Natacha: I can repeat the error with your ex1f.F. The lsqr solver in PETSc was contributed by a user a decade ago. I'll read the original algorithm and investigate it.
I'll let you know the result. Hong Dear PETSc users, > I am trying to solve an over determined linear system of equations Ax =b > with the least square solver LSQR. > The matrix A is rectangular : it has m rows and n columns with m>n. > I set the preconditioner to "PCNONE" (following for instance post > https://lists.mcs.anl.gov/mailman/htdig/petsc-users/2012-May/013591.html) > > Matrix A has the form : > A(1:n,1:n) = Identity(n) > A(n+1:m, 1:n) = 0. > > I define a vector u of size n and set u(1:n) to 1.0 > > The right hand side b= Au. > > The (fortran) test program is attached (it's > petsc-3.5.2/src/ksp/ksp/examples/tutorials/ex1f.F slightly modified) > > The size of matrix A is defined at runtime > > The solver ends OK with m=10, n=2 but goes wrong with m=10, n=3 (KSP > Converged reason = -5) > > The output is shown below: > > First run with n=2 columns > ==================== > ./ex1f -ksp_type lsqr -vec_type seq -ksp_monitor -m 10 -n 2 > > 0 KSP Residual norm 1.414213562373e+00 > 1 KSP Residual norm 3.790370795009e-16 > KSP Object: 1 MPI processes > type: lsqr > maximum iterations=10000, initial guess is zero > tolerances: relative=1e-07, absolute=1e-50, divergence=10000 > left preconditioning > using UNPRECONDITIONED norm type for convergence test > PC Object: 1 MPI processes > type: none > linear system matrix = precond matrix: > Mat Object: 1 MPI processes > type: seqaij > rows=10, cols=2 > total: nonzeros=2, allocated nonzeros=50 > total number of mallocs used during MatSetValues calls =0 > using I-node routines: found 4 nodes, limit used is 5 > KSP Converged Reason 2 > Norm of error < 1.e-12,Iterations = 1 > > Second run, with n=3 > ================ > ./ex1f -ksp_type lsqr -vec_type seq -ksp_monitor -m 10 -n 3 > > 0 KSP Residual norm 1.732050807569e+00 > KSP Object: 1 MPI processes > type: lsqr > maximum iterations=10000, initial guess is zero > tolerances: relative=1e-07, absolute=1e-50, divergence=10000 > left preconditioning > using UNPRECONDITIONED norm type for convergence test > PC Object: 1 MPI processes > type: none > linear system matrix = precond matrix: > Mat Object: 1 MPI processes > type: seqaij > rows=10, cols=3 > total: nonzeros=3, allocated nonzeros=50 > total number of mallocs used during MatSetValues calls =0 > using I-node routines: found 5 nodes, limit used is 5 > KSP Converged Reason -5 > Norm of error = 0.1732E+01, Iterations = 0 > > > I am using version 3.5.2 of PETSc library > > I am probably doing something wrong, but I don't understand what the > problem is. > Does anyone have an idea of what is going on ? > Best regards > Natacha > > > > >
