[R-sig-Geo] 'LDLfactor' error in 'krige' function

[Mauricio Zambrano]

2009/11/17 Edzer Pebesma <edzer.pebesma at uni-muenster.de>:
> I just want to point out that "krige" has no problem with constant
> observations, as long as it is provided with a valid (i.e. semi negative
> definite, or something like that) variogram model.

Thanks for make this point clear.

> The problem is to automatically fit such a function from data that are constant, as they
> have zero (co)variance; this is done by automap/autofitvariogram and the
> like. Replacing an invalid (zero) variogram model with e.g. a
> (numerically) small nugget effect would already help, but raise two
> issues: (i) what is numerically small, and (ii) is that a realistic
> model for your data? Are near-zero prediction variances realistic for
> any process with constant measured values?

If all the measured values are constant, the more realistic
representation of the process should be the constant measured value
itself, because those data doesn't have a spatial structure that can
be represented by a variogram (please correct me if I'm wrong).

So, my solution for this case is returning a spatial grid where all
the cells have the same constant measured value, as suggested by Paul.

Kinds,

Mauricio

> --
> Edzer


>
> Mauricio Zambrano wrote:
>> Dear Paul and Edzer,
>>
>>
>> 2009/11/17 Tomislav Hengl <hengl at spatial-analyst.net>:
>>
>>> Hi Paul, Edzer,
>>>
>>> I understand why the singular matrix problem happens and I know that there is not really a
>>> mathematical solution around it:
>>>
>>>
>>>> x <- matrix(runif(100), nrow=10)
>>>> x.i <- solve(x)
>>>> str(x.i)
>>>>
>>>  num [1:10, 1:10] 0.8191 -1.0293 0.0826 1.068 -0.2106 ...
>>> # add a 'singular' column
>>>
>>>> x[,1:10] <- rep(1, 10)
>>>> x.i <- solve(x)
>>>>
>>> Error in solve.default(x) :
>>>  Lapack routine dgesv: system is exactly singular
>>>
>>>
>>> However, I would very much support if you would integrate an "if" loop to check if it will happen,
>>> and then mask the prediction location using "NA".
>>>
>>
>>
>>> I mean, at the moment every time we want to run predictions, even if only at a single prediction
>>> location the model fails, we are not able to generate any output (this is sometimes really
>>> frustrating).
>>>
>>
>> I agree with Tom that it may be really frustrating not to get any
>> output, even most when this situation happens within a loop that
>> involves many time steps. I know that the user can easily get rid of
>> this manually for a single prediction, but it should be better if the
>> check could be integrated into the 'krige' or the 'autoKrige'
>> function, but of course this is your decision.
>>
>>
>>
>>> Hence, I would support that you allow us to run predictions for all locations first, and then let
>>> the users judge if one should increase the search radius, remove some too-uniform predictors etc
>>> etc.
>>>
>>
>> In case you could allow us to run the predictions first, it shouldn't
>> be better to mask the prediction location with the constant value that
>> caused the error instead of NA ?. Or to have a flag that allow the
>> user to choose if to get an NA or the constant value ?
>>
>>
>> Kinds,
>>
>> Mauricio
>>
>>
>
> --
> Edzer Pebesma
> Institute for Geoinformatics (ifgi), University of Münster
> Weseler Straße 253, 48151 Münster, Germany. Phone: +49 251
> 8333081, Fax: +49 251 8339763 http://ifgi.uni-muenster.de/
> http://www.springer.com/978-0-387-78170-9 e.pebesma at wwu.de
>
>