[GRASS-dev] Fwd: LINEQS solvers and v.surf.rst
Helena Mitasova
hmitaso at unity.ncsu.edu
Wed Sep 5 23:01:44 EDT 2007
Soeren,
I am forwarding the tests to the dev list so that it gets into the
archive and everybody can check it out.
For everybody - this relates to the discussion about the NR lineqs
solver replacement,
Helena
Helena Mitasova
Dept. of Marine, Earth and Atm. Sciences
1125 Jordan Hall, NCSU Box 8208,
Raleigh NC 27695
http://skagit.meas.ncsu.edu/~helena/
Begin forwarded message:
> From: Sören Gebbert <soerengebbert at gmx.de>
> Date: May 6, 2007 6:19:03 AM EDT
> To: Helena Mitasova <hmitaso at unity.ncsu.edu>
> Subject: Re: LINEQS
>
> Helena,
> Thanks for the chapter.
> I have tested the solvers with several vector maps from the
> new demo location.
>
> The script which performs the tests is attached. So you are
> able to reproduce the tests.
> The log file, including time measurement and error log,
> is attached as well.
>
> I have created two simple bar charts. The first represents the
> processed vector maps and
> the cpu time consumption of each solver, measured by the time
> command. The second one
> represents the elev result error between the iterative solvers and
> the nrlu solver
> for each processed vector map.
>
> All the data presented in the charts is available in the log file.
>
> The cg solver is the fastest solver, the new direct lu and gauss
> solver are 20% slower than the nrlu algorithm.
>
> The computation error of the iterative solvers is small enough to be
> accepted. The gpde lu and gauss solver producing exactly the same
> result as the nrlu
> algorithm (see log file).
>
> So the new lu and the cg solver are the best replacement for nrlu.
> I did not tested parallel computation, because i have no
> multi core computer at home.
>
> But, the iterative solvers partially failed on vector maps with low
> data density (contour lines
> in maps elev_contour_3m and elev_ned10m_cont10m),
> in case the npmin was set to 50 or lower. A value of 50 is not
> meaningful for the maps,
> but its the users choice ... .
>
> So much more testing is needed.
> Anyway, the gpde lu solver can handle this.
>
> Important region and v.surf.rst settings:
>
> g.region rural_1m res=2
> npmin=500
>
> Best regards
> Soeren
>
> Helena Mitasova schrieb:
>> On May 5, 2007, at 4:00 PM, Sören Gebbert wrote:
>>> Hi,
>>> now i know the source of the linear equation solver
>>> which you had send me.
>>> Its is the solver implemented in v.vol.rst in user4.c. :D
>> yes - actually v.surf.rst (s.surf.tps) originally looked like
>> v.vol.rst which is a direct
>> rewrite of our original fortran code. There should also be v.volt.rst
>> that interpolates in 3D+time space.
>> I really wanted all 3 programs and r.resamp.rst to be based on a
>> single library as
>> most of the code is almost the same, only the dimensions change,
>> but Irina (one of the russian twins that worked with me at CERL
>> and did a lot of coding for GRASS, you can see Olga and Irina
>> mentioned throughout various GRASS modules)
>> managed to get it to where it is now by the time she finished her
>> Masters
>> and CERL dropped the GRASS project. So it is a quite ugly code
>> right now
>> but it works . I doubt that anybody would have time to rewrite it.
>>>
>>> Looks like good old fortran code converted to C.
>>> I think i will patch v.vol.rst too.
>> yes that would be good. I am thinking that it may be useful to submit
>> the options for solvers that you have added into CVS, I would like
>> to let
>> people from GEON project try it out too (http://lidar.asu.edu/),
>> especially
>> the parallel processing.
>> It would be great if you could try out the performance of the
>> solvers with
>> the new data set - both in terms of how fast they are and whether
>> there are
>> any differences in the results. The data are here, (set the region
>> to rural_1m)
>> http://mpa.itc.it/grasstutor/data_menu3rd.phtml
>> Try it with elev_lid792_bepts, elev_lid792_mrpts,
>> elev_lid792_randpts and
>> elev_contour_3m. I have attached chapter6.tex file that has all
>> the commands
>> so you can just cut and paste them into a script and run it all at
>> once
>> (ignore the figures in the pdf file - they are still for sperafish).
