topic Re: Singular value decomposition function DBDSQR in Intel® oneAPI Math Kernel Library

Singular value decomposition function DBDSQR

CO_Traut — Tue, 18 Aug 2009 21:21:36 GMT

To calculate the singular values of a general matrix, the mkl tutorial says two functions are enough, DGERBD followed by DBDSQR. But it seems like another function (DORGBR) needs to be used in the middle.

Is the tutorial (mkl_man.pdf) right?

Re: Singular value decomposition function DBDSQR

ArturGuzik — Wed, 19 Aug 2009 00:21:57 GMT

Quoting - CO_Traut

DGERBD/DBDSQR should be enough. You can also call GESVD and get your matrix decomposed (including list of singular values (sorted)).

A.

Re: Singular value decomposition function DBDSQR

roland-duerr — Wed, 19 Aug 2009 08:45:44 GMT

Quoting - ArturGuzik

DGERBD/DBDSQR should be enough. You can also call GESVD and get your matrix decomposed (including list of singular values (sorted)).

May I ask which one is better? Is it worth to switch from GEBRD/BDSQR to GESVD?

Especially it is interesting to me which one is faster and whether there are differences in precision.

Re: Singular value decomposition function DBDSQR

ArturGuzik — Thu, 20 Aug 2009 00:58:55 GMT

Quoting - roland-duerr

May I ask which one is better? Is it worth to switch from GEBRD/BDSQR to GESVD?
Especially it is interesting to me which one is faster and whether there are differences in precision.

Roland,

I need to confess that I have not-that-deep knowledge of the algorithm details but I believe GESVD should be fine (this should include calls to GEBRD and BDSQR). You have just a single call. In any case it's superior to LINPACK implementation (as far as I know).

The other algorithm you can use and should be much faster for large problem is ?bdsdc and uses the "divide-and-conquer" algorithm (see MKL docs).

A.

Re: Singular value decomposition function DBDSQR

Michael_C_Intel4 — Wed, 02 Sep 2009 11:01:53 GMT

Quoting - CO_Traut

Hi,

it depends on whether you need singular vectors along with singular values, or not. In case you need full SVD you certainly need dorgbr to restore orthogonal matrix from its elementary reflectors representation. In case you don't need vectors, there's no need to call dorgbr.

MKL manual doesn't state ina general text that dgebrd and dbdsqr is enough, it just describes the decomposition - main (necessary) parts of the algorithm - just because the full description of all the branches would be too excessive. dorgbr isn't a routine making some decomposition - it just restores an orthogonal form.At last, dorgbr is explicitly mentioned in Figure 4-1 Decision Tree: Singular Value Decomposition at the appropriate bar.

Michael,
MKL Engineer.