org.apache.commons.math3.optimization.direct

Class CMAESOptimizer

java.lang.Object

org.apache.commons.math3.optimization.direct.BaseAbstractMultivariateOptimizer<FUNC>

org.apache.commons.math3.optimization.direct.BaseAbstractMultivariateSimpleBoundsOptimizer<MultivariateFunction>

org.apache.commons.math3.optimization.direct.CMAESOptimizer

All Implemented Interfaces:

BaseMultivariateOptimizer<MultivariateFunction>, BaseMultivariateSimpleBoundsOptimizer<MultivariateFunction>, BaseOptimizer<PointValuePair>, MultivariateOptimizer

Deprecated.

As of 3.1 (to be removed in 4.0).

@Deprecated
public class CMAESOptimizer
extends BaseAbstractMultivariateSimpleBoundsOptimizer<MultivariateFunction>
implements MultivariateOptimizer

An implementation of the active Covariance Matrix Adaptation Evolution Strategy (CMA-ES) for non-linear, non-convex, non-smooth, global function minimization. The CMA-Evolution Strategy (CMA-ES) is a reliable stochastic optimization method which should be applied if derivative-based methods, e.g. quasi-Newton BFGS or conjugate gradient, fail due to a rugged search landscape (e.g. noise, local optima, outlier, etc.) of the objective function. Like a quasi-Newton method, the CMA-ES learns and applies a variable metric on the underlying search space. Unlike a quasi-Newton method, the CMA-ES neither estimates nor uses gradients, making it considerably more reliable in terms of finding a good, or even close to optimal, solution.

In general, on smooth objective functions the CMA-ES is roughly ten times slower than BFGS (counting objective function evaluations, no gradients provided). For up to $N=10$ variables also the derivative-free simplex direct search method (Nelder and Mead) can be faster, but it is far less reliable than CMA-ES.

The CMA-ES is particularly well suited for non-separable and/or badly conditioned problems. To observe the advantage of CMA compared to a conventional evolution strategy, it will usually take about $30\; N$ function evaluations. On difficult problems the complete optimization (a single run) is expected to take roughly between $30\; N$ and $300\; N2$ function evaluations.

This implementation is translated and adapted from the Matlab version of the CMA-ES algorithm as implemented in module cmaes.m version 3.51.

For more information, please refer to the following links:

• Matlab code
• Introduction to CMA-ES
• Wikipedia

Since:

3.0

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
private static class	CMAESOptimizer.DoubleIndex Deprecated. Used to sort fitness values.
private class	CMAESOptimizer.FitnessFunction Deprecated. Normalizes fitness values to the range [0,1].
static class	CMAESOptimizer.PopulationSize Deprecated. Population size.
static class	CMAESOptimizer.Sigma Deprecated. Input sigma values.

