sofars 0.6.0

Pure Rust implementation of the IAU SOFA library
Documentation 
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use crate::vm::rz;

use super::pmat06;

///  This function forms three Euler angles which implement general
///  precession from epoch J2000.0, using the IAU 2006 model.  Frame
///  bias (the offset between ICRS and mean J2000.0) is included.
///
///  This function is part of the International Astronomical Union's
///  SOFA (Standards of Fundamental Astronomy) software collection.
///
///  Status:  support function.
///
///  Given:
///     date1,date2  double   TT as a 2-part Julian Date (Note 1)
///
///  Returned (function value):
///     (bzeta, bz, btheta) (f64, f64, f64)
///     bzeta        1st rotation: radians cw around z
///     bz           3rd rotation: radians cw around z
///     btheta       2nd rotation: radians ccw around y
///
///  Notes:
///
///  1) The TT date date1+date2 is a Julian Date, apportioned in any
///     convenient way between the two arguments.  For example,
///     JD(TT)=2450123.7 could be expressed in any of these ways,
///     among others:
///
///            date1          date2
///
///         2450123.7           0.0       (JD method)
///         2451545.0       -1421.3       (J2000 method)
///         2400000.5       50123.2       (MJD method)
///         2450123.5           0.2       (date & time method)
///
///     The JD method is the most natural and convenient to use in
///     cases where the loss of several decimal digits of resolution
///     is acceptable.  The J2000 method is best matched to the way
///     the argument is handled internally and will deliver the
///     optimum resolution.  The MJD method and the date & time methods
///     are both good compromises between resolution and convenience.
///
///  2) The traditional accumulated precession angles zeta_A, z_A,
///     theta_A cannot be obtained in the usual way, namely through
///     polynomial expressions, because of the frame bias.  The latter
///     means that two of the angles undergo rapid changes near this
///     date.  They are instead the results of decomposing the
///     precession-bias matrix obtained by using the Fukushima-Williams
///     method, which does not suffer from the problem.  The
///     decomposition returns values which can be used in the
///     conventional formulation and which include frame bias.
///
///  3) The three angles are returned in the conventional order, which
///     is not the same as the order of the corresponding Euler
///     rotations.  The precession-bias matrix is
///     R_3(-z) x R_2(+theta) x R_3(-zeta).
///
///  4) Should zeta_A, z_A, theta_A angles be required that do not
///     contain frame bias, they are available by calling the SOFA
///     function iauP06e.
///
///  Called:
///     iauPmat06    PB matrix, IAU 2006
///     iauRz        rotate around Z-axis
pub fn pb06(date1: f64, date2: f64) -> (f64, f64, f64) {
    /* Precession matrix via Fukushima-Williams angles. */
    let mut r = pmat06(date1, date2);

    /* Solve for z, choosing the +/- pi alternative. */
    let mut y = r[1][2];
    let mut x = -r[0][2];
    if x < 0.0 {
        y = -y;
        x = -x;
    }
    let bz = if x != 0.0 || y != 0.0 {
        -y.atan2(x)
    } else {
        0.0
    };

    /* Derotate it out of the matrix. */
    rz(bz, &mut r);

    /* Solve for the remaining two angles. */
    y = r[0][2];
    x = r[2][2];
    let btheta = if x != 0.0 || y != 0.0 {
        -y.atan2(x)
    } else {
        0.0
    };

    y = -r[1][0];
    x = r[1][1];
    let bzeta = if x != 0.0 || y != 0.0 {
        -y.atan2(x)
    } else {
        0.0
    };

    (bzeta, bz, btheta)
}