org.hipparchus.analysis.interpolation

Class HermiteInterpolator

java.lang.Object

org.hipparchus.analysis.interpolation.HermiteInterpolator

All Implemented Interfaces:

UnivariateDifferentiableVectorFunction, UnivariateVectorFunction

public class HermiteInterpolator
extends Object
implements UnivariateDifferentiableVectorFunction

Polynomial interpolator using both sample values and sample derivatives.

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 polynomials 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.

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[][]	derivatives(double x, int order) Interpolate value and first derivatives at a specified abscissa.
PolynomialFunction[]	getPolynomials() Compute the interpolation polynomials.
double[]	value(double x) Interpolate value at a specified abscissa.
<T extends Derivative<T>> T[]	value(T x) Compute the value for the function.

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)
                    throws MathIllegalArgumentException,
                           MathRuntimeException

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:

MathIllegalArgumentException - if the abscissa difference between added point and a previous point is zero (i.e. the two points are at same abscissa)

MathRuntimeException - if the number of derivatives is larger than 20, which prevents computation of a factorial

getPolynomials

public PolynomialFunction[] getPolynomials()
                                    throws MathIllegalArgumentException

Compute the interpolation polynomials.

Returns:

interpolation polynomials array

Throws:

MathIllegalArgumentException - if sample is empty

value

public double[] value(double x)
               throws MathIllegalArgumentException

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:

MathIllegalArgumentException - if sample is empty

value

public <T extends Derivative<T>> T[] value(T x)
                                    throws MathIllegalArgumentException

Compute the value for the function..

Specified by:

value in interface UnivariateDifferentiableVectorFunction

Type Parameters:

T - the type of the field elements

Parameters:

x - the point for which the function value should be computed

Returns:

the value

Throws:

MathIllegalArgumentException - if x does not satisfy the function's constraints (argument out of bound, or unsupported derivative order for example)

derivatives

public double[][] derivatives(double x,
                              int order)
                       throws MathIllegalArgumentException,
                              NullArgumentException

Interpolate value and first derivatives at a specified abscissa.

Parameters:

x - interpolation abscissa

order - maximum derivation order

Returns:

interpolated value and derivatives (value in row 0, 1^st derivative in row 1, ... n^th derivative in row n)

Throws:

MathIllegalArgumentException - if sample is empty

NullArgumentException - if x is null