[SciPy-user] Structured matrices

Nils Wagner nwagner@iam.uni-stuttgart...
Wed Mar 14 02:31:06 CDT 2007


Barry Drake wrote:
> Nils,
> Does this matrix come from a particular application?  I'm working on
> algorithms for the non-negative matrix factorization (NMF).  With this
> matrix as input I'm getting some very strange results.  So I'm curious
> about potential applications.
>
> Cheers!
> Barry L. Drake
> GA Tech
>
Barry,

Yes indeed. The mass matrix of a multi-link pendulum (provided that the
equations of motion are linearized) exhibits this structure.
What do you mean by strange results ?

Here are some references

@article{Lobas,
         author={Lobas, L. G.},
         title={Generalized mathematical model of an inverted multilink
pendulum with follower force},
         journal={International Applied Mechanics},
         volume={41},
         pages={566-572},
         year={2005}}

@article{Gallina,
         author={Gallina, P.},
         title={About the stability of non-conservative undamped systems},
         journal={Journal of Sound and Vibration},
         volume={262},
         pages={977-988},
         year={2003}}

@article{Gasparini,
         author={Gasparini, A.~M. and Saetta, A.~V. and Vitaliani, R.~V.},
         title={On the stability and instability regions of non-conservative
                continuous system under partially follower forces},
         journal={Computer Methods in Applied Mechanics and Engineering},
         pages={63-78},
         volume={124},
         year={1995}}

I look forward to hearing from you.

Cheers,
                   Nils

> */Nils Wagner/* wrote:
>
>     Hi all,
>
>     I was wondering if the matrix family (see below) has a special name ?
>     And/or is there a way to construct this matrix via special matrices
>     (like Hankel, Toeplitz, etc.) ?
>
>
>     [[ 3. 1.]
>     [ 1. 1.]]
>
>     [[ 5. 3. 1.]
>     [ 3. 3. 1.]
>     [ 1. 1. 1.]]
>
>     [[ 7. 5. 3. 1.]
>     [ 5. 5. 3. 1.]
>     [ 3. 3. 3. 1.]
>     [ 1. 1. 1. 1.]]
>
>     [[ 9. 7. 5. 3. 1.]
>     [ 7. 7. 5. 3. 1.]
>     [ 5. 5. 5. 3. 1.]
>     [ 3. 3. 3. 3. 1.]
>     [ 1. 1. 1. 1. 1.]]
>
>     Nils
>
>     from scipy import *
>
>     def M(n):
>
>     tmp = ones((n,n))
>     for k in arange(n,0,-1):
>     tmp[:k-1,:k-1] = tmp[:k-1,:k-1] + 2
>     return tmp
>
>     for n in arange(2,8):
>     print M(n)
>     print
>
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