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 <[email protected]>wrote: > On Thu, Dec 6, 2012 at 3:13 PM, Aren Cambre <[email protected]> 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 < > [email protected]> > > wrote: > >> > >> On Thu, Dec 6, 2012 at 3:58 AM, Aren Cambre <[email protected]> > 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@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 <[email protected]> > >> > 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 > >> >> <[email protected]> wrote: > >> >>> > >> >>> On Fri, Nov 23, 2012 at 5:35 PM, Aren Cambre <[email protected]> > >> >>> 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 > >> >>> > <[email protected]> > >> >>> > wrote: > >> >>> >> > >> >>> >> On Fri, Nov 23, 2012 at 2:07 PM, Aren Cambre < > [email protected]> > >> >>> >> 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" > >> >>> >> > <[email protected]> > >> >>> >> > wrote: > >> >>> >> >> > >> >>> >> >> On Fri, Nov 23, 2012 at 4:14 AM, Aren Cambre > >> >>> >> >> <[email protected]> > >> >>> >> >> 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 > >> >>> >> >> > <[email protected]> > >> >>> >> >> > wrote: > >> >>> >> >> >> > >> >>> >> >> >> On Sat, Nov 17, 2012 at 4:06 PM, Aren Cambre > >> >>> >> >> >> <[email protected]> > >> >>> >> >> >> 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 > >> >>> >> >> >> > [email protected] > >> >>> >> >> >> > http://lists.osgeo.org/mailman/listinfo/grass-user > >> >>> >> >> >> > > >> >>> >> >> > > >> >>> >> >> > > >> >>> > > >> >>> > > >> >> > >> >> > >> > > > > > >
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