>> These are all small files so a few tests with millions of points
>> would be useful
>> too (e.g. the Jockey's ridge data from the second edition
>> available at the same web site).
>> That should help to decide which method put as default and which
>> are not
>> needed (to make the life easier for the user). I will then get
>> Jaro and some
>> other people test it more to make sure that the new solvers work
>> for everybody's data.
>> Helena
>>
>>> Best regards
>>> Soeren
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>
> ##########################################################
> ++ Testing solver nrlu with map elev_lid792_bepts
>
> 647.86user 4.10system 10:52.79elapsed 99%CPU (0avgtext+0avgdata
> 0maxresident)k
> 0inputs+0outputs (0major+89167minor)pagefaults 0swaps
>
> ##########################################################
> ++ Testing solver lu with map elev_lid792_bepts
>
> 853.22user 5.02system 14:19.62elapsed 99%CPU (0avgtext+0avgdata
> 0maxresident)k
> 0inputs+0outputs (0major+89451minor)pagefaults 0swaps
>
> -- statistics of differences bewteen nrlu and lu solver based on
> elevation
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: 0
> maximum: 0
> range: 0
> mean: 0
> mean of absolute values: 0
> standard deviation: 0
> variance: 0
> variation coefficient: nan %
> sum: 0
>
> -- statistics of differences bewteen nrlu and lu solver based on slope
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: 0
> maximum: 0
> range: 0
> mean: 0
> mean of absolute values: 0
> standard deviation: 0
> variance: 0
> variation coefficient: nan %
> sum: 0
>
> ##########################################################
> ++ Testing solver gauss with map elev_lid792_bepts
>
> 844.28user 5.10system 14:10.43elapsed 99%CPU (0avgtext+0avgdata
> 0maxresident)k
> 0inputs+0outputs (0major+88890minor)pagefaults 0swaps
>
> -- statistics of differences bewteen nrlu and gauss solver based on
> elevation
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: 0
> maximum: 0
> range: 0
> mean: 0
> mean of absolute values: 0
> standard deviation: 0
> variance: 0
> variation coefficient: nan %
> sum: 0
>
> -- statistics of differences bewteen nrlu and gauss solver based on
> slope
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: 0
> maximum: 0
> range: 0
> mean: 0
> mean of absolute values: 0
> standard deviation: 0
> variance: 0
> variation coefficient: nan %
> sum: 0
>
> ##########################################################
> ++ Testing solver cg with map elev_lid792_bepts
>
> 298.31user 2.34system 5:01.01elapsed 99%CPU (0avgtext+0avgdata
> 0maxresident)k
> 0inputs+0outputs (0major+89731minor)pagefaults 0swaps
>
> -- statistics of differences bewteen nrlu and cg solver based on
> elevation
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: -1.52588e-05
> maximum: 1.52588e-05
> range: 3.05176e-05
> mean: 9.53311e-09
> mean of absolute values: 5.71057e-07
> standard deviation: 2.25911e-06
> variance: 5.10356e-12
> variation coefficient: 23697.5 %
> sum: 0.0012512207
>
> -- statistics of differences bewteen nrlu and cg solver based on slope
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: -1.52588e-05
> maximum: 1.52588e-05
> range: 3.05176e-05
> mean: 9.53311e-09
> mean of absolute values: 5.71057e-07
> standard deviation: 2.25911e-06
> variance: 5.10356e-12
> variation coefficient: 23697.5 %
> sum: 0.0012512207
>
> ##########################################################
> ++ Testing solver bicgstab with map elev_lid792_bepts
>
> 451.35user 3.36system 7:42.13elapsed 98%CPU (0avgtext+0avgdata
> 0maxresident)k
> 0inputs+0outputs (0major+90562minor)pagefaults 0swaps
>
> -- statistics of differences bewteen nrlu and bicgstab solver based
> on elevation
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: -3.8147e-05
> maximum: 1.52588e-05
> range: 5.34058e-05
> mean: -6.01051e-08
> mean of absolute values: 3.5133e-07
> standard deviation: 1.90371e-06
> variance: 3.62411e-12
> variation coefficient: -3167.3 %
> sum: -0.0078887939
>