Field Summary

Fields

Modifier and Type	Field and Description
private RealMatrix	B Deprecated. Coordinate system.
private RealMatrix	BD Deprecated. B*D, stored for efficiency.
private RealMatrix	C Deprecated. Covariance matrix.
private double	cc Deprecated. Cumulation constant.
private double	ccov1 Deprecated. Learning rate for rank-one update.
private double	ccov1Sep Deprecated. Learning rate for rank-one update - diagonalOnly
private double	ccovmu Deprecated. Learning rate for rank-mu update'
private double	ccovmuSep Deprecated. Learning rate for rank-mu update - diagonalOnly
private int	checkFeasableCount Deprecated. Determines how often a new random offspring is generated in case it is not feasible / beyond the defined limits, default is 0.
private double	chiN Deprecated. Expectation of ||N(0,I)|| == norm(randn(N,1)).
private double	cs Deprecated. Cumulation constant for step-size.
private RealMatrix	D Deprecated. Scaling.
private double	damps Deprecated. Damping for step-size.
static int	DEFAULT_CHECKFEASABLECOUNT Deprecated. Default value for checkFeasableCount: 0.
static int	DEFAULT_DIAGONALONLY Deprecated. Default value for diagonalOnly: 0.
static boolean	DEFAULT_ISACTIVECMA Deprecated. Default value for isActiveCMA: true.
static int	DEFAULT_MAXITERATIONS Deprecated. Default value for maxIterations: 30000.
static RandomGenerator	DEFAULT_RANDOMGENERATOR Deprecated. Default value for random.
static double	DEFAULT_STOPFITNESS Deprecated. Default value for stopFitness: 0.0.
private RealMatrix	diagC Deprecated. Diagonal of C, used for diagonalOnly.
private RealMatrix	diagD Deprecated. Diagonal of sqrt(D), stored for efficiency.
private int	diagonalOnly Deprecated. Defines the number of initial iterations, where the covariance matrix remains diagonal and the algorithm has internally linear time complexity.
private int	dimension Deprecated. Number of objective variables/problem dimension
private double[]	fitnessHistory Deprecated. History queue of best values.
private boolean	generateStatistics Deprecated. Indicates whether statistic data is collected.
private int	historySize Deprecated. Size of history queue of best values.
private double[]	inputSigma Deprecated.
private boolean	isActiveCMA Deprecated. Covariance update mechanism, default is active CMA.
private boolean	isMinimize Deprecated. Number of objective variables/problem dimension
private int	iterations Deprecated. Number of iterations already performed.
private int	lambda Deprecated. Population size, offspring number.
private double	logMu2 Deprecated. log(mu + 0.5), stored for efficiency.
private int	maxIterations Deprecated. Maximal number of iterations allowed.
private int	mu Deprecated. Number of parents/points for recombination.
private double	mueff Deprecated. Variance-effectiveness of sum w_i x_i.
private double	normps Deprecated. Norm of ps, stored for efficiency.
private RealMatrix	pc Deprecated. Evolution path.
private RealMatrix	ps Deprecated. Evolution path for sigma.
private RandomGenerator	random Deprecated. Random generator.
private double	sigma Deprecated. Overall standard deviation - search volume.
private java.util.List<RealMatrix>	statisticsDHistory Deprecated. History of D matrix.
private java.util.List<java.lang.Double>	statisticsFitnessHistory Deprecated. History of fitness values.
private java.util.List<RealMatrix>	statisticsMeanHistory Deprecated. History of mean matrix.
private java.util.List<java.lang.Double>	statisticsSigmaHistory Deprecated. History of sigma values.
private double	stopFitness Deprecated. Limit for fitness value.
private double	stopTolFun Deprecated. Stop if fun-changes smaller stopTolFun.
private double	stopTolHistFun Deprecated. Stop if back fun-changes smaller stopTolHistFun.
private double	stopTolUpX Deprecated. Stop if x-changes larger stopTolUpX.
private double	stopTolX Deprecated. Stop if x-change smaller stopTolX.
private RealMatrix	weights Deprecated. Array for weighted recombination.
private RealMatrix	xmean Deprecated. Objective variables.

Fields inherited from class org.apache.commons.math3.optimization.direct.BaseAbstractMultivariateOptimizer

evaluations

Constructor Summary

Constructors

Constructor and Description
CMAESOptimizer() Deprecated. As of version 3.1: Parameter lambda must be passed with the call to optimize (whereas in the current code it is set to an undocumented value).
CMAESOptimizer(int lambda) Deprecated. As of version 3.1: Parameter lambda must be passed with the call to optimize (whereas in the current code it is set to an undocumented value)..
CMAESOptimizer(int lambda, double[] inputSigma) Deprecated. As of version 3.1: Parameters lambda and inputSigma must be passed with the call to optimize.
CMAESOptimizer(int lambda, double[] inputSigma, int maxIterations, double stopFitness, boolean isActiveCMA, int diagonalOnly, int checkFeasableCount, RandomGenerator random, boolean generateStatistics) Deprecated. See SimpleValueChecker.SimpleValueChecker()
CMAESOptimizer(int lambda, double[] inputSigma, int maxIterations, double stopFitness, boolean isActiveCMA, int diagonalOnly, int checkFeasableCount, RandomGenerator random, boolean generateStatistics, ConvergenceChecker<PointValuePair> checker) Deprecated. As of version 3.1: Parameters lambda and inputSigma must be passed with the call to optimize.
CMAESOptimizer(int maxIterations, double stopFitness, boolean isActiveCMA, int diagonalOnly, int checkFeasableCount, RandomGenerator random, boolean generateStatistics, ConvergenceChecker<PointValuePair> checker) Deprecated.

