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Re: calculating matrix inverses (was Re: modifying matrix allocationfunctions for use with R)




On Wed, 10 Oct 2001, James Theiler wrote:

> On Wed, 10 Oct 2001, Faheem Mitha wrote:
>
> ]
> ]
> ] On Wed, 10 Oct 2001, Brian Gough wrote:
> ]
> ] > Faheem Mitha writes:
> ]
> ] >  > Incidentally, it is a little awkward to compute the inverse of a matrix,
> ] >  > since this involves calling both int gsl_linalg_LU_decomp and int
> ] >  > gsl_linalg_LU_invert. Would it not be useful to have a "wrapper" function
> ] >  > which uses both together?
> ] >
> ] > Maybe, but in this case computing the inverse matrix is not something
> ] > I want to encourage, as it's usually better to solve Ax=b instead.
> ]
> ] This is an odd thing to say. I want to calculate the inverse of
> ] (HH^t)^{-1} H, where H is a given matrix, as part of simulating from a
> ] multivariate normal distribution (the given expression is the mean).  How
> ] does this correspond to solving a linear system? I assume you mean here
> ] that A is a matrix and x and b are vectors? I seem to have no option in
> ] this case but to use gsl_linalg_LU_decomp aned gsl_linalg_LU_invert. If
> ] there are any other options I would appreciate being made aware of them.
> ]
> ]                                    Sincerely, Faheem Mitha.
> ]
>
> This is getting away from software and API design and into numerical
> methods, but for this kind of thing, singular value decomposition is
> probably a better tool.  It's a little more expensive than LU, but you
> have a lot more control over the stability of the estimated inverse.

Yes, but gsl does not currently seem to have inverses implemented using
singular value deccmposition, and I don't have the time, or the
appropriate algorithms to hand, to implement it myself. I am looking for
cut and dried, ready to use solutions. Thanks for the suggestion, anyway.

                   Sincerely, Faheem Mitha.


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