I realized BLAS.gbmv works with both orderings using the ’T’ option, so its 
probably worth supporting both formats.

Anyone know if there is a BandedMatrix*BandedMatrix routine in BLAS/LAPack? I 
have it implemented in Julia, but it would probably be a lot faster using an 
inbuilt version.


> On 29 Mar 2016, at 2:25 AM, Tim Holy <[email protected]> wrote:
> 
> On Sunday, March 27, 2016 06:43:19 PM Sheehan Olver wrote:
>> I've split out the BandedMatrix data structure in BandedMatrices.jl:
>> 
>>    https://github.com/ApproxFun/BandedMatrices.jl
>> 
>> Right now the entries are in the "wrong" order for LAPack: the rows are
>> stored  (instead of the columns) .  I'm debating whether to support both
>> orderings, or replace the current implementation with the "correct" column
>> version.
> 
> You internal debate is also going on elsewhere:
> https://github.com/JuliaLang/julia/issues/4774#issuecomment-149349751
> https://github.com/JuliaLang/julialang.github.com/blob/teh/arrays/blog/_posts/2016-03-27-arrays-iteration.md#row-major-matrices-permuteddimensionarrays-and-taking-transposes-seriously
> 
> Best,
> --Tim
> 
>> 
>> On Thursday, March 24, 2016 at 9:10:12 AM UTC+11, Tony Kelman wrote:
>>> +1 for a specific standalone BandedMatrices package. Once it's up and
>>> running and registered, could even move the Lapack bindings for gb*
>>> functions out to the package (and pb* and sb* if you also have symmetric),
>>> since we don't have a type for them in base. I think it'll be important to
>>> work out how to get base to support additional sparse and structured
>>> matrix
>>> formats well, without needing to have the types themselves in base.
>>> 
>>> On Wednesday, March 23, 2016 at 2:43:16 PM UTC-7, Sheehan Olver wrote:
>>>> It would be great to have a broader SparseFormats.jl package.
>>>> 
>>>> Maybe in the time being I'll start it as BandedMatrices.jl (since that's
>>>> already implemented) which can be renamed later.
>>>> 
>>>> Sheehan
>>>> 
>>>> Sent from my iPhone
>>>> 
>>>> On 24 Mar 2016, at 03:07, Christoph Ortner <[email protected]> wrote:
>>>> 
>>>> Here is a short list that in the long-run would be useful:
>>>>  * compressed row
>>>>  * triplet
>>>>  * block-sparse matrices
>>>>  (* linked-list variants of CC and CR??)
>>>> 
>>>> C
>>>> 
>>>> On Wednesday, 23 March 2016 13:53:30 UTC, Tim Holy wrote:
>>>>> Base has UniformScaling, Diagonal, Bidiagonal, Tridiagonal,
>>>>> SymTridiagonal,
>>>>> UpperTriangular, LowerTriangular, in addition to SparseVector and
>>>>> SparseMatrixCSC. But not general banded.
>>>>> 
>>>>> --Tim
>>>>> 
>>>>> On Wednesday, March 23, 2016 04:19:22 AM Christoph Ortner wrote:
>>>>>> I'd be interested as well; more generally: does Julia still only have
>>>>> 
>>>>> CCS
>>>>> 
>>>>>> implemented? For me it would sound productive to start a general
>>>>>> SparseFormats.jl (or similar) package and collect various other
>>>>> 
>>>>> formats,
>>>>> 
>>>>>> which could eventually be incorporated into Base or a
>>>>> 
>>>>> standard-library.
>>>>> 
>>>>>> Christoph
> 

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