BaseAbstractUnivariateSolver (Apache Commons Math 3.6.1 API)

java.lang.Object
- org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver<FUNC>

Type Parameters:
FUNC - Type of function to solve.

All Implemented Interfaces:

BaseUnivariateSolver<FUNC>

Direct Known Subclasses:

AbstractDifferentiableUnivariateSolver, AbstractPolynomialSolver, AbstractUnivariateDifferentiableSolver, AbstractUnivariateSolver
```
public abstract class BaseAbstractUnivariateSolver<FUNC extends UnivariateFunction>
extends Object
implements BaseUnivariateSolver<FUNC>
```
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.

Since:

2.0

Constructor Summary

Constructors
Modifier	Constructor and 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

Methods
Modifier and Type	Method and 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()`
`int`	`getMaxEvaluations()` Get the maximum number of function evaluations.
`double`	`getMin()`
`double`	`getRelativeAccuracy()` Get the relative accuracy of the solver.
`double`	`getStartValue()`
`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, FUNC f, double min, double max, double startValue)` Prepare for computation.
`double`	`solve(int maxEval, FUNC f, double startValue)` Solve for a zero in the vicinity of `startValue`.
`double`	`solve(int maxEval, FUNC f, double min, double max)` Solve for a zero root in the given interval.
`double`	`solve(int maxEval, FUNC 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 Detail
  - 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 Detail
  - getMaxEvaluations
```
public int getMaxEvaluations()
```
    Get the maximum number of function evaluations.
    
    Specified by:
    
    getMaxEvaluations in interface BaseUnivariateSolver<FUNC extends UnivariateFunction>
    
    Returns:
    the maximum number of function evaluations.
  - 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<FUNC extends UnivariateFunction>
    
    Returns:
    the number of evaluations of the objective function.
  - getMin
```
public double getMin()
```
    Returns:
    the lower end of the search interval.
  - getMax
```
public double getMax()
```
    Returns:
    the higher end of the search interval.
  - getStartValue
```
public double getStartValue()
```
    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<FUNC 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<FUNC 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<FUNC extends UnivariateFunction>
    
    Returns:
    the function value accuracy.
  - computeObjectiveValue
```
protected double computeObjectiveValue(double point)
                                throws TooManyEvaluationsException
```
    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:
    
    TooManyEvaluationsException - if the maximal number of evaluations is exceeded.
  - setup
```
protected void setup(int maxEval,
         FUNC 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,
           FUNC f,
           double min,
           double max,
           double startValue)
             throws TooManyEvaluationsException,
                    NoBracketingException
```
    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<FUNC 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:
    
    TooManyEvaluationsException - if the allowed number of evaluations is exceeded.
    
    NoBracketingException
  - solve
```
public double solve(int maxEval,
           FUNC 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<FUNC 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,
           FUNC f,
           double startValue)
             throws TooManyEvaluationsException,
                    NoBracketingException
```
    Solve for a zero in the vicinity of startValue.
    
    Specified by:
    
    solve in interface BaseUnivariateSolver<FUNC 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:
    
    TooManyEvaluationsException - if the allowed number of evaluations is exceeded.
    
    NoBracketingException
  - doSolve
```
protected abstract double doSolve()
                           throws TooManyEvaluationsException,
                                  NoBracketingException
```
    Method for implementing actual optimization algorithms in derived classes.
    
    Returns:
    the root.
    
    Throws:
    
    TooManyEvaluationsException - if the maximal number of evaluations is exceeded.
    
    NoBracketingException - 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 NumberIsTooLargeException
```
    Check that the endpoints specify an interval.
    
    Parameters:
    lower - Lower endpoint.
    upper - Upper endpoint.
    
    Throws:
    
    NumberIsTooLargeException - if lower >= upper.
  - verifySequence
```
protected void verifySequence(double lower,
                  double initial,
                  double upper)
                       throws NumberIsTooLargeException
```
    Check that lower < initial < upper.
    
    Parameters:
    lower - Lower endpoint.
    initial - Initial value.
    upper - Upper endpoint.
    
    Throws:
    
    NumberIsTooLargeException - if lower >= initial or initial >= upper.
  - verifyBracketing
```
protected void verifyBracketing(double lower,
                    double upper)
                         throws NullArgumentException,
                                NoBracketingException
```
    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.
    
    NoBracketingException - if the function has the same sign at the endpoints.
  - incrementEvaluationCount
```
protected void incrementEvaluationCount()
                                 throws TooManyEvaluationsException
```
    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:
    
    TooManyEvaluationsException - when the allowed number of function evaluations has been exhausted.

Class BaseAbstractUnivariateSolver<FUNC extends UnivariateFunction>

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

BaseAbstractUnivariateSolver

BaseAbstractUnivariateSolver

BaseAbstractUnivariateSolver

Method Detail

getMaxEvaluations

getEvaluations

getMin

getMax

getStartValue

getAbsoluteAccuracy

getRelativeAccuracy

getFunctionValueAccuracy

computeObjectiveValue

setup

solve

solve

solve

doSolve

isBracketing

isSequence

verifyInterval

verifySequence

verifyBracketing

incrementEvaluationCount