Package org.apfloat

Class IncompleteGammaHelper

java.lang.Object

org.apfloat.IncompleteGammaHelper

class IncompleteGammaHelper
extends java.lang.Object

Helper class for the incomplete gamma function.

Since:

1.10.0

Version:

1.14.0

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
private static class	IncompleteGammaHelper.ContinuedFraction
private static class	IncompleteGammaHelper.ContinuedFractionResult
private static class	IncompleteGammaHelper.ContinuedFractionType
private static class	IncompleteGammaHelper.GammaValue
private static class	IncompleteGammaHelper.RetryException
private static class	IncompleteGammaHelper.Sequence

Constructor Summary

Constructors

Constructor	Description
IncompleteGammaHelper()

Method Summary

Modifier and Type	Method	Description
private static Apfloat	abs(Apcomplex z)
private static IncompleteGammaHelper.GammaValue	asymptoticLargeA(Apcomplex a, Apcomplex z)
private static IncompleteGammaHelper.GammaValue	asymptoticLargeZ(Apcomplex a, Apcomplex z)
private static IncompleteGammaHelper.GammaValue	attemptUStar(Apcomplex a, Apcomplex z)
private static void	checkPrecision(Apcomplex... z)
private static IncompleteGammaHelper.ContinuedFractionResult	continuedFraction(IncompleteGammaHelper.Sequence s, int radix, long workingPrecision, long minIterations, long maxIterations)
private static Apcomplex	e1(Apcomplex z)
private static long	extraPrecision(int radix)
private static IncompleteGammaHelper.ContinuedFraction	fastestG(Apcomplex a, Apcomplex z, IncompleteGammaHelper.ContinuedFraction[] algorithms)
private static Apcomplex	g(java.util.function.BiFunction<Apcomplex,Apcomplex,IncompleteGammaHelper.Sequence> s, Apcomplex a, Apcomplex z, long minIterations)
static Apcomplex	gamma(Apcomplex a, Apcomplex z)
static Apcomplex	gamma(Apcomplex a, Apcomplex z0, Apcomplex z1)
private static IncompleteGammaHelper.GammaValue	gammaG(Apcomplex a, Apcomplex z, IncompleteGammaHelper.ContinuedFraction algorithm, IncompleteGammaHelper.ContinuedFractionType type)
private static boolean	isCloseToNegativeRealAxis(Apcomplex z)
private static boolean	isMaybeUnstable(Apcomplex a, Apcomplex z)
private static IncompleteGammaHelper.GammaValue	lowerGamma(Apcomplex a, Apcomplex z, IncompleteGammaHelper.ContinuedFraction[] algorithms)
private static IncompleteGammaHelper.Sequence	lowerGammaSequence(Apcomplex a, Apcomplex z)
private static IncompleteGammaHelper.Sequence	lowerGammaSequenceAlternative(Apcomplex a, Apcomplex z)
private static Apcomplex	sum(Apcomplex a, Apcomplex z)
private static Apcomplex	tiny(Apcomplex z, long workingPrecision)
private static Apcomplex	upperGamma(long mn, Apcomplex z)
private static IncompleteGammaHelper.GammaValue	upperGamma(Apcomplex a, Apcomplex z)
private static IncompleteGammaHelper.Sequence	upperGammaSequence(Apcomplex a, Apcomplex z)
private static IncompleteGammaHelper.Sequence	upperGammaSequenceAlternative(Apcomplex a, Apcomplex z)
private static boolean	useAsymptoticLarge(Apcomplex larger, Apcomplex smaller)
private static boolean	useLowerGamma(Apcomplex a, Apcomplex z)
private static boolean	useSum(Apcomplex z)
private static boolean	useUpperGamma(Apcomplex a, Apcomplex z)

Methods inherited from class java.lang.Object

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

Constructor Detail

IncompleteGammaHelper

IncompleteGammaHelper()

Method Detail

gamma

public static Apcomplex gamma(Apcomplex a,
                              Apcomplex z)

gamma

public static Apcomplex gamma(Apcomplex a,
                              Apcomplex z0,
                              Apcomplex z1)

checkPrecision

private static void checkPrecision(Apcomplex... z)

upperGamma

private static IncompleteGammaHelper.GammaValue upperGamma(Apcomplex a,
                                                           Apcomplex z)

useAsymptoticLarge

private static boolean useAsymptoticLarge(Apcomplex larger,
                                          Apcomplex smaller)

lowerGamma

private static IncompleteGammaHelper.GammaValue lowerGamma(Apcomplex a,
                                                           Apcomplex z,
                                                           IncompleteGammaHelper.ContinuedFraction[] algorithms)

useSum

private static boolean useSum(Apcomplex z)

useLowerGamma

private static boolean useLowerGamma(Apcomplex a,
                                     Apcomplex z)

isCloseToNegativeRealAxis

private static boolean isCloseToNegativeRealAxis(Apcomplex z)

useUpperGamma

private static boolean useUpperGamma(Apcomplex a,
                                     Apcomplex z)

isMaybeUnstable

private static boolean isMaybeUnstable(Apcomplex a,
                                       Apcomplex z)

abs

private static Apfloat abs(Apcomplex z)

gammaG

private static IncompleteGammaHelper.GammaValue gammaG(Apcomplex a,
                                                       Apcomplex z,
                                                       IncompleteGammaHelper.ContinuedFraction algorithm,
                                                       IncompleteGammaHelper.ContinuedFractionType type)

upperGammaSequence

private static IncompleteGammaHelper.Sequence upperGammaSequence(Apcomplex a,
                                                                 Apcomplex z)

lowerGammaSequence

private static IncompleteGammaHelper.Sequence lowerGammaSequence(Apcomplex a,
                                                                 Apcomplex z)

upperGammaSequenceAlternative

private static IncompleteGammaHelper.Sequence upperGammaSequenceAlternative(Apcomplex a,
                                                                            Apcomplex z)

lowerGammaSequenceAlternative

private static IncompleteGammaHelper.Sequence lowerGammaSequenceAlternative(Apcomplex a,
                                                                            Apcomplex z)

fastestG

private static IncompleteGammaHelper.ContinuedFraction fastestG(Apcomplex a,
                                                                Apcomplex z,
                                                                IncompleteGammaHelper.ContinuedFraction[] algorithms)

g

private static Apcomplex g(java.util.function.BiFunction<Apcomplex,Apcomplex,IncompleteGammaHelper.Sequence> s,
                           Apcomplex a,
                           Apcomplex z,
                           long minIterations)

extraPrecision

private static long extraPrecision(int radix)

continuedFraction

private static IncompleteGammaHelper.ContinuedFractionResult continuedFraction(IncompleteGammaHelper.Sequence s,
                                                                               int radix,
                                                                               long workingPrecision,
                                                                               long minIterations,
                                                                               long maxIterations)

tiny

private static Apcomplex tiny(Apcomplex z,
                              long workingPrecision)

asymptoticLargeA

private static IncompleteGammaHelper.GammaValue asymptoticLargeA(Apcomplex a,
                                                                 Apcomplex z)

asymptoticLargeZ

private static IncompleteGammaHelper.GammaValue asymptoticLargeZ(Apcomplex a,
                                                                 Apcomplex z)

attemptUStar

private static IncompleteGammaHelper.GammaValue attemptUStar(Apcomplex a,
                                                             Apcomplex z)

upperGamma

private static Apcomplex upperGamma(long mn,
                                    Apcomplex z)

sum

private static Apcomplex sum(Apcomplex a,
                             Apcomplex z)

e1

private static Apcomplex e1(Apcomplex z)