Calculate complex-valued Coulomb and Bessel functions for real-valued arguments.
The original COULCC() has been repackaged here as an
fpm package.
See the original author's article [1] for more detail.
This is largely not my work.
No intentional changes to the algorithm have been made.
Test suite not yet implemented.
Untested.
Building with fpm
In the package directory, just run
$ fpm build --profile release
The archive file liblibcoulcc.a and .mod files will be placed in the generated build subdirectory.
These files are necessary to compile another program that uses this library.
To use this project within your fpm project, add the following to your fpm.toml file:
[dependencies]
libcoulcc = { git="https://github.com/banana-bred/libcoulcc" }
The module libcoulcc contains the following public procedures :
-
coulf(l,eta,x): return the regular Coulomb function$F_l(\eta,x)$ -
coulg(l,eta,x): return the irregular Coulomb function$G_l(\eta,x)$ -
coulcc_wrapper(zlmin, nl, eta, xx, f, fp, g, gp, sig, kfn, mode): a wrapper used to callCOULCC(), used by the above-mentioned procedures -
COULCC(X,ETA1,ZLMIN,NL,FC,GC,FCP,GCP,SIG,MODE1,KFN,IFAIL): the original code described in [1], with some minor modernizations.
Above, nl is the number of l, x, and eta are complex(real64).
The kind real64 (64 bits / 8 bytes) is defined in the intrinsic module iso_fortran_env.
All public procedures other than COULCC() are superfluous — they're provided for convenience or as a simple example of calling COULCC().
The following example program
program test
use libcoulcc, only: coulf
use iso_fortran_env, only: rp => real64, stdout => output_unit
complex(rp) :: l = 0
complex(rp) :: eta = (-0.5_rp, 0.0_rp)
complex(rp) :: x = (20.0_rp, 0.0_rp)
write(stdout, '("F_[", 2(F0.2, X), "i](", 2(F0.2, X), "i,", 2(F0.2, X), "i) = ", &
& 2(e0.15, X))') l, eta, x, coulf(l, eta, x)
end program test
should print the following:
F_[.00 .00 i](-.50 .00 i,20.00 .00 i) = -0.102372301807428 0.000000000000000
[1] Thompson, I. J., and A. R. Barnett. COULCC: A continued-fraction algorithm for Coulomb functions of complex order with complex arguments. Computer physics communications 36.4 (1985): 363-372. URL: http://www.fresco.org.uk/papers/Coulcc-CPC.pdf