org.apache.commons.math.analysis.polynomials

## Class PolynomialFunctionLagrangeForm

• java.lang.Object
• org.apache.commons.math.analysis.polynomials.PolynomialFunctionLagrangeForm
• All Implemented Interfaces:
UnivariateRealFunction

```public class PolynomialFunctionLagrangeForm
extends java.lang.Object
implements UnivariateRealFunction```
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:
1.2
• ### Constructor Summary

Constructors
Constructor and Description
```PolynomialFunctionLagrangeForm(double[] x, double[] y)```
Construct a Lagrange polynomial with the given abscissas and function values.
• ### Method Summary

All Methods
Modifier and Type Method and Description
`int` `degree()`
Returns the degree of the polynomial.
`static double` ```evaluate(double[] x, double[] y, double z)```
Evaluate the Lagrange polynomial using Neville's Algorithm.
`double[]` `getCoefficients()`
Returns a copy of the coefficients array.
`double[]` `getInterpolatingPoints()`
Returns a copy of the interpolating points array.
`double[]` `getInterpolatingValues()`
Returns a copy of the interpolating values array.
`double` `value(double z)`
Compute the value for the function.
`static void` ```verifyInterpolationArray(double[] x, double[] y)```
Verifies that the interpolation arrays are valid.
• ### Methods inherited from class java.lang.Object

`equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`
• ### Constructor Detail

• #### PolynomialFunctionLagrangeForm

```public PolynomialFunctionLagrangeForm(double[] x,
double[] y)
throws java.lang.IllegalArgumentException```
Construct a Lagrange polynomial with the given abscissas and function values. The order of interpolating points are not important.

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

Parameters:
`x` - interpolating points
`y` - function values at interpolating points
Throws:
`java.lang.IllegalArgumentException` - if input arrays are not valid
• ### Method Detail

• #### value

```public double value(double z)
throws FunctionEvaluationException```
Compute the value for the function.
Specified by:
`value` in interface `UnivariateRealFunction`
Parameters:
`z` - the point for which the function value should be computed
Returns:
the value
Throws:
`FunctionEvaluationException` - if the function evaluation fails
• #### degree

`public int degree()`
Returns the degree of the polynomial.
Returns:
the degree of the polynomial
• #### getInterpolatingPoints

`public double[] 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 double[] 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 double[] 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
• #### evaluate

```public static double evaluate(double[] x,
double[] y,
double z)
throws DuplicateSampleAbscissaException,
java.lang.IllegalArgumentException```
Evaluate the Lagrange polynomial using Neville's Algorithm. It takes O(N^2) time.

This function is made public static so that users can call it directly without instantiating PolynomialFunctionLagrangeForm object.

Parameters:
`x` - the interpolating points array
`y` - the interpolating values array
`z` - the point at which the function value is to be computed
Returns:
the function value
Throws:
`DuplicateSampleAbscissaException` - if the sample has duplicate abscissas
`java.lang.IllegalArgumentException` - if inputs are not valid
• #### verifyInterpolationArray

```public static void verifyInterpolationArray(double[] x,
double[] y)
throws java.lang.IllegalArgumentException```
Verifies that the interpolation arrays are valid.

The arrays features checked by this method are that both arrays have the same length and this length is at least 2.

The interpolating points must be distinct. However it is not verified here, it is checked in evaluate() and computeCoefficients().

Parameters:
`x` - the interpolating points array
`y` - the interpolating values array
Throws:
`java.lang.IllegalArgumentException` - if not valid
`evaluate(double[], double[], double)`, `computeCoefficients()`