Package org.hipparchus.analysis.polynomials

Class FieldPolynomialFunctionLagrangeForm<T extends CalculusFieldElement<T>>

java.lang.Object

org.hipparchus.analysis.polynomials.FieldPolynomialFunctionLagrangeForm<T>

Type Parameters:

T - type of the field elements

All Implemented Interfaces:

CalculusFieldUnivariateFunction<T>

public class FieldPolynomialFunctionLagrangeForm<T extends CalculusFieldElement<T>>
extends Object
implements CalculusFieldUnivariateFunction<T>

Implements the representation of a real polynomial function in Lagrange Form. For reference, see Introduction to Numerical Analysis, ISBN 038795452X, chapter 2.

The approximated function should be smooth enough for Lagrange polynomial to work well. Otherwise, consider using splines instead.

Since:

4.0

See Also:

• PolynomialFunctionLagrangeForm

Constructor Summary

Constructors

Constructor	Description
FieldPolynomialFunctionLagrangeForm(T[] x, T[] y)	Construct a Lagrange polynomial with the given abscissas and function values.

Method Summary

Modifier and Type	Method	Description
protected void	computeCoefficients()	Calculate the coefficients of Lagrange polynomial from the interpolation data.
int	degree()	Returns the degree of the polynomial.
T[]	getCoefficients()	Returns a copy of the coefficients array.
T[]	getInterpolatingPoints()	Returns a copy of the interpolating points array.
T[]	getInterpolatingValues()	Returns a copy of the interpolating values array.
T	value(T z)	Calculate the function value at the given point.

Methods inherited from class java.lang.Object

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

Constructor Details

FieldPolynomialFunctionLagrangeForm

public FieldPolynomialFunctionLagrangeForm(T[] x,
 T[] y)
                                    throws MathIllegalArgumentException

Construct a Lagrange polynomial with the given abscissas and function values. The order of interpolating points is important.

The constructor makes copy of the input arrays and assigns them.

Parameters:

x - interpolating points

y - function values at interpolating points

Throws:

MathIllegalArgumentException - if the array lengths are different.

MathIllegalArgumentException - if the number of points is less than 2.

MathIllegalArgumentException - if two abscissae have the same value.

MathIllegalArgumentException - if the abscissae are not sorted.

Method Details

value

public T value(T z)

Calculate the function value at the given point.

Specified by:

value in interface CalculusFieldUnivariateFunction<T extends CalculusFieldElement<T>>

Parameters:

z - Point at which the function value is to be computed.

Returns:

the function value.

Throws:

MathIllegalArgumentException - if x and y have different lengths.

MathIllegalArgumentException - if x is not sorted in strictly increasing order.

MathIllegalArgumentException - if the size of x is less than 2.

degree

public int degree()

Returns the degree of the polynomial.

Returns:

the degree of the polynomial

getInterpolatingPoints

public T[] getInterpolatingPoints()

Returns a copy of the interpolating points array.

Changes made to the returned copy will not affect the polynomial.

Returns:

a fresh copy of the interpolating points array

getInterpolatingValues

public T[] getInterpolatingValues()

Returns a copy of the interpolating values array.

Changes made to the returned copy will not affect the polynomial.

Returns:

a fresh copy of the interpolating values array

getCoefficients

public T[] getCoefficients()

Returns a copy of the coefficients array.

Changes made to the returned copy will not affect the polynomial.

Note that coefficients computation can be ill-conditioned. Use with caution and only when it is necessary.

Returns:

a fresh copy of the coefficients array

computeCoefficients

protected void computeCoefficients()

Calculate the coefficients of Lagrange polynomial from the interpolation data. It takes O(n^2) time. Note that this computation can be ill-conditioned: Use with caution and only when it is necessary.