[petsc-users] Seeking help for analyzing non-convergence (KSP)

Mon Nov 7 03:53:06 CST 2016

Hey Barry!

Am 04.11.2016 um 18:42 schrieb Barry Smith:
> 
>   Try running on one process with the SuperLU direct solver (note superlu NOT superlu_dist). You need to ./configure PETSc with --download-superlu then run your code with -pc_type lu -pc_factor_mat_solver_package superlu

I am having some problems making superlu work, when configuring with --download-superlu.

Firstly, I was getting "libsuperlu.so.5: cannot open shared object file: No such file or directory" errors.
They vanished after adding petsc/arch-linux2-c-debug/lib to LD_LIBRARY_PATH.

But my application (C and python) still do not find the solver:

Traceback (most recent call last):
  File "RBF_Load.py", line 46, in <module>
    main()
  File "RBF_Load.py", line 38, in main
    solver.solve(b, x)
  File "PETSc/KSP.pyx", line 384, in petsc4py.PETSc.KSP.solve (src/petsc4py.PETSc.c:154741)
petsc4py.PETSc.Error: error code 92
[0] KSPSolve() line 600 in /data/scratch/lindnefn/software/petsc/src/ksp/ksp/interface/itfunc.c
[0] KSPSetUpOnBlocks() line 220 in /data/scratch/lindnefn/software/petsc/src/ksp/ksp/interface/itfunc.c
[0] PCSetUpOnBlocks() line 1001 in /data/scratch/lindnefn/software/petsc/src/ksp/pc/interface/precon.c
[0] PCSetUpOnBlocks_ASM() line 428 in /data/scratch/lindnefn/software/petsc/src/ksp/pc/impls/asm/asm.c
[0] KSPSetUp() line 390 in /data/scratch/lindnefn/software/petsc/src/ksp/ksp/interface/itfunc.c
[0] PCSetUp() line 968 in /data/scratch/lindnefn/software/petsc/src/ksp/pc/interface/precon.c
[0] PCSetUp_LU() line 134 in /data/scratch/lindnefn/software/petsc/src/ksp/pc/impls/factor/lu/lu.c
[0] MatGetFactor() line 4244 in /data/scratch/lindnefn/software/petsc/src/mat/interface/matrix.c
[0] See http://www.mcs.anl.gov/petsc/documentation/linearsolvertable.html for possible LU and Cholesky solvers
[0] Could not locate a solver package. Perhaps you must ./configure with --download-<package>

I configured with

python2 configure --with-debugging=1 --download-petsc4py --download-mpi4py --download-superlu

on a recent checkout of the maint branch.

make PETSC_DIR=/data/scratch/lindnefn/software/petsc PETSC_ARCH=arch-linux2-c-debug test reported no errors.

