Integer, Intent (In)	::	m
Integer, Intent (Inout)	::	ifail
Real (Kind=nag_wp), Intent (In)	::	t, sigma, b, acoef(m), errvec(8)
Real (Kind=nag_wp), Intent (Out)	::	finv

C Header Interface

#include <nag.h>

void	c06lcf_ (const double t, const double sigma, const double b, const Integer m, const double acoef[], const double errvec[], double finv, Integer ifail)

The routine may be called by the names c06lcf or nagf_sum_invlaplace_weeks_eval.

3 Description

c06lcf is designed to be used following a call to c06lbf, which computes an inverse Laplace transform by representing it as a Laguerre expansion of the form:

\tilde{f} (t) = e^{σ t} \sum_{i = 0}^{m - 1} a_{i} e^{- b t / 2} L_{i} (b t), σ > σ_{O}, b > 0

where

L_{i} (x)

is the Laguerre polynomial of degree

i

This routine simply evaluates the above expansion for a specified value of

t

c06lcf is derived from the subroutine MODUL2 in Garbow et al. (1988)

4 References

Garbow B S, Giunta G, Lyness J N and Murli A (1988) Algorithm 662: A Fortran software package for the numerical inversion of the Laplace transform based on Weeks' method ACM Trans. Math. Software 14 171–176

5 Arguments

1: $t$ – Real (Kind=nag_wp) Input: On entry: the value $t$ for which the inverse Laplace transform $f (t)$ must be evaluated.
2: $sigma$ – Real (Kind=nag_wp) Input
3: $b$ – Real (Kind=nag_wp) Input
4: $m$ – Integer Input
5: $acoef (m)$ – Real (Kind=nag_wp) array Input
6: $errvec (8)$ – Real (Kind=nag_wp) array Input: On entry: sigma, b, m, acoef and errvec must be unchanged from the previous call of c06lbf.
7: $finv$ – Real (Kind=nag_wp) Output: On exit: the approximation to the inverse Laplace transform at $t$ .
8: $ifail$ – Integer Input/Output: On entry: ifail must be set to $0$ , $−1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $−1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $−1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $- 1$ or $1$ is used it is essential to test the value of ifail on exit.

On exit: $ifail = 0$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

ifail = 0

−1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = 1$: The approximation to $f (t)$ is too large to be representable.

$ifail = 2$: The approximation to $f (t)$ is too small to be representable.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

The error estimate returned by c06lbf in

errvec (1)

has been found in practice to be a highly reliable bound on the pseudo-error

| f (t) - \tilde{f} (t) | e^{- σ t}

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.

c06lcf is not threaded in any implementation.

9 Further Comments

c06lcf is primarily designed to evaluate

\tilde{f} (t)

when

t > 0

. When

t \leq 0

, the result approximates the analytic continuation of

f (t)

; the approximation becomes progressively poorer as

t

becomes more negative.

10 Example

See example for c06lbf.

NAG Library Manual, Mark 30.1

Interfaces: FL CL CPP AD PY MB

NAG FL Interface Introduction

C06 (Sum) Chapter Contents

C06 (Sum) Chapter Introduction

c06lc: FL CL CPP AD PY MB

NAG FL Interfacec06lcf (invlaplace_​weeks_​eval)

▸▿ Contents

1 Purpose

2 Specification