Re: [eigen] Avoid SVD in rotation() for Isometry |

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*To*: eigen <eigen@xxxxxxxxxxxxxxxxxxx>*Subject*: Re: [eigen] Avoid SVD in rotation() for Isometry*From*: Gael Guennebaud <gael.guennebaud@xxxxxxxxx>*Date*: Mon, 14 Jan 2019 16:30:23 +0100*Dkim-signature*: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025; h=mime-version:references:in-reply-to:from:date:message-id:subject:to; bh=4u9yxefIe9zWSu3QLcaTyeqIZr2GIwtm9Pn61aVyqDM=; b=tm0lktRRqhRBP6p3ODyD/BnXj+bm1bJ/Y6l9/NZ+wzuHg2PHqUViulnjrUY2LMunoZ fLwDQI4a5y/SDjbxkAZtY/f04/mSlOQ9aB4S0QSC9wUDb/xssk58BaCo8fO/LfGRWPJ1 Tmcka+D+WgTPOI6FesuyVhYvjf9y7A5zzUbYzZuc1OaMdm9WOm9iQmvE8cVFkv2hnoTn xOCAJYSR0en7oHBWUaPKGg3DFqTOUFD04JH6rxfEPgK5HSwIRav13ATAjeEVRJhHl0Iz iJhEB4dQ/6jF5CXRP02f9u4qxl3TcdOVHVHcu4M9fpedZlv2ng66uU6yQ5dOuU54Ec7E fZ5w==

On Fri, Jan 11, 2019 at 8:30 PM Edward Lam <edward@xxxxxxxxxx> wrote:

This is an aside, but if have a general transform, is doing Jacobi SVD the

fastest? Did anyone investigate using the newton type methods? eg.

https://www.hindawi.com/journals/ddns/2015/649423/

That's a good question. What's sure is that Jacobi SVD is not the fastest among all possible approaches but (1) it's already in Eigen and (2) it's safe.

On my side, I've also written a polar decomposition code based on the direct 3x3 symmetric eigenvalue solver we have in Eigen. IIRC, it's about 5x faster, but it's also numerically less accurate and robust in corner cases.

It would be very interesting to implement the method described in this paper to see how it compares.

gael.

-Edward

**References**:**[eigen] Avoid SVD in rotation() for Isometry***From:*Greg Coombe

**Re: [eigen] Avoid SVD in rotation() for Isometry***From:*Edward Lam

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