Best Thanks,
Florian

> 
>    Barry
> 
>> On Nov 4, 2016, at 10:44 AM, Florian Lindner <mailinglists at xgm.de> wrote:
>>
>> Hello,
>>
>> I have a matrix C that is the result of an RBF interpolation.
>>
>> It is constructured like that:
>>
>> c_ij = phi( |x_i - x_j| )
>>
>> x are supporting points. phi is the radial basis functions, here it is a Gaussian: phi(r) = exp( -(1.5*r)^2 ).
>>
>> The system is augmented by a global polynomial, which results in the first 3 rows being dense.
>>
>> The matrix is symmetric and of size 2309. It is also sparse since the basis functions are decaying very rapidly. A
>> picture of the sparsity pattern I have uploaded at [1]
>>
>> I am having big trouble solving the system.
>>
>> Using default settings on 10 procs I'm not achieving convergence after 40k iterations:
>>
>> 40000 KSP preconditioned resid norm 2.525546749843e+01 true resid norm 5.470906445602e+01 ||r(i)||/||b|| 3.122197420093e-02
>>
>> I have uploaded a small python script using petsc4py that simply loads the matrix and the rhs and tries to solve it. It
>> is bundled with the matrix and rhs and available at [2] (650 KB). Some paths in the Python source need to be adapted.
>>
>> The condition number using -pc_type svd -pc_svd_monitor did not work, due to incompatible matrix formats.
>>
>> The condition number estimate using -pc_type none -ksp_type gmres -ksp_monitor_singular_value -ksp_gmres_restart 1000
>> has been running for over half an hour now, its current line is:
>>
>> 5655 KSP preconditioned resid norm 9.481821216790e-02 true resid norm 9.481821212512e-02 ||r(i)||/||b|| 5.411190635748e-05
>> 5655 KSP Residual norm 9.481821216790e-02 % max 2.853532248325e+02 min 1.073886912921e-06 max/min 2.657199947212e+08
>>
>> The Eigenvalues, computed with -ksp_compute_eigenvalues -ksp_gmres_restart 1000 -pc_type none did not converge after 40k
>> iterations, bit they eigenvalues were printed. They are all real, none is zero, but some are pretty close. I've pasted
>> them at the end of the mail.
>>
>> I tried a bunch of different PCs, but I'm somehow helpless on how to analyse that problem more systematically.
>>
>> I know that RBF interpolation tends to produce badly conditioned matrices, but this seems to be (almost) singular. I
>> have scrutinized my algorithms and in most cases it works just fine, converges and the output results are sane.
>>
>> I am grateful for any help!
>>
>> Best,
>> Florian
>>
>>
>> [1] http://xgm.de/upload/sparsity.png
>> [2] http://xgm.de/upload/RBF.tar.bz2
>>
>> Eigenvalues:
>>
>> Iteratively computed eigenvalues
>> -276.515 + 0.i
>> -276.348 + 0.i
>> -43.5577 + 0.i
>> 3.27753e-09 + 0.i
>> 5.09352e-06 + 0.i
>> 1.56431e-05 + 0.i
>> 2.79046e-05 + 0.i
>> 0.000145571 + 0.i
>> 0.000184333 + 0.i
>> 0.000283665 + 0.i
>> 0.000395128 + 0.i
>> 0.000488579 + 0.i
>> 0.000568982 + 0.i
>> 0.000704054 + 0.i
>> 0.000864538 + 0.i
>> 0.00101309 + 0.i
>> 0.00119913 + 0.i
>> 0.00142954 + 0.i
>> 0.00156907 + 0.i
>> 0.00178931 + 0.i
>> 0.00200295 + 0.i
>> 0.00223425 + 0.i
>> 0.00246876 + 0.i
>> 0.00276749 + 0.i
>> 0.00303141 + 0.i
>> 0.00326647 + 0.i
>> 0.00346721 + 0.i
>> 0.00437335 + 0.i
>> 0.0047525 + 0.i
>> 0.0049999 + 0.i
>> 0.0051701 + 0.i
>> 0.00556462 + 0.i
>> 0.00605938 + 0.i
>> 0.00628264 + 0.i
>> 0.00697463 + 0.i
>> 0.00756472 + 0.i
>> 0.00783031 + 0.i
>> 0.00822392 + 0.i
>> 0.00868428 + 0.i
>> 0.00928107 + 0.i
>> 0.00954981 + 0.i
>> 0.0104767 + 0.i
>> 0.0108791 + 0.i
>> 0.0111159 + 0.i
>> 0.0119535 + 0.i
