Hi David, Thanks so much, this is exactly what I was looking for! For some reason I was trying to use the square bracket notation. Is there any reason why the (i, j) syntax is used rather than [i, j]? Is it just a restriction of c++?
A few follow-up questions about the LAPACKFullMatrix class: is there anywhere that I can find more information about the class besides the reference documentation here <https://www.dealii.org/current/doxygen/deal.II/namespaceLAPACKSupport.html>? In particular, I'm wondering how to deal with the state attribute. It looks like the compute_lu_factorization() method sets the state to lu (reasonable), but I'd like to repopulate the same matrix (meaning it has to be in the matrix state, I think). For now I'm using reinit() because that seems to change the state back to matrix, but I worry that it's expensive to keep reinitializing the matrix every Newton's method iteration. Is there a way to avoid reinitializing it? And is it bad programming practice to *not* reinitialize it? Again, thanks so much for the help. Kind regards, Lucas On Monday, June 21, 2021 at 1:08:50 PM UTC-5 Wells, David wrote: > Hi Lucas, > > You should be able to use syntax like > > A(i, j) = 5; > > to assign values to a FullMatrix - it's what we do in most of the tutorial > programs. TableIndices are somewhat hard to use (you are right) - they are > intended to be used as a generic interface to Table<N, T> where N is not > known until compile time. Once you populate the matrix, you should be able > to do what you mentioned before with the Gauss-Jordan algorithm to get the > inverse. > > That being said - do you need the inverse itself, or the action of the > inverse? If you only ever need the action of the inverse a much better > approach would be to use LAPACKFullMatrix and factorize it (via > LAPACKFullMatrix::compute_lu_factorization() and LAPACKFullMatrix::solve()) > since there is a significant amount of roundoff error accumulation in > computing inverses. > > The Solver classes are more than you need here - they are optimized for > large sparse problems, not small dense ones. > > Best, > David Wells > > > ------------------------------ > *From:* dea...@googlegroups.com <dea...@googlegroups.com> on behalf of > Lucas Myers <lucasm...@gmail.com> > *Sent:* Monday, June 21, 2021 1:50 PM > *To:* deal.II User Group <dea...@googlegroups.com> > *Subject:* [deal.II] 5x5 Matrix Inversion Problem > > Hi Everyone, > > I have a problem wherein one of the terms in my PDE is a 5-component > vector function \Lambda of the 5-component solution vector Q. However, I > only have an explicit formula for Q as a function of \Lambda and so I am > trying to write a numerical inversion class (as a `dealii::Function`) to > get \Lambda as a function of Q. > > I am using Newton's method, and so I need to solve a 5x5 matrix equation. > I was planning on just inverting the Jacobian which I have implemented as a > `dealii::Tensor`, but it looks like the `invert` function is only > implemented up to dimension 3 (?). It looks like the `dealii::FullMatrix` > class can do this via a Gauss Jordan method, but I was having some trouble > using the `FullMatrix` class directly. In particular, to read and write > individual elements I need to create a `dealii::TableIndices` object, which > seems tedious and makes me think it's meant to be used internally. > > Given all this, I am looking for advice at any level: is this a reasonable > way to numerically get \Lambda as a function of Q? Is it recommended to use > a `dealii::Tensor` object as opposed to a `dealii::FullMatrix` object? And > if I am supposed to use the latter, is there a nicer way to index it than > with the `dealii::TableIndices` object? Lastly is it a good idea to be > using an `invert` operation to solve the Newton's method linear equation? I > know that the `Eigen` package recommends against that here > <https://eigen.tuxfamily.org/dox/group__TutorialLinearAlgebra.html>, and > instead recommends one of its solution methods. I haven't seen any of those > here besides one of the `Solver` classes, but those seem like a lot of > overhead for a 5x5 matrix (I'm going to have to do this operation for every > degree of freedom, so I want too minimize overhead). I also don't really > want to use the Eigen package, just because (1) I want to avoid unnecessary > value-copying and (2) I'd like to not have to try to interface multiple > packages. > > Any help is appreciated, and let me know if you need more information > about the problem. > > Kind regards, > Lucas > > -- > The deal.II project is located at http://www.dealii.org/ > For mailing list/forum options, see > https://groups.google.com/d/forum/dealii?hl=en > --- > You received this message because you are subscribed to the Google Groups > "deal.II User Group" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to dealii+un...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/dealii/29d3a1c1-6703-4c98-95a6-44ba96add049n%40googlegroups.com > > <https://groups.google.com/d/msgid/dealii/29d3a1c1-6703-4c98-95a6-44ba96add049n%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/1b2ac5de-338a-4da1-9b93-1bb6718b4ab8n%40googlegroups.com.
