Re: [eigen] Inverse when the (dense) matrix has a known structure |

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] Inverse when the (dense) matrix has a known structure*From*: Matthieu Brucher <matthieu.brucher@xxxxxxxxx>*Date*: Wed, 25 May 2016 15:44:30 +0100*Dkim-signature*: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20120113; h=mime-version:in-reply-to:references:date:message-id:subject:from:to; bh=fA6P/qEqRn/xluuSoNZr+oMAkZXQTOI3w1NAPuBFta0=; b=RarKBOOc5Qtkzt71gmKUHjRxfoEmSM+mLUBb4MyvTnREtU1Rbj3G5PU8PbULWQk8xR dHZqhLdu41+x1bUl//coZ9PVBRRWWB3dABx9j77Ij/jDWgAkoRA0dPGphMDchylH8Xbl kYX/mhyIC1dlybOzr22Xnun6r217V1CR6l2/DFMPS5Sck+PpgdSrZuVC/qBSAODhYOCD KEeSxznTPcwk0DP8hi3FZ2U8YBu2G9vMZ3LzQJNyRS6aYSItYf4qBjDZ2VySLUZq/pCv iFUKF9vugnZtX/bTG4VS2kHnZ8FFNPaLVBvd8W7GAkPa68sxqQlETyVfhYWMUTmJpcMo QRfQ==

I tried using sympy to generate just the operations required, but it seems that even if there are far less operations that a generic inverse, the time spent int he inverse is higher than letting Eigen do it with the current pattern.

Maybe interesting if I have more holes in it though.

Thanks for the feedback!

2016-05-23 22:35 GMT+01:00 Matthieu Brucher <matthieu.brucher@xxxxxxxxx>:

There are other equations that lead to better matrices, but in this case, it is quite dense.The 6D problem may have less off diagonal elements, or small enough that they can be avoided (thus decoupling the computation, allowing to do one after the other instead of both at the same time).Indeed, a CAS could help a little bit if Eigen doesn't do better with vectorisation?X 0 X XX X X X0 X X 0X 0 X XHi,Yes, the zeros are always at the same position. For instance, for one of the 4D problem, the matrix is of the form:--2016-05-22 14:45 GMT+01:00 Dan Čermák <dan.cermak@xxxxxxxxxxxxxxxxxxx>:Hi,

depending on the degree of sparseness (and whether the non-zero elements are

always in the same positions) of your matrix, you could actually try to solve

the underlying equation system "by hand" (read as: use a computer algebra

system) and implement the resulting solution manually.

Hope that helps,

Dan

On Sunday, May 22, 2016 12:39:20 PM Matthieu Brucher wrote:

> Hi,

>

> I'm considering using Eigen for more advanced NR optimization than what I'm

> currently doing in audio real time processing (size 4x4).

> In this case, I know that the matrix has lots of zeros, something I'm not

> currently using to make my 4x4 inverse, but if I'm going for 8x8, it will

> be different.

> I've tried different ways of solving Ax=b, and it seems that computing the

> inverse is currently the best option. With more parameters, this may also

> change...

>

> Any advice as to where I should look for answers?

>

> Cheers,

>

> Matthieu

Information System Engineer, Ph.D.

Blog: http://blog.audio-tk.com/

LinkedIn: http://www.linkedin.com/in/matthieubrucher

Information System Engineer, Ph.D.

Blog: http://blog.audio-tk.com/

LinkedIn: http://www.linkedin.com/in/matthieubrucher

Blog: http://blog.audio-tk.com/

LinkedIn: http://www.linkedin.com/in/matthieubrucher

**References**:**[eigen] Inverse when the (dense) matrix has a known structure***From:*Matthieu Brucher

**Re: [eigen] Inverse when the (dense) matrix has a known structure***From:*Dan Čermák

**Re: [eigen] Inverse when the (dense) matrix has a known structure***From:*Matthieu Brucher

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