[petsc-users] Debugging SNES when "everything" looks okay
Matthew Knepley
knepley at gmail.com
Wed Aug 22 13:19:41 CDT 2018
On Wed, Aug 22, 2018 at 1:33 PM Ellen Price <ellen.price at cfa.harvard.edu>
wrote:
> For Barry:
>
> Okay, I'm stumped. Some of my Jacobian terms match up with the finite
> difference one. Others are off by orders of magnitude.
>
Then your Jacobian does not match your function. This is easy to track down:
1) Reduce your problem size to 10 or so. Lots of people try to avoid
doing this, but that is crazy. Always have a problem of size 10.
2) PETSc uses the all ones (1, 1, ..., 1) and all minus ones (-1, -1,
..., -1) states to check the Jacobian. Feed those into
your PETSc function and your Mathematics function. Do you get the
same vector out?
3) Feed them into your PETSc Jacobian and Mathematics Jacobian. Do you
get the same matrix out?
There is nothing mystical here. PETSc is saying that the analytic Jacobian
must match finite differences in the limit.
Matt
> This led me to think that maybe there was something wrong with my analytic
> Jacobian, so I went back and started trying to track down which term causes
> the problem. The weird thing is that Mathematica gives the same numerical
> result as my code (within a small tolerance), whether i substitute numbers
> into its analytic Jacobian or numerically differentiate the function I'm
> trying to solve using Mathematica. I can't think of anything else to try
> for debugging the Jacobian. Even if the function has a bug in it,
> Mathematica seems pretty sure that I'm using the right Jacobian for what I
> put in... At the suggestion of the FAQ, I also tried "-mat_fd_type ds" to
> see if that made any difference, but it doesn't. Like I said, I'm stumped,
> but I'll keep trying.
>
> For Matt:
>
> Using options "-pc_type lu -snes_view -snes_monitor -snes_converged_reason
> -ksp_monitor_true_residual -ksp_converged_reason -snes_type newtontr", the
> output is below. I thought that the step length convergence message had
> something to do with using NEWTONTR, but I could be wrong about that. It
> doesn't give that message when I switch to NEWTONLS. It also only gives
> that message after the first iteration -- the first one is always
> CONVERGED_RTOL.
>
> 7.533921e-03, 2.054699e+02
> 0 SNES Function norm 6.252612941119e+04
> 0 KSP preconditioned resid norm 1.027204021595e-01 true resid norm
> 6.252612941119e+04 ||r(i)||/||b|| 1.000000000000e+00
> 1 KSP preconditioned resid norm 2.641617517320e-17 true resid norm
> 3.941610607093e-11 ||r(i)||/||b|| 6.303941478885e-16
> Linear solve converged due to CONVERGED_RTOL iterations 1
> 1 SNES Function norm 6.252085930204e+04
> 0 KSP preconditioned resid norm 3.857372064539e-01 true resid norm
> 6.252085930204e+04 ||r(i)||/||b|| 1.000000000000e+00
> 1 KSP preconditioned resid norm 3.664921095158e-16 true resid norm
> 2.434875289829e-10 ||r(i)||/||b|| 3.894500678672e-15
> Linear solve converged due to CONVERGED_STEP_LENGTH iterations 1
> 2 SNES Function norm 6.251886926050e+04
> 0 KSP preconditioned resid norm 4.085000006938e-01 true resid norm
> 6.251886926050e+04 ||r(i)||/||b|| 1.000000000000e+00
> 1 KSP preconditioned resid norm 5.318519617927e-16 true resid norm
> 8.189931340015e-10 ||r(i)||/||b|| 1.309993516660e-14
> Linear solve converged due to CONVERGED_STEP_LENGTH iterations 1
> .....
