Re: how to solve triangular systems

[David Bateman]

Federico Poloni wrote:
> Hi everyone,
>  sorry to bother this mailing list but I don't seem to find this
> anywhere in the docs.
> about operators \ and / :
> When the system matrix is diagonal or triangular does Octave solve it in
> "the smart way" (using O(n) and O(n^2) flops respectively)? Which other
> structures are recognized and supported by these operators (for example,
> matlab says it recognizes permuted-triangular systems)?

If you are using octave 2.9.6 or later then yes octave does indeed solve
only the forward or backward substitution for a triangular matrix. It
detects upper, lower triangular matrices, permuted upper and lower
triangular matrices, and hermitian matrices and does the right thing..

See the matrix_type function for the list of matrix types for sparse and
full matrices that are currently handled automatically by octave 2.9

> If the answer to the first question is no, then:
> Has Octave a "standard" way to solve triangular systems, or does one
> have to write back-substitution from scratch every time?

If you aren't using 2.9.6 or later, then the octave-forge chol function
and triangular matrix type might help. These are available in older
versions of octave-forge.. Although if this is what you want, I'd
strongly recommend using octave 2.9.9 instead..

Regards
David