Package gov.nih.mipav.model.algorithms

Class InverseLaplace2

java.lang.Object

gov.nih.mipav.model.algorithms.InverseLaplace2

Direct Known Subclasses:

AlgorithmFRAP.FitFullModel2, AlgorithmFRAP.FitSineModel, InverseLaplaceTest.FitPiessens1, InverseLaplaceTest.FitPiessens10, InverseLaplaceTest.FitPiessens11, InverseLaplaceTest.FitPiessens12, InverseLaplaceTest.FitPiessens13, InverseLaplaceTest.FitPiessens14, InverseLaplaceTest.FitPiessens15, InverseLaplaceTest.FitPiessens16, InverseLaplaceTest.FitPiessens2, InverseLaplaceTest.FitPiessens3, InverseLaplaceTest.FitPiessens4, InverseLaplaceTest.FitPiessens5, InverseLaplaceTest.FitPiessens6, InverseLaplaceTest.FitPiessens7, InverseLaplaceTest.FitPiessens8, InverseLaplaceTest.FitPiessens9

public abstract class InverseLaplace2
extends java.lang.Object

This is a port of the numerical inverse Laplace transform found as the FORTRAN implementation of Algorithm 619 from the collected algorithms from the ACM found at http://www.netlib.org/toms/619. Ths inversion of the Laplace transform is done using the Durbin formula in combination with the Epsilon Algorithm. This algorithm by R. Piessens and R. Huysmans appeared in ACM Trans. Math. Software, Vol. 10, No. 3, Sep., 1984, pp. 348-353.

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Field Summary

Fields

Modifier and Type	Field	Description
private double	abscissa	abscissa of convergence of the Laplace transform.
private double	absEps	absolute accuracy requested.
private double	epsilon	D1MACH(4).
private int[]	errStatus	Parameter giving information on the termination of the algorithm errStatus[0] = 0 normal and reliable termination of the routine errStatus[0] = 1 The computations are terminated because the bound on the number of evaluations of the user supplied Laplace function has been achieved.
private double[]	estErr	Estimate of the absolute error abs(f(t) - result[0]).
private int[]	evaluations	Number of evaluations of user supplied Laplace function.
private int	it	index of the time variable being used.
private int	maxBound	maxBound is a bound on the number of terms used in the Durbin formula.
private int	nex	DOCUMENT ME!
private int	nres	DOCUMENT ME!
private double	oflow	emax = 1024, the largest exponent E for double precision, is I1MACH(16) D1MACH(2) = 2**(emax)*(1 - 2**(-doubleDigits)) = 2**1024*(1 - 2**-53) D1MACH(2) = Double.MAX_VALUE.
private double	relEps	relative accuracy requested.
private double[]	res3la	DOCUMENT ME!
private double[]	result	The routine tries to satisfy the least stringent of both accuracy requirements.
private double[]	rex	DOCUMENT ME!
private double[]	time	Independent variable for which the inverse Laplace transform has to be computed. time value should be greater than zero.

Constructor Summary

Constructors

Constructor	Description
InverseLaplace2(double[] time, double abscissa, double relEps, double absEps, double[] result, double[] estErr, int[] evaluations, int[] errStatus)	Creates a new InverseLaplace2 object.

Method Summary

Modifier and Type	Method	Description
private void	dqext()	DOCUMENT ME!
void	driver()	driver.
abstract void	fitToLaplace(double realIn, double imagIn, double[] realOut, double[] imagOut)	DOCUMENT ME!

Methods inherited from class java.lang.Object

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

Field Detail

abscissa

private final double abscissa

abscissa of convergence of the Laplace transform.

absEps

private final double absEps

absolute accuracy requested.

epsilon

private double epsilon

D1MACH(4).

errStatus

private final int[] errStatus

Parameter giving information on the termination of the algorithm errStatus[0] = 0 normal and reliable termination of the routine errStatus[0] = 1 The computations are terminated because the bound on the number of evaluations of the user supplied Laplace function has been achieved. This bound is equal to 8*maxBound+ 5. One can allow more Laplace function evalutions by increasing the value of maxBound. errStatus[0] = 2 An input time value is less than or equal to zero

estErr

private final double[] estErr

Estimate of the absolute error abs(f(t) - result[0]).

evaluations

private final int[] evaluations

Number of evaluations of user supplied Laplace function.

it

private int it

index of the time variable being used.

maxBound

private final int maxBound

maxBound is a bound on the number of terms used in the Durbin formula.

See Also:

Constant Field Values

nex

private int nex

DOCUMENT ME!

nres

private int nres

DOCUMENT ME!

oflow

private final double oflow

emax = 1024, the largest exponent E for double precision, is I1MACH(16) D1MACH(2) = 2**(emax)*(1 - 2**(-doubleDigits)) = 2**1024*(1 - 2**-53) D1MACH(2) = Double.MAX_VALUE.

See Also:

Constant Field Values

relEps

private final double relEps

relative accuracy requested.

res3la

private final double[] res3la

DOCUMENT ME!

result

private final double[] result

The routine tries to satisfy the least stringent of both accuracy requirements. That is, the routine tries to satisfy: ABS(f(t) - result[0]) <= max(absEps, relEps*ABS(f(t))) where f(t) is the actual time function Inverse Laplace transform

rex

private final double[] rex

DOCUMENT ME!

time

private final double[] time

Independent variable for which the inverse Laplace transform has to be computed. time value should be greater than zero.

Constructor Detail

InverseLaplace2

public InverseLaplace2(double[] time,
                       double abscissa,
                       double relEps,
                       double absEps,
                       double[] result,
                       double[] estErr,
                       int[] evaluations,
                       int[] errStatus)

Creates a new InverseLaplace2 object.

Parameters:

time - double[]

abscissa - double

relEps - double

absEps - double

result - double[]

estErr - double[]

evaluations - int[]

errStatus - int[]

Method Detail

fitToLaplace

public abstract void fitToLaplace(double realIn,
                                  double imagIn,
                                  double[] realOut,
                                  double[] imagOut)

DOCUMENT ME!

Parameters:

realIn - double real part of independent variable of Laplace transform

imagIn - double imag part of independent varialbe of Laplace transform

realOut - double[] real part of Laplace transform output

imagOut - double[] imag part of Laplace transform output

driver

public void driver()

driver.

dqext

private void dqext()

DOCUMENT ME!