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Bug 233

Summary: Public BandMatrix functionality wish list
Product: Eigen Reporter: Rhys Ulerich <rhys.ulerich>
Component: GeneralAssignee: Nobody <eigen.nobody>
Status: NEW ---    
Severity: enhancement CC: gael.guennebaud, jacob.benoit.1
Priority: ---    
Version: unspecified   
Hardware: All   
OS: All   

Description Rhys Ulerich 2011-03-24 05:10:41 UTC
Following up on, just a kindly plea for public BandMatrix functionality compatible with BLAS/LAPACK's notion of general band storage and interoperable when RowMajor is selected.

Specifically, I'm after...
 - Coefficient access
 - Column and row access
 - {Super,main,sub,main}-diagonal access
 - alpha * BandMatrix + beta * BandMatrix with the result of appropriate size (like BLAST report's GB_ACC).
 - BandMatrix * Vector (like BLAS GBMV)

I've tried to play with internal::BandMatrix (and have noticed diagonal access) but haven't had any luck trying to work with it.

Gravy would be...
 - BandMatrix * Matrix (sadly not in BLAS but level 3-ish)
 - LU factorization and solve a la LAPACK's GBTRF/GBTRS
 - LU solve handling multiple right hand sizes for BandMatrix^-1 * Matrix ops
 - Handling of mixed real/complex arithmetic for the above.

My driving use case is B-spline collocation-based numerics.  These produce discrete operators with small bandwidths.  Turns out besides GBMV/GBTRF/GBTRS these operations tend to fall through the cracks.  The mixed real/complex is for use in Fourier/B-spline pseudospectral techniques.
Comment 1 Gael Guennebaud 2011-03-30 13:48:38 UTC

all your requests are obviously planed. To reach these goals, the next step is to introduce the notion of "range vector" which is a column (or a row) where the nonzeros are known to be inside a given range. Then everything should be fairly easy to implement.

Actually, the most tricky part is probably:

BandMatrix3 = alpha * BandMatrix1 + beta * BandMatrix2;

which have to be implemented as:

1 - allocate space in BandMatrix3 and set it to zero
2 - BandMatrix3 += alpha * BandMatrix1
3 - BandMatrix3 += beta * BandMatrix2

With the work in progress refactoring of our expression tree and evaluation mechanism, such an evaluation of BandMatrix3 = alpha * BandMatrix1 + beta * BandMatrix2; should become possible.
Comment 2 Nobody 2019-12-04 10:34:27 UTC
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