On Thu, Aug 1, 2024 at 12:19 PM Barry Smith <bsm...@petsc.dev> wrote:
>
> The current code is nonsensical. We can "fix" it in a patch to the
> release branch (but the fix may break some current usage) by changing
>
> if (nfields == 1) {
> PetscCall(PCFieldSplitSetIS(pc, fieldNames[ifields[0]],
> compField));
> } else {
> PetscCall(PetscSNPrintf(splitname, sizeof(splitname), "%"
> PetscInt_FMT, i));
> PetscCall(PCFieldSplitSetIS(pc, splitname, compField));
> }
>
> to
>
> PetscCall(PetscSNPrintf(splitname, sizeof(splitname), "%"
> PetscInt_FMT, i));
> PetscCall(PCFieldSplitSetIS(pc, splitname, compField));
>
>
> but a "correct" fix will take some thought. The current model using a
> combination of some "inner" integer fieldnames and some outer fieldnames
> (which are whatever they are including possible integers) doesn't make any
> sense.
>
My fix was going to be a flag that turns off names altogether. I think this
will fix it for Sebastian, and is the only consistent fix I can think of.
Thanks,
Matt
>
> On Aug 1, 2024, at 9:19 AM, Blauth, Sebastian <
> sebastian.bla...@itwm.fraunhofer.de> wrote:
>
> Hello everyone,
>
> I have a follow up on my question. I noticed the following behavior. Let’s
> assume I have 5 fields which I want to group with the following options:
>
> -ksp_type fgmres
> -ksp_max_it 1
> -ksp_monitor_true_residual
> -ksp_view
> -pc_type fieldsplit
> -pc_fieldsplit_type multiplicative
> -pc_fieldsplit_0_fields 0,1
> -pc_fieldsplit_1_fields 2
> -pc_fieldsplit_2_fields 3,4
> -fieldsplit_0_ksp_type preonly
> -fieldsplit_0_pc_type jacobi
> -fieldsplit_2_ksp_type preonly
> -fieldsplit_2_pc_type jacobi
>
> Then, the first split is fine, but both the second and third splits get
> the same prefix, i.e., “fieldsplit_2”. This is shown in the output of the
> ksp_view, which I attach below.
> The first one gets the prefix as there is only a single split (and I
> choose as name the index) and the third split gets the name as it groups
> two other fields, so the “outer” name is taken. Is there any way to
> circumvent this, other than using custom names for the splits which are
> unique?
>
> Thanks for your time and best regards,
> Sebastian Blauth
>
>
> The output of “ksp_view” is the following
>
> KSP Object: 1 MPI process
> type: fgmres
> restart=30, using Classical (unmodified) Gram-Schmidt
> Orthogonalization with no iterative refinement
> happy breakdown tolerance 1e-30
> maximum iterations=1, initial guess is zero
> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
> right preconditioning
> using UNPRECONDITIONED norm type for convergence test
> PC Object: 1 MPI process
> type: fieldsplit
> FieldSplit with MULTIPLICATIVE composition: total splits = 3
> Solver info for each split is in the following KSP objects:
> Split number 0 Defined by IS
> KSP Object: (fieldsplit_0_) 1 MPI process
> type: preonly
> maximum iterations=10000, initial guess is zero
> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
> left preconditioning
> using NONE norm type for convergence test
> PC Object: (fieldsplit_0_) 1 MPI process
> type: jacobi
> type DIAGONAL
> linear system matrix = precond matrix:
> Mat Object: (fieldsplit_0_) 1 MPI process
> type: seqaij
> rows=243, cols=243
> total: nonzeros=4473, allocated nonzeros=4473
> total number of mallocs used during MatSetValues calls=0
> using I-node routines: found 86 nodes, limit used is 5
> Split number 1 Defined by IS
> KSP Object: (fieldsplit_2_) 1 MPI process
