org.apache.commons.math3.analysis.interpolation

## Class FieldHermiteInterpolator<T extends FieldElement<T>>

- java.lang.Object
- - org.apache.commons.math3.analysis.interpolation.FieldHermiteInterpolator<T>

- Type Parameters:
    `T` - Type of the field elements.

      public class FieldHermiteInterpolator<T extends FieldElement<T>>
      extends Object

  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:
    3.2

- - ### Constructor Summary

    Constructors
    Constructor and Description
    `FieldHermiteInterpolator()` Create an empty interpolator.

  - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `void` | `addSamplePoint(T x, T[]... value)` Add a sample point.
    `T[][]` | `derivatives(T x, int order)` Interpolate value and first derivatives at a specified abscissa.
    `T[]` | `value(T x)` Interpolate value at a specified abscissa.

    - ### Methods inherited from class java.lang.Object

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

- - ### Constructor Detail

    - #### FieldHermiteInterpolator

          public FieldHermiteInterpolator()

      Create an empty interpolator.

  - ### Method Detail

    - #### addSamplePoint

          public void addSamplePoint(T x,
                            T[]... value)
                              throws ZeroException,
                                     MathArithmeticException,
                                     DimensionMismatchException,
                                     NullArgumentException

      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:
        `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
        `DimensionMismatchException` - if derivative structures are inconsistent
        `NullArgumentException` - if x is null

    - #### value

          public T[] value(T x)
                                            throws NoDataException,
                                                   NullArgumentException

      Interpolate value at a specified abscissa.
      Parameters:
        `x` - interpolation abscissa
      Returns:
        interpolated value
      Throws:
        `NoDataException` - if sample is empty
        `NullArgumentException` - if x is null

    - #### derivatives

          public T[][] derivatives(T x,
                          int order)
                                                    throws NoDataException,
                                                           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, 1st derivative in row 1, ... nth derivative in row n)
      Throws:
        `NoDataException` - if sample is empty
        `NullArgumentException` - if x is null

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