Class HypergeometricHelper

java.lang.Object

org.apfloat.HypergeometricHelper

class HypergeometricHelper
extends Object

Helper class for hypergeometric functions.

Since:

1.11.0

Version:

1.14.0

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
private class	HypergeometricHelper.Hypergeometric2F1Helper
private static class	HypergeometricHelper.NotConvergingException
private static class	HypergeometricHelper.RetryException
private static enum	HypergeometricHelper.Transformation

Field Summary

Fields

Modifier and Type	Field	Description
private Apcomplex[]	a
private Apcomplex[]	b
private long	extraPrecision
private Apint	one
private int	radix
private long	targetPrecision
private long	workingPrecision
private Apcomplex	z
private Apint	zero

Constructor Summary

Constructors

Modifier	Constructor	Description
private	HypergeometricHelper(Apcomplex[] a, Apcomplex[] b, Apcomplex z)	Helper for the generalized hypergeometric function pFq.

Method Summary

Modifier and Type	Method	Description
private Apfloat	adjustOffset(Apfloat x, Apfloat offset)
private Apcomplex	alternative(Apcomplex a, Apcomplex b, Apcomplex c, Apcomplex z)
private void	checkDivergence(Apcomplex old, Apcomplex term)
private Apcomplex	checkResult()
private Apcomplex	ensureGammaPrecision(Apcomplex z)
private Apcomplex	ensurePrecision(Apcomplex z)
private void	ensurePrecision(Apcomplex[] src, Apcomplex[] dest, long extendedPrecision)
private Apcomplex	evaluate(Apcomplex[] a, Apcomplex[] b, Apcomplex z)
private Apcomplex	hypergeometric0F1(Apcomplex b, Apcomplex z)
private Apcomplex	hypergeometric1F1(Apcomplex a, Apcomplex b, Apcomplex z)
private Apcomplex	hypergeometric1F1series(Apcomplex a, Apcomplex b, Apcomplex z)
private Apcomplex	hypergeometric2F1(Apcomplex a, Apcomplex b, Apcomplex c, Apcomplex z)
private Apcomplex	hypergeometricPFQ()
static Apcomplex	hypergeometricPFQ(Apcomplex[] a, Apcomplex[] b, Apcomplex z)	Generalized hypergeometric function pFq.
private Apcomplex	hypergeometricPFQRegularized()
static Apcomplex	hypergeometricPFQRegularized(Apcomplex[] a, Apcomplex[] b, Apcomplex z)	Regularized generalized hypergeometric function pF̃q.
private Apcomplex	hypergeometricU(boolean fastOnly)
static Apcomplex	hypergeometricU(Apcomplex a, Apcomplex b, Apcomplex z, boolean fastOnly)	Tricomi's confluent hypergeometric function U.
private Apcomplex	hypergeometricUStar(Apcomplex a, Apcomplex b, Apcomplex z)
static Apfloat	maxNonPositiveInteger(Apcomplex... a)
private Apfloat	offset(long scale)
private static long	precision(Apcomplex... z)
private static long	precision(Apcomplex[] z0, Apcomplex[] z1, Apcomplex z2)
private Apcomplex	result(Apcomplex z)

Methods inherited from class Object

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

Field Details

targetPrecision

private long targetPrecision

extraPrecision

private long extraPrecision

workingPrecision

private long workingPrecision

radix

private int radix

a

private Apcomplex[] a

b

private Apcomplex[] b

z

private Apcomplex z

one

private Apint one

zero

private Apint zero

Constructor Details

HypergeometricHelper

private HypergeometricHelper(Apcomplex[] a,
 Apcomplex[] b,
 Apcomplex z)

Helper for the generalized hypergeometric function _pF_q.

Parameters:

a - The first argument.

b - The second argument.

z - The third argument.

Method Details

hypergeometricPFQ

public static Apcomplex hypergeometricPFQ(Apcomplex[] a,
 Apcomplex[] b,
 Apcomplex z)

Generalized hypergeometric function _pF_q.

