Package org.hipparchus.analysis.solvers
Interface BracketedRealFieldUnivariateSolver<T extends CalculusFieldElement<T>>

 Type Parameters:
T
 the type of the field elements
 All Known Implementing Classes:
FieldBracketingNthOrderBrentSolver
public interface BracketedRealFieldUnivariateSolver<T extends CalculusFieldElement<T>>
Interface for(univariate real) rootfinding algorithms
that maintain a bracketed solution. There are several advantages to having such rootfinding algorithms: The bracketed solution guarantees that the root is kept within the interval. As such, these algorithms generally also guarantee convergence.
 The bracketed solution means that we have the opportunity to only
return roots that are greater than or equal to the actual root, or
are less than or equal to the actual root. That is, we can control
whether underapproximations and overapproximations are
allowed solutions
. Other rootfinding algorithms can usually only guarantee that the solution (the root that was found) is around the actual root.
For backwards compatibility, all rootfinding algorithms must have
ANY_SIDE
as default for the allowed solutions. See Also:
AllowedSolution


Nested Class Summary
Nested Classes Modifier and Type Interface Description static class
BracketedRealFieldUnivariateSolver.Interval<T extends CalculusFieldElement<T>>
An interval of a function that brackets a root.

Method Summary
All Methods Instance Methods Abstract Methods Default Methods Modifier and Type Method Description T
getAbsoluteAccuracy()
Get the absolute accuracy of the solver.int
getEvaluations()
Get the number of evaluations of the objective function.T
getFunctionValueAccuracy()
Get the function value accuracy of the solver.int
getMaxEvaluations()
Get the maximum number of function evaluations.T
getRelativeAccuracy()
Get the relative accuracy of the solver.T
solve(int maxEval, CalculusFieldUnivariateFunction<T> f, T min, T max, AllowedSolution allowedSolution)
Solve for a zero in the given interval.T
solve(int maxEval, CalculusFieldUnivariateFunction<T> f, T min, T max, T startValue, AllowedSolution allowedSolution)
Solve for a zero in the given interval, start atstartValue
.default BracketedRealFieldUnivariateSolver.Interval<T>
solveInterval(int maxEval, CalculusFieldUnivariateFunction<T> f, T min, T max)
Solve for a zero in the given interval and return a tolerance interval surrounding the root.BracketedRealFieldUnivariateSolver.Interval<T>
solveInterval(int maxEval, CalculusFieldUnivariateFunction<T> f, T min, T max, T startValue)
Solve for a zero in the given interval and return a tolerance interval surrounding the root.



Method Detail

getMaxEvaluations
int getMaxEvaluations()
Get the maximum number of function evaluations. Returns:
 the maximum number of function evaluations.

getEvaluations
int getEvaluations()
Get the number of evaluations of the objective function. The number of evaluations corresponds to the last call to theoptimize
method. It is 0 if the method has not been called yet. Returns:
 the number of evaluations of the objective function.

getAbsoluteAccuracy
T 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 andv
is a value returned by one of thesolve
methods, then a root of the function should exist somewhere in the interval (v
 ε,v
+ ε). Returns:
 the absolute accuracy.

getRelativeAccuracy
T getRelativeAccuracy()
Get the relative accuracy of the solver. The contract for relative accuracy is the same asgetAbsoluteAccuracy()
, but using relative, rather than absolute error. If ρ is the relative accuracy configured for a solver andv
is a value returned, then a root of the function should exist somewhere in the interval (v
 ρv
,v
+ ρv
). Returns:
 the relative accuracy.

getFunctionValueAccuracy
T getFunctionValueAccuracy()
Get the function value accuracy of the solver. Ifv
is a value returned by the solver for a functionf
, then by contract,f(v)
should be less than or equal to the function value accuracy configured for the solver. Returns:
 the function value accuracy.

solve
T solve(int maxEval, CalculusFieldUnivariateFunction<T> f, T min, T max, AllowedSolution allowedSolution)
Solve for a zero 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. Parameters:
maxEval
 Maximum number of evaluations.f
 Function to solve.min
 Lower bound for the interval.max
 Upper bound for the interval.allowedSolution
 The kind of solutions that the rootfinding algorithm may accept as solutions. 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
T solve(int maxEval, CalculusFieldUnivariateFunction<T> f, T min, T max, T startValue, AllowedSolution allowedSolution)
Solve for a zero in the given interval, start atstartValue
. 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. 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.allowedSolution
 The kind of solutions that the rootfinding algorithm may accept as solutions. 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.

solveInterval
default BracketedRealFieldUnivariateSolver.Interval<T> solveInterval(int maxEval, CalculusFieldUnivariateFunction<T> f, T min, T max) throws MathIllegalArgumentException, MathIllegalStateException
Solve for a zero in the given interval and return a tolerance interval surrounding the root.It is required that the starting interval brackets a root.
 Parameters:
maxEval
 Maximum number of evaluations.f
 Function to solve.min
 Lower bound for the interval. f(min) != 0.0.max
 Upper bound for the interval. f(max) != 0.0. Returns:
 an interval [ta, tb] such that for some t in [ta, tb] f(t) == 0.0 or has a
step wise discontinuity that crosses zero. Both end points also satisfy the
convergence criteria so either one could be used as the root. That is the interval
satisfies the condition ( tb  ta  <=
absolute
accuracy + max(ta, tb) *relative
accuracy) or ( max(f(ta), f(tb)) <=getFunctionValueAccuracy()
) or there are no numbers in the field between ta and tb. The width of the interval (tb  ta) may be zero.  Throws:
MathIllegalArgumentException
 if the arguments do not satisfy the requirements specified by the solver.MathIllegalStateException
 if the allowed number of evaluations is exceeded.

solveInterval
BracketedRealFieldUnivariateSolver.Interval<T> solveInterval(int maxEval, CalculusFieldUnivariateFunction<T> f, T min, T max, T startValue) throws MathIllegalArgumentException, MathIllegalStateException
Solve for a zero in the given interval and return a tolerance interval surrounding the root.It is required that the starting interval brackets a root.
 Parameters:
maxEval
 Maximum number of evaluations.startValue
 start value to use.f
 Function to solve.min
 Lower bound for the interval. f(min) != 0.0.max
 Upper bound for the interval. f(max) != 0.0. Returns:
 an interval [ta, tb] such that for some t in [ta, tb] f(t) == 0.0 or has a
step wise discontinuity that crosses zero. Both end points also satisfy the
convergence criteria so either one could be used as the root. That is the interval
satisfies the condition ( tb  ta  <=
absolute
accuracy + max(ta, tb) *relative
accuracy) or ( max(f(ta), f(tb)) <=getFunctionValueAccuracy()
) or numbers in the field between ta and tb. The width of the interval (tb  ta) may be zero.  Throws:
MathIllegalArgumentException
 if the arguments do not satisfy the requirements specified by the solver.MathIllegalStateException
 if the allowed number of evaluations is exceeded.

