method Summary

Modifier and Type	Method and Description
void	addSamplePoint(double x, double[]... value) Add a sample point.
double[]	derivative(double x) Interpolate first derivative at a specified abscissa.
PolynomialFunction[]	getPolynomials() Compute the interpolation polynomials.
int	getSize() Compute the size of the list of values of the function as created by the UnivariateVectorFunction.value(double) method
DerivativeStructure[]	value(DerivativeStructure x) Interpolate value at a specified abscissa.
double[]	value(double x) Interpolate value at a specified abscissa.
double[][]	valueAndDerivative(double x, boolean computeDoubleDerivative) Interpolate value, first and optionally second derivative at a specified abscissa.

Methods inherited from class java.lang.Object

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

Constructor Detail

HermiteInterpolator

public HermiteInterpolator()

Create an empty interpolator.

Method Detail

addSamplePoint

public void addSamplePoint(double x,
                           double[]... value)

Add a sample point.

This method must be called once for each sample point. It is allowed to mix some calls with values only with calls with values and first derivatives.

The point abscissae for all calls must be different.

Parameters:

x - abscissa of the sample point

value - value and derivatives of the sample point (if only one row is passed, it is the value, if two rows are passed the first one is the value and the second the derivative and so on)

Throws:

IllegalArgumentException - if the abscissa is equals to a previously added sample point

getPolynomials

public PolynomialFunction[] getPolynomials()

Compute the interpolation polynomials.

Returns:

interpolation polynomials array

Throws:

IllegalStateException - if sample is empty

value

public double[] value(double x)

Interpolate value at a specified abscissa.

Calling this method is equivalent to call the value methods of all polynomials returned by getPolynomials, except it does not build the intermediate polynomials, so this method is faster and numerically more stable.

Specified by:

value in interface UnivariateVectorFunction

Parameters:

x - interpolation abscissa

Returns:

interpolated value

Throws:

IllegalStateException - if sample is empty

derivative

public double[] derivative(double x)

Interpolate first derivative at a specified abscissa.

Calling this method is equivalent to call the value methods of the derivatives of all polynomials returned by getPolynomials, except it builds neither the intermediate polynomials nor their derivatives, so this method is faster and numerically more stable.

Parameters:

x - interpolation abscissa

Returns:

interpolated derivative

Throws:

IllegalStateException - if sample is empty

valueAndDerivative

public double[][] valueAndDerivative(double x,
                                     boolean computeDoubleDerivative)

Interpolate value, first and optionally second derivative at a specified abscissa.

Calling this method is equivalent to call the value(DerivativeStructure) method with a structure representing 2 derivatives but is faster since it does not use the generic operations of the DerivativeStructure that are slower.

Calling this method is equivalent to call the value method of the derivatives of all polynomials returned by getPolynomials, except it builds neither the intermediate polynomials nor their derivatives, so this method is faster and numerically more stable.

Parameters:

x - interpolation abscissa

computeDoubleDerivative - Indicates whether the second derivative should be computed

Returns:

interpolated value, derivative and optionally second derivative

Throws:

IllegalStateException - if sample is empty

value

public DerivativeStructure[] value(DerivativeStructure x)

Interpolate value at a specified abscissa.

Calling this method is equivalent to call the value methods of all polynomials returned by getPolynomials, except it does not build the intermediate polynomials, so this method is faster and numerically more stable.

Specified by:

value in interface UnivariateDifferentiableVectorFunction

Parameters:

x - interpolation abscissa

Returns:

interpolated value

Throws:

NoDataException - if sample is empty

getSize

public int getSize()

Compute the size of the list of values of the function as created by the UnivariateVectorFunction.value(double) method

Specified by:

getSize in interface UnivariateVectorFunction

Returns:

the size of the values array