naginterfaces.library.roots.lambertw_complex¶
- naginterfaces.library.roots.lambertw_complex(branch, offset, z)[source]¶
lambertw_complex
computes the values of Lambert’s function .For full information please refer to the NAG Library document for c05bb
https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/c05/c05bbf.html
- Parameters
- branchint
The branch required.
- offsetbool
Controls whether or not is being specified as an offset from .
- zcomplex
If , is the offset from of the intended argument to ; that is, is computed, where .
If , is the argument of the function; that is, is computed, where .
- Returns
- wcomplex
The value : see also the description of .
- residfloat
The residual : see also the description of .
- Warns
- NagAlgorithmicWarning
- (errno )
For the given offset , is negligibly different from : and .
- (errno )
is close to . Enter as an offset to for greater accuracy: and .
- (errno )
The iterative procedure used internally did not converge in iterations. Check the value of for the accuracy of .
- Notes
lambertw_complex
calculates an approximate value for Lambert’s function (sometimes known as the ‘product log’ or ‘Omega’ function), which is the inverse function ofThe function is many-to-one, and so, except at , is multivalued.
lambertw_complex
allows you to specify the branch of on which you would like the results to lie by using the argument . Our choice of branch cuts is as in Corless et al. (1996), and the ranges of the branches of are summarised in Figure [label omitted].[figure omitted]
For more information about the closure of each branch, which is not displayed in Figure [label omitted], see Corless et al. (1996). The dotted lines in the Figure denote the asymptotic boundaries of the branches, at multiples of .
The precise method used to approximate is as described in Corless et al. (1996). For close to greater accuracy comes from evaluating rather than : by setting on entry you inform
lambertw_complex
that you are providing , not , in .
- References
Corless, R M, Gonnet, G H, Hare, D E G, Jeffrey, D J and Knuth, D E, 1996, On the Lambert function, Advances in Comp. Math. (3), 329–359