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    Determines which of a set of angular coordinates on the sky (or on a
    sphere) are within a given angular distance from each of a vector of
    points. New optimized version that uses histograms based on 3D
    locations on the unit sphere and borrows heavily from JD's MATCH_2D.



Calling Sequence

    Result = MATCHALL_SPH(Ra1, Dec1, Ra2, Dec2, Sphrad, Nwithin)


    Ra1: Vector of longitude coordinates, in degrees.
    Dec1: Vector of latitude coordinates, in degrees.
    Ra2: Vector of longitude coordinates, in degrees.
    Dec2: Vector of latitude coordinates, in degrees.
    Sphrad: Maximum angular distance, in degrees.


    The function returns the list of indices of Ra2, Dec2 that lie within
    Sphrad of each point Ra1,Dec1. The format of the returned array is
    similar to the REVERSE_INDICES array from HISTOGRAM: the indices
    into Ra2,Dec2 that are close enough to element i of Ra1,Dec1 are
    contained in Result[Result[i]:Result[i+1]-1] (note, however, that
    these indices are not guaranteed to be sorted). If there are no matches,
    then Result[i] eq Result[i+1].

Optional Outputs

    Nwithin: A vector containing the number of matches for each of Ra1,Dec1.

Keyword Parameters

    DISTANCE: Optional output containing the distances between each pair.
              The distances are stored in the same order as the Result
              array but starting at 0, i.e. if j is match number k to
              element i then
                  j = Result[Result[i]+k]
              and the distance between points i and j is


    Note that the routine is similar to finding
      WHERE(SPHDIST(Ra1,Dec1,Ra2,Dec2,/DEGREE) LE Sphrad, Nwithin)
    for each element of Ra1 and Dec1, but is much more efficient.
    Shows which random points are within 10 degrees of various coordinates:
    nrandcoords = 5000l
    ra_randcoords = 360. * RANDOMU(seed, nrandcoords)
    dec_randcoords = ASIN( 2*RANDOMU(seed, nrandcoords)-1 ) * !RADEG
    ra_centers = 60. * FINDGEN(5)
    dec_centers = [0., 45., 0., -45., 90.]
    matches = MATCHALL_SPH(ra_centers, dec_centers, ra_randcoords, $
      dec_randcoords, 10., nmatches)
    plot, /iso, psym=3, ra_randcoords, dec_randcoords
    oplot, psym=1, color=fsc_color('blue'), ra_centers, dec_centers
    oplot, psym=3, color=fsc_color('red'), ra_randcoords[matches[6:*]], $

Modification History

    Written by: Jeremy Bailin
    10 June 2008 Public release in JBIU as WITHINSPHRAD
    24 April 2009 Vectorized as WITHINSPHRAD_VEC
    25 April 2009 Polished to improve memory use
    9 May 2009 Radical efficiency re-write as WITHINSPHRAD_VEC3D borrowing
                  heavily from JD Smith's MATCH_2D
    13 May 2009 Removed * from LHS index in final remapping for speed
    8 Sept 2010 Renamed MATCHALL_SPH and added DISTANCE keyword
    9 Aug 2011 Bug fix: incorrect bin size caused occasional matches
                  to be missed (thanks to J. Donley for reporting)

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