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**     eraPvppv     pv-vector plus pv_vector
**     eraS2pv      spherical coordinates to pv-vector
**     eraSxp       multiply p-vector by scalar
**
**  References:
**
**     Aoki, S. et al., 1983, "Conversion matrix of epoch B1950.0
**     FK4-based positions of stars to epoch J2000.0 positions in
**     accordance with the new IAU resolutions".  Astron.Astrophys.
**     128, 263-267.
**
**     Seidelmann, P.K. (ed), 1992, "Explanatory Supplement to the
**     Astronomical Almanac", ISBN 0-935702-68-7.
**
**     Smith, C.A. et al., 1989, "The transformation of astrometric
**     catalog systems to the equinox J2000.0".  Astron.J. 97, 265.
**
**     Standish, E.M., 1982, "Conversion of positions and proper motions
**     from B1950.0 to the IAU system at J2000.0".  Astron.Astrophys.,
**     115, 1, 20-22.
**
**     Yallop, B.D. et al., 1989, "Transformation of mean star places
**     from FK4 B1950.0 to FK5 J2000.0 using matrices in 6-space".
**     Astron.J. 97, 274.
**
**  Copyright (C) 2013-2020, NumFOCUS Foundation.
**  Derived, with permission, from the SOFA library.  See notes at end of file.
*/
{
/* Radians per year to arcsec per century */
   const double PMF = 100.0*ERFA_DR2AS;

/* Small number to avoid arithmetic problems */
   const double TINY = 1e-30;

/* Miscellaneous */
   double r, d, ur, ud, px, rv, pxvf, w, rd;
   int i, j, k, l;

/* Pv-vectors */
   double r0[2][3], pv1[2][3], pv2[2][3];

/*
** CANONICAL CONSTANTS (Seidelmann 1992)
*/

/* Km per sec to AU per tropical century */
/* = 86400 * 36524.2198782 / 149597870.7 */
   const double VF = 21.095;

/* Constant pv-vector (cf. Seidelmann 3.591-2, vectors A and Adot) */
   static double a[2][3] = {
                      { -1.62557e-6, -0.31919e-6, -0.13843e-6 },
                      { +1.245e-3,   -1.580e-3,   -0.659e-3   }
                           };

/* 3x2 matrix of pv-vectors (cf. Seidelmann 3.591-4, matrix M) */
   static double em[2][3][2][3] = {

    { { { +0.9999256782,     -0.0111820611,     -0.0048579477     },
        { +0.00000242395018, -0.00000002710663, -0.00000001177656 } },

      { { +0.0111820610,     +0.9999374784,     -0.0000271765     },
        { +0.00000002710663, +0.00000242397878, -0.00000000006587 } },

      { { +0.0048579479,     -0.0000271474,     +0.9999881997,    },
        { +0.00000001177656, -0.00000000006582, +0.00000242410173 } } },

    { { { -0.000551,         -0.238565,         +0.435739        },
        { +0.99994704,       -0.01118251,       -0.00485767       } },

      { { +0.238514,         -0.002667,         -0.008541        },
        { +0.01118251,       +0.99995883,       -0.00002718       } },

      { { -0.435623,         +0.012254,         +0.002117         },
        { +0.00485767,       -0.00002714,       +1.00000956       } } }

                                  };

/*- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

/* The FK4 data (units radians and arcsec per tropical century). */
   r = r1950;
   d = d1950;
   ur = dr1950*PMF;
   ud = dd1950*PMF;
   px = p1950;
   rv = v1950;

/* Express as a pv-vector. */
   pxvf = px*VF;
   w = rv*pxvf;
   eraS2pv(r, d, 1.0, ur, ud, w, r0);

/* Allow for E-terms (cf. Seidelmann 3.591-2). */
   eraPvmpv(r0, a, pv1);
   eraSxp(eraPdp(r0[0], a[0]), r0[0], pv2[0]);
   eraSxp(eraPdp(r0[0], a[1]), r0[0], pv2[1]);
   eraPvppv(pv1, pv2, pv1);

/* Convert pv-vector to Fricke system (cf. Seidelmann 3.591-3). */
   for ( i = 0; i < 2; i++ ) {
      for ( j = 0; j < 3; j++ ) {
         w = 0.0;
         for ( k = 0; k < 2; k++ ) {
            for ( l = 0; l < 3; l++ ) {
               w += em[i][j][k][l] * pv1[k][l];
            }
         }
         pv2[i][j] = w;
      }
   }

/* Revert to catalog form. */
   eraPv2s(pv2, &r, &d, &w, &ur, &ud, &rd);
   if ( px > TINY ) {
      rv = rd/pxvf;
      px = px/w;
   }

/* Return the results. */
   *r2000 = eraAnp(r);
   *d2000 = d;
   *dr2000 = ur/PMF;
   *dd2000 = ud/PMF;
   *v2000 = rv;
   *p2000 = px;