[petsc-dev] PDIPDM questions
Matthew Knepley
knepley at gmail.com
Wed Sep 16 09:59:40 CDT 2020
On Wed, Sep 16, 2020 at 10:57 AM Abhyankar, Shrirang G via petsc-dev <
petsc-dev at mcs.anl.gov> wrote:
> *From: *Pierre Jolivet <pierre.jolivet at enseeiht.fr>
> *Date: *Wednesday, September 16, 2020 at 12:59 AM
> *To: *Barry Smith <bsmith at petsc.dev>
> *Cc: *"Abhyankar, Shrirang G" <shrirang.abhyankar at pnnl.gov>, PETSc
> Development <petsc-dev at mcs.anl.gov>
> *Subject: *Re: [petsc-dev] PDIPDM questions
>
>
>
>
>
> On 15 Sep 2020, at 11:18 PM, Barry Smith <bsmith at petsc.dev> wrote:
>
>
>
>
> I see now, the TaoSetup_PDIPM() code explicitly builds the large matrix
> by calling MatGetRow() on the smaller matrices, no matrix abstractions at
> all and assuming a global AIJ storage of the large matrix.
>
>
>
> I think this can be made more general by building a MatNest() from the
> smaller matrices which allows the smaller matrices to have whatever unique
> structure is appropriate for them. Of course, if needed, for example, for a
> direct solver the MatNest can convert itself to a global AIJ matrix and get
> the current result.
>
>
>
> Before jumping into the PDIPM train, I thought a MatNest was used
> internally. Like you can solve [[A, b],[b^T, 0]] (b of dimension M x 1)
> with a MatNest + fieldsplit or just MatConvert() + LU as you mentioned.
>
>
>
> The current implementation of PDIPM forms a monolithic KKT matrix in AIJ
> format and then passes that to the linear solver. We did try using
> fieldsplit by setting ISes for primal and dual variables. But, the
> performance of the solver using Fieldsplit was not that great. We’ll
> probably try it again after the current development of PDIPM.
>
What solver are you using? There is a nice paper by Yin Zhang from a while
ago about these. There must be something more recent.
Thanks,
Matt
> As Pierre rightly points out, MPIAIJ is just not a good format for many
> constrained optimization problems. This has been something seriously
> neglected in PETSc/TAO. I don't think any single format is ideal for such
> problems, likely hybrid formats are needed and this gets super tricky when
> one needs to use direct solvers such a Cholesky. If MUMPS has non-row
> oriented storage formats we could leverage that but I don't know if it does.
>
>
>
> Just FYI, MUMPS is the most general (direct solver) when it comes to input
> storage. It handles non-sorted coordinate format, possibly with duplicated
> entries which are then summed among processes (so, in theory, it could be
> used to “invert" a MatIS/MatNest, without having to first convert the
> MatIS/MatNest to MatAIJ).
>
>
>
> Thanks for the pointer on MUMPS’s non-sorted coordinate format.
>
>
>
> Thanks,
>
> Pierre
>
>
>
> Thanks,
>
> Shri
>
>
>
> Barry
>
>
>
>
>
>
>
> ierr = MatGetOwnershipRange(tao->hessian,&rjstart,NULL);CHKERRQ(ierr);
>
> for (i=0; i<pdipm->nx; i++){
>
> row = rstart + i;
>
>
>
> ierr = MatGetRow(tao->hessian,i+rjstart,&nc,&aj,NULL);CHKERRQ(ierr);
>
> proc = 0;
>
> for (j=0; j < nc; j++) {
>
> while (aj[j] >= cranges[proc+1]) proc++;
>
> col = aj[j] - cranges[proc] + Jranges[proc];
>
> ierr = MatPreallocateSet(row,1,&col,dnz,onz);CHKERRQ(ierr);
>
> }
>
> ierr =
> MatRestoreRow(tao->hessian,i+rjstart,&nc,&aj,NULL);CHKERRQ(ierr);
>
>
>
