sarkas.utilities.fdints#

Module of Numba’d functions for the calculation of the unnormalized Fermi-Dirac integrals of half integer order p = -9/2,(1),21/2 and integer order p = 0,(1),10 via piecewise minimax rational approximation.

The Numba’d is not necessary for a one time calculation, however, we decided to add the Numba functionality so that future users can use them in Numba’d functions.

The functions contained here are a Python translation of the code xfdh.txt [Fukushima, 2015].

All the credits go to Fukushima, T. email: Toshio.Fukushima at nao.ac.jp.

It was easier than using other packages and/or write our own.

Functions

fd0h(y)

Double precision rational minimax approximation of Fermi-Dirac integral of integer order p=0.

fd10h(y)

Double precision rational minimax approximation of Fermi-Dirac integral of integer order p=5.

fd11h(x)

Double precision rational minimax approximation of Fermi-Dirac integral of half integer order p=11/2.

fd12h(y)

Double precision rational minimax approximation of Fermi-Dirac integral of integer order p=6.

fd13h(x)

Double precision rational minimax approximation of Fermi-Dirac integral of half integer order p=13/2.

fd14h(y)

Double precision rational minimax approximation of Fermi-Dirac integral of integer order p=7.

fd15h(x)

Double precision rational minimax approximation of Fermi-Dirac integral of half integer order p=15/2.

fd16h(y)

Double precision rational minimax approximation of Fermi-Dirac integral of integer order p=8.

fd17h(x)

Double precision rational minimax approximation of Fermi-Dirac integral of half integer order p=17/2.

fd18h(y)

Double precision rational minimax approximation of Fermi-Dirac integral of integer order p=9.

fd19h(x)

Double precision rational minimax approximation of Fermi-Dirac integral of half integer order p=19/2.

fd1h(x)

Double precision rational minimax approximation of Fermi-Dirac integral of half integer order p=1/2.

fd20h(y)

Double precision rational minimax approximation of Fermi-Dirac integral of integer order p=10.

fd21h(x)

Double precision rational minimax approximation of Fermi-Dirac integral of half integer order p=21/2.

fd2h(y)

Double precision rational minimax approximation of Fermi-Dirac integral of integer order p=1.

fd3h(x)

Double precision rational minimax approximation of Fermi-Dirac integral of half integer order p=3/2.

fd4h(y)

Double precision rational minimax approximation of Fermi-Dirac integral of integer order p=2.

fd5h(x)

Double precision rational minimax approximation of Fermi-Dirac integral of half integer order p=5/2.

fd6h(y)

Double precision rational minimax approximation of Fermi-Dirac integral of integer order p=3.

fd7h(x)

Double precision rational minimax approximation of Fermi-Dirac integral of half integer order p=7/2.

fd8h(y)

Double precision rational minimax approximation of Fermi-Dirac integral of integer order p=4.

fd9h(x)

Double precision rational minimax approximation of Fermi-Dirac integral of half integer order p=9/2.

fd_doc_hparams(order)

fd_doc_iparams(order)

fdm1h(x)

Double precision rational minimax approximation of Fermi-Dirac integral of half integer order p=-1/2.

fdm3h(x)

Double precision rational minimax approximation of Fermi-Dirac integral of half integer order p=-3/2.

fdm5h(x)

Double precision rational minimax approximation of Fermi-Dirac integral of half integer order p=-5/2.

fdm7h(x)

Double precision rational minimax approximation of Fermi-Dirac integral of half integer order p=-7/2.

fdm9h(x)

Double precision rational minimax approximation of Fermi-Dirac integral of half integer order p=-9/2.

fermidirac_integral(p, eta)

Wrapper function to calculate the Fermi-Dirac integral using approximation found in Ref.

invfd1h(u)

Approximate the inverse of the Fermi-Dirac integral \(I_{-1/2}(\eta)\) using the fits provided by Fukushima.