> -- statistics of differences bewteen nrlu and bicgstab solver based
> on slope
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: -3.8147e-05
> maximum: 1.52588e-05
> range: 5.34058e-05
> mean: -6.01051e-08
> mean of absolute values: 3.5133e-07
> standard deviation: 1.90371e-06
> variance: 3.62411e-12
> variation coefficient: -3167.3 %
> sum: -0.0078887939
>
> ##########################################################
> ++ Testing solver nrlu with map elev_lidrural_mrpts
>
> 427.92user 2.97system 7:11.51elapsed 99%CPU (0avgtext+0avgdata
> 0maxresident)k
> 0inputs+0outputs (0major+87940minor)pagefaults 0swaps
>
> ##########################################################
> ++ Testing solver lu with map elev_lidrural_mrpts
>
> 587.63user 3.81system 9:52.25elapsed 99%CPU (0avgtext+0avgdata
> 0maxresident)k
> 0inputs+0outputs (0major+88206minor)pagefaults 0swaps
>
> -- statistics of differences bewteen nrlu and lu solver based on
> elevation
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: 0
> maximum: 0
> range: 0
> mean: 0
> mean of absolute values: 0
> standard deviation: 0
> variance: 0
> variation coefficient: nan %
> sum: 0
>
> -- statistics of differences bewteen nrlu and lu solver based on slope
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: 0
> maximum: 0
> range: 0
> mean: 0
> mean of absolute values: 0
> standard deviation: 0
> variance: 0
> variation coefficient: nan %
> sum: 0
>
> ##########################################################
> ++ Testing solver gauss with map elev_lidrural_mrpts
>
> 578.09user 3.75system 9:42.95elapsed 99%CPU (0avgtext+0avgdata
> 0maxresident)k
> 0inputs+0outputs (0major+87672minor)pagefaults 0swaps
>
> -- statistics of differences bewteen nrlu and gauss solver based on
> elevation
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: 0
> maximum: 0
> range: 0
> mean: 0
> mean of absolute values: 0
> standard deviation: 0
> variance: 0
> variation coefficient: nan %
> sum: 0
>
> -- statistics of differences bewteen nrlu and gauss solver based on
> slope
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: 0
> maximum: 0
> range: 0
> mean: 0
> mean of absolute values: 0
> standard deviation: 0
> variance: 0
> variation coefficient: nan %
> sum: 0
>
> ##########################################################
> ++ Testing solver cg with map elev_lidrural_mrpts
>
> 233.33user 1.98system 4:10.17elapsed 94%CPU (0avgtext+0avgdata
> 0maxresident)k
> 0inputs+0outputs (0major+88477minor)pagefaults 0swaps
>
> -- statistics of differences bewteen nrlu and cg solver based on
> elevation
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: -3.05176e-05
> maximum: 3.05176e-05
> range: 6.10352e-05
> mean: -1.02307e-08
> mean of absolute values: 5.68266e-07
> standard deviation: 4.16437e-06
> variance: 1.7342e-11
> variation coefficient: -40704.9 %
> sum: -0.0013427734
>
> -- statistics of differences bewteen nrlu and cg solver based on slope
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: -3.05176e-05
> maximum: 3.05176e-05
> range: 6.10352e-05
> mean: -1.02307e-08
> mean of absolute values: 5.68266e-07
> standard deviation: 4.16437e-06
> variance: 1.7342e-11
> variation coefficient: -40704.9 %
> sum: -0.0013427734
>
> ##########################################################
> ++ Testing solver bicgstab with map elev_lidrural_mrpts
>
> 359.87user 2.86system 6:03.24elapsed 99%CPU (0avgtext+0avgdata
> 0maxresident)k
> 0inputs+0outputs (0major+89273minor)pagefaults 0swaps
>
> -- statistics of differences bewteen nrlu and bicgstab solver based
> on elevation
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: -0.000244141
> maximum: 0.000518799
> range: 0.000762939
> mean: -1.28813e-07
> mean of absolute values: 6.98475e-07
> standard deviation: 9.99815e-06
> variance: 9.99631e-11
> variation coefficient: -7761.74 %
> sum: -0.0169067383
>
> -- statistics of differences bewteen nrlu and bicgstab solver based
> on slope
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: -0.000244141
