[petsc-users] Singlar values of the GMRES Hessenberg matrix
Dave Lee
davelee2804 at gmail.com
Sat May 25 03:18:50 CDT 2019
Thanks Matt, this is where I'm adding in my hookstep code.
Cheers, Dave.
On Fri, May 24, 2019 at 10:49 PM Matthew Knepley <knepley at gmail.com> wrote:
> On Fri, May 24, 2019 at 8:38 AM Dave Lee <davelee2804 at gmail.com> wrote:
>
>> Thanks Matt, great suggestion.
>>
>> I did indeed find a transpose error this way. The SVD as reconstructed
>> via U S V^T now matches the input Hessenberg matrix as derived via the
>> *HES(row,col) macro, and all the singular values are non-zero. However
>> the solution to example src/ksp/ksp/examples/tutorials/ex1.c as
>> determined via the expansion over the singular vectors is still not
>> correct. I suspect I'm doing something wrong with regards to the expansion
>> over the vec array VEC_VV(), which I assume are the orthonormal vectors
>> of the Q_k matrix in the Arnoldi iteration....
>>
>
> Here we are building the solution:
>
>
> https://bitbucket.org/petsc/petsc/src/7c23e6aa64ffbff85a2457e1aa154ec3d7f238e3/src/ksp/ksp/impls/gmres/gmres.c#lines-331
>
> There are some subtleties if you have a nonzero initial guess or a
> preconditioner.
>
> Thanks,
>
> Matt
>
>
>> Thanks again for your advice, I'll keep digging.
>>
>> Cheers, Dave.
>>
>> On Thu, May 23, 2019 at 8:20 PM Matthew Knepley <knepley at gmail.com>
>> wrote:
>>
>>> On Thu, May 23, 2019 at 5:09 AM Dave Lee via petsc-users <
>>> petsc-users at mcs.anl.gov> wrote:
>>>
>>>> Hi PETSc,
>>>>
>>>> I'm trying to add a "hook step" to the SNES trust region solver (at the
>>>> end of the function: KSPGMRESBuildSoln())
>>>>
>>>> I'm testing this using the (linear) example:
>>>> src/ksp/ksp/examples/tutorials/ex1.c
>>>> as
>>>> gdb --args ./test -snes_mf -snes_type newtontr -ksp_rtol 1.0e-12
>>>> -snes_stol 1.0e-12 -ksp_converged_reason -snes_converged_reason
>>>> -ksp_monitor -snes_monitor
>>>> (Ignore the SNES stuff, this is for when I test nonlinear examples).
>>>>
>>>> When I call the LAPACK SVD routine via PETSc as
>>>> PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_(...))
>>>> I get the following singular values:
>>>>
>>>> 0 KSP Residual norm 7.071067811865e-01
>>>> 1 KSP Residual norm 3.162277660168e-01
>>>> 2 KSP Residual norm 1.889822365046e-01
>>>> 3 KSP Residual norm 1.290994448736e-01
>>>> 4 KSP Residual norm 9.534625892456e-02
>>>> 5 KSP Residual norm 8.082545620881e-16
>>>>
>>>> 1 0.5 -7.85046e-16 1.17757e-15
>>>> 0.5 1 0.5 1.7271e-15
>>>> 0 0.5 1 0.5
>>>> 0 0 0.5 1
>>>> 0 0 0 0.5
>>>>
>>>> singular values: 2.36264 0.409816 1.97794e-15 6.67632e-16
>>>>
>>>> Linear solve converged due to CONVERGED_RTOL iterations 5
>>>>
>>>> Where the lines above the singular values are the Hessenberg matrix
>>>> that I'm doing the SVD on.
>>>>
>>>
>>> First, write out all the SVD matrices you get and make sure that they
>>> reconstruct the input matrix (that
>>> you do not have something transposed somewhere).
>>>
>>> Matt
>>>
>>>
>>>> When I build the solution in terms of the leading two right singular
>>>> vectors (and subsequently the first two orthonormal basis vectors in
>>>> VECS_VV I get an error norm as:
>>>> Norm of error 3.16228, Iterations 5
>>>>
>>>> My suspicion is that I'm creating the Hessenberg incorrectly, as I
>>>> would have thought that this problem should have more than two non-zero
>>>> leading singular values.
