On Fri, May 24, 2019 at 8:38 AM Dave Lee <[email protected]> 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 <[email protected]> wrote: > >> On Thu, May 23, 2019 at 5:09 AM Dave Lee via petsc-users < >> [email protected]> 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/>
