Re: [eigen] Instability in LLT and LDLT methods. |

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] Instability in LLT and LDLT methods.*From*: Gael Guennebaud <gael.guennebaud@xxxxxxxxx>*Date*: Wed, 28 Jan 2009 17:45:49 +0100*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=uGo9LbVohhalhLBXj072wtZRXLIcAjdiA3Gg3pPqsbY=; b=MohuSBufYiOK5Iu4Tt82lBI+Lin8cJAxcDOU/u3HhegenpveuG5RADj0/GOtxR15I3 t0dKdtONLQojHIm2vuBqIHvJkNRocTHvQOrxNwVLboSgwnSn0+JelB5oAT4h6ZyBnETe r6/dyWgwKwJoIPWKaSOyXQ+hWI+GEjZCJyyV8=*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=qv7tvaiAKDD4prdSzaY+q77OvTJfHhX6zfPPS8xgZsa/KUE9Fez7WI3yqp7EBKW2X3 pIgJNtpi50rARInF5JORDqzAs/VdXY+2YFxb+H8y1/liWvoXqEw530OysctiBVB7QNem lVOE+wMsNjyZk50BcTOzY5Krwy6d5QUTkrdX4=

see this thread: http://forum.kde.org/solved-lu-only-half-as-fast-as-lapack-t-28265-2.html#pid38539 there is a link to source code under BSD license. that's all I have :( good luck ! On Wed, Jan 28, 2009 at 5:34 PM, Keir Mierle <mierle@xxxxxxxxx> wrote: > I'm working on this now (pivoting in LDLt). Do you have a reference > for the algorithm used? It's pretty simple but a reference would help. > > Keir > > On Tue, Jan 27, 2009 at 11:42 PM, Gael Guennebaud > <gael.guennebaud@xxxxxxxxx> wrote: >> yes, indeed with LDLt we could do full pivoting and be as stable as LU >> for selfadjoint matrices while being faster. My initial motivation >> with LDLt, however, was its performance because it avoids the square >> roots... On the other hand, I remember my benchmark was not really in >> favor of the current LDLt,. I have to check again, but if so, then >> there is no reason not to keep the current LDLt version which could be >> replaced by a more complex one with full pivoting. >> >> On Wed, Jan 28, 2009 at 12:43 AM, Keir Mierle <mierle@xxxxxxxxx> wrote: >>> Probably it's better to do full pivoting. Apparently cholesky is >>> stable for semidefinite matrices when full pivoting is used: >>> >>> http://eprints.ma.man.ac.uk/1101/01/covered/MIMS_ep2008_56.pdf >>> >>> Keir >>> >>> On Tue, Jan 27, 2009 at 3:05 PM, Gael Guennebaud >>> <gael.guennebaud@xxxxxxxxx> wrote: >>>> Hi, >>>> >>>> yes, it seems the test to check whether the matrix is positive >>>> definite was too strict. I changed the absolute tolerance a bit, but >>>> we still need something better. Basically, in Cholesky we compute at >>>> each iteration 1/sqrt(x), and so x must be >0 with some epsilon... >>>> >>>> Gael. >>>> >>>> On Tue, Jan 27, 2009 at 7:35 PM, Keir Mierle <mierle@xxxxxxxxx> wrote: >>>>> Here is a testcase that fails with LLT and LDLT but works fine with >>>>> all of LU, SVD, and QR solving. Depends on my previous patch for QR >>>>> solver (or comment out the qr().solve line). >>>>> >>>>> Keir >>>>> >>>> >>>> >>>> >>> >>> >>> >> >> >> > > >

**Follow-Ups**:**Re: [eigen] Instability in LLT and LDLT methods.***From:*Keir Mierle

**References**:**[eigen] Instability in LLT and LDLT methods.***From:*Keir Mierle

**Re: [eigen] Instability in LLT and LDLT methods.***From:*Gael Guennebaud

**Re: [eigen] Instability in LLT and LDLT methods.***From:*Keir Mierle

**Re: [eigen] Instability in LLT and LDLT methods.***From:*Gael Guennebaud

**Re: [eigen] Instability in LLT and LDLT methods.***From:*Keir Mierle

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