NAG FL Interface
c06lcf (invlaplace_​weeks_​eval)

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1 Purpose

c06lcf evaluates an inverse Laplace transform at a given point, using the expansion coefficients computed by c06lbf.

2 Specification

Fortran Interface
Subroutine c06lcf ( t, sigma, b, m, acoef, errvec, finv, ifail)
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:
f~ (t) = eσt i=0 m-1 ai e -bt/2 Li (bt) ,   σ > σO ,   b > 0  
where Li(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 or −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)-f~(t)| e-σt .

8 Parallelism and Performance

c06lcf is not threaded in any implementation.

9 Further Comments

c06lcf is primarily designed to evaluate f~(t) when t>0 . When t0 , 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.