Hi,
I wanted to use lobpcg to compute some eigenvalues and eigenvectors. Assuming that all matrix types should be supported I chose Magma_ELL as sparse matrix format.
Unfortunately, due to the implementation of magma_d_spmv in magma_d_blaswrapper.cpp this format is only supported for real vectors (num_cols==1). As I am searching for multiple eigenvectors my vector should be a dense matrix with several columns. Yet, Magma_SELLP is supported for my case. That seems a bit strange. Is there an algorithmic reason for this?
It would be nice to have a list of supported matrix formats somewhere.
Please also note that there is some code commented out in function magma_d_spmv that makes it a noop for some formats (e.g. MAGMA_CSR with MagmaRowMajor).
Cheers,
Markus
Matrix formats for lobpcg

 Posts: 283
 Joined: Fri Aug 21, 2009 10:39 pm
Re: Matrix formats for lobpcg
We can easily enable SpMM for any sparse matrix, e.g., just do SpMV for each vector. However, special optimizations for SpMM can do much better than SpMV. We have done this only for the Magma_SELLP format, and have disable the others  just as a reminder to add them (but we can also enable the slow implementation while we add the improvements for the others, e.g., starting from Magma_ELL).
Stan
Stan
Re: Matrix formats for lobpcg
Thanks for your answer Stan.
Unfortunately that would mean patching Magma, as I want to use the lobcpg solver for an ELLP matrix (and not do sparse matrixvector product directly. They are just where it breaks..). I also assume that Magma makes use on BLAS level 3 operations (dense matriymatrix multiplications) for multiple right hand sides and we would loose performance by this approach.
I am going for SELLP now and hope that it works out.
Unfortunately that would mean patching Magma, as I want to use the lobcpg solver for an ELLP matrix (and not do sparse matrixvector product directly. They are just where it breaks..). I also assume that Magma makes use on BLAS level 3 operations (dense matriymatrix multiplications) for multiple right hand sides and we would loose performance by this approach.
I am going for SELLP now and hope that it works out.
Re: Matrix formats for lobpcg
Ok, I did move to using SELLP, but it is not working yet. I am getting an error message "error: number of vectors has to be multiple of 2" in the sparse matrix vector multiplication.
No sure what this is due to.
So I tested lobpcg using testing_dsolver. To make it run through without error mesage I had to use blocksize 32 (for higher one "error: too many threads requested.
error: too many threads requested." but no error code was returned). But it seems like the results differ quite a lot when using SELLP:
Wen requesting the use of SELLP with blocksize=32 and alignment=8 I get this
With CSR using the same matrix
Seems a bit fishy to me.
No sure what this is due to.
So I tested lobpcg using testing_dsolver. To make it run through without error mesage I had to use blocksize 32 (for higher one "error: too many threads requested.
