[petsc-users] norm of KSPBuildResidual does not match norm computed from KSPBuildSolution

[Barry Smith]

  The preconditioner is always built from the second of the two matrices passed in KSPSetOperators() or PCSetOperators(). In the first case below both matrices are the same (the nest matrix) and so diagonal is extracted from the nest matrix (which is the only matrix). In the second case below the first matrix is custom and the second is the next matrix, again the preconditioner is constructed from the second one. 

      linear system matrix = precond matrix:
      Mat Object: 1 MPI process
        type: nest
        rows=524, cols=524
          Matrix object:
        type=nest, rows=3, cols=3
        MatNest structure:
        (0,0) : type=mpiaij, rows=176, cols=176
        (0,1) : NULL
        (0,2) : NULL
        (1,0) : NULL
        (1,1) : type=mpiaij, rows=172, cols=172
        (1,2) : NULL
        (2,0) : NULL
        (2,1) : NULL
        (2,2) : type=mpiaij, rows=176, cols=176
        
Mat Object: 1 MPI process
      type: python
        Python: __main__.LHSOperator
    Mat Object: 1 MPI process
      type: nest
      Matrix object:
        type=nest, rows=3, cols=3
        MatNest structure:
        (0,0) : type=mpiaij, rows=176, cols=176
        (0,1) : NULL
        (0,2) : NULL
        (1,0) : NULL
        (1,1) : type=mpiaij, rows=172, cols=172
        (1,2) : NULL
        (2,0) : NULL
        (2,1) : NULL
        (2,2) : type=mpiaij, rows=176, cols=176
        

The arguments to KSPSetOperators() and PCSetOperators() are stored in the same place (inside the PC) 

In fact,

PetscErrorCode KSPSetOperators(KSP ksp, Mat Amat, Mat Pmat)
{
 ....
  PetscCall(PCSetOperators(ksp->pc, Amat, Pmat));



so when you call

   precond.setOperators(A=nest_mass_matrix, P=None)
   ksp.setPC(precond)

you are overwriting the A = lhs that you passed into  ksp.setOperators(ksp, lhs, None).

Given the names  ksp.setOperators() and precond.setOperators() I can see how this can be confusing. It is reasonable to conclude that ksp.setOperators is providing the linear system and that pc.setOperators() is providing the matrix with which to build the preconditioner, but that is not the case. 

But the code has been this way for 31 years. I am not sure what we can change with the documentation. Perhaps in KSPSetOperators it can say that it sets them into the PC.

Barry




> On Nov 4, 2025, at 4:06 AM, Moral Sanchez, Elena <Elena.Moral.Sanchez at ipp.mpg.de> wrote:
> 
> Dear Barry,
> Thanks for the fast answer. Unfortunately in my case the discrepancy is huge. With the flags
>  -ksp_monitor_true_residual -ksp_norm_type unpreconditioned
> this is the output:
>   0 KSP unpreconditioned resid norm 5.568889644229e-01 true resid norm 5.568889644229e-01 ||r(i)||/||b|| 1.000000000000e+00
>   1 KSP unpreconditioned resid norm 2.831772665189e-01 true resid norm 2.831772665189e-01 ||r(i)||/||b|| 5.084986139245e-01
>   2 KSP unpreconditioned resid norm 1.875950094147e-01 true resid norm 1.875950094147e-01 ||r(i)||/||b|| 3.368625011435e-01
> and this is the output of my own monitor function:
> Iter 0/10 | res = 5.57e-01/1.00e-08 | 0.0 s
> difference KSPBuildSolution and u: 0.0
> UNPRECONDITIONED norm:  0.5568889644229376
> PRECONDITIONED norm:  2.049041078011257
> KSPBuildResidual 2-norm: 0.5568889644229299
> difference KSPBuildResidual and b-A(KSPBuildSolution): 6.573603152700697e-13
> 
> Iter 1/10 | res = 2.83e-01/1.00e-08 | 0.0 s
> difference KSPBuildSolution and u: 0.0
> UNPRECONDITIONED norm:  0.7661983589104541
> PRECONDITIONED norm:  2.7387602134717137
> KSPBuildResidual 2-norm: 0.2831772665189212
> difference KSPBuildResidual and b-A(KSPBuildSolution): 0.1700718741085172
> 
> Iter 2/10 | res = 1.88e-01/1.00e-08 | 0.0 s
> difference KSPBuildSolution and u: 0.0
> UNPRECONDITIONED norm:  0.7050518160900253
> PRECONDITIONED norm:  2.421773833445645
> KSPBuildResidual 2-norm: 0.18759500941469456
> difference KSPBuildResidual and b-A(KSPBuildSolution): 0.19327058976599623
> Here u is the vector in the KSPSolve. 
> After the first iteration, the residual computed from KSPBuildSolution and the residual from KSPBuildResidual diverge. They are the same when I run the same code without preconditioner.
> Another observation is that after convergence (wrt. unpreconditioned norm == 2-norm of KSPBuildResidual) the solution with and without preconditioner looks quite different. How is this possible if my preconditioner is SPD?
> 
> By the way, where can I find your implementation of "My monitor" in src/snes/tutorials/ex5.c? I tried to look at the Gitlab repository but could not find it.
> Thanks for the help.
> Cheers,
> Elena
> 
> 
> 
> 
> 
> On 11/4/25 03:01, Barry Smith wrote:
>>     0 KSP unpreconditioned resid norm 1.265943996096e+00 true resid norm 1.265943996096e+00 ||r(i)||/||b|| 1.000000000000e+00
>> My monitor 0 1.265943996096e+00

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