package edu.northwestern.at.utils.math.rootfinders;
/* Please see the license information at the end of this file. */
import edu.northwestern.at.utils.math.*;
/** Find roots of equations using Newton/Raphson iteration.
*
* <p>
* The Method of NewtonRaphson is a root-finding method which requires an
* initial estimate x0 for a root and that the function be
* continuous and everywhere differentiable.
* </p>
*
* <p>
* If the derivative of the function whose root is being sought
* is difficult or expensive to compute, the Method of Secants or
* Brent's Method is a better choice. If the function is not
* everywhere differentiable, Bisection is the method to use.
* </p>
*/
public class NewtonRaphson implements MonadicFunctionRootFinder
{
/** Find root using the Method of Newton/Raphson.
*
* @param x0 First approximation to root value.
* @param tol Desired accuracy for root value.
* @param maxIter Maximum number of iterations.
* @param function Class implementing MonadicFunction
* interface to provide function values.
* @param derivativeFunction Class implementing MonadicFunction
* interface to provide function
* derivative values.
* @param convergenceTest RootFinderConvergenceTest which
* tests for convergence of the root-finding
* process.
* @param iterationInformation Class implementing
* RootFinderIterationInformation
* for retrieving information about
* each iteration of root finding
* process. Set to null if you don't
* want this information.
*
* @return Approximation to root.
*
* @throws IllegalArgumentException
* if function or
* derivativeFunction is null.
*/
public static double newtonRaphson
(
double x0 ,
double tol ,
int maxIter ,
MonadicFunction function ,
MonadicFunction derivativeFunction ,
RootFinderConvergenceTest convergenceTest ,
RootFinderIterationInformation iterationInformation
)
throws IllegalArgumentException
{
/* Calculated value of x at each iteration. */
double x;
/* Function value at calculated value of x . */
double fx;
/* Function derivative value at calculated value of x . */
double dfx;
/* Previous function value. */
double xPrevious;
// Make sure function and derivativeFunction are not null.
if ( function == null )
{
throw new IllegalArgumentException(
"Function cannot be null" );
}
if ( derivativeFunction == null )
{
throw new IllegalArgumentException(
"Derivative function cannot be null" );
}
// Begin Newton/Raphson iteration loop.
x = x0;
for ( int iter = 0 ; iter < maxIter ; iter++ )
{
// Compute new approximant from first order
// Taylor series.
xPrevious = x;
fx = function.f( xPrevious );
dfx = derivativeFunction.f( xPrevious );
x = xPrevious - ( fx / dfx );
// Post updated iteration information.
if ( iterationInformation != null )
{
iterationInformation.iterationInformation( x , fx , dfx , iter );
}
// See if updated function value is close
// enough to root to stop iterations.
if ( convergenceTest.converged
(
x , xPrevious , fx , tol , tol )
)
{
break;
}
}
return x;
}
/** Find root using the Method of Newton/Raphson.
*
* @param x0 First approximation to root value.
* @param tol Desired accuracy for root value.
* @param maxIter Maximum number of iterations.
* @param function Class implementing MonadicFunction
* interface to provide function values.
* @param derivativeFunction Class implementing MonadicFunction
* interface to provide function
* derivative values.
*
* @return Approximation to root.
*
* @throws IllegalArgumentException
* if function or
* derivativeFunction is null.
*/
public static double newtonRaphson
(
double x0 ,
double tol ,
int maxIter ,
MonadicFunction function ,
MonadicFunction derivativeFunction
)
throws IllegalArgumentException
{
return newtonRaphson(
x0 , tol , maxIter , function , derivativeFunction ,
new StandardRootFinderConvergenceTest() , null );
}
/** Find root using the Method of Newton/Raphson.
*
* @param x0 First approximation to root value.
* @param function Class implementing MonadicFunction
* interface to provide function values.
* @param derivativeFunction Class implementing MonadicFunction
* interface to provide function
* derivative values.
*
* @return Approximation to root.
*
* @throws IllegalArgumentException
* if function or
* derivativeFunction is null.
*
* <p>
* Up to 100 iterations are attempted with the convergence tolerance
* set to Constants.MACHEPS .
* </p>
*/
public static double newtonRaphson
(
double x0 ,
MonadicFunction function ,
MonadicFunction derivativeFunction
)
throws IllegalArgumentException
{
return newtonRaphson(
x0 , Constants.MACHEPS , 100 , function , derivativeFunction ,
new StandardRootFinderConvergenceTest() , null );
}
/** Implementation for {@link MonadicFunctionRootFinder} interface.
*/
public double findRoot
(
double x0 ,
double x1 ,
double tol ,
int maxIter ,
MonadicFunction function ,
MonadicFunction derivativeFunction ,
RootFinderConvergenceTest convergenceTest ,
RootFinderIterationInformation iterationInformation
)
throws IllegalArgumentException
{
return newtonRaphson(
x0 , tol , maxIter , function , derivativeFunction ,
convergenceTest , iterationInformation );
}
/** Constructor if RootFinder interface used.
*/
public NewtonRaphson()
{
}
}
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