Re: [eigen] Positive Definitenes? |

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] Positive Definitenes?*From*: Benoit Jacob <jacob.benoit.1@xxxxxxxxx>*Date*: Wed, 3 Mar 2010 06:56:42 -0500*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; bh=OqoQ2cqjKLB6UXJZHKT63aX4pgOMSS3uoW8muxAXZiw=; b=Op01/PlG0jjqJnwlJ++8bX26D0RvKJJaYlaZAhuN5sCtOqE7/DxRkZzMEfPl9VCe9C hXgivhwafHgIugsKflR9Ia1/S3sKpe+/CHDejoYBfvKTY1cpntif+6AYKoAU/QHcR9Cl 2s7zjARz50wRReCWNyIk1sNetXwr2ZtSIi5mQ=*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; b=MHnqmwthDs8sT4JIrVU2M3LbWwUhRrb0CSHD626V94opcjvUtjizuUmmm7EgTiz6li f3N6wkiCscvNs88XHBoBHgtnNyzoZIywfBLbwjoEKx90HYLHDuULTg1a6Ou0DdVO41Za PAEZpzc7GwccZS0hYWHvXB5XeplVDUakybYBw=

2010/3/3 Cyril Flaig <cflaig@xxxxxxxxxxx>: > On 2010-03-02 19:27, Benoit Jacob wrote: >> 2010/3/2 Cyril Flaig <cflaig@xxxxxxxxxxx>: >>> The Cholesky decomposition works only if the matrix is positive >>> definite. If the decomposition fails then eigen sets a >>> m_isPositiveDefinite to false, doesn't it? >>> >>> Or is this deprecated and not used in the new version? >> >> This is deprecated indeed. > > As far as I know. The fastest way to determine the postive definitnes is > to check the diagonal if all entries are >=0. This is indeed a necessary condition for positiveness. > If this is true then > attempt a Cholesky decomposition. If it exists then the matrix is > positive definite. The problem with this approach is that it's an all-or-nothing test that one has to perform at the time of the decomposition itself. Making this useful in practice would require us to let the user pass a choice of a threshold at the time of the decomposition itself (so an API change) and even then, that would be pretty bad as, if the user passes a higher threshold, he compromises the accuracy of a subsequent solve(). So this forces a compromise between the invertibility check and the precision of solve(). Benoit > > -cyril > >

**Follow-Ups**:**Re: [eigen] Positive Definitenes?***From:*Gabriel

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**Re: [eigen] Positive Definitenes?***From:*Benoit Jacob

**Re: [eigen] Positive Definitenes?***From:*Cyril Flaig

**Re: [eigen] Positive Definitenes?***From:*Benoit Jacob

**Re: [eigen] Positive Definitenes?***From:*Cyril Flaig

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