Package org.hipparchus.analysis.solvers

Class BaseAbstractUnivariateSolver<F extends UnivariateFunction>

java.lang.Object
org.hipparchus.analysis.solvers.BaseAbstractUnivariateSolver<F>
Type Parameters:
F - Type of function to solve.
All Implemented Interfaces:
BaseUnivariateSolver<F>
Direct Known Subclasses:
AbstractPolynomialSolver, AbstractUnivariateDifferentiableSolver, AbstractUnivariateSolver
public abstract class BaseAbstractUnivariateSolver<F extends UnivariateFunction> extends Object implements BaseUnivariateSolver<F>
Provide a default implementation for several functions useful to generic solvers. The default values for relative and function tolerances are 1e-14 and 1e-15, respectively. It is however highly recommended to not rely on the default, but rather carefully consider values that match user's expectations, as well as the specifics of each implementation.

  • Constructor Summary

    Constructors
    Modifier
    Constructor
    Description
    protected
    BaseAbstractUnivariateSolver(double absoluteAccuracy)
    Construct a solver with given absolute accuracy.
    protected
    BaseAbstractUnivariateSolver(double relativeAccuracy, double absoluteAccuracy)
    Construct a solver with given accuracies.
    protected
    BaseAbstractUnivariateSolver(double relativeAccuracy, double absoluteAccuracy, double functionValueAccuracy)
    Construct a solver with given accuracies.

  • Method Summary

    Modifier and Type
    Method
    Description
    protected double
    computeObjectiveValue(double point)
    Compute the objective function value.
    protected abstract double
    doSolve()
    Method for implementing actual optimization algorithms in derived classes.
    double
    getAbsoluteAccuracy()
    Get the absolute accuracy of the solver.
    int
    getEvaluations()
    Get the number of evaluations of the objective function.
    double
    getFunctionValueAccuracy()
    Get the function value accuracy of the solver.
    double
    getMax()
    Get higher end of the search interval.
    double
    getMin()
    Get lower end of the search interval.
    double
    getRelativeAccuracy()
    Get the relative accuracy of the solver.
    double
    getStartValue()
    Get initial guess.
    protected void
    incrementEvaluationCount()
    Increment the evaluation count by one.
    protected boolean
    isBracketing(double lower, double upper)
    Check whether the function takes opposite signs at the endpoints.
    protected boolean
    isSequence(double start, double mid, double end)
    Check whether the arguments form a (strictly) increasing sequence.
    protected void
    setup(int maxEval, F f, double min, double max, double startValue)
    Prepare for computation.
    double
    solve(int maxEval, F f, double startValue)
    Solve for a zero in the vicinity of startValue.
    double
    solve(int maxEval, F f, double min, double max)
    Solve for a zero root in the given interval.
    double
    solve(int maxEval, F f, double min, double max, double startValue)
    Solve for a zero in the given interval, start at startValue.
    protected void
    verifyBracketing(double lower, double upper)
    Check that the endpoints specify an interval and the function takes opposite signs at the endpoints.
    protected void
    verifyInterval(double lower, double upper)
    Check that the endpoints specify an interval.
    protected void
    verifySequence(double lower, double initial, double upper)
    Check that lower < initial < upper.

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • BaseAbstractUnivariateSolver

      protected BaseAbstractUnivariateSolver(double absoluteAccuracy)
      Construct a solver with given absolute accuracy.
      Parameters:
      absoluteAccuracy - Maximum absolute error.

    • BaseAbstractUnivariateSolver

      protected BaseAbstractUnivariateSolver(double relativeAccuracy, double absoluteAccuracy)
      Construct a solver with given accuracies.
      Parameters:
      relativeAccuracy - Maximum relative error.
      absoluteAccuracy - Maximum absolute error.

    • BaseAbstractUnivariateSolver

      protected BaseAbstractUnivariateSolver(double relativeAccuracy, double absoluteAccuracy, double functionValueAccuracy)
      Construct a solver with given accuracies.
      Parameters:
      relativeAccuracy - Maximum relative error.
      absoluteAccuracy - Maximum absolute error.
      functionValueAccuracy - Maximum function value error.

  • Method Details

    • getEvaluations

      public int getEvaluations()
      Get the number of evaluations of the objective function. The number of evaluations corresponds to the last call to the optimize method. It is 0 if the method has not been called yet.
      Specified by:
      getEvaluations in interface BaseUnivariateSolver<F extends UnivariateFunction>
      Returns:
      the number of evaluations of the objective function.

    • getMin

      public double getMin()
      Get lower end of the search interval.
      Returns:
      the lower end of the search interval

    • getMax

      public double getMax()
      Get higher end of the search interval.
      Returns:
      the higher end of the search interval

    • getStartValue

      public double getStartValue()
      Get initial guess.
      Returns:
      the initial guess

    • getAbsoluteAccuracy

      public double getAbsoluteAccuracy()
      Get the absolute accuracy of the solver. Solutions returned by the solver should be accurate to this tolerance, i.e., if ε is the absolute accuracy of the solver and v is a value returned by one of the solve methods, then a root of the function should exist somewhere in the interval (v - ε, v + ε).
      Specified by:
      getAbsoluteAccuracy in interface BaseUnivariateSolver<F extends UnivariateFunction>
      Returns:
      the absolute accuracy.

    • getRelativeAccuracy

      public double getRelativeAccuracy()
      Get the relative accuracy of the solver. The contract for relative accuracy is the same as BaseUnivariateSolver.getAbsoluteAccuracy(), but using relative, rather than absolute error. If ρ is the relative accuracy configured for a solver and v is a value returned, then a root of the function should exist somewhere in the interval (v - ρ v, v + ρ v).
      Specified by:
      getRelativeAccuracy in interface BaseUnivariateSolver<F extends UnivariateFunction>
      Returns:
      the relative accuracy.

