Rank Revealing QR decomposition: obtaining rank

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Hugo Ferreira

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Feb 27, 2017, 12:51:00 PM2/27/17
to Scala Breeze
Hello,

I am trying to use RR QR decomposition to determine collinearity.
I have seen that we can obtain the rank via SVD, however I would
like to use a RR QR with pivoting that will also allow me to identify
the collinear columns (avoid repeated calculation with SVD).

Does Breeze have a RR QR algorithm with pivoting? If so, does
it provide access to the rank? If not, can we calculate it based on
the R matrix?

TIA,
HF

David Hall

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Feb 27, 2017, 3:00:58 PM2/27/17
to scala-...@googlegroups.com
Breeze has a QR with pivoting (qrp) which can (apparently? maybe?) be used to derive the rank. It's supposed to be like [q, r, p] = qr(m) in matlab. Though I honestly don't really know enough to say more. All I know is what I read at this google books link, and that we have qrp. :)


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Hugo Ferreira

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Mar 1, 2017, 1:04:45 PM3/1/17
to Scala Breeze
Hi David,

Appreciate the feedback.

The issue I have is actually finding out how to determine the rank.

I have found 2 methods - one that uses a matrix norm [2] (apache math commons project)
and another that simply checks for non zero diagonal elements in the R matrix
(no.uib.cipr.matrix.QRP, see [1]). The latter uses LAPACK (see
"com.github.fommil.netlib.LAPACK" in [3])

My understanding is that Breeze is using netlib-java. Can you tell me if you are
using DGEQP3? If so I may be able to use the code snippet below taken from [1].
Does this make sense? If this is doable maybe it can also be included into the Beeze code.

Please note that I am not knowledgeable about matrix or any other numeric computation methods, hence the questions.

TIA,
HF
 

1. https://github.com/fommil/matrix-toolkits-java/blob/master/src/main/java/no/uib/cipr/matrix/QRP.java
2. https://en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm
3. https://github.com/fommil/netlib-java

       
 /*
         * Calculate the rank based on a precision EPS
         */
        final double EPS = 1e-12;
        for (rank = 0; rank < k; rank++) {
            if (Math.abs(R.get(rank, rank)) < EPS)
                break;
        }



On Monday, 27 February 2017 20:00:58 UTC, David Hall wrote:
Breeze has a QR with pivoting (qrp) which can (apparently? maybe?) be used to derive the rank. It's supposed to be like [q, r, p] = qr(m) in matlab. Though I honestly don't really know enough to say more. All I know is what I read at this google books link, and that we have qrp. :)

On Mon, Feb 27, 2017 at 5:14 AM, Hugo Ferreira <hugo6f...@gmail.com> wrote:
Hello,

I am trying to use RR QR decomposition to determine collinearity.
I have seen that we can obtain the rank via SVD, however I would
like to use a RR QR with pivoting that will also allow me to identify
the collinear columns (avoid repeated calculation with SVD).

Does Breeze have a RR QR algorithm with pivoting? If so, does
it provide access to the rank? If not, can we calculate it based on
the R matrix?

TIA,
HF

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