> if (pdipm->ng) {
>
> /* Insert grad g' */
>
> ierr =
> MatGetRow(jac_equality_trans,i+rjstart,&nc,&aj,NULL);CHKERRQ(ierr);
>
> ierr =
> MatGetOwnershipRanges(tao->jacobian_equality,&ranges);CHKERRQ(ierr);
>
> proc = 0;
>
> for (j=0; j < nc; j++) {
>
> /* find row ownership of */
>
> while (aj[j] >= ranges[proc+1]) proc++;
>
> nx_all = rranges[proc+1] - rranges[proc];
>
> col = aj[j] - ranges[proc] + Jranges[proc] + nx_all;
>
> ierr = MatPreallocateSet(row,1,&col,dnz,onz);CHKERRQ(ierr);
>
> }
>
> ierr =
> MatRestoreRow(jac_equality_trans,i+rjstart,&nc,&aj,NULL);CHKERRQ(ierr);
>
> }
>
>
>
> /* Insert Jce_xfixed^T' */
>
> if (pdipm->nxfixed) {
>
> ierr =
> MatGetRow(Jce_xfixed_trans,i+rjstart,&nc,&aj,NULL);CHKERRQ(ierr);
>
> ierr =
> MatGetOwnershipRanges(pdipm->Jce_xfixed,&ranges);CHKERRQ(ierr);
>
> proc = 0;
>
> for (j=0; j < nc; j++) {
>
> /* find row ownership of */
>
> while (aj[j] >= ranges[proc+1]) proc++;
>
> nx_all = rranges[proc+1] - rranges[proc];
>
> col = aj[j] - ranges[proc] + Jranges[proc] + nx_all + ng_all[proc];
>
> ierr = MatPreallocateSet(row,1,&col,dnz,onz);CHKERRQ(ierr);
>
> }
>
> ierr =
> MatRestoreRow(Jce_xfixed_trans,i+rjstart,&nc,&aj,NULL);CHKERRQ(ierr);
>
> }
>
>
>
> if (pdipm->nh) {
>
> /* Insert -grad h' */
>
> ierr =
> MatGetRow(jac_inequality_trans,i+rjstart,&nc,&aj,NULL);CHKERRQ(ierr);
>
> ierr =
> MatGetOwnershipRanges(tao->jacobian_inequality,&ranges);CHKERRQ(ierr);
>
> proc = 0;
>
> for (j=0; j < nc; j++) {
>
> /* find row ownership of */
>
> while (aj[j] >= ranges[proc+1]) proc++;
>
> nx_all = rranges[proc+1] - rranges[proc];
>
> col = aj[j] - ranges[proc] + Jranges[proc] + nx_all +
> nce_all[proc];
>
> ierr = MatPreallocateSet(row,1,&col,dnz,onz);CHKERRQ(ierr);
>
> }
>
> ierr =
> MatRestoreRow(jac_inequality_trans,i+rjstart,&nc,&aj,NULL);CHKERRQ(ierr);
>
> }
>
>
>
> /* Insert Jci_xb^T' */
>
> ierr = MatGetRow(Jci_xb_trans,i+rjstart,&nc,&aj,NULL);CHKERRQ(ierr);
>
> ierr = MatGetOwnershipRanges(pdipm->Jci_xb,&ranges);CHKERRQ(ierr);
>
> proc = 0;
>
> for (j=0; j < nc; j++) {
>
> /* find row ownership of */
>
> while (aj[j] >= ranges[proc+1]) proc++;
>
> nx_all = rranges[proc+1] - rranges[proc];
>
> col = aj[j] - ranges[proc] + Jranges[proc] + nx_all + nce_all[proc]
> + nh_all[proc];
>
> ierr = MatPreallocateSet(row,1,&col,dnz,onz);CHKERRQ(ierr);
>
> }
>
> ierr =
> MatRestoreRow(Jci_xb_trans,i+rjstart,&nc,&aj,NULL);CHKERRQ(ierr);
>
> }
>
>
>
> /* 2nd Row block of KKT matrix: [grad Ce, 0, 0, 0] */
>
> if (pdipm->Ng) {
>
> ierr =
> MatGetOwnershipRange(tao->jacobian_equality,&rjstart,NULL);CHKERRQ(ierr);
>
> for (i=0; i < pdipm->ng; i++){
>
> row = rstart + pdipm->off_lambdae + i;
>
>
>
> ierr =
> MatGetRow(tao->jacobian_equality,i+rjstart,&nc,&aj,NULL);CHKERRQ(ierr);
>
> proc = 0;
>
> for (j=0; j < nc; j++) {
>
> while (aj[j] >= cranges[proc+1]) proc++;
>
> col = aj[j] - cranges[proc] + Jranges[proc];
>
> ierr = MatPreallocateSet(row,1,&col,dnz,onz);CHKERRQ(ierr); /*
> grad g */
>
> }
>
> ierr =
> MatRestoreRow(tao->jacobian_equality,i+rjstart,&nc,&aj,NULL);CHKERRQ(ierr);
>
> }
>
> }
>
> /* Jce_xfixed */
>
> if (pdipm->Nxfixed) {
>
> ierr =
> MatGetOwnershipRange(pdipm->Jce_xfixed,&Jcrstart,NULL);CHKERRQ(ierr);
>
> for (i=0; i < (pdipm->nce - pdipm->ng); i++){
>
> row = rstart + pdipm->off_lambdae + pdipm->ng + i;
>
>
>