> 48 SNES Function norm 6.229932776333e+04
> 0 KSP preconditioned resid norm 4.872526135345e+00 true resid norm
> 6.229932776333e+04 ||r(i)||/||b|| 1.000000000000e+00
> 1 KSP preconditioned resid norm 7.281571852581e-15 true resid norm
> 8.562155918387e-09 ||r(i)||/||b|| 1.374357673796e-13
> Linear solve converged due to CONVERGED_STEP_LENGTH iterations 1
> 49 SNES Function norm 6.229663411026e+04
> 0 KSP preconditioned resid norm 4.953303401996e+00 true resid norm
> 6.229663411026e+04 ||r(i)||/||b|| 1.000000000000e+00
> 1 KSP preconditioned resid norm 1.537319689814e-15 true resid norm
> 4.783442569088e-09 ||r(i)||/||b|| 7.678492806886e-14
> Linear solve converged due to CONVERGED_STEP_LENGTH iterations 1
> 50 SNES Function norm 6.229442686875e+04
> Nonlinear solve did not converge due to DIVERGED_MAX_IT iterations 50
> SNES Object: 2 MPI processes
> type: newtontr
> Trust region tolerance (-snes_trtol)
> mu=0.25, eta=0.75, sigma=0.0001
> delta0=0.2, delta1=0.3, delta2=0.75, delta3=2.
> maximum iterations=50, maximum function evaluations=10000
> tolerances: relative=1e-08, absolute=1e-50, solution=1e-08
> total number of linear solver iterations=50
> total number of function evaluations=58
> norm schedule ALWAYS
> SNESLineSearch Object: 2 MPI processes
> type: basic
> maxstep=1.000000e+08, minlambda=1.000000e-12
> tolerances: relative=1.000000e-08, absolute=1.000000e-15,
> lambda=1.000000e-08
> maximum iterations=1
> KSP Object: 2 MPI processes
> type: gmres
> restart=30, using Classical (unmodified) Gram-Schmidt
> Orthogonalization with no iterative refinement
> happy breakdown tolerance 1e-30
> maximum iterations=10000, initial guess is zero
> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
> left preconditioning
> using PRECONDITIONED norm type for convergence test
> PC Object: 2 MPI processes
> type: lu
> out-of-place factorization
> tolerance for zero pivot 2.22045e-14
> matrix ordering: natural
> factor fill ratio given 0., needed 0.
> Factored matrix follows:
> Mat Object: 2 MPI processes
> type: mumps
> rows=20, cols=20
> package used to perform factorization: mumps
> total: nonzeros=112, allocated nonzeros=112
> total number of mallocs used during MatSetValues calls =0
> MUMPS run parameters:
> SYM (matrix type): 0
> PAR (host participation): 1
> ICNTL(1) (output for error): 6
> ICNTL(2) (output of diagnostic msg): 0
> ICNTL(3) (output for global info): 0
> ICNTL(4) (level of printing): 0
> ICNTL(5) (input mat struct): 0
> ICNTL(6) (matrix prescaling): 7
> ICNTL(7) (sequential matrix ordering):7
> ICNTL(8) (scaling strategy): 77
> ICNTL(10) (max num of refinements): 0
> ICNTL(11) (error analysis): 0
> ICNTL(12) (efficiency control): 1
> ICNTL(13) (efficiency control): 0
> ICNTL(14) (percentage of estimated workspace increase): 20
> ICNTL(18) (input mat struct): 3
> ICNTL(19) (Schur complement info): 0
> ICNTL(20) (rhs sparse pattern): 0
> ICNTL(21) (solution struct): 1
> ICNTL(22) (in-core/out-of-core facility): 0
> ICNTL(23) (max size of memory can be allocated locally):0
> ICNTL(24) (detection of null pivot rows): 0
> ICNTL(25) (computation of a null space basis): 0
> ICNTL(26) (Schur options for rhs or solution): 0
> ICNTL(27) (experimental parameter):
> -32
> ICNTL(28) (use parallel or sequential ordering): 1
> ICNTL(29) (parallel ordering): 0
> ICNTL(30) (user-specified set of entries in inv(A)): 0
> ICNTL(31) (factors is discarded in the solve phase): 0
> ICNTL(33) (compute determinant): 0
> ICNTL(35) (activate BLR based factorization): 0
> CNTL(1) (relative pivoting threshold): 0.01
> CNTL(2) (stopping criterion of refinement): 1.49012e-08
> CNTL(3) (absolute pivoting threshold): 0.