Method Summary

Methods

Modifier and Type	Method and Description
private void	checkParameters() Deprecated. Checks dimensions and values of boundaries and inputSigma if defined.
private static void	copyColumn(RealMatrix m1, int col1, RealMatrix m2, int col2) Deprecated. Copies a column from m1 to m2.
private static RealMatrix	diag(RealMatrix m) Deprecated.
private static RealMatrix	divide(RealMatrix m, RealMatrix n) Deprecated.
protected PointValuePair	doOptimize() Deprecated. Perform the bulk of the optimization algorithm.
private static RealMatrix	eye(int n, int m) Deprecated.
java.util.List<RealMatrix>	getStatisticsDHistory() Deprecated.
java.util.List<java.lang.Double>	getStatisticsFitnessHistory() Deprecated.
java.util.List<RealMatrix>	getStatisticsMeanHistory() Deprecated.
java.util.List<java.lang.Double>	getStatisticsSigmaHistory() Deprecated.
private void	initializeCMA(double[] guess) Deprecated. Initialization of the dynamic search parameters
private static int[]	inverse(int[] indices) Deprecated.
private static RealMatrix	log(RealMatrix m) Deprecated.
private static double	max(double[] m) Deprecated.
private static double	max(RealMatrix m) Deprecated.
private static double	min(double[] m) Deprecated.
private static double	min(RealMatrix m) Deprecated.
private static RealMatrix	ones(int n, int m) Deprecated.
protected PointValuePair	optimizeInternal(int maxEval, MultivariateFunction f, GoalType goalType, OptimizationData... optData) Deprecated. Optimize an objective function.
private void	parseOptimizationData(OptimizationData... optData) Deprecated. Scans the list of (required and optional) optimization data that characterize the problem.
private static void	push(double[] vals, double val) Deprecated. Pushes the current best fitness value in a history queue.
private double[]	randn(int size) Deprecated.
private RealMatrix	randn1(int size, int popSize) Deprecated.
private static RealMatrix	repmat(RealMatrix mat, int n, int m) Deprecated.
private static int[]	reverse(int[] indices) Deprecated.
private static RealMatrix	selectColumns(RealMatrix m, int[] cols) Deprecated.
private static RealMatrix	sequence(double start, double end, double step) Deprecated.
private int[]	sortedIndices(double[] doubles) Deprecated. Sorts fitness values.
private static RealMatrix	sqrt(RealMatrix m) Deprecated.
private static RealMatrix	square(RealMatrix m) Deprecated.
private static RealMatrix	sumRows(RealMatrix m) Deprecated.
private static RealMatrix	times(RealMatrix m, RealMatrix n) Deprecated.
private static RealMatrix	triu(RealMatrix m, int k) Deprecated.
private void	updateBD(double negccov) Deprecated. Update B and D from C.
private void	updateCovariance(boolean hsig, RealMatrix bestArx, RealMatrix arz, int[] arindex, RealMatrix xold) Deprecated. Update of the covariance matrix C.
private void	updateCovarianceDiagonalOnly(boolean hsig, RealMatrix bestArz) Deprecated. Update of the covariance matrix C for diagonalOnly > 0
private boolean	updateEvolutionPaths(RealMatrix zmean, RealMatrix xold) Deprecated. Update of the evolution paths ps and pc.
private static RealMatrix	zeros(int n, int m) Deprecated.

Methods inherited from class org.apache.commons.math3.optimization.direct.BaseAbstractMultivariateSimpleBoundsOptimizer

optimize, optimize

Methods inherited from class org.apache.commons.math3.optimization.direct.BaseAbstractMultivariateOptimizer

computeObjectiveValue, getConvergenceChecker, getEvaluations, getGoalType, getLowerBound, getMaxEvaluations, getStartPoint, getUpperBound, optimize, optimizeInternal

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface org.apache.commons.math3.optimization.BaseMultivariateOptimizer

optimize

Methods inherited from interface org.apache.commons.math3.optimization.BaseOptimizer

getConvergenceChecker, getEvaluations, getMaxEvaluations

Field Detail

DEFAULT_CHECKFEASABLECOUNT

public static final int DEFAULT_CHECKFEASABLECOUNT

Deprecated.

Default value for checkFeasableCount: 0.

See Also:

Constant Field Values

DEFAULT_STOPFITNESS

public static final double DEFAULT_STOPFITNESS

Deprecated.

Default value for stopFitness: 0.0.

See Also:

Constant Field Values

DEFAULT_ISACTIVECMA

public static final boolean DEFAULT_ISACTIVECMA

Deprecated.

