[SciPy-User] qr decompostion gives negative q, r ?

Virgil Stokes vs@it.uu...
Wed Nov 21 09:01:17 CST 2012


On 21-Nov-2012 14:22, Alejandro Weinstein wrote:
> On Wed, Nov 21, 2012 at 1:34 AM, Virgil Stokes <vs@it.uu.se 
> <mailto:vs@it.uu.se>> wrote:
>
>     But, again, it is an issue for the algorithm given in Table 3 (p. 2248 of
>     paper).  Look at step 8. and equation (30).
>
>
> I see no Table  3, nor page 2248 in the paper you attached. Which paper are 
> you talking about?
>
>     As stated in this step "The square-root of the filtered state-error
>     covariance" is returned as $T_{22}$ from step 5. where a QR decomposition
>     is performed for the triangularization. The $S_{k+1|k+1}$ matrix must have
>     diagonal elements > 0  (I leave this to you to think about). When I
>     perform step 5. with MATLAB, I *always* get a $T_{22}$ that has diagonal
>     elements > 0 for my application (which is satisfying). When I perform step
>     5. with numpy, for the same matrix on the RHS of (27) I *do not always*
>     get diagonal elements > 0  for $T_{22}$ --- herein lies the problem that I
>     have been trying to explain.
>
>
> Anyway, I would say that an algorithm that depend on the sign of the entries 
> of R is not correct.
>
> Alejandro.
>
>
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I am referring to the following paper:
Arasaratnam, I. and Haykin, S. (2011) Cubature Kalman Smoothers. /Automatica/ 
*47*, pp. 2245-2250.

Sorry about the confusion
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