Re: [eigen] first benchmark of large and sparse matrix |

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] first benchmark of large and sparse matrix*From*: "Gael Guennebaud" <gael.guennebaud@xxxxxxxxx>*Date*: Mon, 23 Jun 2008 10:13:37 +0200*Dkim-signature*: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:received:received:message-id:date:from:to :subject:in-reply-to:mime-version:content-type :content-transfer-encoding:content-disposition:references; bh=7UN9GBICMQ+9rjzP5WsVTHZvs/Eamzy/HdVYwJ6sHLM=; b=Wdps5bJCtEehLc6kv/YDM7QAo8hF4uAvxgmTrgk1i2VE3r/q5JUi5JJQu1JTm+ji6g VBxM35gyNGVvleWaxkwOi7VSOQciPPiznJtzEbKy9X1dZxbjayWPj3G6KXCXZoqQn3Oy 2wY3fpOHd0aW1FOnmKUNbRix1TTMTPHcKX648=*Domainkey-signature*: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=message-id:date:from:to:subject:in-reply-to:mime-version :content-type:content-transfer-encoding:content-disposition :references; b=pCkOgL5srkhLT5L3nhsUKhoaWrdIzeTK8+tx06Nx9Rk5GxoaqtFwxd45BFg8a6jrzL vp/yzypYini5TzDnqGxBef584Y6fnXwdT10NK9GQDCWxWoOGcBRir7RU6kkJ4kJdBlar x1PDSIcGATEHPAW0USkBycCopAqFiB8wFNQiw=

On Mon, Jun 23, 2008 at 7:30 AM, Benoît Jacob <jacob@xxxxxxxxxxxxxxx> wrote: > On Monday 23 June 2008 07:05:30 Benoît Jacob wrote: >> this is of high interest for Krita and for Step and probably has >> countless interesting applications > > I forgot to mention that support for sparse matrices should be of high > interest to OpenBabel (chemistry lib, also considering eigen2): if I remember > well they sometimes apply solving algorithms to the adjacency matrix of a > molecule, so for a molecule with N atoms the matrix is NxN and has 2N nonzero > entries. As far as I remember they used to apply dense algorithms, so N^3 > complexity which is only doable for small N (like 10^2) while some molecules > they deal with have up to 10^5 atoms. hm... if there are only 2N nonzero entries then using a sparse matrix is pointless: the overhead is one int per nonzero entry. Actually, for such a particularly tough problem it has to be reformulated such that you don't have to explicitly form the matrix, then you reformulate it has a set of overlapping local problems and you iterate multiple times till you converge to the global solution (I don't know the name of this kind of approcach but I guess there exist a name for it !) This is standard practice in CG. Also, I think it's very important to support natively linear system solvers as I know many users would never accept a dependency on another lib.... especially if this lib depends itself on lapack that is the case of most of them. > > This example suggests that adjacency matrices of large graphs are a countless > source of applications for sparse matrices... > > Cheers, > > Benoit >

**Follow-Ups**:**Re: [eigen] first benchmark of large and sparse matrix***From:*Benoît Jacob

**References**:**[eigen] first benchmark of large and sparse matrix***From:*Gael Guennebaud

**Re: [eigen] first benchmark of large and sparse matrix***From:*Benoît Jacob

**Re: [eigen] first benchmark of large and sparse matrix***From:*Benoît Jacob

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