Hi Wolfgang,
Thanks for your input. I would be delighted to look into this issue and
potentially make a contribution.
Also, I noticed that SymmetricTensor<2, dim> also has a function called
*eigenvectors,
*which could robustly provide the eigenvalues and eigenvectors for a
symmetric 2nd order tensor. This function performs well regardless of the
scaling. Below is my function to obtain the eigen system of a 2nd order
symmetric tensor:
template <int dim>
void spectrum_decomposition(SymmetricTensor<2, dim> const &
symmetric_tensor,
Vector<double> & myEigenvalues,
std::vector<Tensor<1, dim>> &
myEigenvectors)
{
std::array< std::pair< double, Tensor< 1, dim > >, dim > myEigenSystem;
myEigenSystem = *eigenvectors*(symmetric_tensor);
for (int i = 0; i < dim; i++)
{
myEigenvalues[i] = myEigenSystem[i].first;
myEigenvectors[i] = myEigenSystem[i].second;
}
}
Best,
Tao
On Wednesday, June 14, 2023 at 10:58:37 PM UTC-4 Wolfgang Bangerth wrote:
>
> Tao:
> Yes, this is cumbersome indeed. I looked into this file, and it contains a
> number of places where deal.II outputs to std::cerr. This is not the style
> we
> favor today. I looked it up, and these lines were written in 2005,
> probably
> with the very first version of that file.
>
> I have opened an issue about this:
> https://github.com/dealii/dealii/issues/15363
> As with all things deal.II, we would gladly help any kind of help we can
> get
> -- so if the error message bothers you, perhaps this is your project: Fix
> this
> particular issue, and get it merged into deal.II!
>
> Underlying your question is the issue that dependent on the value of the
> scaling, you either do or do not get an error. I believe that that is
> because
> you need to also scale the upper/lower bounds and the tolerance with which
> you
> call the LAPACK function. When you multiply the 2x2 matrix by a scalar
> factor,
> all of the eigenvalues also scale and consequently the tolerance should
> also
> scale.
>
> Best
> W.
>
> On 6/14/23 09:47, Tao Jin wrote:
> > *** Caution: EXTERNAL Sender ***
> >
> > Dear all,
> >
> > I received the message "LAPACK error in syevx" when using the
> > /*compute_eigenvalues_symmetric*/ of */lapack_full_matrix/* (the
> interface to
> > LAPACK in dealii) to compute the eigenvalues of a symmetric matrix with
> > relatively small matrix entries. I have attached a test file (main.cc)
> in the
> > end.
> >
> > To provide more information, I construct the following 2x2 symmetric
> matrix
> > const double *scalar = 1.0;*
> > for (unsigned int i = 0; i < dim; i++)
> > for (unsigned int j = 0; j <= i; j++)
> > {
> > symmetric_tensor[i][j] = (i + j + 1) * *scalar*;
> > if (j != i)
> > symmetric_tensor[j][i] = symmetric_tensor[i][j];
> > }
> >
> > *In this case, the eigenvalue decomposition runs without error message:*
> > Spectrum decomposition of a symmetric 2nd order tensor
> > Eigenvalues: -0.236068 4.23607
> > Spectrum decomposition succeeded!
> >
> > However, if I set
> > const double *scalar = 1.0e-3; // to make the matrix entries
> relatively small*
> > The eigenvalue decomposition is still successful. However, here is the
> output
> > message:
> > Spectrum decomposition of a symmetric 2nd order tensor
> > *LAPACK error in syevx
> > *Eigenvalues: -0.000236068 0.00423607
> > Spectrum decomposition succeeded!
> >
> > This error message is from "lapack_full_matrix.cc"
> > // Negative return value implies a wrong argument. This should be
> internal.
> > 2049 Assert
> > <
> https://www.dealii.org/current/doxygen/deal.II/group__Exceptions.html#ga70a0bb353656e704acf927945277bbc6>(info
>
> >= 0, ExcInternalError <
> https://www.dealii.org/current/doxygen/deal.II/group__Exceptions.html#gab7a0d88175320d08084b2f40f5e3380b
> >());
> > 2050 if (info != 0)
> > 2051 std::cerr << "*LAPACK error in syevx*" << std::endl;
> > **
> > Since I need to run the spectrum decomposition at each Gauss point, it
> is
> > annoying to receive tons of this error message, even though the
> simulation
> > still finishes with no issue.
> >
> > Any insights to avoid this issue?
> >
> > Best,
> >
> > Tao
> >
> > --
> > The deal.II project is located at http://www.dealii.org/
> > <http://www.dealii.org/>
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> <
> https://groups.google.com/d/msgid/dealii/8adfe7d5-220c-4c4a-b3e5-60c2c9c6b278n%40googlegroups.com?utm_medium=email&utm_source=footer
> >.
>
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth email: bang...@colostate.edu
> www: http://www.math.colostate.edu/~bangerth/
>
>
>
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