Re: [eigen] Small documentation optimizations (tiny test patch)

[Gael Guennebaud <gael.guennebaud@xxxxxxxxx>]

On the other hand I think that the ratio of diagonal coefficients is
still a meaningful information to estimate whether the current LDLt
decomposition is reliable. In not, switch to Column pivoting QR. This
is something you can easily do by yourself since LDLt gives you access
to the diagonal vector which has sorted entries.

Gael.

On Tue, Jun 21, 2011 at 4:47 PM, Benoit Jacob <jacob.benoit.1@xxxxxxxxx> wrote:
> 2011/6/21 Douglas Bates <bates@xxxxxxxxxxxxx>:
>>
>> On Jun 20, 2011 11:38 PM, "Tim Holy" <holy@xxxxxxxxx> wrote:
>>>
>>> Hi Gael/all,
>>>
>>> On Monday, June 20, 2011 02:07:23 pm Gael Guennebaud wrote:
>>> > thanks for the patch. Looking forward for the next ones.
>>>
>>> OK, here's a more complete patch. I'm submitting here because it contains
>>> changes that I expect to be non-controversial. Most pages were barely
>>> touched,
>>> though I couldn't stop myself from getting a bit carried away on the
>>> Sparse
>>> tutorial page (BTW there's a chance that bug #9 could be closed).
>>>
>>> I've also submitted my first documentation "bug" report (#300), this one
>>> without a patch. Currently my main use of Eigen is in C++ functions called
>>> from Matlab (MEX functions), and so I am quite interested in the Map class
>>> to
>>> wrap Matlab arrays. I think there should be a tutorial page titled
>>> something
>>> like "Interfacing with external libraries: the Map class." However, I've
>>> noticed some funny behavior from Map; before writing the tutorial page, I
>>> thought I'd ask whether these inconsistencies are intended or not. (I'm
>>> also
>>> curious for the purposes of moving forward on my own code...)
>>
>> I'm working on a similar interface between R and Eigen using the Rcpp C++
>> template package for interfacing R and C++.  Currently the RcppEigen package
>> passes its tests on Linux but not on Windows. After I fix the Windows glich
>> it will be available as http://cran.R-project.org/web/packages/RcppEigen The
>> sources and development version are on the R-forge site for the Rcpp
>> project.
>>
>> One of our comparisons is on the speed of fitting a linear model (and also
>> simplicity of code, which should not be underestimated). R uses a
>> rank-revealing QR decomposition and Eigen is one of the few high-level
>> linear algebra packages that also provide this so that we can obtain the
>> results we want in the rank-deficient case. I'm pleased to say that Eigen
>> performs very well, twice as fast as the current R code and faster than an
>> implementation using Amarillo, which is not rank-revealing. The fastest code
>> by far uses the LDLT decomposition. I feel that it should be rank-revealing
>> but that is not part of the interface. Should it be possible to check for
>> rank-deficiency according to the ratio of the elements of the diagonal, D,
>> to its largest element or am I missing something here?
>
> We had this conversation a few times in the distant past and the
> conclusion was that LDLT is not rank-revealing.
>
> The pivoting one does in LDLT is akin to partial (columns-only)
> pivoting in LU, whereas only full-pivoting LU is rank-revealing. In
> concrete terms, if you have a big coefficient in the bottom-left
> corner of the matrix, there's nothing in LDLT that will bring it into
> the diagonal.
>
> Benoit
>
>
>