Seeking advice on choice of sparse matrix format

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fletchjp
Posts: 203
Joined: Mon Dec 27, 2010 7:29 pm

Seeking advice on choice of sparse matrix format

Post by fletchjp » Sat Aug 01, 2015 3:55 pm

I have two complex matrices A and B which are generated in memory in setting up a problem.

For a case about 4000 square, A averages 850 elements per row and B has 16 elements per row.

At present I store all the elements of both A and B and for B this is clearly wasteful.

I need to do two operations involving B

1. Add a multiple of it to A
2. Do repeated multiplications Bx with different vectors x.

I want to move to using the sparsity of B, for the moment tackling operation 2 by storing B in a sparse form and using a sparse multiplication. I need to chose a sparse format for B and also find a sparse BLAS which will do the multiplication. I want to start by doing this on the CPU, but have the possibility to move to using Magma sparse routines. I am working in Fortran 90.

I am currently digging into how Magma sparse matrices and routines are defined. I would welcome some advice on the choice of sparse matrix format and sparse BLAS. It would also be useful if this included a routine for adding a sparse matrix to a dense matrix.

Thank you.

John

hartwig anzt
Posts: 90
Joined: Tue Sep 02, 2014 5:44 pm

Re: Seeking advice on choice of sparse matrix format

Post by hartwig anzt » Sat Aug 01, 2015 4:53 pm

Dear John,

a 4000x4000 matrix is still relatively small. Sparse iterative systems typically target problems with more than 100,000 unknowns. So it might be an option to handle this system as dense. However, if you want, you can handle it as sparse. The easiest way is to convert it to csr, and then use the MAGMA-sparse functions for addition and multiplication.

Assuming the elements of your dense matrix is stored in M, you should be able to use the following code:

// pass it to MAGMA-sparse:
// create a MAGMA_Z_MATRIX

magma_z_matrix A, A_CSR, A_dev;
A.num_rows = 4000;
A.num_cols = 4000;
A.storage_type = Magma_DENSE;
A.val = M;

// convert to CSR
magma_zmconvert( A, &A_CSR, Magma_DENSE, Magma_CSR, queue );

// copy to device
magma_zmtransfer( A_CSR, A_dev, Magma_CPU, Magma_DEV, queue );

at this point you are able to throw all linear algebra tools at it, e.g.
* matrix addition
magma_zcuspaxpy ( magmaDoubleComplex * alpha,
magma_z_matrix A,
magmaDoubleComplex * beta,
magma_z_matrix B,
magma_z_matrix * AB,
magma_queue_t queue
)

* sparse matrix sparsematrix multiplication:
magma_zcustomspmv ( magmaDoubleComplex alpha,
magma_z_matrix x,
magmaDoubleComplex beta,
magma_z_matrix y,
magma_queue_t queue
)

* sparse matrix vector product
magma_z_spmv (magmaDoubleComplex alpha, magma_z_matrix A, magma_z_matrix x, magmaDoubleComplex beta, magma_z_matrix y, magma_queue_t queue)


Does this answer your question?

Thanks, Hartwig

fletchjp
Posts: 203
Joined: Mon Dec 27, 2010 7:29 pm

Re: Seeking advice on choice of sparse matrix format

Post by fletchjp » Sat Aug 01, 2015 5:47 pm

Hartwig

Thank you very much for the quick reply. Indeed, my 4000 by 4000 is just a small case, they get much bigger. I use this case for development. I don't see much advantage using Magma at that size, but it can then be used on larger cases.

I think you have dealt with most of the things. There is an argument called queue on some of the calls. Do I have to set that to something or does it have a convenient default?

My main problem with Magma sparse at the moment is that I cannot run with CUDA until I get CUDA 6.5 running and for that I need to update my NVIDIA drivers. I am still figuring out how to do that without crashing my computer, which I have done once already.

I am hoping I can at least use magma_zmconvert to move the matrix around. Is there a FORTRAN wrapper for it?

I then need to find a CPU sparse BLAS to work on it.

Thanks again

John

hartwig anzt
Posts: 90
Joined: Tue Sep 02, 2014 5:44 pm

Re: Seeking advice on choice of sparse matrix format

Post by hartwig anzt » Sat Aug 01, 2015 9:17 pm

John,

are you working on your personal Desktop computer or do you have access to some cluster? In the second case, I could probably help getting the code running - if granted access. For the CPU side, Intel's MKL provides some sparse support. Unfortunately, I have to admit that the FORTRAN support is very limited... Is it a complex code or is switching to C an option?

Thanks, Hartwig

fletchjp
Posts: 203
Joined: Mon Dec 27, 2010 7:29 pm

Re: Seeking advice on choice of sparse matrix format

Post by fletchjp » Sun Aug 02, 2015 7:51 am

Hartwig

Thank you for your message.

I am running with two home computers, both with GTX 460 graphics cards. I bought these systems a few years ago to assist my colleague who does the serious calculations. As I am more or less retired now I have more time to work with them. The idea was that I can run ScaLapack across the two systems. Both the computers are currently on Ubuntu 12.04. I still have the bad memories from the upgrade from 10.04 when a lot of things stopped working, so I have put off the upgrade to 14.04 which is I think coming up soon. I have done upgrades of the NVIDIA drivers in the past, which usually rebuild the kernel module but on the most recent occasion this did not work and I had to step back. So currently I cannot run CUDA 6.5 and I am stuck with CUDA 4.1 until I can sort the drivers.

The code is in historic FORTRAN and I think the way ahead for the Sparse work has to be through interface code. I am already using the magmaf_zgetrf_gpu code. Does that provide a good model? The main problem is in adapting parameters which at the C level are pointers and I think there are facilities for that.

On the Sparse BLAS side there seems to be quite a lot of public domain software. I will look at some of it and post what I find for comment. I was hoping that the Magma team would have some recommendations from the work going on already.

Thank you again.

John

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