> type: preonly
> maximum iterations=10000, initial guess is zero
> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
> left preconditioning
> using NONE norm type for convergence test
> PC Object: (fieldsplit_2_) 1 MPI process
> type: jacobi
> type DIAGONAL
> linear system matrix = precond matrix:
> Mat Object: (fieldsplit_2_) 1 MPI process
> type: seqaij
> rows=81, cols=81
> total: nonzeros=497, allocated nonzeros=497
> total number of mallocs used during MatSetValues calls=0
> not using I-node routines
> Split number 2 Defined by IS
> KSP Object: (fieldsplit_2_) 1 MPI process
> type: preonly
> maximum iterations=10000, initial guess is zero
> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
> left preconditioning
> using NONE norm type for convergence test
> PC Object: (fieldsplit_2_) 1 MPI process
> type: jacobi
> type DIAGONAL
> linear system matrix = precond matrix:
> Mat Object: (fieldsplit_2_) 1 MPI process
> type: seqaij
> rows=243, cols=243
> total: nonzeros=4473, allocated nonzeros=4473
> total number of mallocs used during MatSetValues calls=0
> using I-node routines: found 85 nodes, limit used is 5
> linear system matrix = precond matrix:
> Mat Object: 1 MPI process
> type: seqaij
> rows=567, cols=567
> total: nonzeros=24353, allocated nonzeros=24353
> total number of mallocs used during MatSetValues calls=0
> using I-node routines: found 173 nodes, limit used is 5
>
> --
> Dr. Sebastian Blauth
> Fraunhofer-Institut für
> Techno- und Wirtschaftsmathematik ITWM
> Abteilung Transportvorgänge
> Fraunhofer-Platz 1, 67663 Kaiserslautern
> Telefon: +49 631 31600-4968
> sebastian.bla...@itwm.fraunhofer.de
> https://urldefense.us/v3/__https://www.itwm.fraunhofer.de__;!!G_uCfscf7eWS!an6Idf-f7OiZlsU0N0Ftpr5mM5etD7GF_9ghya_ALFmQP_eL93oONwYYRLmLGz-0FSXHkB0bMsjj0e4-qdCV$
>
>
> *From:* petsc-users <petsc-users-boun...@mcs.anl.gov> *On Behalf Of *Blauth,
> Sebastian
> *Sent:* Tuesday, July 2, 2024 11:47 AM
> *To:* Matthew Knepley <knep...@gmail.com>
> *Cc:* petsc-users@mcs.anl.gov
> *Subject:* Re: [petsc-users] Question regarding naming of fieldsplit
> splits
>
> Hi Matt,
>
> thanks fort he answer and clarification. Then I’ll work around this issue
> in python, where I set the options.
>
> Best,
> Sebastian
>
> --
> Dr. Sebastian Blauth
> Fraunhofer-Institut für
> Techno- und Wirtschaftsmathematik ITWM
> Abteilung Transportvorgänge
> Fraunhofer-Platz 1, 67663 Kaiserslautern
> Telefon: +49 631 31600-4968
> sebastian.bla...@itwm.fraunhofer.de
> https://urldefense.us/v3/__https://www.itwm.fraunhofer.de__;!!G_uCfscf7eWS!an6Idf-f7OiZlsU0N0Ftpr5mM5etD7GF_9ghya_ALFmQP_eL93oONwYYRLmLGz-0FSXHkB0bMsjj0e4-qdCV$
>
>
> *From:* Matthew Knepley <knep...@gmail.com>
> *Sent:* Monday, July 1, 2024 4:30 PM
> *To:* Blauth, Sebastian <sebastian.bla...@itwm.fraunhofer.de>
> *Cc:* petsc-users@mcs.anl.gov
> *Subject:* Re: [petsc-users] Question regarding naming of fieldsplit
> splits
>
> On Mon, Jul 1, 2024 at 9:48 AM Blauth, Sebastian <
> sebastian.bla...@itwm.fraunhofer.de> wrote:
>
> Dear Matt,
>
> thanks a lot for your help. Unfortunately, for me these extra options do
> not have any effect, I still get the “u” and “p” fieldnames. Also, this
> would not help me to get rid of the “c” fieldname – on that level of the
> fieldsplit I am basically using your approach already, and still it does
> show up. The output of the -ksp_view is unchanged, so that I do not attach
> it here again. Maybe I misunderstood you?
