Re: [eigen] Matrix exponential |

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] Matrix exponential*From*: Benoit Jacob <jacob.benoit.1@xxxxxxxxx>*Date*: Thu, 9 Apr 2009 13:58:55 +0200*Dkim-signature*: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:mime-version:received:in-reply-to:references :date:message-id:subject:from:to:content-type :content-transfer-encoding; bh=IIgnPWTjblfXa93Inv+1oWUvFheuOgQ1RMB6Qprz5l0=; b=XMPn8r56kN++FUMP1fEv27xU8idihx42b7t9pqS10pfaRelinQI/3xqMS2X6yY3l13 0XYDZY3S8aetjt+OrrkrOC7r60tD53Xaf7PHlQHCEI3gY9vcKnhMWNCaJwVSoBXFe/b4 We3OmjG9tgTY1/6PjPTr/6gazbJA0eMvsfOl8=*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=gSJAYC2v6KAMDZJALlK7k7/9D70fznevP6GC6c6wW3u37L7sQb/T2yQZNIqZVU7EsV rrMFe9GdhtOTv5V2h5/52F8WCUZusmrM/Wj69RGlWMEYghaA8mrgcDrG9LFYSiFtZklZ +HvNsUUjk10zlor+RlTvYhtrrCEYb136UN87g=

2009/4/9 Jitse Niesen <jitse@xxxxxxxxxxxxxxxxx>: > Hello, > > I'm working on how to calculate the matrix exponential (for sparse > matrices). We programmed it in Matlab, but we're also looking at > implementing it in C++. To my surprise, this task is also listed in the todo > file. However, I don't like the algorithm suggested there, which is to use > the eigendecomposition - that runs into problems when the eigenvalues come > close together. Is there any interest in a routine using > scaling-and-squaring, which is in my opinion the most standard approach? I didn't know that was the standard approach: it sounds much more expensive. But then, I understand the problems you're talking about in the cases where eigenvalues aren't well separated. We could always have both functions. Maybe what we really need is an eigendecomposition that handles well the case of multiple eigenvalues! That would be generally useful. > I already have a working implementation, but it's rather slow because LU > uses complete pivoting. Any progress on implementing a partial pivoting > version? Otherwise, that will have to be tackled first. Yes, I want to add partial pivoting to LU soon, actually i already sent a quick and dirty patch to the list a while ago, and i'll definitely do that for eigen 2.1, but i also want to make it work by taking recursive blocks so it's cache-friendly. So yes, you can implement with the current LU and count on a much faster LU later. Cheers, Benoit

**References**:**[eigen] Matrix exponential***From:*Jitse Niesen

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