Default value for isActiveCMA: true.

See Also:

Constant Field Values

DEFAULT_MAXITERATIONS

public static final int DEFAULT_MAXITERATIONS

Deprecated.

Default value for maxIterations: 30000.

See Also:

Constant Field Values

DEFAULT_DIAGONALONLY

public static final int DEFAULT_DIAGONALONLY

Deprecated.

Default value for diagonalOnly: 0.

See Also:

Constant Field Values

DEFAULT_RANDOMGENERATOR

public static final RandomGenerator DEFAULT_RANDOMGENERATOR

Deprecated.

Default value for random.

lambda

private int lambda

Deprecated.

Population size, offspring number. The primary strategy parameter to play with, which can be increased from its default value. Increasing the population size improves global search properties in exchange to speed. Speed decreases, as a rule, at most linearly with increasing population size. It is advisable to begin with the default small population size.

isActiveCMA

private boolean isActiveCMA

Deprecated.

Covariance update mechanism, default is active CMA. isActiveCMA = true turns on "active CMA" with a negative update of the covariance matrix and checks for positive definiteness. OPTS.CMA.active = 2 does not check for pos. def. and is numerically faster. Active CMA usually speeds up the adaptation.

checkFeasableCount

private int checkFeasableCount

Deprecated.

Determines how often a new random offspring is generated in case it is not feasible / beyond the defined limits, default is 0.

inputSigma

private double[] inputSigma

Deprecated.

See Also:

CMAESOptimizer.Sigma

dimension

private int dimension

Deprecated.

Number of objective variables/problem dimension

diagonalOnly

private int diagonalOnly

Deprecated.

Defines the number of initial iterations, where the covariance matrix remains diagonal and the algorithm has internally linear time complexity. diagonalOnly = 1 means keeping the covariance matrix always diagonal and this setting also exhibits linear space complexity. This can be particularly useful for dimension > 100.

See Also:

A Simple Modification in CMA-ES

isMinimize

private boolean isMinimize

Deprecated.

Number of objective variables/problem dimension

generateStatistics

private boolean generateStatistics

Deprecated.

Indicates whether statistic data is collected.

maxIterations

private int maxIterations

Deprecated.

Maximal number of iterations allowed.

stopFitness

private double stopFitness

Deprecated.

Limit for fitness value.

stopTolUpX

private double stopTolUpX

Deprecated.

Stop if x-changes larger stopTolUpX.

stopTolX

private double stopTolX

Deprecated.

Stop if x-change smaller stopTolX.

stopTolFun

private double stopTolFun

Deprecated.

Stop if fun-changes smaller stopTolFun.

stopTolHistFun

private double stopTolHistFun

Deprecated.

Stop if back fun-changes smaller stopTolHistFun.

mu

private int mu

Deprecated.

Number of parents/points for recombination.

logMu2

private double logMu2

Deprecated.

log(mu + 0.5), stored for efficiency.

weights

private RealMatrix weights

Deprecated.

Array for weighted recombination.

mueff

private double mueff

Deprecated.

Variance-effectiveness of sum w_i x_i.

sigma

private double sigma

Deprecated.

Overall standard deviation - search volume.

cc

private double cc

Deprecated.

Cumulation constant.

cs

private double cs

Deprecated.

Cumulation constant for step-size.

damps

private double damps

Deprecated.

Damping for step-size.

ccov1

private double ccov1

Deprecated.

Learning rate for rank-one update.

ccovmu

private double ccovmu

Deprecated.

Learning rate for rank-mu update'

chiN

private double chiN

Deprecated.

Expectation of ||N(0,I)|| == norm(randn(N,1)).

ccov1Sep

private double ccov1Sep

Deprecated.

Learning rate for rank-one update - diagonalOnly

ccovmuSep

private double ccovmuSep

Deprecated.

Learning rate for rank-mu update - diagonalOnly

xmean

private RealMatrix xmean

Deprecated.

Objective variables.

pc

private RealMatrix pc

Deprecated.

Evolution path.

ps

private RealMatrix ps

Deprecated.

Evolution path for sigma.

normps

private double normps

Deprecated.

Norm of ps, stored for efficiency.

B

private RealMatrix B

Deprecated.

Coordinate system.

D

private RealMatrix D

Deprecated.

Scaling.

BD

private RealMatrix BD

Deprecated.

