Colunm Scaling

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Colunm Scaling

Postby kdallen » Tue Feb 13, 2007 8:01 pm

Hi,

I've seen references to scaling columns to make then have the same norm

http://icl.cs.utk.edu/lapack-forum/view ... 25890fd1a4

and that for least squares problems, A (to solve A'Ax = A'b) can't be row scaled but column scaling might be prudent if using SVD or QR with column pivoting.

http://icl.cs.utk.edu/lapack-forum/view ... 25890fd1a4

Question - is there a BLAS/LAPACK routine that will do column scaling only? I haven't been able to find one so far (row and column scaling, yes, but not column scaling only). If no, is it better to make the column norms be equal to 1 (i.e. use the column norms as the scale factors) or the max value in each column equal to 1 (use the max value in each column as scale factors)? I'm wondering if there is a rule of thumb or is it really problem dependent. Thanks.

Ken
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Postby sven » Wed Feb 14, 2007 9:40 am

Dear Ken,

Yes, it is usually prudent to perform column scaling. The precise choice of scale factor is not critical, so choosing the maximum absolute value in each column would generally be fine. Think of the scaling as making the units of measurement for each variable comparable.

I am afraid that there is not an LAPACK routine to do the scaling, but if efficiency is not too much of a concern, then Level 1 BLAS routines such as IxMAX and xSCAL can help.

Best wishes,

Sven Hammarling.
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Postby kdallen » Wed Feb 14, 2007 4:46 pm

Sven,

Thanks for your reply. Here's some wishful thinking - any discussions going on about including matrix scaling options in DGELSx driver routines in a future LAPACK release?

Thanks again for your help. This user group is great!

Ken
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