Re: [eigen] Re: Eigenvalues and eigenvectors of 2x2 self-adjoint matrix |

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

*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] Re: Eigenvalues and eigenvectors of 2x2 self-adjoint matrix*From*: Alexey Korepanov <khumarahn@xxxxxxxxx>*Date*: Sat, 30 Jun 2012 15:59:56 -0500*Dkim-signature*: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20120113; h=message-id:date:from:user-agent:mime-version:to:subject:references :in-reply-to:content-type:content-transfer-encoding; bh=T91pAqxza9E6BXLBsmO1DQJZTbU1vlYPsRTm89+VkLo=; b=AYcr0Z0rCrReL21ijEiX5Clqlm3QLUL1FL5BwT1IZXcfU7FUhkpI7y3DeRBHFEte8Z AUtf/XvkFnMz277gkppODIGKUVcfUYe0kJlkhZPGebzyRxlts9PtcpMdqgq9y4Te9/r9 ReqPVk3PBrOt8YhZL87fk7xMKlpn/v/uqoKdoXzSgVvXOZ+1GrwpWRTrb8px69hQ5JMP W1ckO6xAiP8ciQYgvFQQ315+VW5Bw5B6RJ58Y0VA1TLmdwul3brlUQD6tOdwpkRD3EIZ 6DjLauH+J/b/Wq/fPvgvfY9wD18AZeEg4aufAeMYWcuIedHimYarxboDo5a2x7TeBroH x8YA==

Thank you much! On 06/30/2012 03:51 PM, Gael Guennebaud wrote:

sorry, its coputeDirect(): http://eigen.tuxfamily.org/dox/classEigen_1_1SelfAdjointEigenSolver.html#a85cda7e77edf4923f3fc0512c83f6323 in short: SeflAdjointEigenSolver<Matrix2f> eig; eig.computeDirect(A); eig.eigenvalues(); eig.eigenvectors(); gael On Sat, Jun 30, 2012 at 10:41 PM, Alexey Korepanov <khumarahn@xxxxxxxxx> wrote:I couldn't find a trace of directCompute() in documentation and source code. How does it work? On 06/30/2012 03:03 PM, Gael Guennebaud wrote:Hi, there is a directCompute() method that does perform the decomposition using closed form formulas for 2x2 and 3x3 real matrices. Maybe the 2x2 algorithm could be used by default if it appears to be 100% reliable, that is clearly not the case for the 3x3 case. gael On Sat, Jun 30, 2012 at 8:49 PM, Alexey Korepanov <khumarahn@xxxxxxxxx> wrote:Hello. I am comparing precision of computation of eigenvectors and eigenvalues of eigen and matlab. I started with a simple 2x2 self-adjoint case, working with long double datatype. The best method seems to be.. "by hand": solving the quadratic equation for eigenvalues, and then computing eigenvectors. Both matlab and eigen are slower and give less precise results. As a measure of precision I take Frobenius norm of AV-VD, where A is original matrix, V is matrix of eigenvectors, D is diagonal matrix of eigenvalues. Difference in precision is probably not a very big deal (like 4 last bits in long double), but it would be interesting to understand what eigen does to compute the decomposition for self-adjoint 2x2 matrix. It looks like eigen gives least precise results when discriminant of equation for eigenvalues is large. Can somebody comment on this? Best

**References**:**[eigen] MPL2 relicensing: tracking 3rd-party code***From:*Benoit Jacob

**Re: [eigen] MPL2 relicensing: tracking 3rd-party code***From:*Keir Mierle

**Re: [eigen] MPL2 relicensing: tracking 3rd-party code***From:*Gael Guennebaud

**Re: [eigen] MPL2 relicensing: tracking 3rd-party code***From:*Benoit Jacob

**Re: [eigen] MPL2 relicensing: tracking 3rd-party code***From:*Gael Guennebaud

**Re: [eigen] MPL2 relicensing: tracking 3rd-party code***From:*Benoit Jacob

**Re: [eigen] MPL2 relicensing: tracking 3rd-party code***From:*Benoit Jacob

**Re: [eigen] MPL2 relicensing: tracking 3rd-party code***From:*orzel

**[eigen] Eigenvalues and eigenvectors of 2x2 self-adjoint matrix***From:*Alexey Korepanov

**Re: [eigen] Eigenvalues and eigenvectors of 2x2 self-adjoint matrix***From:*Gael Guennebaud

**[eigen] Re: Eigenvalues and eigenvectors of 2x2 self-adjoint matrix***From:*Alexey Korepanov

**Re: [eigen] Re: Eigenvalues and eigenvectors of 2x2 self-adjoint matrix***From:*Gael Guennebaud

**Messages sorted by:**[ date | thread ]- Prev by Date:
**Re: [eigen] Re: Eigenvalues and eigenvectors of 2x2 self-adjoint matrix** - Next by Date:
**[no subject]** - Previous by thread:
**Re: [eigen] Re: Eigenvalues and eigenvectors of 2x2 self-adjoint matrix** - Next by thread:
**[eigen] HELP : SVD too slow**

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