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

[Heroux, Mike]

Gyorgy,

The Matrix Market I/O functions are parallel, but only process 0 reads from the file.  The file contents are used to construction an Epetra object on process 0, which is then exported to a distributed object that is split across all processes according to an Epetra map.  The default map splits the data by a uniform distribution.  You can prescribe your own distribution too.

This is the only portable approach to I/O that I know of for reading and writing a plain text file.

In general, text-based file I/O from a single file is not very scalable.  It’s primarily meant as a way to enable problem studies.  You would probably be better off using the HDF5 functionality from EpetraExt.

Mike

From: Gyorgy Matyasfalvi <matyasfalvi at gmail.com<mailto:matyasfalvi at gmail.com>>
Date: Sunday, April 5, 2015 at 10:52 AM
To: "maherou at sandia.gov<mailto:maherou at sandia.gov>" <maherou at sandia.gov<mailto:maherou at sandia.gov>>
Cc: "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>>
Subject: Re: [Trilinos-Users] Epetra - Dense Matrix-Vector multiply basics

Dear Michael:

thanks for your response. Ok that makes sense.
One more question I have in terms of the MatrixMarket I/O routines.
To me it seems that the MatrixMarketFileToCrsMatrix in EpetraExt is actually a serial operation since only processor 0 does the data read-in and then broadcasts the data to the other processors. Is that correct?

Thanks! Best,
Gyorgy

On Sat, Apr 4, 2015 at 8:23 PM, Heroux, Michael A <maherou at sandia.gov<mailto:maherou at sandia.gov>> wrote:
Gyorgy,

I believe the operations you need are supported.  In the case of a wide matrix, for either a sparse or dense matrix, you want to think about storing A^T, and then apply the transpose operation to get the action of A.  This is basically what I described in the previous message.

You are also right about the square case, that doing a 2D decomposition would be appropriate, and Epetra (and similarly Tpetra) is unique in its support for this kind of decomposition, compared to other popular libraries.  Even so, the infrastructure to support construction and management of 2D decompositions can be substantially improved.

If you need more details on what I describe in the first paragraph, let me know.

Mike

On Apr 3, 2015, at 1:33 PM, Gyorgy Matyasfalvi <matyasfalvi at gmail.com<mailto:matyasfalvi at gmail.com><mailto:matyasfalvi at gmail.com<mailto:matyasfalvi at gmail.com>>> wrote:

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<mailto:maherou at sandia.gov><mailto:maherou at sandia.gov<mailto: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><mailto:matyasfalvi at gmail.com<mailto:matyasfalvi at gmail.com>><mailto:matyasfalvi at gmail.com<mailto:matyasfalvi at gmail.com><mailto: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><mailto:maherou at sandia.gov<mailto:maherou at sandia.gov>><mailto:maherou at sandia.gov<mailto:maherou at sandia.gov><mailto: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>><mailto:matyasfalvi at gmail.com<mailto:matyasfalvi at gmail.com><mailto:matyasfalvi at gmail.com<mailto:matyasfalvi at gmail.com>>><mailto:matyasfalvi at gmail.com<mailto:matyasfalvi at gmail.com><mailto:matyasfalvi at gmail.com<mailto:matyasfalvi at gmail.com>><mailto: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>><mailto: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>>><mailto: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>><mailto: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>><mailto: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>>><mailto: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>><mailto: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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