>
>
> Oh, we make an exception for single fields, since we think you would want
> to use the name. I have to make an extra option to shut off naming.
>
> Thanks,
>
> Matt
>
>
> Thanks for the help and best regards,
> Sebastian
>
> --
> Dr. Sebastian Blauth
> Fraunhofer-Institut für
> Techno- und Wirtschaftsmathematik ITWM
> Abteilung Transportvorgänge
> Fraunhofer-Platz 1, 67663 Kaiserslautern
> Telefon: +49 631 31600-4968
> sebastian.bla...@itwm.fraunhofer.de
> https://urldefense.us/v3/__https://www.itwm.fraunhofer.de__;!!G_uCfscf7eWS!an6Idf-f7OiZlsU0N0Ftpr5mM5etD7GF_9ghya_ALFmQP_eL93oONwYYRLmLGz-0FSXHkB0bMsjj0e4-qdCV$
>
>
> *From:* Matthew Knepley <knep...@gmail.com>
> *Sent:* Monday, July 1, 2024 2:27 PM
> *To:* Blauth, Sebastian <sebastian.bla...@itwm.fraunhofer.de>
> *Cc:* petsc-users@mcs.anl.gov
> *Subject:* Re: [petsc-users] Question regarding naming of fieldsplit
> splits
>
> On Fri, Jun 28, 2024 at 4:05 AM Blauth, Sebastian <
> sebastian.bla...@itwm.fraunhofer.de> wrote:
>
> Hello everyone,
>
> I have a question regarding the naming convention using PETSc’s
> PCFieldsplit. I have been following
> https://urldefense.us/v3/__https://lists.mcs.anl.gov/pipermail/petsc-users/2019-January/037262.html__;!!G_uCfscf7eWS!an6Idf-f7OiZlsU0N0Ftpr5mM5etD7GF_9ghya_ALFmQP_eL93oONwYYRLmLGz-0FSXHkB0bMsjj0Qyn5DYX$
> to
> create a DMShell with FEniCS in order to customize PCFieldsplit for my
> application.
> I am using the following options, which work nicely for me:
>
> -ksp_type fgmres
> -pc_type fieldsplit
> -pc_fieldsplit_0_fields 0, 1
> -pc_fieldsplit_1_fields 2
> -pc_fieldsplit_type additive
> -fieldsplit_0_ksp_type fgmres
> -fieldsplit_0_pc_type fieldsplit
> -fieldsplit_0_pc_fieldsplit_type schur
> -fieldsplit_0_pc_fieldsplit_schur_fact_type full
> -fieldsplit_0_pc_fieldsplit_schur_precondition selfp
> -fieldsplit_0_fieldsplit_u_ksp_type preonly
> -fieldsplit_0_fieldsplit_u_pc_type lu
> -fieldsplit_0_fieldsplit_p_ksp_type cg
> -fieldsplit_0_fieldsplit_p_ksp_rtol 1e-14
> -fieldsplit_0_fieldsplit_p_ksp_atol 1e-30
> -fieldsplit_0_fieldsplit_p_pc_type icc
> -fieldsplit_0_ksp_rtol 1e-14
> -fieldsplit_0_ksp_atol 1e-30
> -fieldsplit_0_ksp_monitor_true_residual
> -fieldsplit_c_ksp_type preonly
> -fieldsplit_c_pc_type lu
> -ksp_view
>
>
> By default, we use the field names, but you can prevent this by specifying
> the fields by hand, so
>
> -fieldsplit_0_pc_fieldsplit_0_fields 0
> -fieldsplit_0_pc_fieldsplit_1_fields 1
>
> should remove the 'u' and 'p' fieldnames. It is somewhat hacky, but I
> think easier to remember than
> some extra option.