>>>>
>>>> Within my modified version of the GMRES build solution function
>>>> (attached) I'm creating this (and passing it to LAPACK as):
>>>>
>>>> nRows = gmres->it+1;
>>>> nCols = nRows-1;
>>>>
>>>> ierr = PetscBLASIntCast(nRows,&nRows_blas);CHKERRQ(ierr);
>>>> ierr = PetscBLASIntCast(nCols,&nCols_blas);CHKERRQ(ierr);
>>>> ierr = PetscBLASIntCast(5*nRows,&lwork);CHKERRQ(ierr);
>>>> ierr = PetscMalloc1(5*nRows,&work);CHKERRQ(ierr);
>>>> ierr = PetscMalloc1(nRows*nCols,&R);CHKERRQ(ierr);
>>>> ierr = PetscMalloc1(nRows*nCols,&H);CHKERRQ(ierr);
>>>> for (jj = 0; jj < nRows; jj++) {
>>>> for (ii = 0; ii < nCols; ii++) {
>>>> R[jj*nCols+ii] = *HES(jj,ii);
>>>> }
>>>> }
>>>> // Duplicate the Hessenberg matrix as the one passed to the SVD
>>>> solver is destroyed
>>>> for (ii=0; ii<nRows*nCols; ii++) H[ii] = R[ii];
>>>>
>>>> ierr = PetscMalloc1(nRows*nRows,&U);CHKERRQ(ierr);
>>>> ierr = PetscMalloc1(nCols*nCols,&VT);CHKERRQ(ierr);
>>>> ierr = PetscMalloc1(nRows*nRows,&UT);CHKERRQ(ierr);
>>>> ierr = PetscMalloc1(nCols*nCols,&V);CHKERRQ(ierr);
>>>> ierr = PetscMalloc1(nRows,&p);CHKERRQ(ierr);
>>>> ierr = PetscMalloc1(nCols,&q);CHKERRQ(ierr);
>>>> ierr = PetscMalloc1(nCols,&y);CHKERRQ(ierr);
>>>>
>>>> // Perform an SVD on the Hessenberg matrix - Note: this call
>>>> destroys the input Hessenberg
>>>> ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
>>>>
>>>> PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("A","A",&nRows_blas,&nCols_blas,R,&nRows_blas,S,UT,&nRows_blas,V,&nCols_blas,work,&lwork,&lierr));
>>>> if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SVD
>>>> Lapack routine %d",(int)lierr);
>>>> ierr = PetscFPTrapPop();CHKERRQ(ierr);
>>>>
>>>> // Find the number of non-zero singular values
>>>> for(nnz=0; nnz<nCols; nnz++) {
>>>> if(fabs(S[nnz]) < 1.0e-8) break;
>>>> }
>>>> printf("number of nonzero singular values: %d\n",nnz);
>>>>
>>>> trans(nRows,nRows,UT,U);
>>>> trans(nCols,nCols,V,VT);
>>>>
>>>> // Compute p = ||r_0|| U^T e_1
>>>> beta = gmres->res_beta;
>>>> for (ii=0; ii<nCols; ii++) {
>>>> p[ii] = beta*UT[ii*nRows];
>>>> }
>>>> p[nCols] = 0.0;
>>>>
>>>> // Original GMRES solution (\mu = 0)
>>>> for (ii=0; ii<nnz; ii++) {
>>>> q[ii] = p[ii]/S[ii];
>>>> }
>>>>
>>>> // Expand y in terms of the right singular vectors as y = V q
>>>> for (jj=0; jj<nnz; jj++) {
>>>> y[jj] = 0.0;
>>>> for (ii=0; ii<nCols; ii++) {
>>>> y[jj] += V[jj*nCols+ii]*q[ii]; // transpose of the transpose
>>>> }
>>>> }
>>>>
>>>> // Pass the orthnomalized Krylov vector weights back out
>>>> for (ii=0; ii<nnz; ii++) {
>>>> nrs[ii] = y[ii];
>>>> }
>>>>
>>>> I just wanted to check that this is the correct way to extract the
>>>> Hessenberg from the KSP_GMRES structure, and to pass it to LAPACK, and if
>>>> so, should I really be expecting only two non-zero singular values in
>>>> return for this problem?
>>>>
>>>> Cheers, Dave.
>>>>
>>>
>>>
>>> --
>>> 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/>
>>>
>>
>
> --
> 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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