com.hedgehog.math.functions
Class LagrangianPolynomialFunction

java.lang.Object
  com.hedgehog.HObject
      com.hedgehog.math.functions.Function
          com.hedgehog.math.functions.XYVectorPolynomialFunction
              com.hedgehog.math.functions.LagrangianPolynomialFunction

All Implemented Interfaces:

java.lang.Comparable, java.util.Comparator

public class LagrangianPolynomialFunction
extends XYVectorPolynomialFunction

Title: LagrangianPolynomialFunction - represents the Lagrangian polynomial function.

Description: Lagrangian polynomial function.

Copyright: Copyright (c) Hedgehog Software 2007-2009.

Company: Hedgehog Software

Since:

1.0

Version:

1.1

Field Summary

Fields inherited from class com.hedgehog.math.functions.XYVectorPolynomialFunction

mxi, myi

Fields inherited from class com.hedgehog.math.functions.Function

method

Fields inherited from class com.hedgehog.HObject

mID, mName

Constructor Summary

LagrangianPolynomialFunction(FloatingPointVector xi, FloatingPointVector yi)
Constructor.

LagrangianPolynomialFunction(LagrangianPolynomialFunction object)
Copy constructor.

Method Summary

double	firstDerivative(double x) Evaluates the first derivative.
double	getValue(double x) Evaluates L(x).
OneVariablePolynomial	lagrangianPolynomial() Returns the interpolating Lagrangian polynomial L(x).
OneVariablePolynomial	lagrangianPolynomial(int i) Returns the Lagrangian polynomial for Li(x).
double	Lix(double x, int i) Evaluates Li(x).
double	Lixd(double x, int i) Evaluates Li'(x).

Methods inherited from class com.hedgehog.math.functions.XYVectorPolynomialFunction

findXInterval, getXI, getYI, interpolateY, isValid, setXI, setYI, taylorsSeriesFirstDerivative, taylorsSeriesSecondDerivative, toString

Methods inherited from class com.hedgehog.math.functions.Function

getMethod, setMethod

Methods inherited from class com.hedgehog.HObject

clone, compare, compareTo, copy, equals, getID, getName, hashCode, hasID, hasName, setID, setName

Methods inherited from class java.lang.Object

finalize, getClass, notify, notifyAll, wait, wait, wait

Constructor Detail

LagrangianPolynomialFunction

public LagrangianPolynomialFunction(FloatingPointVector xi,
                                    FloatingPointVector yi)
                             throws java.lang.IllegalArgumentException

Constructor. For example, the following approximates sin(x) in the interval [0:pi]:

  hedgehog.math.vectors.FloatingPointVector xi = new hedgehog.math.vectors.FloatingPointVector(5);
        hedgehog.math.vectors.FloatingPointVector yi = new hedgehog.math.vectors.FloatingPointVector(5);
        xi.setValueOpt(0.0,0); xi.setValueOpt(Math.PI/4.0,1); xi.setValueOpt(Math.PI/2.0,2); xi.setValueOpt(3.0*Math.PI/4.0,3); xi.setValueOpt(Math.PI,4);
        yi.setValueOpt(0.0,0); yi.setValueOpt(0.707,1);       yi.setValueOpt(1.0,2);         yi.setValueOpt(0.707,3);           yi.setValueOpt(0.0,4);
        LagrangianPolynomialFunction lpf = new LagrangianPolynomialFunction(xi,yi);
        System.out.println("lpf: " + lpf);
        System.out.println("lpf.getValue(0.2pi): " + lpf.getValue(0.2*Math.PI));
        System.out.println("lpf.getValue(0.6pi): " + lpf.getValue(0.6*Math.PI));
 

with output:

 lpf.getValue(0.2pi): 0.5871616  // exact: 0.587785
 lpf.getValue(0.6pi): 0.9511936  // exact: 0.951057
 

Parameters:

xi - x values.

yi - y values.

Throws:

java.lang.IllegalArgumentException - Thrown if xi and yi are not of the size.

LagrangianPolynomialFunction

public LagrangianPolynomialFunction(LagrangianPolynomialFunction object)

Copy constructor.

Parameters:

object - Object to copy.

Method Detail

Lix

public double Lix(double x,
                  int i)
           throws java.lang.IllegalArgumentException

Evaluates Li(x).

Parameters:

x - Value of x.

i - Index of x values.

Returns:

Value of Li(x).

Throws:

java.lang.IllegalArgumentException - Thrown if i<0 or i>=mxi.size().

Lixd

public double Lixd(double x,
                   int i)
            throws java.lang.IllegalArgumentException

Evaluates Li'(x).

Parameters:

x - Value of x.

i - Index of x values.

Returns:

Value of Li'(x).

Throws:

java.lang.IllegalArgumentException - Thrown if i<0 or i>=mxi.size().

firstDerivative

public double firstDerivative(double x)

Evaluates the first derivative.

Parameters:

x - Value at which derivative is required.

Returns:

First derivative at x.

lagrangianPolynomial

public OneVariablePolynomial lagrangianPolynomial(int i)
                                           throws java.lang.IllegalArgumentException

Returns the Lagrangian polynomial for Li(x).

Parameters:

i - Index of x values.

Returns:

Lagrangian polynomial for Li(x).

Throws:

java.lang.IllegalArgumentException - Thrown if i is out of range.

lagrangianPolynomial

public OneVariablePolynomial lagrangianPolynomial()

Returns the interpolating Lagrangian polynomial L(x).

Returns:

The interpolating Lagrangian polynomial L(x).

getValue

public double getValue(double x)

Evaluates L(x).

Parameters:

x - x value at which to find y.

Returns:

Interpolated value at the specified x.