class GoldenSectionLS extends LineSearch
The GoldenSectionLS class performs a line search on 'f(x)' to find a minimal
value for 'f'. It requires no derivatives and only one functional evaluation per
iteration. A search is conducted from 'x1' (often 0) to 'xmax'. A guess for 'xmax'
must be given, but can be made larger during the expansion phase, that occurs
before the recursive golden section search is called. It works on scalar functions
(see GoldenSectionLSTest). If starting with a vector function 'f(x)', simply
define a new function 'g(y) = x0 + direction * y' (see GoldenSectionLSTest2).
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- new GoldenSectionLS(f: FunctionS2S, τ: Double = 1E-5)
- f
the scalar objective function to minimize
- τ
the tolerance for breaking the iterations
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- val EPSILON: Double
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- def gsection(left: Boolean, x1: Double, x2: Double, x3: Double, f2: Double): Double
A recursive golden section search requiring only one functional evaluation per call.
A recursive golden section search requiring only one functional evaluation per call. It works by comparing two center points x2 (given) and x4 computed.
- left
whether to search left (true) or right (false) side of last interval
- x1
the left-most point
- x2
the center point (.618 across for left and .382 across for right)
- x3
the right-most point
- f2
the functional value for the x2 center point
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- def lsearch(xmax: Double = 2.0, x1: Double = 0.0): Double
Perform an exact Line Search (LS) using the Golden Search Algorithm.
Perform an exact Line Search (LS) using the Golden Search Algorithm. Two phases are used: an expansion phase (moving the end-point) to find a down-up pattern, followed by a traditional golden section search.
- xmax
a rough guess for the right end-point of the line search
- x1
the left (smallest) anchor point for the search (usually 0)
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- GoldenSectionLS → LineSearch
- final def ne(arg0: AnyRef): Boolean
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- def printGolden(): Unit
Print the golden ratio and the golden section.
- def search(step: Double = 2.0): Double
Perform an exact Line Search (LS) using the Golden Search Algorithm with defaults.
Perform an exact Line Search (LS) using the Golden Search Algorithm with defaults.
- step
the initial step size
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- GoldenSectionLS → LineSearch
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