sofars 0.6.0

Pure Rust implementation of the IAU SOFA library
Documentation 
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use crate::vm::{anp, anpm, c2s, s2c, trxp};

/// Transformation from Galactic coordinates to ICRS.
///
/// Status:  support function.
///
/// Given:
///    dl     f64      Galactic longitude (radians)
///    db     f64      Galactic latitude (radians)
///
/// Returned:
///    dr     f64      ICRS right ascension (radians)
///    dd     f64      ICRS declination (radians)
///
/// Notes:
///
/// 1) The IAU 1958 system of Galactic coordinates was defined with
///    respect to the now obsolete reference system FK4 B1950.0.  When
///    interpreting the system in a modern context, several factors have
///    to be taken into account:
///
///    . The inclusion in FK4 positions of the E-terms of aberration.
///
///    . The distortion of the FK4 proper motion system by differential
///      Galactic rotation.
///
///    . The use of the B1950.0 equinox rather than the now-standard
///      J2000.0.
///
///    . The frame bias between ICRS and the J2000.0 mean place system.
///
///    The Hipparcos Catalogue (Perryman & ESA 1997) provides a rotation
///    matrix that transforms directly between ICRS and Galactic
///    coordinates with the above factors taken into account.  The
///    matrix is derived from three angles, namely the ICRS coordinates
///    of the Galactic pole and the longitude of the ascending node of
///    the Galactic equator on the ICRS equator.  They are given in
///    degrees to five decimal places and for canonical purposes are
///    regarded as exact.  In the Hipparcos Catalogue the matrix
///    elements are given to 10 decimal places (about 20 microarcsec).
///    In the present SOFA function the matrix elements have been
///    recomputed from the canonical three angles and are given to 30
///    decimal places.
///
/// 2) The inverse transformation is performed by the function icrs2g.
///
/// Reference:
///    Perryman M.A.C. & ESA, 1997, ESA SP-1200, The Hipparcos and Tycho
///    catalogues.  Astrometric and photometric star catalogues
///    derived from the ESA Hipparcos Space Astrometry Mission.  ESA
///    Publications Division, Noordwijk, Netherlands.
pub fn g2icrs(dl: f64, db: f64) -> (f64, f64) {
    let mut v2 = [0.0; 3];

    /*
    **  L2,B2 system of Galactic coordinates in the form presented in the
    **  Hipparcos Catalogue.  In degrees:
    **
    **  P = 192.85948    right ascension of the Galactic north pole in ICRS
    **  Q =  27.12825    declination of the Galactic north pole in ICRS
    **  R =  32.93192    Galactic longitude of the ascending node of
    **                   the Galactic equator on the ICRS equator
    **
    **  ICRS to Galactic rotation matrix, obtained by computing
    **  R_3(-R) R_1(pi/2-Q) R_3(pi/2+P) to the full precision shown:
    */
    let r = [
        [
            -0.054875560416215368492398900454,
            -0.873437090234885048760383168409,
            -0.483835015548713226831774175116,
        ],
        [
            0.494109427875583673525222371358,
            -0.444829629960011178146614061616,
            0.746982244497218890527388004556,
        ],
        [
            -0.867666149019004701181616534570,
            -0.198076373431201528180486091412,
            0.455983776175066922272100478348,
        ],
    ];

    /* Spherical to Cartesian. */
    let v1 = s2c(dl, db);

    /* Galactic to ICRS. */
    trxp(&r, &v1, &mut v2);

    /* Cartesian to spherical. */
    let (dr_raw, dd_raw) = c2s(&v2);

    /* Express in conventional ranges. */
    (anp(dr_raw), anpm(dd_raw))
}