B C D E F G I L M N O P R S U

B

BEALE_SORENSON_HESTENES_STIEFEL_UPDATE - Static variable in class pal.math.ConjugateGradientSearch

Binomial - Class in pal.math

Binomial coefficients

Binomial() - Constructor for class pal.math.Binomial

BoundsCheckedFunction - Class in pal.math

returns a very large number instead of the function value if arguments are out of bound (useful for minimization with minimizers that don't check argument boundaries)

BoundsCheckedFunction(MultivariateFunction) - Constructor for class pal.math.BoundsCheckedFunction

construct bound-checked multivariate function (a large number will be returned on function evaluation if argument is out of bounds; default is 1000000)

BoundsCheckedFunction(MultivariateFunction, double) - Constructor for class pal.math.BoundsCheckedFunction

construct constrained multivariate function

C

checkDirection(double[], double[]) - Method in class pal.math.LineFunction

check direction vector.

checkPoint(double[]) - Method in class pal.math.LineFunction

check (and modify, if necessary) whether a point lies properly within the predefined bounds

checkVariables(double[], double[], boolean[]) - Method in class pal.math.LineFunction

determine active variables at a point p and corresponding gradient grad (if a component of p lies on a border and the corresponding component of the gradient points out of the border the variable is considered inactive)

choose(double, double) - Method in class pal.math.Binomial

Binomial coefficient n choose k

computeEpsilon() - Static method in class pal.math.MachineAccuracy

compute EPSILON from scratch

computeGradient(double[], double[]) - Method in interface pal.math.MFWithGradient

compute gradient at a point

ConjugateDirectionSearch - Class in pal.math

methods for minimization of a real-valued function of several variables without using derivatives (Brent's modification of a conjugate direction search method proposed by Powell)

ConjugateDirectionSearch() - Constructor for class pal.math.ConjugateDirectionSearch

constructor

ConjugateDirectionSearch.OptimizationError - Exception in pal.math

ConjugateGradientSearch - Class in pal.math

minimization of a real-valued function of several variables using a the nonlinear conjugate gradient method where several variants of the direction update are available (Fletcher-Reeves, Polak-Ribiere, Beale-Sorenson, Hestenes-Stiefel) and bounds are respected.

ConjugateGradientSearch() - Constructor for class pal.math.ConjugateGradientSearch

ConjugateGradientSearch(int) - Constructor for class pal.math.ConjugateGradientSearch

conjugateGradientStyle - Variable in class pal.math.ConjugateGradientSearch

conjugateGradientStyle determines the method for the conjugate gradient direction update update (0 = Fletcher-Reeves, 1 = Polak-Ribiere, 2 = Beale-Sorenson, Hestenes-Stiefel), the default is 2.

copy(double[], double[]) - Method in class pal.math.MultivariateMinimum

Copy source vector into target vector

CR - Variable in class pal.math.DifferentialEvolution

Crossing over factor (default 0.9)

D

defaultStep - Variable in class pal.math.ConjugateGradientSearch

defaultStep is a steplength parameter and should be set equal to the expected distance from the solution (in a line search) exceptionally small or large values of defaultStep lead to slower convergence on the first few iterations (the step length itself is adapted during search), the default value is 1.0

diagonalHessian(MultivariateFunction, double[]) - Static method in class pal.math.NumericalDerivative

determine diagonal of Hessian

DifferentialEvolution - Class in pal.math

global minimization of a real-valued function of several variables without using derivatives using a genetic algorithm (Differential Evolution)

DifferentialEvolution(int) - Constructor for class pal.math.DifferentialEvolution

construct DE optimization modul (population size is selected automatically)

DifferentialEvolution(int, int) - Constructor for class pal.math.DifferentialEvolution

construct optimization modul

drawDontPutBack() - Method in class pal.math.UrnModel

draw a number without putting back

drawPutBack() - Method in class pal.math.UrnModel

draws a number with putting back

E

EPSILON - Static variable in class pal.math.MachineAccuracy

machine accuracy constant

erf(double) - Static method in class pal.math.ErrorFunction

error function

erfc(double) - Static method in class pal.math.ErrorFunction

complementary error function = 1-erf(x)

ErrorFunction - Class in pal.math

error function and related stuff

ErrorFunction() - Constructor for class pal.math.ErrorFunction

evaluate(double[]) - Method in class pal.math.BoundsCheckedFunction

computes function value, taking into account the constraints on the argument

evaluate(double) - Method in class pal.math.LineFunction

evaluate f(start+lambda*dir)

evaluate(double[], double[]) - Method in interface pal.math.MFWithGradient

compute both function value and gradient at a point

evaluate(double[]) - Method in interface pal.math.MultivariateFunction

compute function value

evaluate(double) - Method in class pal.math.OrthogonalLineFunction

evaluate(double) - Method in interface pal.math.UnivariateFunction

compute function value

F

F - Variable in class pal.math.DifferentialEvolution

weight factor (default 0.7)

f2minx - Variable in class pal.math.UnivariateMinimum

curvature at minimum

findMinimum() - Method in class pal.math.LineFunction

find parameter lambda within the given bounds that minimizes the univariate function (due to numerical inaccuaries it may happen that getPoint for the returned lambda produces a point that lies slightly out of bounds)

findMinimum(MultivariateFunction, double[]) - Method in class pal.math.MultivariateMinimum

