org.apache.commons.math3.analysis.solvers
Class BaseAbstractUnivariateSolver<FUNC extends UnivariateFunction>

java.lang.Object
  extended by 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.

Since:
2.0
Version:
$Id: BaseAbstractUnivariateSolver.java 1455194 2013-03-11 15:45:54Z luc $

Constructor Summary
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
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.


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