Re: [eigen] Eigenvalues of (lower) Hessenberg matrix |

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] Eigenvalues of (lower) Hessenberg matrix*From*: Yixuan Qiu <yixuanq@xxxxxxxxx>*Date*: Tue, 4 Apr 2017 20:16:56 -0400*Dkim-signature*: v=1; a=rsa-sha256; c=relaxed/relaxed; d=cos-name.20150623.gappssmtp.com; s=20150623; h=mime-version:sender:in-reply-to:references:from:date:message-id :subject:to; bh=mjb4KJmErW3o3lQ8uvpsA18jvHLMZpolaoQ8OMlfOdg=; b=aEcEYz4RoSjnGk6YosQnDmZw8//XwAno5Atf7lV8quZ7k41XzCnM9mGrf38X8JNkHA fL3ey7LyuO5EKj8TzyR7B9kTgWpgZIeidU3toTB3UvQuvcUt4/FM7ynJvOthYQS8q0p8 2B4HvTCQrcUkC0J1j8dhfj4Vmw3lgShuTPHT2in+zvPYbu1RvSI06m9GS42LR138Bf5U L1lB4ELeHd0jd58fEe+LnHmevCHQdF0f1YKf84D2vySy8EnBlzY48e9j12zESzYDUXuF RvRCHjAXfGeTDN5BZp8vBSc7ho8CzINi4Pn12BSRwnZvCs2Mx+0f4ZAr0Jr5JbwOLmJY 2l6A==*Dkim-signature*: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025; h=mime-version:sender:in-reply-to:references:from:date:message-id :subject:to; bh=mjb4KJmErW3o3lQ8uvpsA18jvHLMZpolaoQ8OMlfOdg=; b=DksYUXqMZh7EWc1a/SdwQYFz1M+rbjQNMuaLVyNAaA+Kkgl97V/c8//IhvJwAro7Ba omjBiZ0MCu1bR0tQf0m/xCr1Xxa5Qxlym7HaqqvVHVjIgQ9U7RlwqqAe57DQ2bmafUDg y412WKL1hYHQJdIvGw2QJVVJKhF0TsPEJ0Tb/zA6T2squh09cwmhwBfu3xnh/tjgQU2Q zDlM1pxNY3Cv7dKnzwiHLx3wgBcXf1/XVfEHZA2hJHlPFyoZyHcRqZtxC0LhYHzq5WgT aKGtAhSENnDF3/+8YFErngHfa33ZxoG2xJ1xsK8U32eQ8goenCMm+l1gIlWqnM1BeD+8 P4ew==

There is a parameter you can set in the constructor: http://eigen.tuxfamily.org/dox/classEigen_1_1EigenSolver.html#a7e8ab3d89ea525af5f27f1a8e805fae1

Best,2017-04-04 18:07 GMT-04:00 Ian Bell <ian.h.bell@xxxxxxxxx>:

Kind Regards, and thanks for your help,For future reference, how does one "select "computeEigenvectors = false" in EigenSolve"?For these sizes, there just isn't much more to do in Eigen-based eigenvalue solving. The solver in LAPACK for Hessenberg matrices is about two times (very roughly) faster for 16 x 16 matrices. So this is not the end, I guess, but it might be the end of my capabilities in the world of linear algebra.Yixuan,For sure I took many replicates - the timings were actually carried out in a python library built with pybind11 on top of your code, Eigen, and some of my own code. The library is actually for working with Chebyshev expansions of continuous functions and doing rootfinding with them. I'm relatively familiar with the pitfalls of profiling, so I think this is a pretty fair test.

That's certainly much better - on par at these sizes now with the naive eigenvalues() function in Eigen. I guess if you are focused on larger matrices (as most people seem to be), my matrices are rather tiny, and perhaps, less interesting.Ian

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**References**:**[eigen] Eigenvalues of (lower) Hessenberg matrix***From:*Ian Bell

**Re: [eigen] Eigenvalues of (lower) Hessenberg matrix***From:*Yixuan Qiu

**Re: [eigen] Eigenvalues of (lower) Hessenberg matrix***From:*Ian Bell

**Re: [eigen] Eigenvalues of (lower) Hessenberg matrix***From:*Ian Bell

**Re: [eigen] Eigenvalues of (lower) Hessenberg matrix***From:*Yixuan Qiu

**Re: [eigen] Eigenvalues of (lower) Hessenberg matrix***From:*Ian Bell

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