Class HermiteInterpolator
- java.lang.Object
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- org.apache.commons.math3.analysis.interpolation.HermiteInterpolator
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- All Implemented Interfaces:
UnivariateDifferentiableVectorFunction
,UnivariateVectorFunction
public class HermiteInterpolator extends java.lang.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.
- Since:
- 3.1
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Field Summary
Fields Modifier and Type Field Description private java.util.List<java.lang.Double>
abscissae
Sample abscissae.private java.util.List<double[]>
bottomDiagonal
Bottom diagonal of the divided differences array.private java.util.List<double[]>
topDiagonal
Top diagonal of the divided differences array.
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Constructor Summary
Constructors Constructor Description HermiteInterpolator()
Create an empty interpolator.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description void
addSamplePoint(double x, double[]... value)
Add a sample point.private void
checkInterpolation()
Check interpolation can be performed.PolynomialFunction[]
getPolynomials()
Compute the interpolation polynomials.private PolynomialFunction
polynomial(double... c)
Create a polynomial from its coefficients.double[]
value(double x)
Interpolate value at a specified abscissa.DerivativeStructure[]
value(DerivativeStructure x)
Interpolate value at a specified abscissa.
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Field Detail
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abscissae
private final java.util.List<java.lang.Double> abscissae
Sample abscissae.
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topDiagonal
private final java.util.List<double[]> topDiagonal
Top diagonal of the divided differences array.
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bottomDiagonal
private final java.util.List<double[]> bottomDiagonal
Bottom diagonal of the divided differences array.
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Method Detail
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addSamplePoint
public void addSamplePoint(double x, double[]... value) throws ZeroException, MathArithmeticException
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 pointvalue
- 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:
ZeroException
- if the abscissa difference between added point and a previous point is zero (i.e. the two points are at same abscissa)MathArithmeticException
- if the number of derivatives is larger than 20, which prevents computation of a factorial
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getPolynomials
public PolynomialFunction[] getPolynomials() throws NoDataException
Compute the interpolation polynomials.- Returns:
- interpolation polynomials array
- Throws:
NoDataException
- if sample is empty
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value
public double[] value(double x) throws NoDataException
Interpolate value at a specified abscissa.Calling this method is equivalent to call the
value
methods of all polynomials returned bygetPolynomials
, except it does not build the intermediate polynomials, so this method is faster and numerically more stable.- Specified by:
value
in interfaceUnivariateVectorFunction
- Parameters:
x
- interpolation abscissa- Returns:
- interpolated value
- Throws:
NoDataException
- if sample is empty
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value
public DerivativeStructure[] value(DerivativeStructure x) throws NoDataException
Interpolate value at a specified abscissa.Calling this method is equivalent to call the
value
methods of all polynomials returned bygetPolynomials
, except it does not build the intermediate polynomials, so this method is faster and numerically more stable.- Specified by:
value
in interfaceUnivariateDifferentiableVectorFunction
- Parameters:
x
- interpolation abscissa- Returns:
- interpolated value
- Throws:
NoDataException
- if sample is empty
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checkInterpolation
private void checkInterpolation() throws NoDataException
Check interpolation can be performed.- Throws:
NoDataException
- if interpolation cannot be performed because sample is empty
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polynomial
private PolynomialFunction polynomial(double... c)
Create a polynomial from its coefficients.- Parameters:
c
- polynomials coefficients- Returns:
- polynomial
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