On 10/30/12 6:34 AM, Dima Pasechnik wrote:
On 2012-10-29, Raniere Gaia Silva <[email protected]> wrote:
Hi,
I need to performe a (numerical) cholesky factorization of a sparse
matrix (20x20) but I'm getting a error.
the error message is clear: there is no implementation for RDF matrices,
only for exact matrices. So you can do this for QQ, for instance.
This is of course a deficiency in Sage matrices. There are Cholesky
implementations available for RDF matrices from numpy, for instance,
it's just absense of proper hooks in Sage.
You can do the following as a workaround:
sage: import numpy as np
sage: D = matrix(RDF, 2, 2, [[1, 1],[1,2]])
sage: np.linalg.cholesky(D.numpy())
array([[ 1., 0.],
[ 1., 1.]])
sage:
you can get Sage matrix out of it, too:
sage: L=matrix(np.linalg.cholesky(D.numpy())); L
[1.0 0.0]
[1.0 1.0]
HTH,
Dmitrii
I think the point was that cholesky was not implemented for *sparse*
matrices. Dense RDF matrices in Sage do have cholesky implemented (and
that calls scipy).
Of course, converting sparse to dense RDF and using cholesky on the
dense matrix works if the matrix is small enough. Scipy had some
interest in adding sparse cholesky [1], but it seems that nothing came
of it.
On the other hand, it would be cool if we wrapped something like CHOLMOD
[2] to compute sparse cholesky decompositions. Even cooler would be
supporting the SuiteSparse package [3] and its various algorithms.
Sparse matrices in Sage need some attention.
Thanks,
Jason
[1] http://projects.scipy.org/scipy/ticket/261
[2] http://www.cise.ufl.edu/research/sparse/cholmod/
[3] http://www.cise.ufl.edu/research/sparse/SuiteSparse/
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