[petsc-users] Debugging SNES when "everything" looks okay
Ellen Price
ellen.price at cfa.harvard.edu
Wed Aug 22 12:33:18 CDT 2018
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. 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/>
>
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