No, it is of size 9
Jose E. Roman <jro...@dsic.upv.es>, 10 Tem 2020 Cum, 19:31 tarihinde şunu yazdı: > > [Please respond to the list.] > > Is your matrix of size 8? This would explain the residuals. > > Jose > > > El 10 jul 2020, a las 17:10, Eda Oktay <eda.ok...@metu.edu.tr> escribió: > > > > I computed residual norm via -eps_error_relative::ascii_info_detail > > for different tolerance numbers (e-4, e-6, e-8, e-10). In each > > tolerance, I got the same table below: > > > > ---------------------- -------------------- > > k ||Ax-kx||/||kx|| > > ---------------------- -------------------- > > 3.000000 6.25528e-16 > > 3.000000 7.13774e-16 > > 3.438447 2.64362e-16 > > 5.000000 4.39333e-16 > > 6.000000 1.63943e-16 > > 6.000000 2.93737e-16 > > 6.000000 3.95997e-16 > > 7.561553 3.48664e-16 > > ---------------------- -------------------- > > > > I understood that since relative error is E-16 and this table shows > > eigenvalues whose relative error are below the tolerance, I am getting > > the same table but I still couldn't understand although relative > > errors are so small, how am I getting the most qualified partition in > > e-4 tolerance, not e-8. I am not computing zero eigenvalue I believe, > > since I am using EPSSetWhichEigenpairs(eps,EPS_SMALLEST_MAGNITUDE); > > and I am not getting zero eigenvalue. > > > > Thanks so much for answering! > > > > Jose E. Roman <jro...@dsic.upv.es>, 10 Tem 2020 Cum, 14:09 tarihinde şunu > > yazdı: > >> > >> > >> > >>> El 10 jul 2020, a las 12:54, Eda Oktay <eda.ok...@metu.edu.tr> escribió: > >>> > >>>> How do you measure accuracy? > >>> Using the word accuracy may be not true actually, I am sorry. I am > >>> using eigenvectors corresponding to these eigenvalues in k-means > >>> algorithm, then do spectral graph partitioning. I must look at the > >>> partition quality. By quality, I mean, the resulting edge cut of my > >>> partitioned graph. I thought that the less tolerance results in more > >>> accuracy, hence more qualified partition. > >>> > >>>> What do you mean "the result was still the same"? > >>> I mean I am still not getting the most qualified solution in E-10, > >>> still E-2 or E-6 gives more qualified partitions, i.e. they give less > >>> edge cut. > >>> > >>>> What is the eigenvalue you are computing? > >>> I am computing the smallest eigenvalue of a Laplacian matrix. > >> > >> You should compute the residual norm, for instance with > >> -eps_error_relative ::ascii_info_detail (see section 2.5.4 of the manual). > >> The relative residual error should be in the order of the tolerance (or > >> smaller) if using the default convergence test, but if you are computing a > >> zero eigenvalue then you may want to use an absolute convergence criterion > >> (see table 2.6 or the manual). A graph Laplacian has at least one zero > >> eigenvalue, unless you deflate it as explained in section 2.6.2 of the > >> manual, see also ex11.c > >> https://slepc.upv.es/documentation/current/src/eps/tutorials/ex11.c.html > >> > >> Jose > >> >