Can I use slicot to solve this particular problem? #33
Replies: 7 comments
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PS: I apologize if this is not the right place to ask this kind of questions. |
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It is ok to ask this question. I wrote the first version of MB04PB 25 years ago. I did have a version for skew-Hamiltonians, that might be a lower-level support function or never made it into SLICOT. I will check my files, but this might take a few days. |
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Wow this is great, thank you very much! |
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Currently, SLICOT does not include a routine for computing the PVL form of a skew-Hamiltonian matrix. We do have one for skew-Hamiltonian/Hamiltonian pencils. An appropriate routine for item 1 above could be DSHPVB from HAPACK package. It might be possible to include its adaptation into SLICOT Library in the near future. |
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Sounds great! I had never heard of HAPACK before. A quick google search leads me to believe the project home page is https://www.tu-chemnitz.de/mathematik/industrie_technik/software/hapack.php?lang=en . The download links are all down though :-( |
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Maybe a project for your next visit?
Best regards,
Peter
…On Wed, Feb 08, 2023 at 11:01:27PM -0800, VasileSima4 wrote:
Currently, SLICOT does not include a routine for computing the PVL form of a skew-Hamiltonian matrix. We do have one for skew-Hamiltonian/Hamiltonian pencils. An appropriate routine for item 1 above could be DSHPVB from HAPACK package. It might be possible to include its adaptation into SLICOT Library in the near future.
I don't know now an answer for item 2.
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Sure! Most HAPACK routines are already integrated into SLICOT. From the six routines you sent, two are already there, under the names MB01MD and MB01ND. |
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Here is my numerical problem: I want to compute a Hamiltonian square root of a given skew-Hamiltonian matrix.
The following article Structure-Preserving Schur Methods for Computing Square Roots of Real Skew-Hamiltonian Matrices by Zhongyun Liu, Yulin Zhang, Carla Ferreira, and Rui Ralha proposes an algorithm involving the following steps:
I think I can use Lapack to deal with 3. and 4.
My question is: can I use SLICOT to deal with 1. and/or 2. ?
I see in the doc that there is a subroutine for the Paige/Van Loan form of a Hamiltonian matrix MB04PB, but I don't see anything for the skew-Hamiltonian case.
Any tips would be greatly appreciated
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