error: too many threads requested." but no error code was returned). But it seems like the results differ quite a lot when using SELLP:
Wen requesting the use of SELLP with blocksize=32 and alignment=8 I get this
Code: Select all
matrixinfo = [
% size (m x n)  nonzeros (nnz)  nnz/m  stored nnz
%============================================================================%
132 132 4347 32 5888
%============================================================================%
];
Eigenvalues:
1.617020e+01 1.205513e+01 9.965225e+00 8.563851e+00 3.259683e+00 2.923920e+00 5.317256e01 1.116960e03 9.093301e+00 5.388978e+01 6.490582e+01 7.867743e+01 8.791892e+01 9.520502e+01 1.079634e+02 1.094998e+02 1.163479e+02 1.246189e+02 1.305209e+02 1.355360e+02 1.502891e+02 1.649066e+02 1.672114e+02 1.879650e+02 2.056203e+02 2.406668e+02 2.580640e+02 2.768265e+02 3.229031e+02 3.427514e+02 3.691790e+02 4.366912e+02
Final residuals:
[ 48.5361 39.8537 38.7237 31.7085 23.0854 22.6478 9.4308 0.4406 19.1769 77.2629 80.1439 92.7044 115.0919 103.4186 107.4072 117.2513 106.8727 118.3167 143.3277 156.7057 113.8573 155.3311 149.2352 149.7174 173.7212 226.6655 261.0226 226.0232 319.8264 303.9063 318.7915 373.8634 ];
Residuals are stored in file residualNorms
Plot the residuals using: myplot
convergence = [
% iter  residualnrm2  runtime  SpMVcount  info
%=================================================================================%
1 0.000000e+00 0.009271 2 0
%=================================================================================%
%=================================================================================%
% LOBPCG iteration solver summary:
% initial residual: 0.000000e+00
% preconditioner setup: 0.0000 sec
% iterations: 1
% SpMVcount: 2
% exact final residual: 0.000000e+00
% runtime: 0.0093 sec
% preconditioner runtime: 0.0000 sec
%=================================================================================%
];
solverinfo = [
% iter  residualnrm2  runtime  SpMVcount  info
%=================================================================================%
1 0.000000e+00 0.009271 2 0
%=================================================================================%
%=================================================================================%
% LOBPCG iteration solver summary:
% initial residual: 0.000000e+00
% preconditioner setup: 0.0000 sec
% iterations: 1
% SpMVcount: 2
% exact final residual: 0.000000e+00
% runtime: 0.0093 sec
% preconditioner runtime: 0.0000 sec
%=================================================================================%
];
Code: Select all
matrixinfo = [
% size (m x n)  nonzeros (nnz)  nnz/m  stored nnz
%============================================================================%
132 132 4347 32 4347
%============================================================================%
];
restart at step #6
restart at step #19
restart at step #20
restart at step #21
restart at step #22
restart at step #23
restart at step #24
restart at step #25
restart at step #26
restart at step #27
restart at step #28
restart at step #29
Eigenvalues:
9.938945e14 4.197015e14 3.383334e14 3.243467e14 2.336373e14 2.892851e15 6.606877e01 6.606877e01 1.568701e+00 4.108731e+00 4.108731e+00 6.121250e+00 1.221696e+01 1.274937e+01 1.274937e+01 1.321201e+01 2.214689e+01 2.792283e+01 2.792283e+01 3.205128e+01 4.195567e+01 4.743933e+01 4.983593e+01 4.983593e+01 5.089055e+01 5.798131e+01 6.253386e+01 6.410256e+01 7.745958e+01 7.745958e+01 9.381312e+01 9.382367e+01
Final residuals:
[ 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0003 ];
Residuals are stored in file residualNorms
Plot the residuals using: myplot
convergence = [
% iter  residualnrm2  runtime  SpMVcount  info
%=================================================================================%
29 3.506094e09 1.185907 30 0
%=================================================================================%
%=================================================================================%
% LOBPCG iteration solver summary:
% initial residual: 3.288210e+01
% preconditioner setup: 0.0000 sec
% iterations: 29
% SpMVcount: 30
% exact final residual: 2.015266e09
% runtime: 1.1859 sec
% preconditioner runtime: 0.0009 sec
%=================================================================================%
];
solverinfo = [
% iter  residualnrm2  runtime  SpMVcount  info
%=================================================================================%
29 3.506094e09 1.185907 30 0
%=================================================================================%
%=================================================================================%
% LOBPCG iteration solver summary:
% initial residual: 3.288210e+01
% preconditioner setup: 0.0000 sec
% iterations: 29
% SpMVcount: 30
% exact final residual: 2.015266e09
% runtime: 1.1859 sec
% preconditioner runtime: 0.0009 sec
%=================================================================================%
];
Re: Matrix formats for lobpcg
Well, if I only request one eigenvalue, then the results seem similar. But this seems to be the only case. In all others lobpcg with SELLP thinks the initial residual is already small enough. Tested with up to 9 Eigen values.