> CNTL(4) (value of static pivoting): -1.
> CNTL(5) (fixation for null pivots): 0.
> CNTL(7) (dropping parameter for BLR): 0.
> RINFO(1) (local estimated flops for the elimination after
> analysis):
> [0] 127.
> [1] 155.
> RINFO(2) (local estimated flops for the assembly after
> factorization):
> [0] 16.
> [1] 16.
> RINFO(3) (local estimated flops for the elimination after
> factorization):
> [0] 127.
> [1] 155.
> INFO(15) (estimated size of (in MB) MUMPS internal data
> for running numerical factorization):
> [0] 1
> [1] 1
> INFO(16) (size of (in MB) MUMPS internal data used during
> numerical factorization):
> [0] 1
> [1] 1
> INFO(23) (num of pivots eliminated on this processor after
> factorization):
> [0] 10
> [1] 10
> RINFOG(1) (global estimated flops for the elimination
> after analysis): 282.
> RINFOG(2) (global estimated flops for the assembly after
> factorization): 32.
> RINFOG(3) (global estimated flops for the elimination
> after factorization): 282.
> (RINFOG(12) RINFOG(13))*2^INFOG(34) (determinant):
> (0.,0.)*(2^0)
> INFOG(3) (estimated real workspace for factors on all
> processors after analysis): 112
> INFOG(4) (estimated integer workspace for factors on all
> processors after analysis): 225
> INFOG(5) (estimated maximum front size in the complete
> tree): 4
> INFOG(6) (number of nodes in the complete tree): 9
> INFOG(7) (ordering option effectively use after analysis):
> 2
> INFOG(8) (structural symmetry in percent of the permuted
> matrix after analysis): 100
> INFOG(9) (total real/complex workspace to store the matrix
> factors after factorization): 112
> INFOG(10) (total integer space store the matrix factors
> after factorization): 225
> INFOG(11) (order of largest frontal matrix after
> factorization): 4
> INFOG(12) (number of off-diagonal pivots): 0
> INFOG(13) (number of delayed pivots after factorization):
> 0
> INFOG(14) (number of memory compress after factorization):
> 0
> INFOG(15) (number of steps of iterative refinement after
> solution): 0
> INFOG(16) (estimated size (in MB) of all MUMPS internal
> data for factorization after analysis: value on the most memory consuming
> processor): 1
> INFOG(17) (estimated size of all MUMPS internal data for
> factorization after analysis: sum over all processors): 2
> INFOG(18) (size of all MUMPS internal data allocated
> during factorization: value on the most memory consuming processor): 1
> INFOG(19) (size of all MUMPS internal data allocated
> during factorization: sum over all processors): 2
> INFOG(20) (estimated number of entries in the factors):
> 112
> INFOG(21) (size in MB of memory effectively used during
> factorization - value on the most memory consuming processor): 1
> INFOG(22) (size in MB of memory effectively used during
> factorization - sum over all processors): 2
> INFOG(23) (after analysis: value of ICNTL(6) effectively
> used): 0
> INFOG(24) (after analysis: value of ICNTL(12) effectively
> used): 1
> INFOG(25) (after factorization: number of pivots modified
> by static pivoting): 0
> INFOG(28) (after factorization: number of null pivots
> encountered): 0
> INFOG(29) (after factorization: effective number of
> entries in the factors (sum over all processors)): 112
> INFOG(30, 31) (after solution: size in Mbytes of memory
> used during solution phase): 0, 0
> INFOG(32) (after analysis: type of analysis done): 1
> INFOG(33) (value used for ICNTL(8)): 7
> INFOG(34) (exponent of the determinant if determinant is
> requested): 0
> linear system matrix = precond matrix:
> Mat Object: 2 MPI processes
> type: mpiaij
> rows=20, cols=20, bs=2
> total: nonzeros=112, allocated nonzeros=240
> total number of mallocs used during MatSetValues calls =0
>
> Ellen
>
> On Tue, Aug 21, 2018 at 10:16 PM Matthew Knepley <knepley at gmail.com>
> wrote:
>
>> On Tue, Aug 21, 2018 at 10:00 PM Ellen M. Price <
>> ellen.price at cfa.harvard.edu> wrote:
>>
>>> Hi PETSc users,
>>>
>>> I'm having trouble applying SNES to a new problem I'm working on. I'll
>>> try to be as complete as possible but can't post the full code because
>>> it's ongoing research and is pretty long anyway.
