[SciPy-User] cholesky of sparse symmetric banded matrix

[Nathaniel Smith]

On Wed, Aug 22, 2012 at 12:16 AM,  <josef.pktd at gmail.com> wrote:
> I would like to get a cholesky decomposition of a symmetric banded matrix
> and multiply it with a dense array
>
> I found
> http://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.cholesky_banded.html
> and this
> http://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.dia_matrix.html
>
> either
> 1) is there a way to do linear algebra (dot multiplication) directly in the
> "upper diagonal ordered form"?
> or
> 2) is there an efficient way to go from the "upper diagonal ordered form" to
> a sparse diagonal matrix (or both ways)?
>
> Is there code that uses this and that I can look at for the pattern?
>
>
> -------
> my problem is standard linear least squares, where I have an explicit banded
> form for the (nobs, nobs) weighting matrix
>
> X'WX and X'Wy
>
> and I need a transformation X2 = W^(0.5) X and y2 = W^(0.5) y
>
> so I get X2'X2 and X2'y2
>
> (nobs: number of observations, prime is transpose)
> My first example only has one upper and one lower off-diagonal, so working
> with dense is wasteful.

If you only have one off-diagonal, then you may be best off using
CHOLMOD on the CSC representation:
  http://packages.python.org/scikits.sparse/cholmod.html
  http://lists.vorpus.org/pipermail/scikits-sparse-discuss/2012-August/000038.html

Of course this uses GPLed code.

-n