naginterfaces.library.sum.invlaplace_​weeks_​eval

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

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://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/c06/c06lcf.html

Parameters
tfloat

The value for which the inverse Laplace transform must be evaluated.

sigmafloat

must be unchanged from the previous call of invlaplace_weeks()

bfloat

must be unchanged from the previous call of invlaplace_weeks()

acoeffloat, array-like, shape

must be unchanged from the previous call of invlaplace_weeks()

errvecfloat, array-like, shape

must be unchanged from the previous call of invlaplace_weeks()

Returns
finvfloat

The approximation to the inverse Laplace transform at .

Warns
NagAlgorithmicWarning
(errno )

The approximation to is too large to be representable.

(errno )

The approximation to 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:

where is the Laguerre polynomial of degree .

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

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