Class BrentOptimizer
java.lang.Object
org.apache.commons.math3.optim.BaseOptimizer<UnivariatePointValuePair>
org.apache.commons.math3.optim.univariate.UnivariateOptimizer
org.apache.commons.math3.optim.univariate.BrentOptimizer
For a function defined on some interval
This code is an adaptation, partly based on the Python code from SciPy (module "optimize.py" v0.5); the original algorithm is also modified
(lo, hi)
, this class
finds an approximation x
to the point at which the function
attains its minimum.
It implements Richard Brent's algorithm (from his book "Algorithms for
Minimization without Derivatives", p. 79) for finding minima of real
univariate functions.
This code is an adaptation, partly based on the Python code from SciPy (module "optimize.py" v0.5); the original algorithm is also modified
- to use an initial guess provided by the user,
- to ensure that the best point encountered is the one returned.
- Since:
- 2.0
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Field Summary
FieldsModifier and TypeFieldDescriptionprivate final double
Absolute threshold.private static final double
Golden section.private static final double
Minimum relative tolerance.private final double
Relative threshold.Fields inherited from class org.apache.commons.math3.optim.BaseOptimizer
evaluations, iterations
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Constructor Summary
ConstructorsConstructorDescriptionBrentOptimizer
(double rel, double abs) The arguments are used for implementing the original stopping criterion of Brent's algorithm.BrentOptimizer
(double rel, double abs, ConvergenceChecker<UnivariatePointValuePair> checker) The arguments are used implement the original stopping criterion of Brent's algorithm. -
Method Summary
Modifier and TypeMethodDescriptionprivate UnivariatePointValuePair
best
(UnivariatePointValuePair a, UnivariatePointValuePair b, boolean isMinim) Selects the best of two points.protected UnivariatePointValuePair
Performs the bulk of the optimization algorithm.Methods inherited from class org.apache.commons.math3.optim.univariate.UnivariateOptimizer
computeObjectiveValue, getGoalType, getMax, getMin, getStartValue, optimize, parseOptimizationData
Methods inherited from class org.apache.commons.math3.optim.BaseOptimizer
getConvergenceChecker, getEvaluations, getIterations, getMaxEvaluations, getMaxIterations, incrementEvaluationCount, incrementIterationCount, optimize
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Field Details
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GOLDEN_SECTION
private static final double GOLDEN_SECTIONGolden section. -
MIN_RELATIVE_TOLERANCE
private static final double MIN_RELATIVE_TOLERANCEMinimum relative tolerance. -
relativeThreshold
private final double relativeThresholdRelative threshold. -
absoluteThreshold
private final double absoluteThresholdAbsolute threshold.
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Constructor Details
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BrentOptimizer
The arguments are used implement the original stopping criterion of Brent's algorithm.abs
andrel
define a tolerancetol = rel |x| + abs
.rel
should be no smaller than 2 macheps and preferably not much less than sqrt(macheps), where macheps is the relative machine precision.abs
must be positive.- Parameters:
rel
- Relative threshold.abs
- Absolute threshold.checker
- Additional, user-defined, convergence checking procedure.- Throws:
NotStrictlyPositiveException
- ifabs <= 0
.NumberIsTooSmallException
- ifrel < 2 * Math.ulp(1d)
.
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BrentOptimizer
public BrentOptimizer(double rel, double abs) The arguments are used for implementing the original stopping criterion of Brent's algorithm.abs
andrel
define a tolerancetol = rel |x| + abs
.rel
should be no smaller than 2 macheps and preferably not much less than sqrt(macheps), where macheps is the relative machine precision.abs
must be positive.- Parameters:
rel
- Relative threshold.abs
- Absolute threshold.- Throws:
NotStrictlyPositiveException
- ifabs <= 0
.NumberIsTooSmallException
- ifrel < 2 * Math.ulp(1d)
.
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Method Details
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doOptimize
Performs the bulk of the optimization algorithm.- Specified by:
doOptimize
in classBaseOptimizer<UnivariatePointValuePair>
- Returns:
- the point/value pair giving the optimal value of the objective function.
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best
private UnivariatePointValuePair best(UnivariatePointValuePair a, UnivariatePointValuePair b, boolean isMinim) Selects the best of two points.- Parameters:
a
- Point and value.b
- Point and value.isMinim
-true
if the selected point must be the one with the lowest value.- Returns:
- the best point, or
null
ifa
andb
are bothnull
. Whena
andb
have the same function value,a
is returned.
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