Examples of PegasusSolver

org.apache.commons.math3.analysis.solvers.PegasusSolver
Implements the Pegasus method for root-finding (approximating a zero of a univariate real function). It is a modified {@link RegulaFalsiSolver Regula Falsi} method.
Like the Regula Falsi method, convergence is guaranteed by maintaining a bracketed solution. The Pegasus method however, should converge much faster than the original Regula Falsi method. Furthermore, this implementation of the Pegasus method should not suffer from the same implementation issues as the Regula Falsi method, which may fail to convergence in certain cases. Also, the Pegasus method should converge faster than the {@link IllinoisSolver Illinois} method, another RegulaFalsi-based method.

The Pegasus method assumes that the function is continuous, but not necessarily smooth.

Implementation based on the following article: M. Dowell and P. Jarratt, The "Pegasus" method for computing the root of an equation, BIT Numerical Mathematics, volume 12, number 4, pages 503-508, Springer, 1972.
@since 3.0

Examples of org.apache.commons.math3.analysis.solvers.PegasusSolver

                        final double baseRoot = forward ?
                                                solver.solve(maxIterationCount, f, ta, tb) :
                                                solver.solve(maxIterationCount, f, tb, ta);
                        final int remainingEval = maxIterationCount - solver.getEvaluations();
                        BracketedUnivariateSolver<UnivariateFunction> bracketing =
                                new PegasusSolver(solver.getRelativeAccuracy(), solver.getAbsoluteAccuracy());
                        root = forward ?
                               UnivariateSolverUtils.forceSide(remainingEval, f, bracketing,
                                                                   baseRoot, ta, tb, AllowedSolution.RIGHT_SIDE) :
                               UnivariateSolverUtils.forceSide(remainingEval, f, bracketing,
                                                                   baseRoot, tb, ta, AllowedSolution.LEFT_SIDE);

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Examples of org.apache.commons.math3.analysis.solvers.PegasusSolver

                        final double baseRoot = forward ?
                                                solver.solve(maxIterationCount, f, ta, tb) :
                                                solver.solve(maxIterationCount, f, tb, ta);
                        final int remainingEval = maxIterationCount - solver.getEvaluations();
                        BracketedUnivariateSolver<UnivariateFunction> bracketing =
                                new PegasusSolver(solver.getRelativeAccuracy(), solver.getAbsoluteAccuracy());
                        root = forward ?
                               UnivariateSolverUtils.forceSide(remainingEval, f, bracketing,
                                                                   baseRoot, ta, tb, AllowedSolution.RIGHT_SIDE) :
                               UnivariateSolverUtils.forceSide(remainingEval, f, bracketing,
                                                                   baseRoot, tb, ta, AllowedSolution.LEFT_SIDE);

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Examples of org.apache.commons.math3.analysis.solvers.PegasusSolver

                        final double baseRoot = forward ?
                                                solver.solve(maxIterationCount, f, ta, tb) :
                                                solver.solve(maxIterationCount, f, tb, ta);
                        final int remainingEval = maxIterationCount - solver.getEvaluations();
                        BracketedUnivariateSolver<UnivariateFunction> bracketing =
                                new PegasusSolver(solver.getRelativeAccuracy(), solver.getAbsoluteAccuracy());
                        root = forward ?
                               UnivariateSolverUtils.forceSide(remainingEval, f, bracketing,
                                                                   baseRoot, ta, tb, AllowedSolution.RIGHT_SIDE) :
                               UnivariateSolverUtils.forceSide(remainingEval, f, bracketing,
                                                                   baseRoot, tb, ta, AllowedSolution.LEFT_SIDE);

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Examples of org.apache.commons.math3.analysis.solvers.PegasusSolver

        double e = 1e-15;
        FirstOrderIntegrator integrator;
        integrator = (integratorType == 1)
                     ? new DormandPrince853Integrator(e, 100.0, 1e-7, 1e-7)
                     : new GraggBulirschStoerIntegrator(e, 100.0, 1e-7, 1e-7);
        PegasusSolver rootSolver = new PegasusSolver(e, e);
        integrator.addEventHandler(new Event(), 0.1, e, 1000, rootSolver);
        double t0 = 6.0;
        double tEnd = 10.0;
        double[] y = {2.0, 2.0, 2.0, 4.0, 2.0, 7.0, 15.0};
        return integrator.integrate(new Ode(), t0, y, tEnd, y);

