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

Thu Dec 6 13:19:27 PST 2012

OK, I think I get it now. After you've hit 4 SDs (or even arguably 3 SDs!)
the contribution of more points to that square fades to almost nothing
without extreme clusters of points.

Seems like this ought to be clarified in the UI and documentation? Should I
file an enhancement request?

BTW, I dropped down to a SD of 200, and it ran in 212 minutes. I'm trying a
SD of 300 now but on a grid with 1/4 as many squares as I cut the rows and
cols by half. We'll see how it does.

Aren

On Thu, Dec 6, 2012 at 12:17 PM, Markus Metz
<markus.metz.giswork at gmail.com>wrote:

> On Thu, Dec 6, 2012 at 3:13 PM, Aren Cambre <aren at arencambre.com> wrote:
> > Thanks. I am using EPSG:3081, and its unit is meters. So is it the case
> that
> > a SD of x on EPSG:3081 means a search radius of 4x meters? If so, why 4x?
>
> Because the gaussian function is infinite, a cutoff of 3 to 6 SDs is
> usually applied when using a gaussian function as kernel density
> function. In theory, an alternative is to combine the infinite
> gaussian function with a finite function, e.g. uniform. I think
> historically v.kernel had only one kernel function, gaussian. The
> original authors decided to ask for SD and not for the search radius
> as input and have set the cutoff to 4 x SD where the gaussian function
> is reasonably close to zero.
>
> BTW, search radius = 4 x SD applies only to the gaussian kernel, for
> all other kernel functions the search radius is equal to SD.
>
> Markus M
>
> >
> > On Thu, Dec 6, 2012 at 2:29 AM, Markus Metz <
> markus.metz.giswork at gmail.com>
> > wrote:
> >>
> >> On Thu, Dec 6, 2012 at 3:58 AM, Aren Cambre <aren at arencambre.com>
> wrote:
> >> > It's gotten slow again. This run will probably take more than 10
> hours.
> >> > However, I am using a standard deviation of 1000. Is that what could
> be
> >> > causing this?
> >>
> >> Yes. With a standard deviation of 1000, the search radius is now 4000,
> >> that is, for each cell a 8000x8000 box is searched. With many densely
> >> packed points, this can take quite some time.
> >>
> >> Markus M
> >>
> >> >
> >> > v.kernel input=tickets at PERMANENT output=tickets_new_heatmap_1000
> >> > stddeviation=1000
> >> > STDDEV: 1000.000000
> >> > RES: 18.290457 ROWS: 2370 COLS: 2650
> >> >
> >> > Writing output raster map using smooth parameter=1000.000000.
> >> >
> >> > Normalising factor=6482635.018778.
> >> >
> >> > On Sat, Nov 24, 2012 at 9:03 PM, Aren Cambre <aren at arencambre.com>
> >> > wrote:
> >> >>
> >> >> I installed r53983. The v.kernel execution that took almost a day now
> >> >> executes in 25.5 minutes. Thank you!
> >> >>
> >> >> Aren
> >> >>
> >> >>
> >> >> On Fri, Nov 23, 2012 at 12:51 PM, Markus Metz
> >> >> <markus.metz.giswork at gmail.com> wrote:
> >> >>>
> >> >>> On Fri, Nov 23, 2012 at 5:35 PM, Aren Cambre <aren at arencambre.com>
> >> >>> wrote:
> >> >>> > Thanks!
> >> >>> >
> >> >>> > I am not familiar with GRASS's release customs. Will this become
> >> >>> > part
> >> >>> > of a
> >> >>> > binary release soon, or should I just pull down the latest release
> >> >>> > in
> >> >>> > the
> >> >>> > 6.4.2 trunk? I'm assuming this has been merged into the trunk...
> >> >>>
> >> >>> It should be available as a binary for Windows by tomorrow in the
> >> >>> nightly builds [0].
> >> >>>
> >> >>> Markus M
> >> >>>
> >> >>> [0] http://wingrass.fsv.cvut.cz/grass64/
> >> >>>
> >> >>> >
> >> >>> > Aren
> >> >>> >
> >> >>> >
> >> >>> > On Fri, Nov 23, 2012 at 7:32 AM, Markus Metz
> >> >>> > <markus.metz.giswork at gmail.com>
> >> >>> > wrote:
> >> >>> >>
> >> >>> >> On Fri, Nov 23, 2012 at 2:07 PM, Aren Cambre <
> aren at arencambre.com>
> >> >>> >> wrote:
> >> >>> >> > Isn't taking about 10,000% too much time considered a bug? :-)
> >> >>> >>
> >> >>> >> Hmm, yes. v.kernel is fixed in devbr6 and relbr6 with r53982 and
> >> >>> >> r53983, respectively.
> >> >>> >>
> >> >>> >> Markus M
> >> >>> >>
> >> >>> >> >
> >> >>> >> > On Nov 23, 2012 5:11 AM, "Markus Metz"
> >> >>> >> > <markus.metz.giswork at gmail.com>
> >> >>> >> > wrote:
> >> >>> >> >>
> >> >>> >> >> 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
> >> >>> >> >> >> >
> >> >>> >> >> >> > _______________________________________________
> >> >>> >> >> >> > grass-user mailing list
> >> >>> >> >> >> > grass-user at lists.osgeo.org
> >> >>> >> >> >> > http://lists.osgeo.org/mailman/listinfo/grass-user
> >> >>> >> >> >> >
> >> >>> >> >> >
> >> >>> >> >> >
> >> >>> >
> >> >>> >
> >> >>
> >> >>
> >> >
> >
> >
>
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