On 06/03/2015 10:12 AM, Ruben Smits wrote:
> What was the return value of svd_eigen_HH, maybe the computation
> failed and the results should not be trusted? (This is a long shot I
> know ;)
The return value was/is OK, also the result is numerically ok, just not
for the convention of no negative singular values.
It seems that the algorithm only checks for negative singular values
half-way, so doing this again at the end should solve the problem.
I'll test and make a patch.

Nick

>
> R.
>
> On Thu, May 21, 2015 at 7:02 PM, Dominick Vanthienen
> <nick [dot] vanthienen [..] ... nick [dot] vanthienen [..] ...>> wrote:
>
> Hi,
>
> We're using the svd_eigen_HH algorithm of KDL
> https://github.com/orocos/orocos_kinematics_dynamics/blob/master/orocos_...
> Which should do a singular value decomposition of eigenmatrices using
> the Householder transformations.
>
> One of the properties of singular values is that the values are always
> positive.
> However, the algorithm does output sometimes negative values!
> Typically a 1 becomes a -1.
> The returned result does make some sense (U*S*V' does return the
> original matrix),
> hence we ruled out that the algorithm was interrupted somehow, or used
> bad data.
>
> However, we are unable to recreate the problem in a small subset,
> even with exact the same inputs as given at runtime.
>
> There is very little documentation on input and output, only the
> required size of matrices,
> and variable names in the code are not descriptive...
> Does anyone have an idea whether the algorithm can return negative
> S values?
> Line 174 mentions (and does) 'Singular value is made nonnegative.',
> although the values are manipulated further on...
> Does anyone could give us possible causes or a hint on how to recreate
> the problem?
>
> example:
> if you run the algorithm on the matrix Jf below, you would
> normally get:
> Sf: (the singular values)
> 1.16694
> 1.16694
> 1
> 1
> 0.856941
> 0.856941
>
> However now it returns:
> Sf:
> 1.16694
> 1.16694
> 1
> 0.856941
> 0.856941
> -1
>
> the algorithm:
> svd_eigen_HH(Jf, Uf, Sf, Vf, temp)
>
> input:
> temp:
> 0
> 7.52316e-36
> 0
> 0
> 1.24602e-35
> 0
>
> Jf: 1 0 0 0 -0.31
> -1.70024e-33
> 0 -1 -1.22461e-16 -0.31 0 0
> 0 1.22461e-16 -1 3.79628e-17 0 0
> 0 0 0 1 0 0
> 0 0 0 0 -1
> -1.22461e-16
> 0 0 0 0
> 1.22461e-16 -1
> (The matrix is negative definite, hence you would expect negative
> _eigenvalues_...)
>
> output:
> Uf: -0.759332 1.84585e-17 -1.86641e-32 0.638111 -0.127391
> -3.05582e-32
> -9.69548e-17 -0.759332 -8.91122e-17 -0.127391 -0.638111
> 6.88099e-17
> -8.71483e-33 -3.58457e-16 -0.797647 6.76459e-17 3.38842e-16
> 0.603124
> 5.50775e-17 0.650703 -2.8027e-16 -0.148658 -0.744638
> 2.17033e-16
> -0.650703 1.33574e-16 7.3859e-17 -0.744638 0.148658
> 9.76804e-17
> 7.96855e-17 -4.55151e-32 0.603124 9.11889e-17 -1.82048e-17
> 0.797647
>
> Sf:
> 1.16694
> 1.16694
> 1
> 0.856941
> 0.856941
> -1
> Vf:
> -0.650703 -3.14419e-18 -1.86641e-32 0.744638 -0.148658 3.05582e-32
> 1.14627e-16 0.650703 8.65715e-17 0.148658 0.744638
> 6.51196e-17
> 1.6563e-32 1.79184e-16 0.797647 -5.36816e-17 -2.68894e-16
> 0.603124
> 7.48371e-17 0.759332 -3.01999e-16 -0.127391 -0.638111
> -2.27218e-16
> 0.759332 -1.53333e-16 9.24941e-33 0.638111 -0.127391
> 3.99573e-35
> 2.73502e-32 -6.13455e-32 -0.603124 5.50262e-32 3.956e-31
> 0.797647
> temp:
> 0
> 2.26598e-17
> 0
> -5.50571e-21
> 0
> 3.90313e-17
>
>
> Nick
>
>
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