Find minimum close to vector x

findMinimum(MultivariateFunction, double[], int, int) - Method in class pal.math.MultivariateMinimum

Find minimum close to vector x (desired fractional digits for each parameter is specified)

findMinimum(double, UnivariateFunction) - Method in class pal.math.UnivariateMinimum

Find minimum (first estimate given)

findMinimum(double, UnivariateFunction, int) - Method in class pal.math.UnivariateMinimum

Find minimum (first estimate given, desired number of fractional digits specified)

findMinimum(UnivariateFunction) - Method in class pal.math.UnivariateMinimum

Find minimum (no first estimate given)

findMinimum(UnivariateFunction, int) - Method in class pal.math.UnivariateMinimum

Find minimum (no first estimate given, desired number of fractional digits specified)

firstDerivative(UnivariateFunction, double) - Static method in class pal.math.NumericalDerivative

determine first derivative

FLETCHER_REEVES_UPDATE - Static variable in class pal.math.ConjugateGradientSearch

fminx - Variable in class pal.math.UnivariateMinimum

function value at minimum

G

GammaFunction - Class in pal.math

gamma function

GammaFunction() - Constructor for class pal.math.GammaFunction

GeneralizedDEOptimizer - Class in pal.math

Provides an general interface to the DifferentialEvolution class that is not tied to a certain number of parameters (as DifferentialEvolution is).

GeneralizedDEOptimizer() - Constructor for class pal.math.GeneralizedDEOptimizer

getLowerBound(int) - Method in class pal.math.BoundsCheckedFunction

getLowerBound() - Method in class pal.math.LineFunction

getLowerBound(int) - Method in interface pal.math.MultivariateFunction

get lower bound of argument n

getLowerBound() - Method in class pal.math.OrthogonalLineFunction

getLowerBound() - Method in interface pal.math.UnivariateFunction

get lower bound of argument

getLowerBoundParameter() - Method in class pal.math.LineFunction

get parameter that limits the lower bound

getNChoose2(int) - Method in class pal.math.Binomial

get (precomputed) n choose 2

getNextBoolean() - Static method in class pal.math.MersenneTwisterFast

Access a default instance of this class, access is synchronized

getNextByte() - Static method in class pal.math.MersenneTwisterFast

Access a default instance of this class, access is synchronized

getNextBytes(byte[]) - Static method in class pal.math.MersenneTwisterFast

Access a default instance of this class, access is synchronized

getNextChar() - Static method in class pal.math.MersenneTwisterFast

Access a default instance of this class, access is synchronized

getNextDouble() - Static method in class pal.math.MersenneTwisterFast

Access a default instance of this class, access is synchronized

getNextFloat() - Static method in class pal.math.MersenneTwisterFast

Access a default instance of this class, access is synchronized

getNextInt() - Static method in class pal.math.MersenneTwisterFast

Access a default instance of this class, access is synchronized

getNextLong() - Static method in class pal.math.MersenneTwisterFast

Access a default instance of this class, access is synchronized

getNextShort() - Static method in class pal.math.MersenneTwisterFast

Access a default instance of this class, access is synchronized

getNormalized(double[]) - Static method in class pal.math.MathUtils

getNumArguments() - Method in class pal.math.BoundsCheckedFunction

getNumArguments() - Method in interface pal.math.MultivariateFunction

get number of arguments

getPoint(double, double[]) - Method in class pal.math.LineFunction

get point associated with the one-dimensional parameter (bounds of of multivariate function are NOT checked)

getRandomArguments(MultivariateFunction) - Static method in class pal.math.MathUtils

getTotal(double[], int, int) - Static method in class pal.math.MathUtils

getTotal(double[]) - Static method in class pal.math.MathUtils

getUpperBound(int) - Method in class pal.math.BoundsCheckedFunction

getUpperBound() - Method in class pal.math.LineFunction

getUpperBound(int) - Method in interface pal.math.MultivariateFunction

get upper bound of argument n

getUpperBound() - Method in class pal.math.OrthogonalLineFunction

getUpperBound() - Method in interface pal.math.UnivariateFunction

get upper bound of argument

getUpperBoundParameter() - Method in class pal.math.LineFunction

get parameter that limits the upper bound

gradient(MultivariateFunction, double[]) - Static method in class pal.math.NumericalDerivative

determine gradient

gradient(MultivariateFunction, double[], double[]) - Static method in class pal.math.NumericalDerivative

determine gradient

I

illc - Variable in class pal.math.ConjugateDirectionSearch

illc should be set to true if the problem is known to be ill-conditioned.

