# [SciPy-User] cholesky of sparse symmetric banded matrix

josef.pktd@gmai... josef.pktd@gmai...
Tue Aug 21 18:16:29 CDT 2012

```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.

Josef
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