`vp.special.plasma_z`

The plasma dispersion function Z(zeta) = i sqrt(pi) w(zeta) and its derivative Z'(zeta) = -2 (1 + zeta Z(zeta)), anywhere in the plane.

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

Signature

vp.special.plasma_z(zeta)

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

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.

import vipyr as vp
r = vp.special.plasma_z(zeta=1.0 + 0.5j)
print(r.Z, r.Zp)
assert r.check()

(-0.6077242989405138+0.6290444616787879j) (-0.15550694044018432-0.650364624417062j)

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

Reference: Z = 1j*sqrt(pi)*scipy.special.wofz(zeta); Z' = -2*(1 + zeta*Z) from that Z
Compared by: relative error |a - b| / |b|, Z and Z' separately
Domain: -6 <= Re zeta <= 6, -1 <= Im zeta <= 4: the region lib/zfunc_ref.py measured
Tolerance: rel 2 × 10⁻¹⁴, rel_prime 10⁻¹²
Why that tolerance: w is 10⁻¹⁴ relative on the domain (lib/zfunc_ref.py); Z' = -2(1 + zeta Z) cancels where Z ~ -1/zeta, which multiplies Z's error by up to 2|zeta|^2 = 104 on the domain