> ierr =
> MatGetRow(pdipm->Jce_xfixed,i+Jcrstart,&nc,&cols,NULL);CHKERRQ(ierr);
>
> if (nc != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"nc != 1");
>
>
>
> proc = 0;
>
> j = 0;
>
> while (cols[j] >= cranges[proc+1]) proc++;
>
> col = cols[j] - cranges[proc] + Jranges[proc];
>
> ierr = MatPreallocateSet(row,1,&col,dnz,onz);CHKERRQ(ierr);
>
> ierr =
> MatRestoreRow(pdipm->Jce_xfixed,i+Jcrstart,&nc,&cols,NULL);CHKERRQ(ierr);
>
> }
>
> }
>
>
>
> /* 3rd Row block of KKT matrix: [ gradCi, 0, 0, -I] */
>
> if (pdipm->Nh) {
>
> ierr =
> MatGetOwnershipRange(tao->jacobian_inequality,&rjstart,NULL);CHKERRQ(ierr);
>
> for (i=0; i < pdipm->nh; i++){
>
> row = rstart + pdipm->off_lambdai + i;
>
>
>
> ierr =
> MatGetRow(tao->jacobian_inequality,i+rjstart,&nc,&aj,NULL);CHKERRQ(ierr);
>
> proc = 0;
>
> for (j=0; j < nc; j++) {
>
> while (aj[j] >= cranges[proc+1]) proc++;
>
> col = aj[j] - cranges[proc] + Jranges[proc];
>
> ierr = MatPreallocateSet(row,1,&col,dnz,onz);CHKERRQ(ierr); /*
> grad h */
>
> }
>
> ierr =
> MatRestoreRow(tao->jacobian_inequality,i+rjstart,&nc,&aj,NULL);CHKERRQ(ierr);
>
> }
>
> /* -I */
>
> for (i=0; i < pdipm->nh; i++){
>
> row = rstart + pdipm->off_lambdai + i;
>
> col = rstart + pdipm->off_z + i;
>
> ierr = MatPreallocateSet(row,1,&col,dnz,onz);CHKERRQ(ierr);
>
> }
>
> }
>
>
>
> /* Jci_xb */
>
> ierr = MatGetOwnershipRange(pdipm->Jci_xb,&Jcrstart,NULL);CHKERRQ(ierr);
>
> for (i=0; i < (pdipm->nci - pdipm->nh); i++){
>
> row = rstart + pdipm->off_lambdai + pdipm->nh + i;
>
>
>
> ierr =
> MatGetRow(pdipm->Jci_xb,i+Jcrstart,&nc,&cols,NULL);CHKERRQ(ierr);
>
> if (nc != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"nc != 1");
>
> proc = 0;
>
> for (j=0; j < nc; j++) {
>
> while (cols[j] >= cranges[proc+1]) proc++;
>
> col = cols[j] - cranges[proc] + Jranges[proc];
>
> ierr = MatPreallocateSet(row,1,&col,dnz,onz);CHKERRQ(ierr);
>
> }
>
> ierr =
> MatRestoreRow(pdipm->Jci_xb,i+Jcrstart,&nc,&cols,NULL);CHKERRQ(ierr);
>
> /* -I */
>
> col = rstart + pdipm->off_z + pdipm->nh + i;
>
> ierr = MatPreallocateSet(row,1,&col,dnz,onz);CHKERRQ(ierr);
>
> }
>
>
>
> /* 4-th Row block of KKT matrix: Z and Ci */
>
> for (i=0; i < pdipm->nci; i++) {
>
> row = rstart + pdipm->off_z + i;
>
> cols1[0] = rstart + pdipm->off_lambdai + i;
>
> cols1[1] = row;
>
> ierr = MatPreallocateSet(row,2,cols1,dnz,onz);CHKERRQ(ierr);
>
> }
>
>
>
>
>
> On Sep 15, 2020, at 4:03 PM, Abhyankar, Shrirang G <
> shrirang.abhyankar at pnnl.gov> wrote:
>
>
>
> There is some code in PDIPM that copies over matrix elements from user
> jacobians/hessians to the big KKT matrix. I am not sure how/if that will
> work with MatMPI_Column. We’ll have to try out and we need an example for
> that 😊
>
>
>
> Thanks,
>
> Shri
>
>
>
>
>
> *From: *Barry Smith <bsmith at petsc.dev>
> *Date: *Tuesday, September 15, 2020 at 1:21 PM
> *To: *Pierre Jolivet <pierre.jolivet at enseeiht.fr>
> *Cc: *"Abhyankar, Shrirang G" <shrirang.abhyankar at pnnl.gov>, PETSc
> Development <petsc-dev at mcs.anl.gov>
> *Subject: *Re: [petsc-dev] PDIPDM questions
>
>
>
>
>
> Pierre,
>
>
>
> Based on my previous mail I am hoping that the PDIPM algorithm itself
> won't need a major refactorization to be scalable, only a custom matrix
> type is needed to store and compute with the Hessian in a scalable way.
