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From Koobas <koo...@gmail.com>
Subject Re: Detecting rank-deficiency, or worse, via QR decomposition
Date Sun, 07 Apr 2013 00:45:27 GMT
Okay, you do have a problem.
Y'*Y is 10x10, but it's rank is 5.
Has to have something to do with the input data.



On Sat, Apr 6, 2013 at 7:47 PM, Sean Owen <srowen@gmail.com> wrote:

> For example, here's Y:
>
> Y =
>
>   -0.278098  -0.256438   0.127559  -0.045869  -0.769172  -0.255599
> 0.150450  -0.436548   0.209881  -0.526238
>    0.613175  -0.600739  -0.291662  -1.142282   0.277204  -0.296846
> -0.175122   0.031656  -0.202138  -0.254480
>   -0.187816  -0.889571   0.052191  -0.304053   0.498097  -0.049822
> -0.972282  -0.240532   0.155711  -0.627668
>   -0.065179  -0.055424   0.977480   0.104342   0.594501   0.033205
> -0.896222  -0.345715  -0.371288  -0.489602
>   -0.434807  -0.403650   0.264583  -0.110285  -1.318951  -0.452470
> 0.274445  -0.755704   0.313150  -0.903234
>
> and R from the QR decomposition of Y' * Y:
>
> R =
>
>    2.56259  -1.35164  -2.43837   1.27844  -0.17692  -0.30514   1.09366
>  -0.84664   0.58601   1.06875
>    0.00000   1.03316   2.61600  -0.46070  -1.46785  -0.10841   0.24828
>  -2.32186  -2.00163  -0.71470
>    0.00000   0.00000   2.11507   1.15523   1.10757   0.36407  -0.31567
>   2.77361   0.77367  -0.84055
>    0.00000   0.00000   0.00000   0.54242  -0.01545   0.21761   0.26630
>   0.13972   0.44089   0.02783
>    0.00000   0.00000   0.00000   0.00000   0.00000  -0.00000  -0.00000
>   0.00000   0.00000  -0.00000
>    0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
>  -0.00000   0.00000   0.00000
>    0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
>   0.00000   0.00000  -0.00000
>    0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
>   0.00000   0.00000  -0.00000
>    0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
>   0.00000   0.00000   0.00000
>    0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
>   0.00000   0.00000   0.00000
>
>
> Separately I tried avoiding the inverse altogether here and just using
> the QR decomposition to solve a system where necessary. Probably a
> better move anyway. But same result. I think I'm not really
> quantifying the problem properly, but it's not really a matter of
> condition number or machine precision. Condition numbers are >1 in
> these cases but not that large.
>
>
> On Sun, Apr 7, 2013 at 12:19 AM, Koobas <koobas@gmail.com> wrote:
> > I don't see why the inverse of Y'*Y does not exist.
> > What Y do you end up with?
>

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