NAME

       v.kernel  - Generates a raster density map from vector point data using a moving kernel or
       optionally generates a vector density map on a vector network.

KEYWORDS

       vector, kernel density

SYNOPSIS

       v.kernel
       v.kernel help
       v.kernel [-oqnmv] input=name  [net=name]   output=name  stddeviation=float   [dsize=float]
       [segmax=float]      [distmax=float]     [mult=float]     [node=string]     [kernel=string]
       [--verbose]  [--quiet]

   Flags:
       -o
           Try to calculate an optimal standard deviation with 'stddeviation'  taken  as  maximum
           (experimental)

       -q
           Only calculate optimal standard deviation and exit (no map is written)

       -n
           In  network  mode,  normalize  values  by  sum of density multiplied by length of each
           segment. Integral over the output map then gives 1.0 * mult

       -m
           In network mode, multiply the result by number of input points.

       -v
           Verbose module output (retained for backwards compatibility)

       --verbose
           Verbose module output

       --quiet
           Quiet module output

   Parameters:
       input=name
           Input vector with training points

       net=name
           Input network vector map

       output=name
           Output raster/vector map

       stddeviation=float
           Standard deviation in map units

       dsize=float
           Discretization error in map units
           Default: 0.

       segmax=float
           Maximum length of segment on network
           Default: 100.

       distmax=float
           Maximum distance from point to network
           Default: 100.

       mult=float
           Multiply the density result by this number
           Default: 1.

       node=string
           Node method
           Options: none,split
           Default: none
           none: No method applied at nodes with more than 2 arcs
           split: Equal split (Okabe 2009) applied at nodes

       kernel=string
           Kernel function
           Options: uniform,triangular,epanechnikov,quartic,triweight,gaussian,cosine
           Default: gaussian

DESCRIPTION

       v.kernel generates a raster density map from vector points data  using  a  moving  kernel.
       Available  kernel  density  functions  are  uniform,  triangular,  epanechnikov,  quartic,
       triweight, gaussian, cosine, default is gaussian.

       The module can also generate a vector density  map  on  a  vector  network.   Conventional
       kernel  functions  produce biased estimates by overestimating the densities around network
       nodes, whereas the equal split method of Okabe et al.  (2009)  produces  unbiased  density
       estimates. The equal split method uses the kernel function selected with the kernel option
       and can be enabled with node=split.

NOTES

       The mult option is needed to overcome the limitation that the resulting density in case of
       a vector map output is stored as category (Integer). The density result stored as category
       may be multiplied by this number.

       With the -o flag (experimental)  the  command  tries  to  calculate  an  optimal  standard
       deviation.  The  value  of  stddeviation  is taken as maximum value. Standard deviation is
       calculated using ALL points, not just those in the current region.

LIMITATIONS

       The module only considers the presence of points, but not (yet) any attribute values.

SEE ALSO

       v.surf.rst

REFERENCES

       Okabe, A., Satoh, T.,  Sugihara,  K.  (2009).  A  kernel  density  estimation  method  for
       networks,  its  computational  method  and  a  GIS-based  tool.   International Journal of
       Geographical Information Science, Vol 23(1), pp. 7-32.
       DOI: 10.1080/13658810802475491

AUTHORS

       Stefano Menegon, ITC-irst, Trento, Italy
       Radim Blazek (additional kernel density functions and network part)

       Last changed: $Date: 2011-11-08 03:29:50 -0800 (Tue, 08 Nov 2011) $

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