>
>
>
> Barry
>
>
>
>
>
>
> On Sep 15, 2020, at 12:50 PM, Pierre Jolivet <pierre.jolivet at enseeiht.fr>
> wrote:
>
>
>
>
>
>
>
>
> On 15 Sep 2020, at 5:40 PM, Abhyankar, Shrirang G <
> shrirang.abhyankar at pnnl.gov> wrote:
>
>
>
> Pierre,
>
> You are right. There are a few MatMultTransposeAdd that may need
> conforming layouts for the equality/inequality constraint vectors and
> equality/inequality constraint Jacobian matrices. I need to check if that’s
> the case. We only have ex1 example currently, we need to add more examples.
> We are currently working on making PDIPM robust and while doing it will
> work on adding another example.
>
>
>
> Very naive question, but given that I have a single constraint, how do I
> split a 1 x N matrix column-wise? I thought it was not possible.
>
>
>
> When setting the size of the constraint vector, you need to set the local
> size on one rank to 1 and all others to zero. For the Jacobian, the local
> row size on that rank will be 1 and all others to zero. The column layout
> for the Jacobian should follow the layout for vector x. So each rank will
> set the local column size of the Jacobian to local size of x.
>
>
>
> That is assuming I don’t want x to follow the distribution of the Hessian,
> which is not my case.
>
> Is there some plan to make PDIPM handle different layouts?
>
> I hope I’m not the only one thinking that having a centralized Hessian
> when there is a single constraint is not scalable?
>
>
>
> Thanks,
>
> Pierre
>
>
>
> Shri
>
>
>
> On 15 Sep 2020, at 2:21 AM, Abhyankar, Shrirang G <
> shrirang.abhyankar at pnnl.gov> wrote:
>
>
>
> Hello Pierre,
>
> PDIPM works in parallel so you can have distributed Hessian, Jacobians,
> constraints, variables, gradients in any layout you want. If you are using
> a DM then you can have it generate the Hessian.
>
>
>
> Could you please show an example where this is the case?
>
> pdipm->x, which I’m assuming is a working vector, is both used as input
> for Hessian and Jacobian functions, e.g.,
> https://gitlab.com/petsc/petsc/-/blob/master/src/tao/constrained/impls/ipm/pdipm.c#L369 (Hessian)
> +
> https://gitlab.com/petsc/petsc/-/blob/master/src/tao/constrained/impls/ipm/pdipm.c#L473
> (Jacobian)
>
> I thus doubt that it is possible to have different layouts?