incompleteGammaP(double, double) - Static method in class pal.math.GammaFunction

Incomplete Gamma function P(a,x) = 1-Q(a,x) (a cleanroom implementation of Numerical Recipes gammp(a,x); in Mathematica this function is 1-GammaRegularized)

incompleteGammaP(double, double, double) - Static method in class pal.math.GammaFunction

Incomplete Gamma function P(a,x) = 1-Q(a,x) (a cleanroom implementation of Numerical Recipes gammp(a,x); in Mathematica this function is 1-GammaRegularized)

incompleteGammaQ(double, double) - Static method in class pal.math.GammaFunction

Incomplete Gamma function Q(a,x) (a cleanroom implementation of Numerical Recipes gammq(a,x); in Mathematica this function is called GammaRegularized)

interrupt - Variable in class pal.math.ConjugateDirectionSearch

MHL: added this so we can interrupt the optimization if we need to.

inverseErf(double) - Static method in class pal.math.ErrorFunction

inverse error function

L

LineFunction - Class in pal.math

converts a multivariate function into a univariate function

LineFunction(MultivariateFunction) - Constructor for class pal.math.LineFunction

construct univariate function from multivariate function

lnGamma(double) - Static method in class pal.math.GammaFunction

log Gamma function: ln(gamma(alpha)) for alpha>0, accurate to 10 decimal places

M

MachineAccuracy - Class in pal.math

determines machine accuracy

MachineAccuracy() - Constructor for class pal.math.MachineAccuracy

MathUtils - Class in pal.math

Handy utility functions which have some Mathematical relavance.

MathUtils() - Constructor for class pal.math.MathUtils

maxFun - Variable in class pal.math.MultivariateMinimum

maxFun is the maximum number of calls to fun allowed.

maxFun - Variable in class pal.math.UnivariateMinimum

maximum number of function evaluations (default 0 indicates no limit on calls)

MersenneTwisterFast - Class in pal.math

MersenneTwisterFast: A simulation quality fast random number generator (MT19937) with the same public methods as java.util.Random.

MersenneTwisterFast() - Constructor for class pal.math.MersenneTwisterFast

Constructor using the time of day as default seed.

MersenneTwisterFast(long) - Constructor for class pal.math.MersenneTwisterFast

Constructor using a given seed.

MFWithGradient - Interface in pal.math

interface for a function of several variables with a gradient

minx - Variable in class pal.math.UnivariateMinimum

last minimum

MultivariateFunction - Interface in pal.math

interface for a function of several variables

MultivariateMinimum - Class in pal.math

abstract base class for minimisation of a multivariate function

MultivariateMinimum() - Constructor for class pal.math.MultivariateMinimum

N

nextBoolean() - Method in class pal.math.MersenneTwisterFast

nextByte() - Method in class pal.math.MersenneTwisterFast

nextBytes(byte[]) - Method in class pal.math.MersenneTwisterFast

nextChar() - Method in class pal.math.MersenneTwisterFast

nextDouble() - Method in class pal.math.MersenneTwisterFast

nextFloat() - Method in class pal.math.MersenneTwisterFast

nextGaussian() - Method in class pal.math.MersenneTwisterFast

nextInt() - Method in class pal.math.MersenneTwisterFast

nextInt(int) - Method in class pal.math.MersenneTwisterFast

Returns an integer drawn uniformly from 0 to n-1.

nextLong() - Method in class pal.math.MersenneTwisterFast

nextShort() - Method in class pal.math.MersenneTwisterFast

NumericalDerivative - Class in pal.math

approximates numerically the first and second derivatives of a function of a single variable and approximates gradient and diagonal of Hessian for multivariate functions

NumericalDerivative() - Constructor for class pal.math.NumericalDerivative

numFun - Variable in class pal.math.MultivariateMinimum

total number of function evaluations necessary

numFun - Variable in class pal.math.UnivariateMinimum

total number of function evaluations neccessary

numFuncStops - Variable in class pal.math.MultivariateMinimum

numFuncStops is the number of consecutive positive evaluations of the stop criterion based on function evaluation necessary to cause the abortion of the optimization (default is 4)

O

OptimizationError(String) - Constructor for exception pal.math.ConjugateDirectionSearch.OptimizationError

optimize(MultivariateFunction, double[], double, double) - Method in class pal.math.ConjugateDirectionSearch

optimize(MultivariateFunction, double[], double, double) - Method in class pal.math.ConjugateGradientSearch

optimize(MultivariateFunction, double[], double, double) - Method in class pal.math.DifferentialEvolution

optimize(MultivariateFunction, double[], double, double) - Method in class pal.math.GeneralizedDEOptimizer

