rfa 0.5.9

A port ERFA to Rust.
Documentation 
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use crate::vector_matrix::vector_ops::pdp::pdp;
use crate::rfam::*;
use crate::utils::*;
/*
**  - - - - - -
**   e r a A b
**  - - - - - -
**
**  Apply aberration to transform natural direction into proper
**  direction.
**
**  Given:
**    pnat    double[3]   natural direction to the source (unit vector)
**    v       double[3]   observer barycentric velocity in units of c
**    s       double      distance between the Sun and the observer (au)
**    bm1     double      sqrt(1-|v|^2): reciprocal of Lorenz factor
**
**  Returned:
**    ppr     double[3]   proper direction to source (unit vector)
**
**  Notes:
**
**  1) The algorithm is based on Expr. (7.40) in the Explanatory
**     Supplement (Urban & Seidelmann 2013), but with the following
**     changes:
**
**     o  Rigorous rather than approximate normalization is applied.
**
**     o  The gravitational potential term from Expr. (7) in
**        Klioner (2003) is added, taking into account only the Sun's
**        contribution.  This has a maximum effect of about
**        0.4 microarcsecond.
**
**  2) In almost all cases, the maximum accuracy will be limited by the
**     supplied velocity.  For example, if the ERFA eraEpv00 function is
**     used, errors of up to 5 microarcseconds could occur.
**
**  References:
**
**     Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to
**     the Astronomical Almanac, 3rd ed., University Science Books
**     (2013).
**
**     Klioner, Sergei A., "A practical relativistic model for micro-
**     arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003).
**
**  Called:
**     eraPdp       scalar product of two p-vectors
**
**  This revision:   2021 February 24
**
**  Copyright (C) 2013-2021, NumFOCUS Foundation.
**  Derived, with permission, from the SOFA library.  See notes at end of file.
*/
pub fn ab(pnat: &[f64; 3], v: &[f64; 3], s: f64, bm1: f64,
    ppr: &mut [f64; 3])
{
    let mut p = [0.0;3];
 
 
    let pdv = pdp(pnat, v);
    let w1 = 1.0 + pdv/(1.0 + bm1);
    let w2 = URSA_SRS/s;
    let mut r2 = 0.0;
    for i in 0..3 {
       let w = pnat[i]*bm1 + w1*v[i] + w2*(v[i] - pdv*pnat[i]);
       p[i] = w;
       r2 += w*w;
    }
    let r = sqrt(r2);
    for i in 0..3 {
       ppr[i] = p[i]/r;
    }
 
 /* Finished. */
 
 }