Re: [eigen] unpleasant surprise mit math functions |

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*To*: "eigen@xxxxxxxxxxxxxxxxxxx" <eigen@xxxxxxxxxxxxxxxxxxx>*Subject*: Re: [eigen] unpleasant surprise mit math functions*From*: "Wood, Tobias" <tobias.wood@xxxxxxxxx>*Date*: Thu, 27 Sep 2012 10:02:05 +0100*Accept-language*: en-US*Acceptlanguage*: en-US*Thread-index*: Ac2cjsSN7DiibZEqRh2udTUz95+dvQ==*Thread-topic*: [eigen] unpleasant surprise mit math functions

On 26 Sep 2012, at 20:13, Helmut Jarausch wrote: > On 09/26/2012 06:43:10 PM, rupp@xxxxxxxxxxxxxxxx wrote: >> Hi Helmut, >> >> just out of curiosity: >> which unified behavior do you expect for exp(A), sin(A) and cos(A), >> with A being a dense matrix? If you want it to act on each entry >> separately, then the result of exp(A) is probably not what a >> significant number of people may expect. However, using a power >> series expansion for exp, sin and cos is clearly not equivalent to >> sin(t.array())... > > There are 2 papers title "19 )(new) dubious ways to compute the matrix > exponential". > Therefore, a general package like Eigen shouldn't even try to compute > the "matrix versions". I'm not totally sure what you mean by this statement, but just to point out that Eigen does provide a matrix exponential function in unsupported/Eigen/MatrixFunctions. Although there are (at least) 19 ways to compute the matrix exponential, Eigen uses the algorithm from N Higham's 2005 paper, which is good enough to be the default in Matlab. However, this seems a good time to mention this article: http://blogs.mathworks.com/cleve/2012/07/23/a-balancing-act-for-the-matrix-exponential/?s_eid=PSM_2096 which does highlight some situations where the algorithm can fail (if you have to have matrix elements that differ by 18 orders of magnitude!). There is a link at the bottom of the article to an improved algorithm developed by Higham's PhD student. I wanted to implement and contribute this to Eigen, but frankly the new algorithm makes my head spin, so I feel under-qualified for such work. Toby

**References**:**Re: [eigen] unpleasant surprise mit math functions***From:*Helmut Jarausch

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