Class 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.

    • Method Detail

      • addSamplePoint

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

        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)
        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
      • 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 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
        x - interpolation abscissa
        interpolated value
        NoDataException - if sample is empty