[petsc-users] interpreting data from SNESSolve profiling

[Barry Smith]

     Yes, the "basic" line search updates the solution vector and evaluates the function at the new solution point; not much else.

     There are no duplicate or extra function evaluations in PETSc, (most of them occur in the linesearch function). When the code returns from the line search routine it "knows" the function evaluation has already been done (at the newest solution) so it does not need to do it again.

     The line search does not perform the Newton step, it takes the step computed by the linear solve and decides how to use that step (you will see that KSPSolve time is not part of the line search time). 

   Barry


> On Feb 8, 2023, at 7:56 AM, Matteo Semplice <matteo.semplice at uninsubria.it> wrote:
> 
> Dear all,
> 
>     I am trying to optimize the nonlinear solvers in a code of mine, but I am having a hard time at interpreting the profiling data from the SNES. In particular, if I run with -snesCorr_snes_lag_jacobian 5 -snesCorr_snes_linesearch_monitor -snesCorr_snes_monitor -snesCorr_snes_linesearch_type basic -snesCorr_snes_view I get, for all timesteps an output like
> 
>  0 SNES Function norm 2.204257292307e+00  
>  1 SNES Function norm 5.156376709750e-03  
>  2 SNES Function norm 9.399026338316e-05  
>  3 SNES Function norm 1.700505246874e-06  
>  4 SNES Function norm 2.938127043559e-08  
> SNES Object: snesCorr (snesCorr_) 1 MPI process 
>  type: newtonls 
>  maximum iterations=50, maximum function evaluations=10000 
>  tolerances: relative=1e-08, absolute=1e-50, solution=1e-08 
>  total number of linear solver iterations=4 
>  total number of function evaluations=5 
>  norm schedule ALWAYS 
>  Jacobian is rebuilt every 5 SNES iterations 
>  SNESLineSearch Object: (snesCorr_) 1 MPI process 
>    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=40 
>  KSP Object: (snesCorr_) 1 MPI process 
>    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: (snesCorr_) 1 MPI process 
>    type: ilu 
>      out-of-place factorization 
>      0 levels of fill 
>      tolerance for zero pivot 2.22045e-14 
>      matrix ordering: natural 
>      factor fill ratio given 1., needed 1. 
>        Factored matrix follows: 
>          Mat Object: (snesCorr_) 1 MPI process 
>            type: seqaij 
>            rows=1200, cols=1200 
>            package used to perform factorization: petsc 
>            total: nonzeros=17946, allocated nonzeros=17946 
>              using I-node routines: found 400 nodes, limit used is 5 
>    linear system matrix = precond matrix: 
>    Mat Object: 1 MPI process 
>      type: seqaij 
>      rows=1200, cols=1200 
>      total: nonzeros=17946, allocated nonzeros=17946 
>      total number of mallocs used during MatSetValues calls=0 
>        using I-node routines: found 400 nodes, limit used is 5
> 
> I guess that this means that no linesearch is performed and the full Newton step is always performed (I did not report the full output, but all timesteps are alike). Also, with the default (bt) LineSearch, the total CPU time does not change, which seems in line with this.
> 
> However, I'd have expected that the time spent in SNESLineSearch would be negligible, but the flamegraph is showing that about 38% of the time spent by SNESSolve is actually spent in SNESLineSearch. Furthermore, SNESLineSearch seems to cause more SNESFunction evaluations (in terms of CPU time) than the SNESSolve itself. The flamegraph is attached.
> 
> Could some expert help me in understanding these data? Is the LineSearch actually performing the newton step? Given that the full step is always taken, can the SNESFunction evaluations from the LineSearch be skipped?
> 
> Thanks a lot!
> 
> Matteo
> 
> <flame.svg>

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