>
> Thanks,
>
> Matt
>
>
> Note that this is just an academic example (sorry for the low solver
> tolerances) to test the approach, consisting of a Stokes equation and some
> concentration equation (which is not even coupled to Stokes, just for
> testing).
> Completely analogous to
> https://urldefense.us/v3/__https://lists.mcs.anl.gov/pipermail/petsc-users/2019-January/037262.html__;!!G_uCfscf7eWS!an6Idf-f7OiZlsU0N0Ftpr5mM5etD7GF_9ghya_ALFmQP_eL93oONwYYRLmLGz-0FSXHkB0bMsjj0Qyn5DYX$
> ,
> I translate my IS’s to a PETSc Section, which is then supplied to a DMShell
> and assigned to a KSP. I am not so familiar with the code or how / why this
> works, but it seems to do so perfectly. I name my sections with petsc4py
> using
>
> section.setFieldName(0, "u")
> section.setFieldName(1, "p")
> section.setFieldName(2, "c")
>
> However, this is also reflected in the way I can access the fieldsplit
> options from the command line. My question is: Is there any way of not
> using the FieldNames specified in python but use the index of the field as
> defined with “-pc_fieldsplit_0_fields 0, 1” and “-pc_fieldsplit_1_fields
> 2”, i.e., instead of the prefix “fieldsplit_0_fieldsplit_u” I want to write
> “fieldsplit_0_fieldsplit_0”, instead of “fieldsplit_0_fieldsplit_p” I want
> to use “fieldsplit_0_fieldsplit_1”, and instead of “fieldsplit_c” I want to
> use “fieldsplit_1”. Just changing the names of the fields to
>
> section.setFieldName(0, "0")
> section.setFieldName(1, "1")
> section.setFieldName(2, "2")
>
> does obviously not work as expected, as it works for velocity and
> pressure, but not for the concentration – the prefix there is then
> “fieldsplit_2” and not “fieldsplit_1”. In the docs, I have found
> https://urldefense.us/v3/__https://petsc.org/main/manualpages/PC/PCFieldSplitSetFields/__;!!G_uCfscf7eWS!an6Idf-f7OiZlsU0N0Ftpr5mM5etD7GF_9ghya_ALFmQP_eL93oONwYYRLmLGz-0FSXHkB0bMsjj0X9GdD2a$
> which seems
> to suggest that the fieldname can potentially be supplied, but I don’t see
> how to do so from the command line. Also, for the sake of completeness, I
> attach the output of the solve with “-ksp_view” below.
>
> Thanks a lot in advance and best regards,
> Sebastian
>
>
> The output of ksp_view is the following:
> KSP Object: 1 MPI processes
> type: fgmres
> 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-11, divergence=10000.
> right preconditioning
> using UNPRECONDITIONED norm type for convergence test
> PC Object: 1 MPI processes
> type: fieldsplit
> FieldSplit with ADDITIVE composition: total splits = 2
> Solver info for each split is in the following KSP objects:
> Split number 0 Defined by IS
> KSP Object: (fieldsplit_0_) 1 MPI processes
> type: fgmres
> 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-14, absolute=1e-30, divergence=10000.
