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:
The approximation to f(t) is too large to be representable.
The approximation to f(t) is too small to be representable.
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.
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.
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

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 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.