    • getFunctionValueAccuracy

      public double getFunctionValueAccuracy()
      Get the function value accuracy of the solver. If v is a value returned by the solver for a function f, then by contract, |f(v)| should be less than or equal to the function value accuracy configured for the solver.
      Specified by:
      getFunctionValueAccuracy in interface BaseUnivariateSolver<F extends UnivariateFunction>
      Returns:
      the function value accuracy.

    • computeObjectiveValue

      protected double computeObjectiveValue(double point) throws MathIllegalStateException
      Compute the objective function value.
      Parameters:
      point - Point at which the objective function must be evaluated.
      Returns:
      the objective function value at specified point.
      Throws:
      MathIllegalStateException - if the maximal number of evaluations is exceeded.

    • setup

      protected void setup(int maxEval, F f, double min, double max, double startValue) throws NullArgumentException
      Prepare for computation. Subclasses must call this method if they override any of the solve methods.
      Parameters:
      f - Function to solve.
      min - Lower bound for the interval.
      max - Upper bound for the interval.
      startValue - Start value to use.
      maxEval - Maximum number of evaluations.
      Throws:
      NullArgumentException - if f is null

    • solve

      public double solve(int maxEval, F f, double min, double max, double startValue) throws MathIllegalArgumentException, MathIllegalStateException
      Solve for a zero in the given interval, start at startValue. A solver may require that the interval brackets a single zero root. Solvers that do require bracketing should be able to handle the case where one of the endpoints is itself a root.
      Specified by:
      solve in interface BaseUnivariateSolver<F extends UnivariateFunction>
      Parameters:
      maxEval - Maximum number of evaluations.
      f - Function to solve.
      min - Lower bound for the interval.
      max - Upper bound for the interval.
      startValue - Start value to use.
      Returns:
      a value where the function is zero.
      Throws:
      MathIllegalArgumentException - if the arguments do not satisfy the requirements specified by the solver.
      MathIllegalStateException - if the allowed number of evaluations is exceeded.

    • solve

      public double solve(int maxEval, F f, double min, double max)
      Solve for a zero root in the given interval. A solver may require that the interval brackets a single zero root. Solvers that do require bracketing should be able to handle the case where one of the endpoints is itself a root.
      Specified by:
      solve in interface BaseUnivariateSolver<F extends UnivariateFunction>
      Parameters:
      maxEval - Maximum number of evaluations.
      f - Function to solve.
      min - Lower bound for the interval.
      max - Upper bound for the interval.
      Returns:
      a value where the function is zero.

    • solve

      public double solve(int maxEval, F f, double startValue) throws MathIllegalArgumentException, MathIllegalStateException
      Solve for a zero in the vicinity of startValue.
      Specified by:
      solve in interface BaseUnivariateSolver<F extends UnivariateFunction>
      Parameters:
      maxEval - Maximum number of evaluations.
      f - Function to solve.
      startValue - Start value to use.
      Returns:
      a value where the function is zero.
      Throws:
      MathIllegalArgumentException - if the arguments do not satisfy the requirements specified by the solver.
      MathIllegalStateException - if the allowed number of evaluations is exceeded.

    • doSolve

      protected abstract double doSolve() throws MathIllegalArgumentException, MathIllegalStateException
      Method for implementing actual optimization algorithms in derived classes.
      Returns:
      the root.
      Throws:
      MathIllegalStateException - if the maximal number of evaluations is exceeded.
      MathIllegalArgumentException - if the initial search interval does not bracket a root and the solver requires it.

    • isBracketing

      protected boolean isBracketing(double lower, double upper)
      Check whether the function takes opposite signs at the endpoints.
      Parameters:
      lower - Lower endpoint.
      upper - Upper endpoint.
      Returns:
      true if the function values have opposite signs at the given points.

    • isSequence

      protected boolean isSequence(double start, double mid, double end)
      Check whether the arguments form a (strictly) increasing sequence.
      Parameters:
      start - First number.
      mid - Second number.
      end - Third number.
      Returns:
      true if the arguments form an increasing sequence.

    • verifyInterval

      protected void verifyInterval(double lower, double upper) throws MathIllegalArgumentException
      Check that the endpoints specify an interval.
      Parameters:
      lower - Lower endpoint.
      upper - Upper endpoint.
      Throws:
      MathIllegalArgumentException - if lower >= upper.

    • verifySequence

      protected void verifySequence(double lower, double initial, double upper) throws MathIllegalArgumentException
      Check that lower < initial < upper.
      Parameters:
      lower - Lower endpoint.
      initial - Initial value.
      upper - Upper endpoint.
      Throws:
      MathIllegalArgumentException - if lower >= initial or initial >= upper.

    • verifyBracketing

      protected void verifyBracketing(double lower, double upper) throws MathIllegalArgumentException, NullArgumentException
      Check that the endpoints specify an interval and the function takes opposite signs at the endpoints.
      Parameters:
      lower - Lower endpoint.
      upper - Upper endpoint.
      Throws:
      NullArgumentException - if the function has not been set.
      MathIllegalArgumentException - if the function has the same sign at the endpoints.

    • incrementEvaluationCount

      protected void incrementEvaluationCount() throws MathIllegalStateException
      Increment the evaluation count by one. Method computeObjectiveValue(double) calls this method internally. It is provided for subclasses that do not exclusively use computeObjectiveValue to solve the function. See e.g. AbstractUnivariateDifferentiableSolver.
      Throws:
      MathIllegalStateException - when the allowed number of function evaluations has been exhausted.