This is the mail archive of the
gsl-discuss@sources.redhat.com
mailing list for the GSL project.
Re: calculating matrix inverses (was Re: modifying matrix allocationfunctions for use with R)
- To: Faheem Mitha <faheem at email dot unc dot edu>
- Subject: Re: calculating matrix inverses (was Re: modifying matrix allocationfunctions for use with R)
- From: James Theiler <jt at lanl dot gov>
- Date: Wed, 10 Oct 2001 11:52:30 -0600 (MDT)
- cc: Brian Gough <bjg at network-theory dot co dot uk>, <gsl-discuss at sources dot redhat dot com>
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.
jt
---------------------------------------------
James Theiler jt@lanl.gov
MS-D436, NIS-2, LANL tel: 505/665-5682
Los Alamos, NM 87545 fax: 505/665-4414
----- Space and Remote Sensing Sciences -----