> right preconditioning
> using UNPRECONDITIONED norm type for convergence test
> PC Object: (fieldsplit_0_) 1 MPI processes
> type: fieldsplit
> FieldSplit with Schur preconditioner, factorization FULL
> Preconditioner for the Schur complement formed from Sp, an assembled
> approximation to S, which uses A00's diagonal's inverse
> Split info:
> Split number 0 Defined by IS
> Split number 1 Defined by IS
> KSP solver for A00 block
> KSP Object: (fieldsplit_0_fieldsplit_u_) 1 MPI processes
> type: preonly
> maximum iterations=10000, initial guess is zero
> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
> left preconditioning
> using NONE norm type for convergence test
> PC Object: (fieldsplit_0_fieldsplit_u_) 1 MPI processes
> type: lu
> out-of-place factorization
> tolerance for zero pivot 2.22045e-14
> matrix ordering: nd
> factor fill ratio given 5., needed 3.92639
> Factored matrix follows:
> Mat Object: 1 MPI processes
> type: seqaij
> rows=4290, cols=4290
> package used to perform factorization: petsc
> total: nonzeros=375944, allocated nonzeros=375944
> using I-node routines: found 2548 nodes, limit used is
> 5
> linear system matrix = precond matrix:
> Mat Object: (fieldsplit_0_fieldsplit_u_) 1 MPI processes
> type: seqaij
> rows=4290, cols=4290
> total: nonzeros=95748, allocated nonzeros=95748
> total number of mallocs used during MatSetValues calls=0
> using I-node routines: found 3287 nodes, limit used is 5
> KSP solver for S = A11 - A10 inv(A00) A01
> KSP Object: (fieldsplit_0_fieldsplit_p_) 1 MPI processes
> type: cg
> maximum iterations=10000, initial guess is zero
> tolerances: relative=1e-14, absolute=1e-30, divergence=10000.
> left preconditioning
> using PRECONDITIONED norm type for convergence test
> PC Object: (fieldsplit_0_fieldsplit_p_) 1 MPI processes
> type: icc
> out-of-place factorization
> 0 levels of fill
> tolerance for zero pivot 2.22045e-14
> using Manteuffel shift [POSITIVE_DEFINITE]
> matrix ordering: natural
> factor fill ratio given 1., needed 1.
> Factored matrix follows:
> Mat Object: 1 MPI processes
> type: seqsbaij
> rows=561, cols=561
> package used to perform factorization: petsc
> total: nonzeros=5120, allocated nonzeros=5120
> block size is 1
> linear system matrix followed by preconditioner matrix:
> Mat Object: (fieldsplit_0_fieldsplit_p_) 1 MPI processes
> type: schurcomplement
> rows=561, cols=561
> Schur complement A11 - A10 inv(A00) A01
> A11
> Mat Object: (fieldsplit_0_fieldsplit_p_) 1 MPI processes
> type: seqaij
> rows=561, cols=561
> total: nonzeros=3729, allocated nonzeros=3729
> total number of mallocs used during MatSetValues calls=0
> not using I-node routines
> A10
> Mat Object: 1 MPI processes
> type: seqaij
> rows=561, cols=4290
> total: nonzeros=19938, allocated nonzeros=19938
> total number of mallocs used during MatSetValues calls=0
> not using I-node routines
> KSP of A00
> KSP Object: (fieldsplit_0_fieldsplit_u_) 1 MPI processes
> type: preonly
> maximum iterations=10000, initial guess is zero
> tolerances: relative=1e-05, absolute=1e-50,
> divergence=10000.
> left preconditioning
> using NONE norm type for convergence test
> PC Object: (fieldsplit_0_fieldsplit_u_) 1 MPI processes
> type: lu
> out-of-place factorization
> tolerance for zero pivot 2.22045e-14
> matrix ordering: nd
> factor fill ratio given 5., needed 3.92639
> Factored matrix follows:
> Mat Object: 1 MPI processes
> type: seqaij
> rows=4290, cols=4290
> package used to perform factorization: petsc
> total: nonzeros=375944, allocated nonzeros=375944
> using I-node routines: found 2548 nodes, limit
> used is 5
> linear system matrix = precond matrix:
