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

[David Bateman]

Le 27 sept. 2012 à 21:04, Sergei Steshenko <address@hidden> a écrit :

> 
> 
> --- 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.
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You can explicitly set full matrix types as

Upper
Lower
Positive definite
Full
Singular

But you can't set it to "banded". In any case there is no banded full solver in 
octave

D,