please see this https://groups.google.com/d/topic/cvxopt/xQ-lR9ESijg/discussion far a way to make it more sane. It turns out that cvxopt has un undocumented function to extract the Cholesky factor directly.
On Tuesday, 30 October 2012 21:49:48 UTC+8, Dima Pasechnik wrote: > > On 2012-10-29, Raniere Gaia Silva <r.gaia...@gmail.com> wrote: > > Hi, > > I need to performe a (numerical) cholesky factorization of a sparse > > matrix (20x20) but I'm getting a error. > > OK, my previous reply didn't make much sense, so here is one that is > meaningful. In cvxopt (a standard Sage spkg) there is an interface to > sparse Cholesky > factorization. > There aren't too many hooks for cvxopt in Sage, and, moreover, cvxopt > does not provide a straightforward interface, you need to solve matrix > linear equations to get L, see > > http://abel.ee.ucla.edu/cvxopt/userguide/spsolvers.html#positive-definite-linear-equations > > > so it's a bit of a walk: > > sage: preparser(False) # somehow, preparser breaks cvxopt :( > sage: import cvxopt > sage: from cvxopt import cholmod > sage: A=cvxopt.sparse(cvxopt.matrix([[1,1],[1,2]])); A > <2x2 sparse matrix, tc='d', nnz=4> > sage: print A > [ 1.00e+00 1.00e+00] > [ 1.00e+00 2.00e+00] > sage: F = cholmod.symbolic(A) > sage: cholmod.numeric(A,F) > sage: Lt=cvxopt.cholmod.spsolve(F,A,sys=4); Lt > <2x2 sparse matrix, tc='d', nnz=3> > sage: print Lt > [ 1.00e+00 1.00e+00] > [ 0 1.00e+00] > > Achtung! This only works in the case the decomposition PAP^T=LL^T > computed by cholmod (and stored in F), where P is a permutation > matrix, has P=identity. More generally, you need to be more careful: > either cvxopt.cholmod.symbolic() must be called with the parameter > p specified to be the identity (permutation) matrix, or it can (perhaps) > be retrieved using cvxopt.cholmod.spsolve() with appropriate B and sys=... > > Well, perhaps you actually do not need to know L explicitly, just to > solve these matrix equations... > > By the way, you can extract entries of Lt using syntax like this: > sage: Lt[1,0] > 0.0 > sage: Lt[1,1] > 1.0 > > note that > sage: type(Lt[1,0]) > <type 'float'> > > so they can be converted back to Sage types. > > HTH, > Dmitrii > > PS. cvxopt has its own google group: > https://groups.google.com/forum/?fromgroups=#!forum/cvxopt > > > I look at this thread > > > https://groups.google.com/forum/?fromgroups=#!searchin/sage-devel/cholesky/sage-devel/AW4pmKx49H4/7iuet3rWYQgJ > > > but it didn't help very much (and is a little old). > > > > Bellow a minimal example of the problem. > > > > {{{ > > sage: D = matrix(RDF, 2, 2, [[1, 1],[1,2]]) > > sage: D > > [1.0 1.0] > > [1.0 2.0] > > sage: D.cholesky() > > [1.0 0.0] > > [1.0 1.0] > > sage: D = matrix(RDF, 2, 2, [[1, 1],[1,2]], sparse=True) > > sage: D > > [1.0 1.0] > > [1.0 2.0] > > sage: D.cholesky() > > > --------------------------------------------------------------------------- > > TypeError Traceback (most recent call > last) > > > > /home/raniere/documents/cnpq_126874_2012-3/src_sage/<ipython console> > > in <module>() > > > > > /home/raniere/opt/sage/local/lib/python2.7/site-packages/sage/matrix/matrix2.so > > > > in sage.matrix.matrix2.Matrix.cholesky (sage/matrix/matrix2.c:47860)() > > > > TypeError: base ring of the matrix must be exact, not Real Double Field > > }}} > > > > Thanks, > > Raniere > > > > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To post to this group, send email to sage-support@googlegroups.com. To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en.
