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

Alejandro Weinstein alejandro.weinstein@gmail....
Tue Nov 20 20:47:46 CST 2012

On Tue, Nov 20, 2012 at 5:56 PM, Virgil Stokes <vs@it.uu.se> wrote:
> On 2012-11-21 01:48, Alejandro Weinstein wrote:
>> On Tue, Nov 20, 2012 at 5:36 PM, Virgil Stokes <vs@it.uu.se> wrote:
>>> which is clearly not PD, since the it's 3 eigenvalues (diagonal
>>> elements) are all negative.
>> But why you expect R to be PD?
> Because    R*R^T = P (a covariance matrix). One important reason for
> using the QR factorization in the KF is to ensure that R is always PD
> during the recursions.

As you said, P = R * R^T, which is PD, even if R is not. Please check
the definition of QR decomposition: R is _not_ required to be PD.

Looking at the paper, they in fact use P = R * R ^ T, as in eq. (1).
They never use R alone. So the fact that R is not PD should not be an
issue. Can you show your code? I'm curious to see how the fact that R
is not PD makes a difference.


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