>>>
>>> The nonlinear problem arises from trying to solve a set of two coupled
>>> ODEs using a Galerkin method. I am using Mathematica to generate the
>>> objective function to solve and the Jacobian, so I *think* I can rule
>>> out human error on that front.
>>>
>>> There are four things I can easily change:
>>>
>>> - number of DMDA grid points N (I've tried 100 and 1000)
>>> - preconditioner (I've tried LU and SVD, LU appears to work better, and
>>> SVD is too slow for N = 1000)
>>> - linear solver (haven't played with this much, but sometimes smaller
>>> tolerances work better)
>>> - nonlinear solver (what I'm having trouble with)
>>>
>>> Trying different solvers should, as far as I'm aware, give comparable
>>> answers, but that's not the case here. NEWTONTR works best of the ones
>>> I've tried, but I'm suspicious that the function value barely decreases
>>> before SNES "converges" -- and none of the options I've tried changing
>>> seem to affect this, as it just finds another reason to converge without
>>> making any real progress. For example:
>>>
>>> 0 SNES Function norm 7.197788479418e+00
>>> 0 KSP Residual norm 1.721996766619e+01
>>> 1 KSP Residual norm 5.186021549059e-14
>>> Linear solve converged due to CONVERGED_STEP_LENGTH iterations 1
>>>
>>
>> This makes no sense. LU should converge due to atol or rtol. Send the
>> output of
>>
>> -snes_view -snes_monitor -snes_converged_reason
>> -ksp_monitor_true_residual -ksp_converged_reason
>>
>> Thanks,
>>
>> Matt
>>
>>
>>> 1 SNES Function norm 7.197777674987e+00
>>> 0 KSP Residual norm 3.296112185897e+01
>>> 1 KSP Residual norm 2.713415432045e-13
>>> Linear solve converged due to CONVERGED_STEP_LENGTH iterations 1
>>> .....
>>> 50 SNES Function norm 7.197376803542e+00
>>> 0 KSP Residual norm 6.222518656302e+02
>>> 1 KSP Residual norm 9.630659996504e-12
>>> Linear solve converged due to CONVERGED_STEP_LENGTH iterations 1
>>> 51 SNES Function norm 7.197376803542e+00
>>> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 50
>>>
>>> I've tried everything I can think of and the FAQ suggestions, including
>>> non-dimensionalizing the problem; I observe the same behavior either
>>> way. The particularly strange thing I can't understand is why some of
>>> the SNES methods fail outright, after just one iteration (NCG, NGMRES,
>>> and others) with DIVERGED_DTOL. Unless I've misunderstood, it seems
>>> like, for the most part, I should be able to substitute in one method
>>> for another, possibly adjusting a few parameters along the way.
>>> Furthermore, the default method, NEWTONLS, diverges with
>>> DIVERGED_LINE_SEARCH, which I'm not sure how to debug.
>>>
>>> So the only viable method is NEWTONTR, and that doesn't appear to
>>> "really" converge. Any suggestions for further things to try are
>>> appreciated. My current options are:
>>>
>>> -pc_type lu -snes_monitor -snes_converged_reason -ksp_converged_reason
>>> -snes_max_it 10000 -ksp_monitor -snes_type newtonls
>>>
>>> Thanks in advance,
>>> Ellen Price
>>>
>>
>>
>> --
>> What most experimenters take for granted before they begin their
>> experiments is infinitely more interesting than any results to which their
>> experiments lead.
>> -- Norbert Wiener
>>
>> https://www.cse.buffalo.edu/~knepley/ <http://www.caam.rice.edu/~mk51/>
>>
>
--
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
https://www.cse.buffalo.edu/~knepley/ <http://www.caam.rice.edu/~mk51/>
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