From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: (qmail 29572 invoked by alias); 20 Nov 2007 21:41:11 -0000 Received: (qmail 29564 invoked by uid 22791); 20 Nov 2007 21:41:10 -0000 X-Spam-Check-By: sourceware.org Received: from qmta09.westchester.pa.mail.comcast.net (HELO QMTA09.westchester.pa.mail.comcast.net) (76.96.62.96) by sourceware.org (qpsmtpd/0.31) with ESMTP; Tue, 20 Nov 2007 21:41:02 +0000 Received: from OMTA11.westchester.pa.mail.comcast.net ([76.96.62.36]) by QMTA09.westchester.pa.mail.comcast.net with comcast id F8mb1Y00C0mv7h00507t00; Tue, 20 Nov 2007 21:41:00 +0000 Received: from hippogriff.homeunix.org ([75.70.82.180]) by OMTA11.westchester.pa.mail.comcast.net with comcast id F9gx1Y00V3tRyZn0300000; Tue, 20 Nov 2007 21:40:59 +0000 X-Authority-Analysis: v=1.0 c=1 a=OpBoXAIT8TsA:10 a=kW6L00vQvgl9A4mUGIoA:9 a=LxCk12REhsDEnKi1lZEDWlcyG-cA:4 a=MxZ3bB5I4kYA:10 Received: by hippogriff.homeunix.org (Postfix, from userid 1000) id 992763177F; Tue, 20 Nov 2007 14:41:09 -0700 (MST) Date: Tue, 20 Nov 2007 21:41:00 -0000 From: Patrick Alken To: gsl-discuss@sourceware.org Subject: Re: gsl_multifit_linear fails in a certain case Message-ID: <20071120214109.GA4016@hippogriff.physics.drexel.edu> References: <20071120060732.GB8438@hippogriff.physics.drexel.edu> <87sl307idd.wl%bjg@network-theory.co.uk> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline In-Reply-To: <87sl307idd.wl%bjg@network-theory.co.uk> User-Agent: Mutt/1.4.2.2i Mailing-List: contact gsl-discuss-help@sourceware.org; run by ezmlm Precedence: bulk List-Id: List-Subscribe: List-Archive: List-Post: List-Help: , Sender: gsl-discuss-owner@sourceware.org X-SW-Source: 2007-q4/txt/msg00034.txt.bz2 > Perhaps the manual needs to be clearer about what is computed, which > is the unique least squares solution that has minimum norm solution > coefficients |c|^2 (this only comes into play if there's a null space > - otherwise there's only one solution anyway). The idea is to > minimise any spurious components of the solution. This is usually > what is needed when fitting data and pretty standard. > > When the rhs=0 and there is one singular value there is still an > infinite number of solutions, as the overall scale is > undetermined. The least squares choice is to return the minimum norm > solution, i.e. zero. > > In the help-gsl question, which was about fitting the equation for a > plane, the appropriate method is orthogonal regression rather than > linear regression, as there's no dependent variable. Yes, after thinking about the problem some more I realized its a bit more complicated than I originally thought.