[Trilinos-Users] Epetra - Dense Matrix-Vector multiply basics

[Gyorgy Matyasfalvi]

Dear Michael:

We're solving the following optimization problem:

min ||A(x^+ - x^-) - b||^2_2 + \nu * 1^T (x^+ + x^-)
x^+, x^- \in R^n

s.t. x^+, x^- >= 0

aka (LASSO) using a first order method called the Nonmonotone Spectral
Projected Gradient (SPG).
( You can find more details in this paper:
http://www.optimization-online.org/DB_FILE/2015/01/4748.pdf )

The matrix A in the objective function comes in many different forms: tall,
wide, square. In one of our test problems A is a wide matrix, with
dimensions: 19,996 rows and 1.355,191 columns.
Our most "expensive" operations are mtx-vec multiplies when computing the
objective function value or the gradient.

What I'd like to achieve is that our code can handle matrices of arbitrary
form "appropriately". For example if A is wide i.e. few rows but many
columns then we partition A along it's columns (domain decomposition), if A
is tall i.e. many rows and few columns then we partition A along it's rows
(range decomposition). If A is square and huge than maybe do both range and
domain decomposition.
It seems to me this is actually doable for sparse matrices using the
Epetra_CrsMatrix class. My question is can I do this in the dense case with
the Epetra_MultiVector class?

Thanks a lot for your help!
Best,
Gyorgy

On Fri, Apr 3, 2015 at 1:24 AM, Heroux, Michael A <maherou at sandia.gov>
wrote:

> Gyorgy,
>
> Please give me some details about your problem:  Algorithm, size of
> matrices, type of data distribution.  Just the basics to start.
>
> Thanks.
>
> Mike
>
> On Apr 2, 2015, at 11:03 PM, Gyorgy Matyasfalvi <matyasfalvi at gmail.com
> <mailto:matyasfalvi at gmail.com>> wrote:
>
> Dear Mike:
>
> Thanks for your help. Indeed I got an error code of -2 and I suspect that,
> as you pointed out, the issue is that *this is not a row vector.
>
> My other question then would be: Is it possible to define a "Domain Map"
> for Multivectors? i.e I want processors to own columns of the matrix
> instead of rows. So basically spread out the columns among different
> processors. I know think this is possible for sparse matrices.
>
> Thanks! Best,
> Gyorgy
>
>
>
> On Thu, Apr 2, 2015 at 9:02 AM, Heroux, Michael A <maherou at sandia.gov
> <mailto:maherou at sandia.gov>> wrote:
> Gyorgy,
>
> Assuming your x, y and A are dense objects, you are using the correct
> function, Multiply().  Chances are that you have some detail incorrect.
> First you should check for error codes that are being returned.  Multiply()
> will return integer error codes if it runs into issues:
>
> Int ierr = y.Multiply(...)
>
> If (ierr!=0) ...
>
> Regarding your transpose operation, if I understand the situation
> correctly, x should also be transposed to be a row vector.  Multiply() is
> probably complaining about this.  There is no way in the Epetra framework
> to specify that the "this" argument is transposed.
>
> I think it is best to perform the transpose operation as
>
> x = A^T y
>
> This expression keeps the dimensions correct.
>
> Try this and see how it goes.
>
> Mike
>
> From: Gyorgy Matyasfalvi <matyasfalvi at gmail.com<mailto:
> matyasfalvi at gmail.com><mailto:matyasfalvi at gmail.com<mailto:
> matyasfalvi at gmail.com>>>
> Date: Wednesday, April 1, 2015 at 10:41 PM
> To: "trilinos-users at software.sandia.gov<mailto:
> trilinos-users at software.sandia.gov><mailto:
> trilinos-users at software.sandia.gov<mailto:
> trilinos-users at software.sandia.gov>>" <trilinos-users at software.sandia.gov
> <mailto:trilinos-users at software.sandia.gov><mailto:
> trilinos-users at software.sandia.gov<mailto:
> trilinos-users at software.sandia.gov>>>
> Subject: [EXTERNAL] [Trilinos-Users] Epetra - Dense Matrix-Vector multiply
> basics
>
> Dear Developers/Users:
>
> I have a question concerning matrix-vector multiplies:
>
> 1) Is there a document or example file that explains the basics of
> matrix-vector multiplies? Preferably isolated examples of mtx-vec mults.
> instead of being embedded in some algorithm.
>
> If this doesn't exist. Then I'd be interested in finding out:
>
> 2) How to do dense matrix, dense vector multiplies?
> I assume it's done via the Epetra_MultiVector class. However, the only
> operation that seems to have an effect is the following:
>
> y = A x
> using
> y.Multiply('N', 'N', 1.0, A, x, 0.0)
> (x was constructed using an Epetra_LocalMap
> A, and y were constructed using the same Epetra_Map)
>
> The problem is that if I want to compute for example:
>
> x = y^T A
> using
> x.Multiply('T', 'N', 1.0, y, A, 0.0)
>
> it seems the Multiply() operation doesn't do anything x remains unchanged.
>
> What am I doing incorrectly here?
> Thanks a lot! Best,
> Gyorgy
>
>
>
>
>
>
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