B*D, stored for efficiency.

diagD

private RealMatrix diagD

Deprecated.

Diagonal of sqrt(D), stored for efficiency.

C

private RealMatrix C

Deprecated.

Covariance matrix.

diagC

private RealMatrix diagC

Deprecated.

Diagonal of C, used for diagonalOnly.

iterations

private int iterations

Deprecated.

Number of iterations already performed.

fitnessHistory

private double[] fitnessHistory

Deprecated.

History queue of best values.

historySize

private int historySize

Deprecated.

Size of history queue of best values.

random

private RandomGenerator random

Deprecated.

Random generator.

statisticsSigmaHistory

private java.util.List<java.lang.Double> statisticsSigmaHistory

Deprecated.

History of sigma values.

statisticsMeanHistory

private java.util.List<RealMatrix> statisticsMeanHistory

Deprecated.

History of mean matrix.

statisticsFitnessHistory

private java.util.List<java.lang.Double> statisticsFitnessHistory

Deprecated.

History of fitness values.

statisticsDHistory

private java.util.List<RealMatrix> statisticsDHistory

Deprecated.

History of D matrix.

Constructor Detail

CMAESOptimizer

@Deprecated
public CMAESOptimizer()

Deprecated. As of version 3.1: Parameter lambda must be passed with the call to optimize (whereas in the current code it is set to an undocumented value).

Default constructor, uses default parameters

CMAESOptimizer

@Deprecated
public CMAESOptimizer(int lambda)

Deprecated. As of version 3.1: Parameter lambda must be passed with the call to optimize (whereas in the current code it is set to an undocumented value)..

Parameters:

lambda - Population size.

CMAESOptimizer

@Deprecated
public CMAESOptimizer(int lambda,
                         double[] inputSigma)

Deprecated. As of version 3.1: Parameters lambda and inputSigma must be passed with the call to optimize.

Parameters:

lambda - Population size.

inputSigma - Initial standard deviations to sample new points around the initial guess.

CMAESOptimizer

@Deprecated
public CMAESOptimizer(int lambda,
                         double[] inputSigma,
                         int maxIterations,
                         double stopFitness,
                         boolean isActiveCMA,
                         int diagonalOnly,
                         int checkFeasableCount,
                         RandomGenerator random,
                         boolean generateStatistics)

Deprecated. See SimpleValueChecker.SimpleValueChecker()

Parameters:

lambda - Population size.

inputSigma - Initial standard deviations to sample new points around the initial guess.

maxIterations - Maximal number of iterations.

stopFitness - Whether to stop if objective function value is smaller than stopFitness.

isActiveCMA - Chooses the covariance matrix update method.

diagonalOnly - Number of initial iterations, where the covariance matrix remains diagonal.

checkFeasableCount - Determines how often new random objective variables are generated in case they are out of bounds.

random - Random generator.

generateStatistics - Whether statistic data is collected.

CMAESOptimizer

@Deprecated
public CMAESOptimizer(int lambda,
                         double[] inputSigma,
                         int maxIterations,
                         double stopFitness,
                         boolean isActiveCMA,
                         int diagonalOnly,
                         int checkFeasableCount,
                         RandomGenerator random,
                         boolean generateStatistics,
                         ConvergenceChecker<PointValuePair> checker)

Deprecated. As of version 3.1: Parameters lambda and inputSigma must be passed with the call to optimize.

Parameters:

lambda - Population size.

inputSigma - Initial standard deviations to sample new points around the initial guess.

maxIterations - Maximal number of iterations.

stopFitness - Whether to stop if objective function value is smaller than stopFitness.

isActiveCMA - Chooses the covariance matrix update method.

diagonalOnly - Number of initial iterations, where the covariance matrix remains diagonal.

checkFeasableCount - Determines how often new random objective variables are generated in case they are out of bounds.

random - Random generator.

generateStatistics - Whether statistic data is collected.

checker - Convergence checker.

CMAESOptimizer

public CMAESOptimizer(int maxIterations,
              double stopFitness,
              boolean isActiveCMA,
              int diagonalOnly,
              int checkFeasableCount,
              RandomGenerator random,
              boolean generateStatistics,
              ConvergenceChecker<PointValuePair> checker)

Deprecated.

