[GRASS-dev] [GRASS-user] compare a DCELL and FCELL question

[Markus Metz]

A note about the usage of GRASS_EPSILON = 1.0e-15:

The range of single precision floating point is about 1.4012984643e−45 to
3.4028234664e38
That means for large numbers, using GRASS_EPSILON will also detect floating
point precision limits, not only meaningful differences. For small numbers,
GRASS_EPSILON will not detect meaningful differences. GRASS_EPSILON could
instead be modified with something like "max(abs(map_A), abs(map_B)) *
1.0e-15" to test for meaningful differences.

Markus M


On Sun, Jan 24, 2021 at 5:32 PM Markus Metz <markus.metz.giswork at gmail.com>
wrote:
>
>
>
> On Sun, Jan 24, 2021 at 5:06 PM ming han <dustming at gmail.com> wrote:
> >
> > Hi Everyone
> >
> >    Many thanks for your help. Is if(fabs(map_A - map_B) <= 1.0e-15, ...
) approach may increase the runtime compare to '==' way?
>
> The formulas are very simple, I don't think that differences in runtime
can be reliably measured. (De-)compression of the data and the operating
system's file cache have a much stronger influence on the runtime.
>
> Markus M
> >
> > Thanks
> > Ming
> >
> > Markus Metz <markus.metz.giswork at gmail.com> 于2021年1月24日周日 上午10:57写道：
> >>
> >> Trying to answer the original question: with a DCELL map
"cat1_acc_riv" and a FCELL map "cat1_minacc", why is "float(cat1_acc_riv)
== float(cat1_minacc)" not equal to "int(cat1_acc_riv) == int(cat1_minacc)"
?
> >>
> >> int truncates to integer while float converts to single precision
floating point. E.g. with cat1_acc_riv = 1.1 and cat1_minacc = 1.9,
"float(cat1_acc_riv) == float(cat1_minacc)" becomes "1.1 == 1.9" whereas
"int(cat1_acc_riv) == int(cat1_minacc)" becomes "1 == 1", thus the results
are different.
> >>
> >> Another reason for possible differences is that float can only
represent max 7 decimal digits. E.g. float(194320567) becomes 194320560 but
int(194320567) preserves the value 194320567.
> >>
> >> Thus the safest is to cast everything to the type with the highest
precision. In this case with FCELL and DCELL, use "double(cat1_acc_riv) ==
double(cat1_minacc)" or even better the suggestion of Markus N.
> >>
> >> Markus M
> >>
> >>
> >> On Sun, Jan 24, 2021 at 3:51 PM ming han <dustming at gmail.com> wrote:
> >> >
> >> > Hi Markus and Micha
> >> >
> >> >      I am just trying to find grids have the same values in these
two rasters, I will try the threshold approach.
> >> >
> >> > Thanks
> >> > Ming
> >> >
> >> > Markus Neteler <neteler at osgeo.org> 于2021年1月24日周日 上午6:58写道：
> >> >>
> >> >> Hi Ming,
> >> >>
> >> >> On Sun, Jan 24, 2021 at 10:49 AM ming han <dustming at gmail.com>
wrote:
> >> >> >
> >> >> > Hi Micha
> >> >> >
> >> >> >      Many thanks for your reply.
> >> >> >      Here is the command I am using:
> >> >> >
> >> >> >      if(float(cat1_acc_riv) == float(cat1_minacc), str_r, null())
> >> >> >
> >> >> >       The str_r is a CELL raster. the result is different when I
change it to:
> >> >> >        if(int(cat1_acc_riv) == int(cat1_minacc), str_r, null())
> >> >>
> >> >> Note that numerical "equality" is better tested with a threshold
test
> >> >> against the map pixel difference.
> >> >> As the threshold, we use GRASS_EPSILON which is defined as 1.0e-15.
> >> >>
> >> >> Hence the test needs to be implemented in a different way, i.e. by
> >> >> using an epsilon.
> >> >> Essentially something like this:
> >> >>
> >> >> if(fabs(map_A - map_B) <= 1.0e-15, ... )
> >> >>
> >> >> In your case (untested):
> >> >> r.mapcalc diffepsilon = if( abs( map_A - map_B) <= 1.0e-15, str_r ,
null())
> >> >>
> >> >> See related discussions here: [1], [2] and elsewhere.
> >> >>
> >> >> [1] Comment by Glynn:
https://trac.osgeo.org/grass/ticket/2854#comment:9
> >> >> [2] Comment by Glynn:
> >> >>
https://lists.osgeo.org/pipermail/grass-user/2015-October/073200.html
> >> >>
> >> >> Best,
> >> >> Markus
> >> >
> >> > _______________________________________________
> >> > grass-dev mailing list
> >> > grass-dev at lists.osgeo.org
> >> > https://lists.osgeo.org/mailman/listinfo/grass-dev
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