Hello David,
Yes, that is very helpful. Thanks for getting back to me. That is very helpful!
I am tried to copy what you've done, see below. But I do have a few questions.
1) Do you have a topetsc function defined like what I have at the top?
2) When you define the petsc matrix, petsc_a, how did you define that?
3) I guess you are solving a regular eigenvalue problem, or is it a generalized eigenvalue problem? If it's in Finite elements i presume it's generalized?
In the case of a generalized eigenvalue problem I wonder if I should have
es.setOperators(A,M)
where A and M are petsc matrices.
4) If yes, then when you have
vr, vi = petsc_A.getVec
I guess this is solving the eigenvalue problem but should you give it an A and M?
Sorry to bother you but I feel like I'm close, just missing an important detail.
Cheers, Francis
def topetsc(A):
A.force_evaluation()
return A.petscmat
# Set up Eigenvalue Problem: QG Basin modes
a = beta*phi*psi.dx(0)*dx
m = -inner(grad(psi), grad(phi))*dx - F*psi*phi*dx
# Assemble Weak Form into a PETSc Matrix
# Impose Boundary Conditions on Mass Matrix
A = topetsc(assemble(a))
M = topetsc(assemble(m, bcs=[bc]))
# Create solver
es = SLEPc.EPS().create(comm=COMM_WORLD)
# Set type of eigenvalues
es.setWhichEigenpairs(es.Which.SMALLEST_IMAGINARY)
# Set number of eigenvalues to compute
num_eigenvalues = 5
es.setDimensions(num_eigenvalues)
#setting the matrix (petsc_a is a PETSc matrix)
es.setOperators(petsc_a)
# Fin eigenvalues an eigenvectors
vr, vi = petsc_a.getVecs()
for i in range(num_eigenvalues):
lam = es.getEigenpair(i, vr, vi)
eigenvalue[i] = lam.real
eigenfunction[i].vector()[:] = vr
Hi Francis, I’m working on a project involving a SLEPc eigensolver in Firedrake so I’ve done some of what you mentioned.
For instance: creating an eigensolver:
es = SLEPc.EPS().create(comm=COMM_WORLD)
setting type of eigenvalues:
es.setWhichEigenpairs(self.eigensolver.Which.SMALLEST_REAL)
setting number of eigenvalues to compute:
es.setDimensions(self.num_eigenvalues)
setting the matrix (petsc_a is a PETSc matrix)
es.setOperators(petsc_a)
getting eigenvectors (in my case the eigenvalues are all real, petsc_a is the matrix)
vr, vi = petsc_a.getVecs()
for i in range(num_eigenvalues):
lmbda = es.getEigenpair(i, vr, vi)
eigenvalue[i] = lmbda.real
eigenfunction[i].vector()[:] = vr
Here eigenfunction is an array of Firedrake functions in the right space that has already been allocated.
Hope that helps,
Dave
Dear
Francis,
On
30/11/16 03:23, Francis Poulin wrote:
Hello,
A while ago someone pointed me towards test_slepc.py for an example
on how to solve an eigenvalue problem. I have been using this as a
model to compute Quasi-Geostrophic basin modes in a closed basin.
We have a version working in FENicS and I am very keen to get it
working in Firedrake as well.
I have a good start, which can be found on github,
https://github.com/francispoulin/firedrakeQG/blob/master/basin_modes_qg.py
Unfortunately, I don't know how to do a lot of things. For
example specify number of eigenvalues to determine, specify a
target eigenvalue, what method to use, or even just look at the
eigenvector.
Doing
this is strictly in the realm of SLEPc, rather than Firedrake
itself.
We're "just" providing the operators. The SLEPc
documentation
is therefore probably helpful:
http://slepc.upv.es/documentation/manual.htm
It
describes everything in terms of the C API, but fortunately,
slepc4py
has somewhat useful documentation strings (type
help(some_slepc_function)
in ipython). The translation from C
functions
to slepc4py functions is quite mechanical:
EPSFooBar(eps,
...)
translates
to:
eps.fooBar(...)
and
so forth.
Thanks,
Lawrence
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