topic accessing LU matrices in Pardiso in Intel® oneAPI Math Kernel Library

accessing LU matrices in Pardiso

amaslov — Thu, 16 Sep 2010 18:21:46 GMT

Hi,

is it possible to access directly the LU matrices after the factorization stage in Pardiso?

Alex

accessing LU matrices in Pardiso

Alexander_K_Intel2 — Thu, 16 Sep 2010 19:00:46 GMT

Hi,

LU matrices stored internally but you can get diagonal elements of Cholesky decomposition, number of positive and negative elements on diagonal an so on. What exactly you what to do with LU matrices obtained from PARDISO?

With best regards,

Alexander Kalinkin

accessing LU matrices in Pardiso

amaslov — Thu, 16 Sep 2010 19:08:59 GMT

Hi,
I am thinking of using LU matrices to compute some elements (or blocks) of the inverse matrix using recursive
algorithms. For this, I need full access to LU (or L for Cholesky factorization) matrices.

Alex

accessing LU matrices in Pardiso

Alexander_K_Intel2 — Thu, 16 Sep 2010 19:16:16 GMT

Could you provide block-scheme of this algorithms or some articles about them? Maybe I could provide some ideas how PARDISO can be used to improve it.

With best regards,

Alexander Kalinkin

accessing LU matrices in Pardiso

amaslov — Fri, 17 Sep 2010 00:36:32 GMT

Hi Alexander,

thank you for your help. An example of recursive computing of inverse elements using LU matrices is given in Niessner et al. "On computing the inverse of a sparse matrix," International Journal for Numerical Methods in Engineering, Vol. 19, 1513-1526 (1983).
(I can send a pdf file vie email).

I am thinking of putting the block that I need in the lower right part of the inverse matrix and then applying formulas (21) and (22) [see also Figs.3,4]. My original matrix is symmetric and I was wondering whether PARDISO could be used to make Cholesky factorization and return the L-matrix (instead of actually solving the linear system of equations).

--Alex

accessing LU matrices in Pardiso

Alexander_K_Intel2 — Fri, 17 Sep 2010 09:53:51 GMT

Hi,

Could you upload this pdf by this forum? You can do it by private reply on this topic if there are some problem with sharing this article.

With best regards,

Alexander Kalinkin

accessing LU matrices in Pardiso

Russ_Taylor — Sat, 18 Sep 2010 00:49:19 GMT

Hi Alexander,

I need to access diagonal elements of sparse Cholesky, could you please show how these may be accessed? Thanks, RT

accessing LU matrices in Pardiso

Alexander_K_Intel2 — Sat, 18 Sep 2010 03:47:04 GMT

Hi Russ,

Are your matrix symmetric? If yes the way how to find diagonal elements from Cholesky decomposition describe in this topic: (http://software.intel.com/en-us/forums/showthread.php?t=77082) or in PARDISO example folder (example name -pardiso_sym_getdiag_c.c).

With best regards,

Alexander Kalinkin

accessing LU matrices in Pardiso

Russ_Taylor — Sat, 18 Sep 2010 04:22:41 GMT

Thanks for the very quick reply. Yes, matrix is SPD.
thanks again,

RT

accessing LU matrices in Pardiso

Russ_Taylor — Mon, 20 Sep 2010 01:50:16 GMT

Hi Alexander,

Two questions:

(1) I couldn't tell if LDL' or LL' is being computed?
(2) What is the cost of the two extra steps?

Thanks again,

Russ

accessing LU matrices in Pardiso

Alexander_K_Intel2 — Mon, 20 Sep 2010 01:54:42 GMT

Hi Russ,

1. If mtype is equal 2 than LL^T decomposition will be computed,if mtype is equal -2 then LDL^T decomposition will be computed.

2. It's depend on initial matrix size and structure.

With best regards,

Alexander Kalinkin