Re: solving triadiagonal (and banded in general) systems of linear equations

[Sergei Steshenko]

--- On Thu, 9/27/12, Jordi Gutiérrez Hermoso <address@hidden> wrote:

> From: Jordi Gutiérrez Hermoso <address@hidden>
> Subject: Re: solving triadiagonal (and banded in general) systems of linear 
> equations
> To: "Sergei Steshenko" <address@hidden>
> Cc: "Octave users list" <address@hidden>
> Date: Thursday, September 27, 2012, 6:12 AM
> On 26 September 2012 18:48, Sergei
> Steshenko <address@hidden>
> wrote:
> 
> > So, do I understand it correctly, that I simply need to
> provide
> > matrix to the solver, and it will detect automatically
> that the
> > matrix is banded and choose the most optimal algorithm
> ?
> 
>     
> http://hg.savannah.gnu.org/hgweb/octave/file/46dd555edd33/liboctave/array/MatrixType.cc#l268
> 
> Note that the argument for this function is a sparse matrix,
> so the
> check only occurs for sparse matrices. For full matrices the
> check is
> 
>      
> http://hg.savannah.gnu.org/hgweb/octave/file/46dd555edd33/liboctave/array/MatrixType.cc#l60
> 
> only upper, lower, and hermitian matrices. No bandedness is
> checked if
> the matrix isn't of sparse type. This is consistent with
> the
> documentation:
> 
>     octave:1> x = toeplitz ([1 2 0 0 0 0]); y =
> toeplitz ([1 2 3 0 0 0]);
>     octave:2> matrix_type (x), matrix_type (y)
>     ans = Full
>     ans = Full
>     octave:3> matrix_type (sparse (x)),
> matrix_type (sparse (y))
>     ans = Tridiagonal
>     ans = Banded
> 
> HTH,
> - Jordi G. H.
> 

So, can I explicitly specify type (banded) of traditional (not sparse) matrix ?

If yes, will it improve performance ?

Thanks,
  Sergei.