Re: [eigen] Problem inverting a Matrix4f with Eigen 2.0.0 |

[ Thread Index | Date Index | More lists.tuxfamily.org/eigen Archives ]

*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] Problem inverting a Matrix4f with Eigen 2.0.0*From*: Benoit Jacob <jacob.benoit.1@xxxxxxxxx>*Date*: Mon, 19 Jul 2010 09:51:53 -0400*Dkim-signature*: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:mime-version:received:received:in-reply-to :references:date:message-id:subject:from:to:content-type :content-transfer-encoding; bh=rzAnnPNR/JgaxzG6He1RlYUr0FtoXLwZQf+Nfarhk+M=; b=A6e72JKVp9uRVnqEkpOqwZCTOuvhR2l7A+cKiLUFBMsOJ8wtQI+5dm8b4IwSLJfMBO oYXrA03zloGBgmvZPEIFKxZqo9asFyVsAI0AZ14UOVUvYv9I6Xp8JO4D0+ccfJuVzPNb GMnoOvr9w3PykZraJlsR9gTxMKJPfe6HoncXg=*Domainkey-signature*: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=mime-version:in-reply-to:references:date:message-id:subject:from:to :content-type:content-transfer-encoding; b=P2i3kGRRp5agYsdN7qE9bcLLMqejEaS/IEJ47OaKEPkdO5uJmH1OXnq6IDRG1bMk5B 5MIAXZtECx0EDHIe6BMQRigcZlSO4IdIgmN5yJd6WbNiodRRufs4fbbMzryG8ILty2y5 Hzr/abNlyUed3wpoZIi2sSN+50V+3rq7oky6A=

2010/7/19 Helmut Jarausch <jarausch@xxxxxxxxxxxxxxxxxxx>: > On 07/18/10 00:32:26, Benoit Jacob wrote: >> 2010/7/17 Jitse Niesen <jitse@xxxxxxxxxxxxxxxxx>: >> > On Sat, 17 Jul 2010, Benoit Jacob wrote: >> > >> >> Another reason why we decided not to expose condition numbers in >> Eigen >> >> is that for the main purpose they're used for, namely checking if >> a >> >> result is reliable, there is a better approach which is: check the >> >> result itself. For example, if you want to check how accurate your >> >> matrix inverse is, just compute matrix*inverse and see how close >> it >> is >> >> to the identity matrix. Nothing beats that! When it comes to more >> >> general solving with potentially non full rank matrices, this is >> even >> >> better, because the condition number of the lhs matrix alone >> doesn't >> >> tell all you need to know (it also depends on your particular >> rhs), >> so >> >> the approach we're recommending in Eigen, to compute lhs*solution >> and >> >> compare with rhs, is the only way to know for sure how good your >> >> solution is. >> > >> > I'm not sure I agree. The residual (lhs * solution - rhs) is >> certainly >> > useful, but so is the condition number (norm of A multiplied by >> norm >> of >> > A^{-1}, where I deliberately don't specify the norm used). If the >> residual >> > is zero but the condition number is huge then you probably should >> not trust >> > the solution, >> >> If (lhs * solution - rhs) is small compared to rhs, then what more >> could you ask for? > > A lot more! > A linear equation A x = b is a mathematical problem. > If it has a solution the users wants an approximation to that. > If I find a vector x which satisfies norm(A*x-b) = tiny in finite > arithmetic, that doesn't say much about norm(x_computed - x_true) > unless I have a bound on the condition number. I see, x = A^{-1} A x ~= A^{-1} b so what you need to conclude how accurate x is, is a bound on the norm of A^{-1} which is closely related to certain notions of condition number. OK, that makes sense. Good point! Benoit

**References**:**Re: [eigen] Problem inverting a Matrix4f with Eigen 2.0.0***From:*Benoit Jacob

**Re: [eigen] Problem inverting a Matrix4f with Eigen 2.0.0***From:*Helmut Jarausch

**Messages sorted by:**[ date | thread ]- Prev by Date:
**[eigen] Compiling Eigen2-based code in Eigen3** - Next by Date:
**Re: [eigen] Problem inverting a Matrix4f with Eigen 2.0.0** - Previous by thread:
**Re: [eigen] Problem inverting a Matrix4f with Eigen 2.0.0** - Next by thread:
**Re: [eigen] Problem inverting a Matrix4f with Eigen 2.0.0**

Mail converted by MHonArc 2.6.19+ | http://listengine.tuxfamily.org/ |