Class UnivariateRealSolverUtils


  • public class UnivariateRealSolverUtils
    extends java.lang.Object
    Utility routines for UnivariateRealSolver objects.
    Version:
    $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 févr. 2011) $
    • Method Summary

      All Methods Static Methods Concrete Methods 
      Modifier and Type Method Description
      static double[] bracket​(UnivariateRealFunction function, double initial, double lowerBound, double upperBound)
      This method attempts to find two values a and b satisfying lowerBound <= a < initial < b <= upperBound f(a) * f(b) < 0 If f is continuous on [a,b], this means that a and b bracket a root of f.
      static double[] bracket​(UnivariateRealFunction function, double initial, double lowerBound, double upperBound, int maximumIterations)
      This method attempts to find two values a and b satisfying lowerBound <= a < initial < b <= upperBound f(a) * f(b) <= 0 If f is continuous on [a,b], this means that a and b bracket a root of f.
      static double midpoint​(double a, double b)
      Compute the midpoint of two values.
      static double solve​(UnivariateRealFunction f, double x0, double x1)
      Convenience method to find a zero of a univariate real function.
      static double solve​(UnivariateRealFunction f, double x0, double x1, double absoluteAccuracy)
      Convenience method to find a zero of a univariate real function.
      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
    • Method Detail

      • solve

        public static double solve​(UnivariateRealFunction f,
                                   double x0,
                                   double x1)
                            throws ConvergenceException,
                                   FunctionEvaluationException
        Convenience method to find a zero of a univariate real function. A default solver is used.
        Parameters:
        f - the function.
        x0 - the lower bound for the interval.
        x1 - the upper bound for the interval.
        Returns:
        a value where the function is zero.
        Throws:
        ConvergenceException - if the iteration count was exceeded
        FunctionEvaluationException - if an error occurs evaluating the function
        java.lang.IllegalArgumentException - if f is null or the endpoints do not specify a valid interval
      • solve

        public static double solve​(UnivariateRealFunction f,
                                   double x0,
                                   double x1,
                                   double absoluteAccuracy)
                            throws ConvergenceException,
                                   FunctionEvaluationException
        Convenience method to find a zero of a univariate real function. A default solver is used.
        Parameters:
        f - the function
        x0 - the lower bound for the interval
        x1 - the upper bound for the interval
        absoluteAccuracy - the accuracy to be used by the solver
        Returns:
        a value where the function is zero
        Throws:
        ConvergenceException - if the iteration count is exceeded
        FunctionEvaluationException - if an error occurs evaluating the function
        java.lang.IllegalArgumentException - if f is null, the endpoints do not specify a valid interval, or the absoluteAccuracy is not valid for the default solver
      • bracket

        public static double[] bracket​(UnivariateRealFunction function,
                                       double initial,
                                       double lowerBound,
                                       double upperBound)
                                throws ConvergenceException,
                                       FunctionEvaluationException
        This method attempts to find two values a and b satisfying
        • lowerBound <= a < initial < b <= upperBound
        • f(a) * f(b) < 0
        If f is continuous on [a,b], this means that a and b bracket a root of f.

        The algorithm starts by setting a := initial -1; b := initial +1, examines the value of the function at a and b and keeps moving the endpoints out by one unit each time through a loop that terminates when one of the following happens:

        • f(a) * f(b) < 0 -- success!
        • a = lower and b = upper -- ConvergenceException
        • Integer.MAX_VALUE iterations elapse -- ConvergenceException

        Note: this method can take Integer.MAX_VALUE iterations to throw a ConvergenceException. Unless you are confident that there is a root between lowerBound and upperBound near initial, it is better to use bracket(UnivariateRealFunction, double, double, double, int), explicitly specifying the maximum number of iterations.

        Parameters:
        function - the function
        initial - initial midpoint of interval being expanded to bracket a root
        lowerBound - lower bound (a is never lower than this value)
        upperBound - upper bound (b never is greater than this value)
        Returns:
        a two element array holding {a, b}
        Throws:
        ConvergenceException - if a root can not be bracketted
        FunctionEvaluationException - if an error occurs evaluating the function
        java.lang.IllegalArgumentException - if function is null, maximumIterations is not positive, or initial is not between lowerBound and upperBound
      • bracket

        public static double[] bracket​(UnivariateRealFunction function,
                                       double initial,
                                       double lowerBound,
                                       double upperBound,
                                       int maximumIterations)
                                throws ConvergenceException,
                                       FunctionEvaluationException
        This method attempts to find two values a and b satisfying
        • lowerBound <= a < initial < b <= upperBound
        • f(a) * f(b) <= 0
        If f is continuous on [a,b], this means that a and b bracket a root of f.

        The algorithm starts by setting a := initial -1; b := initial +1, examines the value of the function at a and b and keeps moving the endpoints out by one unit each time through a loop that terminates when one of the following happens:

        • f(a) * f(b) <= 0 -- success!
        • a = lower and b = upper -- ConvergenceException
        • maximumIterations iterations elapse -- ConvergenceException

        Parameters:
        function - the function
        initial - initial midpoint of interval being expanded to bracket a root
        lowerBound - lower bound (a is never lower than this value)
        upperBound - upper bound (b never is greater than this value)
        maximumIterations - maximum number of iterations to perform
        Returns:
        a two element array holding {a, b}.
        Throws:
        ConvergenceException - if the algorithm fails to find a and b satisfying the desired conditions
        FunctionEvaluationException - if an error occurs evaluating the function
        java.lang.IllegalArgumentException - if function is null, maximumIterations is not positive, or initial is not between lowerBound and upperBound
      • midpoint

        public static double midpoint​(double a,
                                      double b)
        Compute the midpoint of two values.
        Parameters:
        a - first value.
        b - second value.
        Returns:
        the midpoint.