>> 0.0125402 + 0.i
>> 0.0131083 + 0.i
>> 0.0135975 + 0.i
>> 0.0142472 + 0.i
>> 0.0148179 + 0.i
>> 0.0156007 + 0.i
>> 0.0160567 + 0.i
>> 0.0169899 + 0.i
>> 0.0174895 + 0.i
>> 0.0182683 + 0.i
>> 0.0189543 + 0.i
>> 0.0196781 + 0.i
>> 0.0206413 + 0.i
>> 0.0212257 + 0.i
>> 0.0220118 + 0.i
>> 0.0229829 + 0.i
>> 0.023606 + 0.i
>> 0.0244077 + 0.i
>> 0.0253428 + 0.i
>> 0.0263089 + 0.i
>> 0.0269905 + 0.i
>> 0.0278572 + 0.i
>> 0.028664 + 0.i
>> 0.0293435 + 0.i
>> 0.0306571 + 0.i
>> 0.0315797 + 0.i
>> 0.0320843 + 0.i
>> 0.0334732 + 0.i
>> 0.0344048 + 0.i
>> 0.0349148 + 0.i
>> 0.0361261 + 0.i
>> 0.037176 + 0.i
>> 0.0382401 + 0.i
>> 0.0390156 + 0.i
>> 0.0404156 + 0.i
>> 0.0413084 + 0.i
>> 0.0421763 + 0.i
>> 0.0434521 + 0.i
>> 0.0452247 + 0.i
>> 0.0460417 + 0.i
>> 0.0467954 + 0.i
>> 0.0479258 + 0.i
>> 0.0489899 + 0.i
>> 0.0506182 + 0.i
>> 0.0512171 + 0.i
>> 0.0529938 + 0.i
>> 0.0537732 + 0.i
>> 0.0549977 + 0.i
>> 0.056272 + 0.i
>> 0.0574546 + 0.i
>> 0.0585867 + 0.i
>> 0.0595438 + 0.i
>> 0.0614507 + 0.i
>> 0.0625339 + 0.i
>> 0.0634786 + 0.i
>> 0.0651556 + 0.i
>> 0.066393 + 0.i
>> 0.067585 + 0.i
>> 0.0701521 + 0.i
>> 0.0709748 + 0.i
>> 0.0725257 + 0.i
>> 0.073676 + 0.i
>> 0.0739372 + 0.i
>> 0.0758159 + 0.i
>> 0.078728 + 0.i
>> 0.0803127 + 0.i
>> 0.0813565 + 0.i
>> 0.0819371 + 0.i
>> 0.0824692 + 0.i
>> 0.0847166 + 0.i
>> 0.0878818 + 0.i
>> 0.0901822 + 0.i
>> 0.0906192 + 0.i
>> 0.0912192 + 0.i
>> 0.0921386 + 0.i
>> 0.0964252 + 0.i
>> 0.0978271 + 0.i
>> 0.0991256 + 0.i
>> 0.100197 + 0.i
>> 0.101757 + 0.i
>> 0.103163 + 0.i
>> 0.104427 + 0.i
>> 0.105316 + 0.i
>> 0.108255 + 0.i
>> 0.110149 + 0.i
>> 0.111963 + 0.i
>> 0.113533 + 0.i
>> 0.114857 + 0.i
>> 0.11807 + 0.i
>> 0.119241 + 0.i
>> 0.121196 + 0.i
>> 0.124063 + 0.i
>> 0.124824 + 0.i
>> 0.125867 + 0.i
>> 0.129153 + 0.i
>> 0.129692 + 0.i
>> 0.130804 + 0.i
>> 0.13186 + 0.i
>> 0.136671 + 0.i
>> 0.137159 + 0.i
>> 0.139948 + 0.i
>> 0.140338 + 0.i
>> 0.143836 + 0.i
>> 0.145398 + 0.i
>> 0.146868 + 0.i
>> 0.14813 + 0.i
>> 0.149113 + 0.i
>> 0.152292 + 0.i
>> 0.154569 + 0.i
>> 0.1592 + 0.i
>> 0.159868 + 0.i
>> 0.16113 + 0.i
>> 0.163854 + 0.i
>> 0.16612 + 0.i
>> 0.167395 + 0.i
>> 0.169089 + 0.i
>> 0.171137 + 0.i
>> 0.173693 + 0.i
>> 0.176847 + 0.i
>> 0.177794 + 0.i
>> 0.178951 + 0.i
>> 0.179342 + 0.i
>> 0.185936 + 0.i
>> 0.18772 + 0.i
>> 0.189272 + 0.i
>> 0.191293 + 0.i
>> 0.193085 + 0.i
>> 0.195212 + 0.i
>> 0.197571 + 0.i
>> 0.199457 + 0.i
>> 0.201105 + 0.i
>> 0.204097 + 0.i
>> 0.207915 + 0.i
>> 0.208748 + 0.i
>> 0.212964 + 0.i
>> 0.214298 + 0.i
>> 0.217664 + 0.i
>> 0.218679 + 0.i
>> 0.220846 + 0.i
>> 0.222277 + 0.i
>> 0.226707 + 0.i
>> 0.228239 + 0.i
>> 0.229806 + 0.i
>> 0.231871 + 0.i
>> 0.235329 + 0.i
>> 0.237857 + 0.i
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>> 0.242546 + 0.i
>> 0.244337 + 0.i
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>> 0.250223 + 0.i
>> 0.252628 + 0.i
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>> 0.256945 + 0.i
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>> 0.269103 + 0.i
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>> 0.338197 + 0.i
>> 0.34279 + 0.i
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>> 0.34954 + 0.i
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>> 0.355576 + 0.i
>> 0.359178 + 0.i
>> 0.361957 + 0.i
>> 0.364873 + 0.i
>> 0.367973 + 0.i
>> 0.370043 + 0.i
>> 0.3732 + 0.i
>> 0.375047 + 0.i
>> 0.376219 + 0.i
>> 0.38884 + 0.i
>> 0.390239 + 0.i
>> 0.392451 + 0.i
>> 0.394641 + 0.i
>> 0.39603 + 0.i
