vp.special.faddeeva_w

The Faddeeva function w(z) = exp(-z^2) erfc(-i z).

Part of the distribution vipyr; it runs from a checkout of the repository. Planned on PyPI as pip install vipyr.

Signature

vp.special.faddeeva_w(z)

Parameters

z : complex, required

Returns

A frozen FaddeevaWResult. Iterating it gives the fields below in order; it also has params, tests, log and check().

w : complex

Raises

TypeError

An argument of the wrong type, or an unknown keyword.

vipyr.VivBuildError

An ImportError: no C compiler, or the program's C does not build.

Examples

import vipyr as vp
r = vp.special.faddeeva_w(z=2.0 + 1.0j)
print(r.w)
assert r.check()

(0.14023958136627798+0.22221344017989914j)

Each example ran as written when these pages were generated, and the output shown is what it printed.

Checked against

Reference

scipy.special.wofz

Compared by

relative error |a - b| / |b|

Domain

-6 <= Re z <= 6, -1 <= Im z <= 4

Tolerance

rel 2 × 10⁻¹⁴

Why that tolerance

Weideman's expansion with N = 40 terms is 10⁻¹⁴ relative on the domain (lib/zfunc_ref.py); wofz itself is good to a few ulps

Source

• Manifest: kernels/k1/k1.export.toml
• Viv: kernels/k1/special.viv
• Viv: lib/zfunc.viv
• The defs it reaches and the calls between them: map of the code