>
> In practice, I end up with the following error when I try this (2
> processes, distributed Hessian with centralized Jacobian):
>
> [1]PETSC ERROR: --------------------- Error Message
> --------------------------------------------------------------
>
> [1]PETSC ERROR: Nonconforming object sizes
>
> [1]PETSC ERROR: Vector wrong size 14172 for scatter 0 (scatter reverse and
> vector to != ctx from size)
>
> [1]PETSC ERROR: #1 VecScatterBegin() line 96 in
> /Users/jolivet/Documents/repositories/petsc/src/vec/vscat/interface/vscatfce.c
>
> [1]PETSC ERROR: #2 MatMultTransposeAdd_MPIAIJ() line 1223 in
> /Users/jolivet/Documents/repositories/petsc/src/mat/impls/aij/mpi/mpiaij.c
>
> [1]PETSC ERROR: #3 MatMultTransposeAdd() line 2648 in
> /Users/jolivet/Documents/repositories/petsc/src/mat/interface/matrix.c
>
> [0]PETSC ERROR: Nonconforming object sizes
>
> [0]PETSC ERROR: Vector wrong size 13790 for scatter 27962 (scatter reverse
> and vector to != ctx from size)
>
> [1]PETSC ERROR: #4 TaoSNESFunction_PDIPM() line 510 in
> /Users/jolivet/Documents/repositories/petsc/src/tao/constrained/impls/ipm/pdipm.c
>
> [0]PETSC ERROR: #5 TaoSolve_PDIPM() line 712 in
> /Users/jolivet/Documents/repositories/petsc/src/tao/constrained/impls/ipm/pdipm.c
>
> [1]PETSC ERROR: #6 TaoSolve() line 222 in
> /Users/jolivet/Documents/repositories/petsc/src/tao/interface/taosolver.c
>
> [0]PETSC ERROR: #1 VecScatterBegin() line 96 in
> /Users/jolivet/Documents/repositories/petsc/src/vec/vscat/interface/vscatfce.c
>
> [0]PETSC ERROR: #2 MatMultTransposeAdd_MPIAIJ() line 1223 in
> /Users/jolivet/Documents/repositories/petsc/src/mat/impls/aij/mpi/mpiaij.c
>
> [0]PETSC ERROR: #3 MatMultTransposeAdd() line 2648 in
> /Users/jolivet/Documents/repositories/petsc/src/mat/interface/matrix.c
>
> [0]PETSC ERROR: #4 TaoSNESFunction_PDIPM() line 510 in
> /Users/jolivet/Documents/repositories/petsc/src/tao/constrained/impls/ipm/pdipm.c
>
> [0]PETSC ERROR: #5 TaoSolve_PDIPM() line 712 in
> /Users/jolivet/Documents/repositories/petsc/src/tao/constrained/impls/ipm/pdipm.c
>
> [0]PETSC ERROR: #6 TaoSolve() line 222 in
> /Users/jolivet/Documents/repositories/petsc/src/tao/interface/taosolver.c
>
>
>
> I think this can be reproduced by ex1.c by just distributing the Hessian
> instead of having it centralized on rank 0.
>
>
>
>
>
> Ideally, you want to have the layout below to minimize movement of
> matrix/vector elements across ranks.
>
> · The layout of vectors x, bounds on x, and gradient is same.
>
> · The row layout of the equality/inequality Jacobian is same as
> the equality/inequality constraint vector layout.
>
> · The column layout of the equality/inequality Jacobian is same
> as that for x.
>
>
>
> Very naive question, but given that I have a single constraint, how do I
> split a 1 x N matrix column-wise? I thought it was not possible.
>
>
>
> Thanks,
>
> Pierre
>
>
>
>
>
> · The row and column layout for the Hessian is same as x.
>
>
>
> The tutorial example ex1 is extremely small (only 2 variables) so its
> implementation is very simplistic. I think, in parallel, it ships off
> constraints etc. to rank 0. It’s not an ideal example w.r.t demonstrating a
> parallel implementation. We aim to add more examples as we develop PDIPM.
> If you have an example to contribute then we would most welcome it and
> provide help on adding it.
>
>
>
> Thanks,
>
> Shri
>
> *From: *petsc-dev <petsc-dev-bounces at mcs.anl.gov> on behalf of Pierre
> Jolivet <pierre.jolivet at enseeiht.fr>
> *Date: *Monday, September 14, 2020 at 1:52 PM
> *To: *PETSc Development <petsc-dev at mcs.anl.gov>
> *Subject: *[petsc-dev] PDIPDM questions
>
>
>
> Hello,
>
> In my quest to help users migrate from Ipopt to Tao, I’ve a new question.
>
> When looking at src/tao/constrained/tutorials/ex1.c, it seems that almost
> everything is centralized on rank 0 (local sizes are 0 but on rank 0).
>
> I’d like to have my Hessian distributed more naturally, as in (almost?)
> all other SNES/TS examples, but still keep the Jacobian of my equality
> constraint, which is of dimension 1 x N (N >> 1), centralized on rank 0.
>
> Is this possible?
>
> If not, is it possible to supply the transpose of the Jacobian, of
> dimension N x 1, which could then be distributed row-wise like the Hessian?
>
> Or maybe use some trick to distribute a MatAIJ/MatDense of dimension 1 x N
> column-wise? Use a MatNest with as many blocks as processes?
>
>
>
> So, just to sum up, how can I have a distributed Hessian with a Jacobian
> with a single row?
>
>
>
> Thanks in advance for your help,
>
> Pierre
>
>
>
>
--
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.cse.buffalo.edu/~knepley/>
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