[petsc-users] Least Square solver LSQR

Natacha BEREUX natacha.bereux at gmail.com
Tue Jan 6 03:57:48 CST 2015

```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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