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POINT_CONVOLVE

POINT_CONVOLVE

Name


    POINT_CONVOLVE

Purpose


    Convolves a list of N-dimensional points with a Gaussian kernel.

Category


    Math

Calling Sequence


    Result = POINT_CONVOLVE()

Keyword Parameters


    POINTS: Array of MxN points for M dimensions and N particles (required).
    BINSIZE: Bin sizes for final output grid. Either a scalar or an
              array of length M. (required)
    RANGE: Array of Mx2, containing the extent of output grid
              in each dimension. (required)
    SIGMA: Width of Gaussian kernel. May either be a scalar that is
              applied to all dimensions, an array of length M for
              different widths in each dimension, OR an MxN array
              containing a separate width for each particle and
              dimension (this option uses manual summation as if
              /NOCONVOL were set, and is therefore much slower).
              (required)
    WEIGHT: An array of length N containing the weight to assign to
            each point. A weight of 1 (default) corresponds to a Gaussian
            normalized such that its integral over the entire M-dimensional
            space is unity.
   
    CUTOFF: Assume that the kernel may be safely truncated after this many
            SIGMAs. Default: 8 (corresponding to a dynmical range of 7.9e13).
    NOCONVOL: If /NOCONVOL is set than use manual summation rather than an FFT.
    NOFFT: If /NOFFT is set then use the built-in CONVOL routine rather
              than an FFT.

Outputs


    An grid containing the output density field. Each dimension i in the output
    grid has length (RANGE[i,1]-RANGE[i,0])/BINSIZE[i]. Returns -1 on error.

Procedure


    By default, this function uses an FFT and the convolution theorem.
    If /NOFFT is set, then it uses the built-in CONVOL function. If
    either /NOCONVOL is set or SIGMA is an MxN array, then it uses
    manual summation.

Example


    xpos = 10.*RANDOMU(seed,100)
    ypos = 20.*RANDOMU(seed,100)
    density = POINT_CONVOLVE(POINTS=TRANSPOSE([[xpos],[ypos]]),
      BINSIZE=1., RANGE=[[0.,0.], [10.,20.]], SIGMA=[2.,4.])

Modification History


    Written by: Jeremy Bailin
    12 June 2008 Public release in JBIU
    15 Apr 2008 Fixed off-by-one bug and improved memory usage
    27 March 2013 Speed improvements



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