Parameters:

a - The first argument.

b - The second argument.

z - The third argument.

Returns:

_pF_q(a₁, …, a_p; b₁, …, b_q; z)

Throws:

ArithmeticException - If the series does not converge.

hypergeometricPFQRegularized

public static Apcomplex hypergeometricPFQRegularized(Apcomplex[] a,
 Apcomplex[] b,
 Apcomplex z)

Regularized generalized hypergeometric function _pF̃_q.

Parameters:

a - The first argument.

b - The second argument.

z - The third argument.

Returns:

_pF̃_q(a₁, …, a_p; b₁, …, b_q; z)

Throws:

ArithmeticException - If the series does not converge.

Since:

1.13.0

hypergeometricPFQRegularized

private Apcomplex hypergeometricPFQRegularized()

hypergeometricU

public static Apcomplex hypergeometricU(Apcomplex a,
 Apcomplex b,
 Apcomplex z,
 boolean fastOnly)

Tricomi's confluent hypergeometric function U. Also known as the confluent hypergeometric function of the second kind.

Parameters:

a - The first argument.

b - The second argument.

z - The third argument.

fastOnly - Only attempt relatively fast algorithms and return null if not applicable

Returns:

U(a, b, z)

Since:

1.13.0

hypergeometricPFQ

private Apcomplex hypergeometricPFQ()
                             throws ArithmeticException,
ApfloatRuntimeException

Throws:

ArithmeticException

ApfloatRuntimeException

hypergeometric0F1

private Apcomplex hypergeometric0F1(Apcomplex b,
 Apcomplex z)
                             throws ArithmeticException,
ApfloatRuntimeException

Throws:

ArithmeticException

ApfloatRuntimeException

hypergeometric1F1

private Apcomplex hypergeometric1F1(Apcomplex a,
 Apcomplex b,
 Apcomplex z)
                             throws ArithmeticException,
ApfloatRuntimeException

Throws:

ArithmeticException

ApfloatRuntimeException

hypergeometric1F1series

private Apcomplex hypergeometric1F1series(Apcomplex a,
 Apcomplex b,
 Apcomplex z)

hypergeometricUStar

private Apcomplex hypergeometricUStar(Apcomplex a,
 Apcomplex b,
 Apcomplex z)
                               throws ArithmeticException,
ApfloatRuntimeException

Throws:

ArithmeticException

ApfloatRuntimeException

hypergeometricU

private Apcomplex hypergeometricU(boolean fastOnly)
                           throws ArithmeticException,
ApfloatRuntimeException

Throws:

ArithmeticException

ApfloatRuntimeException

hypergeometric2F1

private Apcomplex hypergeometric2F1(Apcomplex a,
 Apcomplex b,
 Apcomplex c,
 Apcomplex z)
                             throws ArithmeticException,
ApfloatRuntimeException

Throws:

ArithmeticException

ApfloatRuntimeException

precision

private static long precision(Apcomplex[] z0,
 Apcomplex[] z1,
 Apcomplex z2)

precision

private static long precision(Apcomplex... z)

checkResult

private Apcomplex checkResult()

maxNonPositiveInteger

public static Apfloat maxNonPositiveInteger(Apcomplex... a)

evaluate

private Apcomplex evaluate(Apcomplex[] a,
 Apcomplex[] b,
 Apcomplex z)

checkDivergence

private void checkDivergence(Apcomplex old,
 Apcomplex term)

alternative

private Apcomplex alternative(Apcomplex a,
 Apcomplex b,
 Apcomplex c,
 Apcomplex z)

offset

private Apfloat offset(long scale)

adjustOffset

private Apfloat adjustOffset(Apfloat x,
 Apfloat offset)

ensurePrecision

private Apcomplex ensurePrecision(Apcomplex z)

ensurePrecision

private void ensurePrecision(Apcomplex[] src,
 Apcomplex[] dest,
 long extendedPrecision)

ensureGammaPrecision

private Apcomplex ensureGammaPrecision(Apcomplex z)

result

private Apcomplex result(Apcomplex z)