Class AkimaSplineInterpolator
java.lang.Object
org.apache.commons.math3.analysis.interpolation.AkimaSplineInterpolator
- All Implemented Interfaces:
UnivariateInterpolator
Computes a cubic spline interpolation for the data set using the Akima
algorithm, as originally formulated by Hiroshi Akima in his 1970 paper
"A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures."
J. ACM 17, 4 (October 1970), 589-602. DOI=10.1145/321607.321609
http://doi.acm.org/10.1145/321607.321609
This implementation is based on the Akima implementation in the CubicSpline class in the Math.NET Numerics library. The method referenced is CubicSpline.InterpolateAkimaSorted
The interpolate
method returns a
PolynomialSplineFunction
consisting of n cubic polynomials, defined
over the subintervals determined by the x values, x[0] < x[i] ... < x[n]
.
The Akima algorithm requires that n >= 5
.
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Field Summary
FieldsModifier and TypeFieldDescriptionprivate static final int
The minimum number of points that are needed to compute the function. -
Constructor Summary
Constructors -
Method Summary
Modifier and TypeMethodDescriptionprivate double
differentiateThreePoint
(double[] xvals, double[] yvals, int indexOfDifferentiation, int indexOfFirstSample, int indexOfSecondsample, int indexOfThirdSample) Three point differentiation helper, modeled off of the same method in the Math.NET CubicSpline class.interpolate
(double[] xvals, double[] yvals) Computes an interpolating function for the data set.private PolynomialSplineFunction
interpolateHermiteSorted
(double[] xvals, double[] yvals, double[] firstDerivatives) Creates a Hermite cubic spline interpolation from the set of (x,y) value pairs and their derivatives.
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Field Details
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MINIMUM_NUMBER_POINTS
private static final int MINIMUM_NUMBER_POINTSThe minimum number of points that are needed to compute the function.- See Also:
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Constructor Details
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AkimaSplineInterpolator
public AkimaSplineInterpolator()
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Method Details
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interpolate
public PolynomialSplineFunction interpolate(double[] xvals, double[] yvals) throws DimensionMismatchException, NumberIsTooSmallException, NonMonotonicSequenceException Computes an interpolating function for the data set.- Specified by:
interpolate
in interfaceUnivariateInterpolator
- Parameters:
xvals
- the arguments for the interpolation pointsyvals
- the values for the interpolation points- Returns:
- a function which interpolates the data set
- Throws:
DimensionMismatchException
- ifxvals
andyvals
have different sizes.NonMonotonicSequenceException
- ifxvals
is not sorted in strict increasing order.NumberIsTooSmallException
- if the size ofxvals
is smaller than 5.
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differentiateThreePoint
private double differentiateThreePoint(double[] xvals, double[] yvals, int indexOfDifferentiation, int indexOfFirstSample, int indexOfSecondsample, int indexOfThirdSample) Three point differentiation helper, modeled off of the same method in the Math.NET CubicSpline class. This is used by both the Apache Math and the Math.NET Akima Cubic Spline algorithms- Parameters:
xvals
- x values to calculate the numerical derivative withyvals
- y values to calculate the numerical derivative withindexOfDifferentiation
- index of the elemnt we are calculating the derivative aroundindexOfFirstSample
- index of the first element to sample for the three point methodindexOfSecondsample
- index of the second element to sample for the three point methodindexOfThirdSample
- index of the third element to sample for the three point method- Returns:
- the derivative
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interpolateHermiteSorted
private PolynomialSplineFunction interpolateHermiteSorted(double[] xvals, double[] yvals, double[] firstDerivatives) Creates a Hermite cubic spline interpolation from the set of (x,y) value pairs and their derivatives. This is modeled off of the InterpolateHermiteSorted method in the Math.NET CubicSpline class.- Parameters:
xvals
- x values for interpolationyvals
- y values for interpolationfirstDerivatives
- first derivative values of the function- Returns:
- polynomial that fits the function
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