Parameters:

maxIterations - Maximal number of iterations.

stopFitness - Whether to stop if objective function value is smaller than stopFitness.

isActiveCMA - Chooses the covariance matrix update method.

diagonalOnly - Number of initial iterations, where the covariance matrix remains diagonal.

checkFeasableCount - Determines how often new random objective variables are generated in case they are out of bounds.

random - Random generator.

generateStatistics - Whether statistic data is collected.

checker - Convergence checker.

Since:

3.1

Method Detail

getStatisticsSigmaHistory

public java.util.List<java.lang.Double> getStatisticsSigmaHistory()

Deprecated.

Returns:

History of sigma values.

getStatisticsMeanHistory

public java.util.List<RealMatrix> getStatisticsMeanHistory()

Deprecated.

Returns:

History of mean matrix.

getStatisticsFitnessHistory

public java.util.List<java.lang.Double> getStatisticsFitnessHistory()

Deprecated.

Returns:

History of fitness values.

getStatisticsDHistory

public java.util.List<RealMatrix> getStatisticsDHistory()

Deprecated.

Returns:

History of D matrix.

optimizeInternal

protected PointValuePair optimizeInternal(int maxEval,
                              MultivariateFunction f,
                              GoalType goalType,
                              OptimizationData... optData)

Deprecated.

Optimize an objective function.

Overrides:

optimizeInternal in class BaseAbstractMultivariateOptimizer<MultivariateFunction>

Parameters:

maxEval - Allowed number of evaluations of the objective function.

f - Objective function.

goalType - Optimization type.

optData - Optimization data. The following data will be looked for:

• InitialGuess
• CMAESOptimizer.Sigma
• CMAESOptimizer.PopulationSize

Returns:

the point/value pair giving the optimal value for objective function.

doOptimize

protected PointValuePair doOptimize()

Deprecated.

Perform the bulk of the optimization algorithm.

Specified by:

doOptimize in class BaseAbstractMultivariateOptimizer<MultivariateFunction>

Returns:

the point/value pair giving the optimal value of the objective function.

parseOptimizationData

private void parseOptimizationData(OptimizationData... optData)

Deprecated.

Scans the list of (required and optional) optimization data that characterize the problem.

Parameters:

optData - Optimization data. The following data will be looked for:

• CMAESOptimizer.Sigma
• CMAESOptimizer.PopulationSize

checkParameters

private void checkParameters()

Deprecated.

Checks dimensions and values of boundaries and inputSigma if defined.

initializeCMA

private void initializeCMA(double[] guess)

Deprecated.

Initialization of the dynamic search parameters

Parameters:

guess - Initial guess for the arguments of the fitness function.

updateEvolutionPaths

private boolean updateEvolutionPaths(RealMatrix zmean,
                           RealMatrix xold)

Deprecated.

Update of the evolution paths ps and pc.

Parameters:

zmean - Weighted row matrix of the gaussian random numbers generating the current offspring.

xold - xmean matrix of the previous generation.

Returns:

hsig flag indicating a small correction.

updateCovarianceDiagonalOnly

private void updateCovarianceDiagonalOnly(boolean hsig,
                                RealMatrix bestArz)

Deprecated.

Update of the covariance matrix C for diagonalOnly > 0

Parameters:

hsig - Flag indicating a small correction.

bestArz - Fitness-sorted matrix of the gaussian random values of the current offspring.

updateCovariance

private void updateCovariance(boolean hsig,
                    RealMatrix bestArx,
                    RealMatrix arz,
                    int[] arindex,
                    RealMatrix xold)

Deprecated.

Update of the covariance matrix C.

Parameters:

hsig - Flag indicating a small correction.

bestArx - Fitness-sorted matrix of the argument vectors producing the current offspring.

arz - Unsorted matrix containing the gaussian random values of the current offspring.

arindex - Indices indicating the fitness-order of the current offspring.

xold - xmean matrix of the previous generation.

updateBD

private void updateBD(double negccov)

Deprecated.

Update B and D from C.

Parameters:

negccov - Negative covariance factor.

push

private static void push(double[] vals,
        double val)

Deprecated.

Pushes the current best fitness value in a history queue.

Parameters:

vals - History queue.

val - Current best fitness value.

sortedIndices

private int[] sortedIndices(double[] doubles)

Deprecated.

Sorts fitness values.

Parameters:

doubles - Array of values to be sorted.

Returns:

a sorted array of indices pointing into doubles.

log

private static RealMatrix log(RealMatrix m)

Deprecated.