The actual optimization routine It finds a minimum close to vector x when the absolute tolerance for each parameter is specified.

optimize(MultivariateFunction, double[], double, double) - Method in class pal.math.MultivariateMinimum

The actual optimization routine (needs to be implemented in a subclass of MultivariateMinimum).

optimize(MultivariateFunction, double[], double, double) - Method in class pal.math.OrthogonalSearch

optimize(MultivariateFunction, double[], double, double) - Method in class pal.math.StochasticOSearch

optimize(UnivariateFunction, double) - Method in class pal.math.UnivariateMinimum

The actual optimization routine (Brent's golden section method)

optimize(double, UnivariateFunction, double) - Method in class pal.math.UnivariateMinimum

The actual optimization routine (Brent's golden section method)

OrthogonalLineFunction - Class in pal.math

converts a multivariate function into a univariate function by keeping all but one argument constant

OrthogonalLineFunction(MultivariateFunction) - Constructor for class pal.math.OrthogonalLineFunction

construct univariate function from multivariate function

OrthogonalSearch - Class in pal.math

minimization of a real-valued function of several variables without using derivatives, using the simple strategy of optimizing variables one by one.

OrthogonalSearch() - Constructor for class pal.math.OrthogonalSearch

Initialization

P

pal.math - package pal.math

POLAK_RIBIERE_UPDATE - Static variable in class pal.math.ConjugateGradientSearch

prin - Variable in class pal.math.ConjugateDirectionSearch

controls the printed output from the routine (0 = no output, 1 = print only starting and final values, 2 = detailed map of the minimization process, 3 = print also eigenvalues and vectors of the search directions), the default value is 0

prin - Variable in class pal.math.ConjugateGradientSearch

controls the printed output from the routine (0 = no output, 1 = print only starting and final values, 2 = detailed map of the minimisation process), the default value is 0

prin - Variable in class pal.math.DifferentialEvolution

variable controlling print out, default value = 0 (0 = no output, 1 = print final value, 2 = detailed map of optimization process)

R

random - Static variable in class pal.math.MathUtils

A random number generator that is initialized with the clock when this class is loaded into the JVM.

reset() - Method in class pal.math.UrnModel

refill urn

S

same(double, double) - Static method in class pal.math.MachineAccuracy

scbd - Variable in class pal.math.ConjugateDirectionSearch

scbd is a scaling parameter.

secondDerivative(UnivariateFunction, double) - Static method in class pal.math.NumericalDerivative

determine second derivative

selectArgument(int) - Method in class pal.math.OrthogonalLineFunction

use only the specified argument in the constructed univariate function and keep all others constant

setAllArguments(double[]) - Method in class pal.math.OrthogonalLineFunction

set (change) values of all arguments (start values)

setArgument(double) - Method in class pal.math.OrthogonalLineFunction

set (change) value of a single argument (the one currently active)

setMax(int) - Method in class pal.math.Binomial

set capacity and precompute the n choose 2 values

setSeed(long) - Method in class pal.math.MersenneTwisterFast

Initalize the pseudo random number generator.

shuffle(int[]) - Method in class pal.math.MersenneTwisterFast

Shuffles an array.

shuffle(int[], int) - Method in class pal.math.MersenneTwisterFast

Shuffles an array.

shuffled(int) - Method in class pal.math.MersenneTwisterFast

Returns an array of shuffled indices of length l.

SQRT_EPSILON - Static variable in class pal.math.MachineAccuracy

SQRT_SQRT_EPSILON - Static variable in class pal.math.MachineAccuracy

step - Variable in class pal.math.ConjugateDirectionSearch

step is a steplength parameter and should be set equal to the expected distance from the solution.

StochasticOSearch - Class in pal.math

minimization of a real-valued function of several variables without using derivatives, using the simple strategy of optimizing variables one by one.

StochasticOSearch() - Constructor for class pal.math.StochasticOSearch

Initialization

stopCondition(double, double[], double, double, boolean) - Method in class pal.math.MultivariateMinimum

Checks whether optimization should stop

U

UnivariateFunction - Interface in pal.math

interface for a function of one variable

UnivariateMinimum - Class in pal.math

minimization of a real-valued function of one variable without using derivatives.

UnivariateMinimum() - Constructor for class pal.math.UnivariateMinimum

update(double[], double[]) - Method in class pal.math.LineFunction

update start point and direction (bounds and search direction are NOT checked)

UrnModel - Class in pal.math

class for drawing numbers from an urn with and without laying back

UrnModel(int) - Constructor for class pal.math.UrnModel

create urn model

B C D E F G I L M N O P R S U