com.numericalmethod.suanshu.analysis.uniroot
Class Uniroot

java.lang.Object
  com.numericalmethod.suanshu.analysis.uniroot.Uniroot

Direct Known Subclasses:

Brent, Halley, Newton

public abstract class Uniroot
extends java.lang.Object

One dimensional root (zero) finding algorithm for univariate function. All uniroot implementations extends this class.

A root-finding algorithm is a numerical algorithm for finding a value x such that f(x) = 0, for a given function f. Such an x is called a root of the function f.

See Also:

Wikipedia: Root-finding algorithm

Nested Class Summary

static class

Uniroot.NoRootFoundException Exception thrown when it fails to find a root.

Field Summary

UnivariateRealFunction	f the univariate function to be solved for 0, f
double	tol the convergence criterion such that the search succeeds when |f(x)| < tol

Constructor Summary

Uniroot(UnivariateRealFunction f, double tol)
Construct a uniroot solver.

Method Summary

abstract double	solve(int maxIterations, double lower, double upper, double... guess) The implementation of a specific uniroot finding algorithm.
double	solve(int maxIterations, double lower, double upper, double guess) Search for a root in the interval [lower, upper] for the maximum number of maxIterations.

Methods inherited from class java.lang.Object

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

Field Detail

f

public final UnivariateRealFunction f

the univariate function to be solved for 0, f

tol

public final double tol

the convergence criterion such that the search succeeds when |f(x)| < tol

Constructor Detail

Uniroot

public Uniroot(UnivariateRealFunction f,
               double tol)

Construct a uniroot solver.

Parameters:

f - a univariate function

tol - the convergence tolerance

Method Detail

solve

public double solve(int maxIterations,
                    double lower,
                    double upper,
                    double guess)
             throws Uniroot.NoRootFoundException

Search for a root in the interval [lower, upper] for the maximum number of maxIterations.

If the search fails, it throws a Uniroot.NoRootFoundException exception.

Parameters:

lower - the lower bound for the root

upper - the upper bound for the root

maxIterations - the maximum number of iterations to repeat the procedure

guess - an initial guess

Returns:

an approximate root

Throws:

Uniroot.NoRootFoundException

solve

public abstract double solve(int maxIterations,
                             double lower,
                             double upper,
                             double... guess)

The implementation of a specific uniroot finding algorithm.

Parameters:

maxIterations - the maximum number of iterations

lower - the lower bound of the bracketing interval

upper - the upper bound of the bracketing interval

guess - an initial guess of the root. It should lie between [lower, upper]. Note that guess is a double[] array. This signature allows multiple initial guesses for certain types of uniroot algorithms, e.g., Brent's algorithm.

Returns:

an approximate root