Purpose

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  This procedure creates a smoothed map of some function on the sky,
  sampled at discrete points. It relies on adxy and gcirc from the
  IDL astronomy user's library to handle all of the hard
  spherical geometry stuff.

Inputs

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  map: A blank map and fits header. Use map_init.pro to create
      this structure.
  x: The x location (sky coordinates in degrees) of the data
  y: The y location (sky coordinates in degrees) of the data
  val: The value at each (x,y) point
  dval: The 1-sigma error at each point.

Keyword Parameters

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  fwhm: The fwhm of the smoothing kernel, in degrees. Defaults to
        1/100 of the map size
  truncate: The radius at which to truncate the smoothing. This can
            considerably speed up execution time. See PROCEDURE for
            details. Defaults to 2 * fwhm.
  emap: Set to a named variable to hold the estimated variance
        map.

Outputs

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  On output, the map.map array will be populated with the smoothed
  map. Pixels which are further than (truncate) from the nearest
  source are set to NAN.

Procedure

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  This function uses weighted mean smoothing with a Gaussian
  smoothing kernel.
   
    V(x,y) = sum(w_i * val_i) / sum(w_i)
  where
    w_i = 1/dval_i^2 * exp[-((x-x_i)^2 + (y-y_i)^2) / 2 sigma^2]
    w_i truncated to 0 at (x - x_i)^2 + (y - y_i)^2 > truncate^2
  The variance map is given by
  dV(x,y) = sum(w_i * dval_i^2) / sum(w_i)^2
  In other words, it is the interpolated value of the variance, divided
  by the "effective" number of points which contribute to each pixel.
  The procedure only calculates weights out to the truncation radius
  to speed things up. The procedure takes O(stamp_size * n_data)
  operations, instead of O(map_size * n_data).

Modification History

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  March 2010: Written by Chris Beaumont. Meant to replace
  SMOOTHMAP.pro.
  Dec 2010: Added /SAMPLE to REBIN calls. cnb.