>> 0.40011 + 0.i
>> 0.402863 + 0.i
>> 0.40477 + 0.i
>> 0.407166 + 0.i
>> 0.409253 + 0.i
>> 0.41114 + 0.i
>> 0.417392 + 0.i
>> 0.419475 + 0.i
>> 0.421597 + 0.i
>> 0.42226 + 0.i
>> 0.425458 + 0.i
>> 0.432817 + 0.i
>> 0.434498 + 0.i
>> 0.437448 + 0.i
>> 0.440073 + 0.i
>> 0.441784 + 0.i
>> 0.44471 + 0.i
>> 0.449445 + 0.i
>> 0.450416 + 0.i
>> 0.454865 + 0.i
>> 0.456899 + 0.i
>> 0.459119 + 0.i
>> 0.464975 + 0.i
>> 0.466739 + 0.i
>> 0.470461 + 0.i
>> 0.473138 + 0.i
>> 0.473366 + 0.i
>> 0.482849 + 0.i
>> 0.487335 + 0.i
>> 0.487996 + 0.i
>> 0.490971 + 0.i
>> 0.492149 + 0.i
>> 0.498317 + 0.i
>> 0.49924 + 0.i
>> 0.501193 + 0.i
>> 0.502928 + 0.i
>> 0.505282 + 0.i
>> 0.507326 + 0.i
>> 0.5094 + 0.i
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>> 0.678938 + 0.i
>> 0.6845 + 0.i
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>> 0.693601 + 0.i
>> 0.711189 + 0.i
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>> 0.72405 + 0.i
>> 0.730072 + 0.i
>> 0.730319 + 0.i
>> 0.732633 + 0.i
>> 0.73299 + 0.i
>> 0.737779 + 0.i
>> 0.74204 + 0.i
>> 0.744661 + 0.i
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>> 0.746947 + 0.i
>> 0.751408 + 0.i
>> 0.751786 + 0.i
>> 0.753859 + 0.i
>> 0.761784 + 0.i
>> 0.762905 + 0.i
>> 0.765961 + 0.i
>> 0.767479 + 0.i
>> 0.769471 + 0.i
>> 0.769529 + 0.i
>> 0.774108 + 0.i
>> 0.794173 + 0.i
>> 0.799031 + 0.i
>> 0.799111 + 0.i
>> 0.811928 + 0.i
>> 0.812351 + 0.i
>> 0.813483 + 0.i
>> 0.815524 + 0.i
>> 0.815749 + 0.i
>> 0.826079 + 0.i
>> 0.826832 + 0.i
>> 0.831323 + 0.i
>> 0.832443 + 0.i
>> 0.8415 + 0.i
>> 0.842963 + 0.i
>> 0.843567 + 0.i
>> 0.84377 + 0.i
>> 0.847571 + 0.i
>> 0.8493 + 0.i
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>> 0.85882 + 0.i
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>> 0.862321 + 0.i
>> 0.863661 + 0.i
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>> 0.884266 + 0.i
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>> 0.907204 + 0.i
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>> 0.908615 + 0.i
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>> 1.14715 + 0.i
>> 1.14717 + 0.i
>> 1.14717 + 0.i
>> 1.14746 + 0.i
>> 1.14758 + 0.i
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>> 1.17845 + 0.i
>> 1.18206 + 0.i
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>> 1.20113 + 0.i
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>> 1.20318 + 0.i
>> 1.2033 + 0.i
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>> 1.22727 + 0.i
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>> 1.25919 + 0.i
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>> 1.25961 + 0.i
>> 1.26135 + 0.i
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>> 1.27463 + 0.i
>> 1.27486 + 0.i
>> 1.30179 + 0.i
>> 1.30211 + 0.i
>> 1.30257 + 0.i
>> 1.30268 + 0.i
>> 1.34742 + 0.i
>> 1.34745 + 0.i
>> 1.34827 + 0.i
>> 1.34845 + 0.i
>> 1.35084 + 0.i
>> 1.35085 + 0.i
>> 1.36396 + 0.i
>> 1.36397 + 0.i
>> 1.36462 + 0.i
>> 1.36466 + 0.i
>> 1.36931 + 0.i
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>> 1.37666 + 0.i
>> 1.37668 + 0.i
>> 1.3813 + 0.i
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>> 1.4043 + 0.i
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>> 1.4236 + 0.i
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>> 1.45085 + 0.i
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>> 1.53664 + 0.i
>> 1.53809 + 0.i
>> 1.53809 + 0.i
>> 1.53813 + 0.i
>> 1.5383 + 0.i
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>> 285.353 + 0.i
> 