> maximum: 0.000518799
> range: 0.000762939
> mean: -1.28813e-07
> mean of absolute values: 6.98475e-07
> standard deviation: 9.99815e-06
> variance: 9.99631e-11
> variation coefficient: -7761.74 %
> sum: -0.0169067383
>
> ##########################################################
> ++ Testing solver nrlu with map elev_contour_3m
>
> 126.94user 0.88system 2:08.91elapsed 99%CPU (0avgtext+0avgdata
> 0maxresident)k
> 0inputs+0outputs (0major+13106minor)pagefaults 0swaps
>
> ##########################################################
> ++ Testing solver lu with map elev_contour_3m
>
> 157.57user 1.10system 2:38.99elapsed 99%CPU (0avgtext+0avgdata
> 0maxresident)k
> 0inputs+0outputs (0major+13143minor)pagefaults 0swaps
>
> -- statistics of differences bewteen nrlu and lu solver based on
> elevation
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: 0
> maximum: 0
> range: 0
> mean: 0
> mean of absolute values: 0
> standard deviation: 0
> variance: 0
> variation coefficient: nan %
> sum: 0
>
> -- statistics of differences bewteen nrlu and lu solver based on slope
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: 0
> maximum: 0
> range: 0
> mean: 0
> mean of absolute values: 0
> standard deviation: 0
> variance: 0
> variation coefficient: nan %
> sum: 0
>
> ##########################################################
> ++ Testing solver gauss with map elev_contour_3m
>
> 158.20user 1.08system 2:39.61elapsed 99%CPU (0avgtext+0avgdata
> 0maxresident)k
> 0inputs+0outputs (0major+13074minor)pagefaults 0swaps
>
> -- statistics of differences bewteen nrlu and gauss solver based on
> elevation
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: 0
> maximum: 0
> range: 0
> mean: 0
> mean of absolute values: 0
> standard deviation: 0
> variance: 0
> variation coefficient: nan %
> sum: 0
>
> -- statistics of differences bewteen nrlu and gauss solver based on
> slope
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: 0
> maximum: 0
> range: 0
> mean: 0
> mean of absolute values: 0
> standard deviation: 0
> variance: 0
> variation coefficient: nan %
> sum: 0
>
> ##########################################################
> ++ Testing solver cg with map elev_contour_3m
>
> 69.81user 0.65system 1:10.61elapsed 99%CPU (0avgtext+0avgdata
> 0maxresident)k
> 0inputs+0outputs (0major+13184minor)pagefaults 0swaps
>
> -- statistics of differences bewteen nrlu and cg solver based on
> elevation
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: -1.52588e-05
> maximum: 1.52588e-05
> range: 3.05176e-05
> mean: -8.77162e-08
> mean of absolute values: 5.67859e-07
> standard deviation: 2.28233e-06
> variance: 5.20904e-12
> variation coefficient: -2601.95 %
> sum: -0.0115127563
>
> -- statistics of differences bewteen nrlu and cg solver based on slope
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: -1.52588e-05
> maximum: 1.52588e-05
> range: 3.05176e-05
> mean: -8.77162e-08
> mean of absolute values: 5.67859e-07
> standard deviation: 2.28233e-06
> variance: 5.20904e-12
> variation coefficient: -2601.95 %
> sum: -0.0115127563
>
> ##########################################################
> ++ Testing solver bicgstab with map elev_contour_3m
>
> 93.88user 0.72system 1:34.81elapsed 99%CPU (0avgtext+0avgdata
> 0maxresident)k
> 0inputs+0outputs (0major+13286minor)pagefaults 0swaps
>
> -- statistics of differences bewteen nrlu and bicgstab solver based
> on elevation
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: -3.8147e-05
> maximum: 3.8147e-05
> range: 7.62939e-05
> mean: -2.70705e-07
> mean of absolute values: 5.87391e-07
> standard deviation: 3.21259e-06
> variance: 1.03207e-11
> variation coefficient: -1186.75 %
> sum: -0.0355300903
>
> -- statistics of differences bewteen nrlu and bicgstab solver based
> on slope
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: -3.8147e-05
> maximum: 3.8147e-05
> range: 7.62939e-05
> mean: -2.70705e-07
> mean of absolute values: 5.87391e-07
> standard deviation: 3.21259e-06
> variance: 1.03207e-11
> variation coefficient: -1186.75 %
