FABuLOuS numericals results

This graphic seems to indicate than a larger restart parameter help to speed up the convergence (but this is not necessarily true, a collection of references in IB-BGMRES-DR, Section 4.5, show that the contrary is possible)

In this experience, I try to mimic the parameters of section 4.2, example 8. The experience results are different because the right hand side are generated randomly with different random number generator, the kernels used may be different and some algorithms may differ a little.

For IB versions, the algorithms do differ: the experience presented here implement an extension computing 'Inexact breakdown on R0', while the result presented in the article do not (Figure 2, Example 8, left side)

The max and min displayed here are the max and min of the "not yet discarded" direction This is why the min may be increasing on this graphic: This means a direction was discarded and its norm is not taken into account anymore.

As the CG algorithm minimize the A-norm of the error and not directly the residual. It is not an error if the norm of the residual is not decreasing.

When using random loader "-l RD" with BCG algorithm, the test program, ensure to have a SPD matrix by computing

A <- rand_mat()
A <- A^{T} * A

Using the exemple file example\_gcro.cpp

The curve for "full_gels facto" is zero because there is no factorization part in the "full_gels". But even if it may be unexpected, the curve for "incremental_gels solve" is also zero because since GMRES is not a short term recurrence algorithm, computing the complete least square solution is not mandatory at each iteration. Only the residual norm is needed is this can be obtained from the incremental factorization without computing the actual residual

DOES NOT WORK Try to compare PAPI hw counter with estimation of Gflops/s we computed:

In this section they may have big test cases which may not work if your machine do not have enough memory.

Reminder:

• "-p" is number of right hand sides
• "-m" is maximum krylov space
• "-M" is maximum matrix vector product

"BAD" matrices are matrices that theorically have a bad convergence:

• real case: they are tridiagonal with 4 on diagonal, -1.0 under the diagonal and -2.99 over the diagonal
• complex case: diag = 4 - 2i, sub-diag: -2.99+i and over-diag: -1+i.

There is two kinds of test: MAX_KRYLOV_SPACE = 2000 AND DIMENSION = 5000 and MAX_KRYLOV_SPACE = 5000 AND DIMENSION = 20000

MAX_MVP is set to a very big value in order that all test reach convergence (100000)

The ORTHOGONALIZATION_SCHEME used is CGS (the cheapest)

There are two kind of graphic:

• Time or percentage of time of certain steps in a iteration with respect to size of the krylov space. (therefore data from different restart are grouped together by krylov space size)
• Time of steps of total time of iterations with respect to the number of the current iteration in the globality of the algorithm

The tests in this section compare badly against each other because part that does not use chameleon in the executable linked with chameleon does not profit from multi-threaded kernels (as chameleon requires to be linked against sequential blas. See [[ile:NOTES.org] Section "linking with lapacke/cblas kernels"]]

Setup connection with plafrim

export TERM=xterm
hostname
echo $WORKDIR

Launch the experiments

cd ${WORKDIR}
#git pull origin develop
emacs -batch --load ~/.emacs.d/init.el RESULTS.org --funcall org-babel-tangle
sbatch scripts/batch_perf1.sh
squeue -u tmijieux