> Mat Object: (fieldsplit_0_fieldsplit_u_) 1 MPI processes
> type: seqaij
> rows=4290, cols=4290
> total: nonzeros=95748, allocated nonzeros=95748
> total number of mallocs used during MatSetValues
> calls=0
> using I-node routines: found 3287 nodes, limit used
> is 5
> A01
> Mat Object: 1 MPI processes
> type: seqaij
> rows=4290, cols=561
> total: nonzeros=19938, allocated nonzeros=19938
> total number of mallocs used during MatSetValues calls=0
> using I-node routines: found 3287 nodes, limit used is
> 5
> Mat Object: 1 MPI processes
> type: seqaij
> rows=561, cols=561
> total: nonzeros=9679, allocated nonzeros=9679
> total number of mallocs used during MatSetValues calls=0
> not using I-node routines
> linear system matrix = precond matrix:
> Mat Object: (fieldsplit_0_) 1 MPI processes
> type: seqaij
> rows=4851, cols=4851
> total: nonzeros=139353, allocated nonzeros=139353
> total number of mallocs used during MatSetValues calls=0
> using I-node routines: found 3830 nodes, limit used is 5
> Split number 1 Defined by IS
> KSP Object: (fieldsplit_c_) 1 MPI processes
> type: preonly
> maximum iterations=10000, initial guess is zero
> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
> left preconditioning
> using NONE norm type for convergence test
> PC Object: (fieldsplit_c_) 1 MPI processes
> type: lu
> out-of-place factorization
> tolerance for zero pivot 2.22045e-14
> matrix ordering: nd
> factor fill ratio given 5., needed 4.24323
> Factored matrix follows:
> Mat Object: 1 MPI processes
> type: seqaij
> rows=561, cols=561
> package used to perform factorization: petsc
> total: nonzeros=15823, allocated nonzeros=15823
> not using I-node routines
> linear system matrix = precond matrix:
> Mat Object: (fieldsplit_c_) 1 MPI processes
> type: seqaij
> rows=561, cols=561
> total: nonzeros=3729, allocated nonzeros=3729
> total number of mallocs used during MatSetValues calls=0
> not using I-node routines
> linear system matrix = precond matrix:
> Mat Object: 1 MPI processes
> type: seqaij
> rows=5412, cols=5412
> total: nonzeros=190416, allocated nonzeros=190416
> total number of mallocs used during MatSetValues calls=0
> using I-node routines: found 3833 nodes, limit used is 5
>
> --
> Dr. Sebastian Blauth
> Fraunhofer-Institut für
> Techno- und Wirtschaftsmathematik ITWM
> Abteilung Transportvorgänge
> Fraunhofer-Platz 1, 67663 Kaiserslautern
> Telefon: +49 631 31600-4968
> sebastian.bla...@itwm.fraunhofer.de
> https://urldefense.us/v3/__https://www.itwm.fraunhofer.de__;!!G_uCfscf7eWS!an6Idf-f7OiZlsU0N0Ftpr5mM5etD7GF_9ghya_ALFmQP_eL93oONwYYRLmLGz-0FSXHkB0bMsjj0e4-qdCV$
>
>
>
>
>
> --
> 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://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!an6Idf-f7OiZlsU0N0Ftpr5mM5etD7GF_9ghya_ALFmQP_eL93oONwYYRLmLGz-0FSXHkB0bMsjj0dkG26YT$
>
> <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!an6Idf-f7OiZlsU0N0Ftpr5mM5etD7GF_9ghya_ALFmQP_eL93oONwYYRLmLGz-0FSXHkB0bMsjj0VN-barz$
> >
>
>
>
> --
> 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://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!an6Idf-f7OiZlsU0N0Ftpr5mM5etD7GF_9ghya_ALFmQP_eL93oONwYYRLmLGz-0FSXHkB0bMsjj0dkG26YT$
>
> <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!an6Idf-f7OiZlsU0N0Ftpr5mM5etD7GF_9ghya_ALFmQP_eL93oONwYYRLmLGz-0FSXHkB0bMsjj0VN-barz$
> >
>
>
>
--
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://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!an6Idf-f7OiZlsU0N0Ftpr5mM5etD7GF_9ghya_ALFmQP_eL93oONwYYRLmLGz-0FSXHkB0bMsjj0dkG26YT$
<https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!an6Idf-f7OiZlsU0N0Ftpr5mM5etD7GF_9ghya_ALFmQP_eL93oONwYYRLmLGz-0FSXHkB0bMsjj0VN-barz$
>
