gmx::NelderMeadSimplex Class Reference

#include <gromacs/math/neldermead.h>

Description

The simplex for the Nelder-Mead algorithm.

Contains the N+1 simplex N-dimensional coordinates and its function values. Allows for simplex manipulations as needed for the Nelder-Mead algorithm.

Note

Keeps the simplex sorted according to function values with the simplex at the lowest function value first.

Public Member Functions
	NelderMeadSimplex (const std::function< real(ArrayRef< const real >)> &f, ArrayRef< const real > initalGuess)
	Set up Nelder-Mead simplex from an initial guess. More...
const RealFunctionvalueAtCoordinate &	bestVertex () const
	Return the vertex with the lowest function value at any of the simplex vertices.
const RealFunctionvalueAtCoordinate &	worstVertex () const
	Return the vertex of the simplex with the highest (worst) function value.
real	secondWorstValue () const
	Return the second largest function value at any of the simplex vertices.
RealFunctionvalueAtCoordinate	evaluateReflectionPoint (const std::function< real(ArrayRef< const real >)> &f) const
	Return the reflection point and the evaluated function value at this point.
RealFunctionvalueAtCoordinate	evaluateExpansionPoint (const std::function< real(ArrayRef< const real >)> &f) const
	Evaluate and return the expansion point and function value.
RealFunctionvalueAtCoordinate	evaluateContractionPoint (const std::function< real(ArrayRef< const real >)> &f) const
	Evaluate and return the contraction point and function value.
void	swapOutWorst (const RealFunctionvalueAtCoordinate &newVertex)
	Replace the simplex vertex with the largest function value. More...
void	shrinkSimplexPointsExceptBest (const std::function< real(ArrayRef< const real >)> &f)
	Shrink the simplex. More...
real	orientedLength () const
	The oriented length of the vertex. More...

Constructor & Destructor Documentation

gmx::NelderMeadSimplex::NelderMeadSimplex	(	const std::function< real(ArrayRef< const real >)> &	f,
		ArrayRef< const real >	initalGuess
	)

Set up Nelder-Mead simplex from an initial guess.

Note

Triggers N+1 function evaluations at all simplex points.

Parameters

[in]	f	the function to be evaluated
[in]	initalGuess	initial guess of the coordinates.

Member Function Documentation

real gmx::NelderMeadSimplex::orientedLength

(

)

const

The oriented length of the vertex.

The oriented length of the simplex is defined as the largest distance between the first simplex vertex coordinate (with the lowest, best function value) and any other simplex coordinate.

The oriented length is used as a computationally fast and simple convergence criterion because it is proven that orientedLegnth < simplex_diameter < 2 * orientedLength

void gmx::NelderMeadSimplex::shrinkSimplexPointsExceptBest

(

const std::function< real(ArrayRef< const real >)> &

f

)

Shrink the simplex.

All points move closer to the best point by a factor .

Replace all point coordinates, except the best, with

void gmx::NelderMeadSimplex::swapOutWorst

(

const RealFunctionvalueAtCoordinate &

newVertex

)

Replace the simplex vertex with the largest function value.

Parameters

[in]

newVertex

to replace the worst vertex with

Note

keeps the simplex list sorted and reevaluates the reflection point

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The documentation for this class was generated from the following files:

• src/gromacs/math/neldermead.h
• src/gromacs/math/neldermead.cpp