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Examples of org.apache.commons.math3.analysis.solvers.PegasusSolver

                        final double baseRoot = forward ?
                                                solver.solve(maxIterationCount, f, ta, tb) :
                                                solver.solve(maxIterationCount, f, tb, ta);
                        final int remainingEval = maxIterationCount - solver.getEvaluations();
                        BracketedUnivariateSolver<UnivariateFunction> bracketing =
                                new PegasusSolver(solver.getRelativeAccuracy(), solver.getAbsoluteAccuracy());
                        root = forward ?
                               UnivariateSolverUtils.forceSide(remainingEval, f, bracketing,
                                                                   baseRoot, ta, tb, AllowedSolution.RIGHT_SIDE) :
                               UnivariateSolverUtils.forceSide(remainingEval, f, bracketing,
                                                                   baseRoot, tb, ta, AllowedSolution.LEFT_SIDE);

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Examples of org.apache.commons.math3.analysis.solvers.PegasusSolver

    public void test(int eventType)
        throws DimensionMismatchException, NumberIsTooSmallException,
               MaxCountExceededException, NoBracketingException {
        double e = 1e-15;
        FirstOrderIntegrator integrator = new DormandPrince853Integrator(e, 100.0, 1e-7, 1e-7);
        BaseSecantSolver rootSolver = new PegasusSolver(e, e);
        EventHandler evt1 = new Event(0, eventType);
        EventHandler evt2 = new Event(1, eventType);
        integrator.addEventHandler(evt1, 0.1, e, 999, rootSolver);
        integrator.addEventHandler(evt2, 0.1, e, 999, rootSolver);
        double t = 0.0;

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Examples of org.apache.commons.math3.analysis.solvers.PegasusSolver

        double e = 1e-15;
        FirstOrderIntegrator integrator;
        integrator = (integratorType == 1)
                     ? new DormandPrince853Integrator(e, 100.0, 1e-7, 1e-7)
                     : new GraggBulirschStoerIntegrator(e, 100.0, 1e-7, 1e-7);
        PegasusSolver rootSolver = new PegasusSolver(e, e);
        integrator.addEventHandler(new Event(), 0.1, e, 1000, rootSolver);
        double t0 = 6.0;
        double tEnd = 10.0;
        double[] y = {2.0, 2.0, 2.0, 4.0, 2.0, 7.0, 15.0};
        return integrator.integrate(new Ode(), t0, y, tEnd, y);

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Examples of org.apache.commons.math3.analysis.solvers.PegasusSolver

     * EventHandler.g(double, double[])}.
     */
    public void test(int eventType) {
        double e = 1e-15;
        FirstOrderIntegrator integrator = new DormandPrince853Integrator(e, 100.0, 1e-7, 1e-7);
        BaseSecantSolver rootSolver = new PegasusSolver(e, e);
        EventHandler evt1 = new Event(0, eventType);
        EventHandler evt2 = new Event(1, eventType);
        integrator.addEventHandler(evt1, 0.1, e, 999, rootSolver);
        integrator.addEventHandler(evt2, 0.1, e, 999, rootSolver);
        double t = 0.0;

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Examples of org.apache.commons.math3.analysis.solvers.PegasusSolver

        double e = 1e-15;
        FirstOrderIntegrator integrator;
        integrator = (integratorType == 1)
                     ? new DormandPrince853Integrator(e, 100.0, 1e-7, 1e-7)
                     : new GraggBulirschStoerIntegrator(e, 100.0, 1e-7, 1e-7);
        PegasusSolver rootSolver = new PegasusSolver(e, e);
        integrator.addEventHandler(new Event(), 0.1, e, 1000, rootSolver);
        double t0 = 6.0;
        double tEnd = 10.0;
        double[] y = {2.0, 2.0, 2.0, 4.0, 2.0, 7.0, 15.0};
        return integrator.integrate(new Ode(), t0, y, tEnd, y);

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