> El 17 ago 2020, a las 14:27, Barry Smith <bsm...@petsc.dev> escribió:
>
>
> Nidish,
>
> Your matrix is dense, correct? MUMPS is for sparse matrices.
>
> Then I guess you could use Scalapack
> http://netlib.org/scalapack/slug/node48.html#SECTION04323200000000000000 to
> do the SVD. The work is order N^3 and parallel efficiency may not be great
> but it might help you solve your problem.
>
> I don't know if SLEPc has an interface to Scalapack for SVD or not.
Yes, SLEPc (master) has interfaces for ScaLAPACK and Elemental for both SVD and
(symmetric) eigenvalues.
Jose
>
> Barry
>
>
>
>
>
>
>
>> On Aug 17, 2020, at 2:51 AM, Jose E. Roman <jro...@dsic.upv.es> wrote:
>>
>> You can use SLEPc's SVD to compute the nullspace, but it has pitfalls: make
>> sure you use an absolute convergence test (not relative); for the particular
>> case of zero singular vectors, accuracy may not be very good and convergence
>> may be slow (with the corresponding high computational cost).
>>
>> MUMPS has functionality to get a basis of the nullspace, once you have
>> computed the factorization. But I don't know if this is easily accessible
>> via PETSc.
>>
>> Jose
>>
>>
>>
>>> El 17 ago 2020, a las 3:10, Nidish <n...@rice.edu> escribió:
>>>
>>> Oh damn. Alright, I'll keep trying out the different options.
>>>
>>> Thank you,
>>> Nidish
>>>
>>> On 8/16/20 8:05 PM, Barry Smith wrote:
>>>>
>>>> SVD is enormously expensive, needs to be done on a full dense matrix so
>>>> completely impractical. You need the best tuned iterative method, Jose is
>>>> the by far the most knowledgeable about that.
>>>>
>>>> Barry
>>>>
>>>>
>>>>> On Aug 16, 2020, at 7:46 PM, Nidish <n...@rice.edu> wrote:
>>>>>
>>>>> Thank you for the suggestions.
>>>>>
>>>>> I'm getting a zero pivot error for the LU in slepc while calculating the
>>>>> rest of the modes.
>>>>>
>>>>> Would conducting an SVD for just the stiffness matrix and then using the
>>>>> singular vectors as bases for the nullspace work? I haven't tried this
>>>>> out just yet, but I'm wondering if you could provide me insights into
>>>>> whether this will.
>>>>>
>>>>> Thanks,
>>>>> Nidish
>>>>>
>>>>> On 8/16/20 2:50 PM, Barry Smith wrote:
>>>>>>
>>>>>> If you know part of your null space explicitly (for example the rigid
>>>>>> body modes) I would recommend you always use that information explicitly
>>>>>> since it is extremely expensive numerically to obtain. Thus rather than
>>>>>> numerically computing the entire null space compute the part orthogonal
>>>>>> to the part you already know. Presumably SLEPc has tools to help do
>>>>>> this, naively I would just orthogonalized against the know subspace
>>>>>> during the computational process but there are probably better ways.
>>>>>>
>>>>>> Barry
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>> On Aug 16, 2020, at 11:26 AM, Nidish <n...@rice.edu> wrote:
>>>>>>>
>>>>>>> Well some of the zero eigenvectors are rigid body modes, but there are
>>>>>>> some more which are introduced by lagrange-multiplier based constraint
>>>>>>> enforcement, which are non trivial.
>>>>>>>
>>>>>>> My final application is for a nonlinear simulation, so I don't mind the
>>>>>>> extra computational effort initially. Could you have me the suggested
>>>>>>> solver configurations to get this type of eigenvectors in slepc?
>>>>>>>
>>>>>>> Nidish
>>>>>>> On Aug 16, 2020, at 00:17, Jed Brown <j...@jedbrown.org> wrote:
>>>>>>> It's possible to use this or a similar algorithm in SLEPc, but keep in
>>>>>>> mind that it's more expensive to compute these eigenvectors than to
>>>>>>> solve a linear system. Do you have a sequence of systems with the same
>>>>>>> null space?
>>>>>>>
>>>>>>> You referred to the null space as "rigid body modes". Why can't those
>>>>>>> be written down? Note that PETSc has convenience routines for
>>>>>>> computing rigid body modes from coordinates.
>>>>>>>
>>>>>>> Nidish <
>>>>>>> n...@rice.edu
>>>>>>>> writes:
>>>>>>>
>>>>>>>
>>>>>>> I just use the standard eigs function
>>>>>>> (https://www.mathworks.com/help/matlab/ref/eigs.html
>>>>>>> ) as a black box. I think it uses a lanczos type method under the hood.
>>>>>>>
>>>>>>> Nidish
>>>>>>>
>>>>>>> On Aug 15, 2020, 21:42, at 21:42, Barry Smith <
>>>>>>> bsm...@petsc.dev
>>>>>>>> wrote:
>>>>>>>
>>>>>>>
>>>>>>> Exactly what algorithm are you using in Matlab to get the 10 smallest
>>>>>>> eigenvalues and their corresponding eigenvectors?
>>>>>>>
>>>>>>> Barry
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> On Aug 15, 2020, at 8:53 PM, Nidish <n...@rice.edu
>>>>>>>> wrote:
>>>>>>>
>>>>>>> The section on solving singular systems in the manual starts with
>>>>>>>
>>>>>>> assuming that the singular eigenvectors are already known.
>>>>>>>
>>>>>>>
>>>>>>> I have a large system where finding the singular eigenvectors is not
>>>>>>>
>>>>>>> trivially written down. How would you recommend I proceed with making
>>>>>>> initial estimates? In MATLAB (with MUCH smaller matrices), I conduct an
>>>>>>> eigensolve for the first 10 smallest eigenvalues and take the
>>>>>>> eigenvectors corresponding to the zero eigenvalues from this. This
>>>>>>> approach doesn't work here since I'm unable to use SLEPc for solving
>>>>>>>
>>>>>>>
>>>>>>> K.v = lam*M.v
>>>>>>>
>>>>>>> for cases where K is positive semi-definite (contains a few "rigid
>>>>>>>
>>>>>>> body modes") and M is strictly positive definite.
>>>>>>>
>>>>>>>
>>>>>>> I'd appreciate any assistance you may provide with this.
>>>>>>>
>>>>>>> Thank you,
>>>>>>> Nidish
>>>>>>>
>>>>>>
>>>>> --
>>>>> Nidish
>>>>
>>> --
>>> Nidish
>>
>
