naginterfaces.library.sum.invlaplace_​weeks_​eval

naginterfaces.library.sum.invlaplace_weeks_eval(t, sigma, b, acoef, errvec)

invlaplace_weeks_eval evaluates an inverse Laplace transform at a given point, using the expansion coefficients computed by invlaplace_weeks().

For full information please refer to the NAG Library document for c06lc

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/c06/c06lcf.html

Parameters

tfloat

The value $t$ for which the inverse Laplace transform $f\left(t\right)$ must be evaluated.

sigmafloat

$sigma$ must be unchanged from the previous call of invlaplace_weeks()

bfloat

$b$ must be unchanged from the previous call of invlaplace_weeks()

acoeffloat, array-like, shape $\left(m\right)$

$acoef$ must be unchanged from the previous call of invlaplace_weeks()

errvecfloat, array-like, shape $\left(8\right)$

$errvec$ must be unchanged from the previous call of invlaplace_weeks()

Returns

finvfloat

The approximation to the inverse Laplace transform at $t$.

Warns

NagAlgorithmicWarning

(errno $1$)

The approximation to $f\left(t\right)$ is too large to be representable.

(errno $2$)

The approximation to $f\left(t\right)$ is too small to be representable.

Notes

No equivalent traditional C interface for this routine exists in the NAG Library.

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

$$\tilde{f}\left(t\right)=e^{\sigma t}\sum _{i=0}^{m-1}{a}_i{e}^{-bt/2}{L}_i\left(bt\right)\text{,}\sigma >{\sigma }_O\text{,}b>0$$

where $L_i\left(x\right)$ is the Laguerre polynomial of degree $i$.

This function simply evaluates the above expansion for a specified value of $t$.

invlaplace_weeks_eval is derived from the function MODUL2 in Garbow et al. (1988)

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