Class BrentOptimizer
- java.lang.Object
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- org.apache.commons.statistics.inference.BrentOptimizer
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final class BrentOptimizer extends java.lang.Object
For a function defined on some interval(lo, hi)
, this class finds an approximationx
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.
This class has been extracted from
o.a.c.math4.optim.univariate
and simplified to remove support for the UnivariateOptimizer interface. This removed the options: to find the maximum; use a custom convergence checker on the function value; and remove the maximum function evaluation count. The class now implements a single optimize method within the provided bracket from the given start position (with value).- Since:
- 1.1
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Nested Class Summary
Nested Classes Modifier and Type Class Description (package private) static class
BrentOptimizer.PointValuePair
This class holds a point and the value of an objective function at this point.
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Field Summary
Fields Modifier and Type Field Description private double
absoluteThreshold
Absolute threshold.private int
evaluations
The number of function evaluations from the most recent call to optimize.private static double
GOLDEN_SECTION
Golden section.private static double
MIN_RELATIVE_TOLERANCE
Minimum relative tolerance.private double
relativeThreshold
Relative threshold.
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Constructor Summary
Constructors Constructor Description BrentOptimizer(double rel, double abs)
The arguments are used to implement the original stopping criterion of Brent's algorithm.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description (package private) int
getEvaluations()
Gets the number of function evaluations from the most recent call tooptimize
.(package private) BrentOptimizer.PointValuePair
optimize(java.util.function.DoubleUnaryOperator func, double lo, double hi, double mid, double fMid)
Search for the minimum inside the provided interval.
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Field Detail
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GOLDEN_SECTION
private static final double GOLDEN_SECTION
Golden section. (3 - sqrt(5)) / 2.- See Also:
- Constant Field Values
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MIN_RELATIVE_TOLERANCE
private static final double MIN_RELATIVE_TOLERANCE
Minimum relative tolerance. 2 * eps = 2^-51.- See Also:
- Constant Field Values
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relativeThreshold
private final double relativeThreshold
Relative threshold.
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absoluteThreshold
private final double absoluteThreshold
Absolute threshold.
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evaluations
private int evaluations
The number of function evaluations from the most recent call to optimize.
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Constructor Detail
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BrentOptimizer
BrentOptimizer(double rel, double abs)
The arguments are used to 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.- Throws:
java.lang.IllegalArgumentException
- ifabs <= 0
; or ifrel < 2 * Math.ulp(1.0)
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Method Detail
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getEvaluations
int getEvaluations()
Gets the number of function evaluations from the most recent call tooptimize
.- Returns:
- the function evaluations
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optimize
BrentOptimizer.PointValuePair optimize(java.util.function.DoubleUnaryOperator func, double lo, double hi, double mid, double fMid)
Search for the minimum inside the provided interval. The bracket must satisfy the equalitieslo < mid < hi
orhi < mid < lo
.Note: This function accepts the initial guess and the function value at that point. This is done for convenience as this internal class is used where the caller already knows the function value.
- Parameters:
func
- Function to solve.lo
- Lower bound of the search interval.hi
- Higher bound of the search interval.mid
- Start point.fMid
- Function value at the start point.- Returns:
- the value where the function is minimum.
- Throws:
java.lang.IllegalArgumentException
- if start point is not within the search intervaljava.lang.IllegalStateException
- if the maximum number of iterations is exceeded
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