> sum: -0.0355300903
>
> ##########################################################
> ++ Testing solver nrlu with map elev_ned10m_cont10m
>
> 57.10user 0.52system 0:57.80elapsed 99%CPU (0avgtext+0avgdata
> 0maxresident)k
> 0inputs+0outputs (0major+22349minor)pagefaults 0swaps
>
> ##########################################################
> ++ Testing solver lu with map elev_ned10m_cont10m
>
> 71.86user 0.62system 1:12.66elapsed 99%CPU (0avgtext+0avgdata
> 0maxresident)k
> 0inputs+0outputs (0major+22374minor)pagefaults 0swaps
>
> -- statistics of differences bewteen nrlu and lu solver based on
> elevation
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: 0
> maximum: 0
> range: 0
> mean: 0
> mean of absolute values: 0
> standard deviation: 0
> variance: 0
> variation coefficient: nan %
> sum: 0
>
> -- statistics of differences bewteen nrlu and lu solver based on slope
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: 0
> maximum: 0
> range: 0
> mean: 0
> mean of absolute values: 0
> standard deviation: 0
> variance: 0
> variation coefficient: nan %
> sum: 0
>
> ##########################################################
> ++ Testing solver gauss with map elev_ned10m_cont10m
>
> 71.32user 0.56system 1:12.09elapsed 99%CPU (0avgtext+0avgdata
> 0maxresident)k
> 0inputs+0outputs (0major+22339minor)pagefaults 0swaps
>
> -- statistics of differences bewteen nrlu and gauss solver based on
> elevation
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: 0
> maximum: 0
> range: 0
> mean: 0
> mean of absolute values: 0
> standard deviation: 0
> variance: 0
> variation coefficient: nan %
> sum: 0
>
> -- statistics of differences bewteen nrlu and gauss solver based on
> slope
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: 0
> maximum: 0
> range: 0
> mean: 0
> mean of absolute values: 0
> standard deviation: 0
> variance: 0
> variation coefficient: nan %
> sum: 0
>
> ##########################################################
> ++ Testing solver cg with map elev_ned10m_cont10m
>
> 40.79user 0.38system 0:41.30elapsed 99%CPU (0avgtext+0avgdata
> 0maxresident)k
> 0inputs+0outputs (0major+22403minor)pagefaults 0swaps
>
> -- statistics of differences bewteen nrlu and cg solver based on
> elevation
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: -1.52588e-05
> maximum: 1.52588e-05
> range: 3.05176e-05
> mean: 5.26356e-07
> mean of absolute values: 1.0859e-06
> standard deviation: 2.93473e-06
> variance: 8.61265e-12
> variation coefficient: 557.557 %
> sum: 0.0690841675
>
> -- statistics of differences bewteen nrlu and cg solver based on slope
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: -1.52588e-05
> maximum: 1.52588e-05
> range: 3.05176e-05
> mean: 5.26356e-07
> mean of absolute values: 1.0859e-06
> standard deviation: 2.93473e-06
> variance: 8.61265e-12
> variation coefficient: 557.557 %
> sum: 0.0690841675
>
> ##########################################################
> ++ Testing solver bicgstab with map elev_ned10m_cont10m
>
> 50.83user 0.52system 0:51.49elapsed 99%CPU (0avgtext+0avgdata
> 0maxresident)k
> 0inputs+0outputs (0major+22467minor)pagefaults 0swaps
>
> -- statistics of differences bewteen nrlu and bicgstab solver based
> on elevation
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: -1.52588e-05
> maximum: 1.52588e-05
> range: 3.05176e-05
> mean: -1.2271e-07
> mean of absolute values: 4.69854e-07
> standard deviation: 2.02924e-06
> variance: 4.1178e-12
> variation coefficient: -1653.69 %
> sum: -0.0161056519
>
> -- statistics of differences bewteen nrlu and bicgstab solver based
> on slope
> total null and non-null cells: 131250
> total null cells: 0
>
> Of the non-null cells:
> ----------------------
> n: 131250
> minimum: -1.52588e-05
> maximum: 1.52588e-05
> range: 3.05176e-05
> mean: -1.2271e-07
> mean of absolute values: 4.69854e-07
> standard deviation: 2.02924e-06
> variance: 4.1178e-12
> variation coefficient: -1653.69 %
> sum: -0.0161056519
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