[petsc-users] KSPLSQR convergence criterion

[Chetan Jhurani]

Thanks for the quick fix.  I'll check it out and let you know if
there is any trouble.

Chetan

> -----Original Message-----
> From: petsc-users-bounces at mcs.anl.gov [mailto:petsc-users-bounces at mcs.anl.gov] On Behalf Of Barry
> Smith
> Sent: Friday, August 06, 2010 10:29 PM
> To: PETSc users list
> Subject: Re: [petsc-users] KSPLSQR convergence criterion
> 
> 
>    Ok, here is my understanding of the situation:  LSQR actually solves the normal equations A'*Ax =
> A'x. When Ax = b has a solution then Matlab and PETSc use || b - Ax|| < tol to determine convergence.
> Matlab also checks || A'*b - A'*Ax || < tol for convergence.
> 
>    In petsc-dev http://www.mcs.anl.gov/petsc/petsc-as/developers/index.html I have added an additional
> test based on the residual norm of the normal equations || A'*b - A'*Ax || < tol    I also added -
> ksp_monitor_lsqr that prints the residual norm and the residual norm of the normal equations. For
> example
> 
> [barry-smiths-macbook-pro:~/Downloads] barrysmith% ./ex1 -ksp_max_it 10 -ksp_converged_reason -
> ksp_monitor_lsqr
>   0 KSP Residual norm 5.000000000000e+00
>   1 KSP Residual norm 8.944271909999e-01 Residual norm normal equations 1.807443084090e-15
> Linear solve converged due to CONVERGED_RTOL_NORMAL iterations 1
> 
> Please let me know if you have any troubles.
> 
>   Barry
> 
> Note that I use a different scaling of tol for convergence test than Matlab (they try to approximate
> the norm of the preconditioned matrix and include that inside the bound, in PETSc we never do this).
> 
> 
> 
> On Aug 6, 2010, at 11:40 AM, Chetan Jhurani wrote:
> 
> > Hello!
> >
> > Could someone help me figure out the correct way to
> > to use KSPLSQR?  Maybe I'm missing something simple.
> >
> > I'm trying to use it to solve an over-determined set
> > of equations.  It seems like the KSP iterations keep on
> > going because the residual is not small enough.  But
> > since the system is over-determined, in general, the
> > exact residual Ax - b will not be zero.
> >
> > For example, to solve the system
> >
> > min_x ||Ax - b||, with A = [1;2], b = [3;4],
> >
> > x must be inv(A'A)A'b = 2.2.  Relative residual is 0.17888.
> > See the Matlab code below too, which gives the correct
> > value in 1 iteration.
> >
> > KSPLSQR, however, stagnates after 1 iteration.  At that
> > point, the relative residual and true residual norm
> > match the correct values exactly.
> >
> > Is there an assumption in KSPLSQR that the system is always
> > invertible or under-determined?  This is petsc-3.1p2 if
> > it matters.
> >
> > Thanks,
> >
> > Chetan
> >
> > ----------------------------------------------------
> > KSPLSQR:
> >
> >  0 KSP preconditioned resid norm 5.000000000000e+000 true resid norm 5.000000000000e+000
> ||Ae||/||Ax|| 1.000000000000e+000
> >  1 KSP preconditioned resid norm 8.944271909999e-001 true resid norm 8.944271909999e-001
> ||Ae||/||Ax|| 1.788854382000e-001
> >  2 KSP preconditioned resid norm 8.944271909999e-001 true resid norm 8.944271909999e-001
> ||Ae||/||Ax|| 1.788854382000e-001
> >  3 KSP preconditioned resid norm 8.944271909999e-001 true resid norm 8.944271909999e-001
> ||Ae||/||Ax|| 1.788854382000e-001
> >  4 KSP preconditioned resid norm 8.944271909999e-001 true resid norm 8.944271909999e-001
> ||Ae||/||Ax|| 1.788854382000e-001
> >  5 KSP preconditioned resid norm 8.944271909999e-001 true resid norm 8.944271909999e-001
> ||Ae||/||Ax|| 1.788854382000e-001
> >
> > Matlab:
> >
> >>> a = [1;2];
> >>> b = [3;4];
> >>> [x,FLAG,RELRES,ITER] = lsqr(a,b, 1e-10, 10)
> > x =
> >   2.200000000000000
> > FLAG =
> >     1
> > RELRES =
> >   0.178885438199983
> > ITER =
> >     1
> >>> norm(a*x-b)
> > ans =
> >   0.894427190999916
> >
> > ----------------------------------------------------
> >
> >