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

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] Re: Eigenvalues and eigenvectors of 2x2 self-adjoint matrix*From*: Gael Guennebaud <gael.guennebaud@xxxxxxxxx>*Date*: Sat, 30 Jun 2012 22:51:42 +0200*Dkim-signature*: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20120113; h=mime-version:in-reply-to:references:from:date:message-id:subject:to :content-type:content-transfer-encoding; bh=8w7ScE1HbRzyLVZau8adXCmszjKdZ4uWyJgkXeo+zdk=; b=GkhuACS/TkFnCNItJqohNTX3HdS21GobrovKfS+3ke2PhtqHWbefCcFgFFEPsFMZz5 qOpQ8pUsKOUJ9qfDbR3pLCsKGg5rlWm114Md7uLlS0KuQ+I7Jcdx9Z6msp2D+hoJGwy+ RgeHKetJiO62kMQn9vYa/0HDkORvtMnW3jJx9yL9OQ6UbrS0kN+9gXuv/ysG8pUt/hL5 D7+4eSmLquBo21wAs94F2+QJIgPMsuBVm6/PAg/z6ofRldJnpqeEIkKBwSAH3tKzzxKQ 5txuS+U+u2V8MbQXP4cmvAWCtlojkjb2BKiVQKCs64gns4W5wE+oWsLVhxN942udop05 UYnw==

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 >>> >>> >> > > > >

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

**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

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