# [petsc-users] Least Square solver LSQR

Hong hzhang at mcs.anl.gov
Tue Jan 6 11:52:28 CST 2015

```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
>
>
>
>
>
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