Parameters:

m - Input matrix

Returns:

Matrix representing the element-wise logarithm of m.

sqrt

private static RealMatrix sqrt(RealMatrix m)

Deprecated.

Parameters:

m - Input matrix.

Returns:

Matrix representing the element-wise square root of m.

square

private static RealMatrix square(RealMatrix m)

Deprecated.

Parameters:

m - Input matrix.

Returns:

Matrix representing the element-wise square of m.

times

private static RealMatrix times(RealMatrix m,
               RealMatrix n)

Deprecated.

Parameters:

m - Input matrix 1.

n - Input matrix 2.

Returns:

the matrix where the elements of m and n are element-wise multiplied.

divide

private static RealMatrix divide(RealMatrix m,
                RealMatrix n)

Deprecated.

Parameters:

m - Input matrix 1.

n - Input matrix 2.

Returns:

Matrix where the elements of m and n are element-wise divided.

selectColumns

private static RealMatrix selectColumns(RealMatrix m,
                       int[] cols)

Deprecated.

Parameters:

m - Input matrix.

cols - Columns to select.

Returns:

Matrix representing the selected columns.

triu

private static RealMatrix triu(RealMatrix m,
              int k)

Deprecated.

Parameters:

m - Input matrix.

k - Diagonal position.

Returns:

Upper triangular part of matrix.

sumRows

private static RealMatrix sumRows(RealMatrix m)

Deprecated.

Parameters:

m - Input matrix.

Returns:

Row matrix representing the sums of the rows.

diag

private static RealMatrix diag(RealMatrix m)

Deprecated.

Parameters:

m - Input matrix.

Returns:

the diagonal n-by-n matrix if m is a column matrix or the column matrix representing the diagonal if m is a n-by-n matrix.

copyColumn

private static void copyColumn(RealMatrix m1,
              int col1,
              RealMatrix m2,
              int col2)

Deprecated.

Copies a column from m1 to m2.

Parameters:

m1 - Source matrix.

col1 - Source column.

m2 - Target matrix.

col2 - Target column.

ones

private static RealMatrix ones(int n,
              int m)

Deprecated.

Parameters:

n - Number of rows.

m - Number of columns.

Returns:

n-by-m matrix filled with 1.

eye

private static RealMatrix eye(int n,
             int m)

Deprecated.

Parameters:

n - Number of rows.

m - Number of columns.

Returns:

n-by-m matrix of 0 values out of diagonal, and 1 values on the diagonal.

zeros

private static RealMatrix zeros(int n,
               int m)

Deprecated.

Parameters:

n - Number of rows.

m - Number of columns.

Returns:

n-by-m matrix of zero values.

repmat

private static RealMatrix repmat(RealMatrix mat,
                int n,
                int m)

Deprecated.

Parameters:

mat - Input matrix.

n - Number of row replicates.

m - Number of column replicates.

Returns:

a matrix which replicates the input matrix in both directions.

sequence

private static RealMatrix sequence(double start,
                  double end,
                  double step)

Deprecated.

Parameters:

start - Start value.

end - End value.

step - Step size.

Returns:

a sequence as column matrix.

max

private static double max(RealMatrix m)

Deprecated.

Parameters:

m - Input matrix.

Returns:

the maximum of the matrix element values.

min

private static double min(RealMatrix m)

Deprecated.

Parameters:

m - Input matrix.

Returns:

the minimum of the matrix element values.

max

private static double max(double[] m)

Deprecated.

Parameters:

m - Input array.

Returns:

the maximum of the array values.

min

private static double min(double[] m)

Deprecated.

Parameters:

m - Input array.

Returns:

the minimum of the array values.

inverse

private static int[] inverse(int[] indices)

Deprecated.

Parameters:

indices - Input index array.

Returns:

the inverse of the mapping defined by indices.

reverse

private static int[] reverse(int[] indices)

Deprecated.

Parameters:

indices - Input index array.

Returns:

the indices in inverse order (last is first).

randn

private double[] randn(int size)

Deprecated.

Parameters:

size - Length of random array.

Returns:

an array of Gaussian random numbers.

randn1

private RealMatrix randn1(int size,
                int popSize)

Deprecated.

Parameters:

size - Number of rows.

popSize - Population size.

Returns:

a 2-dimensional matrix of Gaussian random numbers.