[GRASS-user] Does v.kernel have to take 16+ hours?

[Markus Metz]

On Fri, Nov 23, 2012 at 4:14 AM, Aren Cambre <aren at arencambre.com> wrote:
> I'm able to reproduce reliably here. I'll email you details privately.

Thanks. I can confirm that v.kernel takes a long time in GRASS 6 with
the settings provided by you. It does not crash, however.

I can speed up v.kernel in GRASS 6 to complete in 10 minutes instead
of 16+ hours, but I am not sure if this fix can/will go into GRASS 6.4
because by now only bugs should be fixed.

Markus M

>
> Aren
>
>
> On Thu, Nov 22, 2012 at 9:02 AM, Markus Metz <markus.metz.giswork at gmail.com>
> wrote:
>>
>> On Sat, Nov 17, 2012 at 4:06 PM, Aren Cambre <aren at arencambre.com> wrote:
>> > I have a dataset of just over 700,000 incidents that happened in
>> > square-ish
>> > Texas county that's about 30 miles on each side.
>> >
>> > Here's the parameters reported by v.kernel as it's executing:
>> >
>> > STDDEV: 1000.000000
>> > RES: 111.419043 ROWS: 458   COLS: 447
>> >
>> > Writing output raster map using smooth parameter=1000.000000.
>> >
>> > Normalising factor=6482635.018778.
>> >
>> >
>> > I am running this on a Windows 7 x64 machine with 8 GB RAM and an Intel
>> > Core
>> > i7 Q720 1.6 GHz with 4 physical cores. I notice that it's not
>> > multithreaded,
>> > only using 1 core.
>> >
>> > It takes about 16 hours to complete. Is this correct? I'd like to use
>> > this
>> > on a dataset with closer to 5 million records, and I'm really concerned
>> > how
>> > long it may take.
>>
>> The time required by v.kernel is a function of the number of cells and
>> the input parameter stddeviation. The larger any of these values is,
>> the more time v.kernel will need. Nevertheless, I think that the 16+
>> hours are not correct. I tested with a vector with 3 million points
>> for a grid with 2700 rows and 1087 columns, magnitudes larger than the
>> grid used by you. v.kernel completes in just over one minute.
>>
>> >
>> > I posted my question about the 16+ hours at
>> >
>> > http://gis.stackexchange.com/questions/41058/how-do-i-compute-v-kernel-maps-in-less-than-16-hours/.
>> > Bill Huber, who si apparently knowledgeable about kernel density
>> > calculations in general, posted a response, and he felt like a kernel
>> > density map shouldn't take much time at all. But digging more deeply,
>> > turns
>> > out he had come up with a kernel density calculation method over a
>> > decade
>> > ago using Fourier transforms. See
>> > http://www.directionsmag.com/features/convolution/129753 and the next
>> > two
>> > articles linked to it (they are short articles). Apparently this
>> > transforms
>> > it from an O(n^2) problem to an O(n ln n) complexity problem.
>>
>> The approach of Bill Huber is raster-based, not vector based, making
>> some things easier, at the cost of precision. The coordinate
>> precision, however, is only needed for kernel functions other than
>> uniform. In GRASS, you could get something like a raster-based density
>> map by
>>
>> - exporting the points with v.out.ascii
>> - re-importing the points with r.in.xyz method=n to get the number of
>> points per cell
>> - running a neighborhood analysis using a circular window with
>> r.neighbors method=sum -c
>>
>> Optionally you could use the gauss option of r.neighbors to get an
>> equivalent to v.kernel kernel=gaussian
>>
>> HTH,
>>
>> Markus M
>>
>> >
>> > I inspected v.kernel's main.c
>> >
>> > (http://trac.osgeo.org/grass/browser/grass/trunk/vector/v.kernel/main.c),
>> > and looks like v.kernel uses an output-centric method (using Bill's
>> > wording)
>> > of calculating the output, which seems like O(n^2) complexity.
>> >
>> > So I guess what I'm getting at is it appears to me that the algorithm
>> > behind
>> > GRASS GIS's v.kernel is straightforward but is a greedy algorithm
>> > (http://en.wikipedia.org/wiki/Greedy_algorithm), which is fine, but it
>> > make
>> > take a while to execute. Is this true?
>> >
>> > Is there not spatial indexing I could add to the dataset? I've done
>> > various
>> > Google searches on that and can't come up with anything clear.
>> >
>> > Aren
>> >
>> > _______________________________________________
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>> > http://lists.osgeo.org/mailman/listinfo/grass-user
>> >
>
>