Dear I've been reading all the advices that (all of them) speak about the need to normalize the data in order to avoid the ill-conditioned issues (and to be the closest as possible to the value 1.0) ; the example shared by Serge Steer is quite interesting and highlights the ill-conditioning issue.
Nevertheless I'm a bit confuse on how to do it in order to rebuild the results afterward: [u,v] = eigs(K((ddl_elem+1):$,(ddl_elem+1):$),M((ddl_elem+1):$,(ddl_elem+1):$),n,"SM"); pulse_ =sqrt(diag(u)) //pulse - circular frequency freq_ = pulse_/(2*%pi); //natural frequency Naively I thought that the following would have fix the problem: - using max(K) and max(M) to normalize the sparse matrix, - removing the smallest values (i.e. bellow a threshold value) ... but the matrix becomes singular (why ?). So is there any additional advice ? Paul -----Message d'origine----- De : users [mailto:[email protected]] De la part de Serge Steer Envoyé : jeudi 18 juin 2015 10:08 À : [email protected] Objet : Re: [Scilab-users] eigs calculation Le 17/06/2015 22:18, Carrico, Paul a écrit : > Dear All > > Thanks for the answers. > > To give more information's on what I'm doing (That's quite new I confess), > I'm performing a (basic) finite element calculation with beams using sparse > matrix (stiffness matrix K and mass matrix M). > [u,v] = > eigs(K((ddl_elem+1):$,(ddl_elem+1):$),M((ddl_elem+1):$,(ddl_elem+1):$) > ,n,"SM"); > > Nota: ddl means dof > > I'm calculated first the natural frequencies using (K - omega^2.M).x=0 ... > the pulse (or circular frequencies) are no more and no less than the > eigenvalues of the above system (u = omega^2). > > Just a "mechanical" remark: since the beam is clamped in one side (and free > on the tip), it is absolutely normal that you find twice the same natural > frequency (1rst mode in one direction, the second one in a new direction at > 90°) .... I've been really surprised to find it, but happy at the same time > ... > > The origin of my question was: since it obvious that the results are strongly > sensitive to the "units" (i.e. the numbers), I'm wondering if there is a way > to control the accuracy of the eigenvalues calculation using eigs keywords > ... There is no way to improve accurary with an option. In general the numerical algorithms try to return the best solution. But it should be possible to improve accuracy by a well suited normalisation (unit change for example!) The condition number of u gives a measure of the numerical difficulty to solve the problem Note that as stated the eigenvalue computation may be a ill conditionned problem in particular when there are clusters of eigenvalues Please find below a little script which illustrate a typicall case A=zeros(10,10)+diag(ones(1,9),1);A(10,1)=%eps; s=spec(A); clf;plot(real(s),imag(s),'+'); Serge Steer > In any way, thanks for the debate > > Paul _______________________________________________ users mailing list [email protected] https://urldefense.proofpoint.com/v2/url?u=http-3A__lists.scilab.org_mailman_listinfo_users&d=AwIF-g&c=0hKVUfnuoBozYN8UvxPA-w&r=4TCz--8bXfJhZZvIxJAemAJyz7Vfx78XvgYu3LN7eLo&m=S2zme-g7wK4GeuiYqaod2UALQUgCMA5H4YAmnwGMSjE&s=yrKeTLe9iyrw3ACr0KvvHnUusYyMaXo-RoPpv8yhipg&e= EXPORT CONTROL : Cet email ne contient pas de données techniques This email does not contain technical data _______________________________________________ users mailing list [email protected] http://lists.scilab.org/mailman/listinfo/users
