RFC: General 1-norm estimation for some functions of sparse matrices #12609
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+ Add tests + Remove check for parallel columns in complex matrices + Remove redundant capping of number of blocks + Add more robust default value for number of blocks + Minor change in complex "sign" for type stability
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I have changed my approach slightly, and the generalization seems to work (this branch includes some minor changes to @mfasi's implementation of Higham and Tisseur's algorithm for norm estimation, but this first commit with the minor changes has been submited as a separate pull request). I had to change how |
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trailing whitespace on these - make sure they pass make check-whitespace locally
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@mfasi I have a fully working version now. I am curious to hear what you think. There maybe a slight performance hit with |
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Before you complicate the code with |
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Any updates here? Did other later PR's cover this functionality? |
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No, not yet. I haven't had time to do careful benchmarking of this code vs what @mfasi suggested. |
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I have some code elsewhere that does, but I have not delved into detailed On Wed, Oct 14, 2015 at 4:24 PM Tony Kelman notifications@github.com
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why this pr is not merged yet? |
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Would be nice to revive this, but it is also really old and may just need a fresh start. |
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I'd be happy to see it revived — I don't think I have the bandwidth to get
back into it.
Indeed my motivation was to use this in sparse expmv, so I'm sure there
will be many users for it.
…On Mon, Dec 17, 2018, 3:11 AM Viral B. Shah ***@***.*** wrote:
Would be nice to revive this, but it is also really old and may just need
a fresh start.
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Enough has changed since this was created that we'll need to substantially redo this if we want it. |
@mfasi @tkelman
Here is what I had in mind for a more general
normestroutine. At the moment there is something wrong withAc_ldiv_B!that I don't quite understand (something about the types keeps this from compiling).This attempt of a general
normestis also not type stable (thepreroutine in particular mucks that up) but that is probably fixable by replacing it with an object instead of a function.I also put
normestin a separate file just to make it easier to test it while I play with it. This pull request is really just meant to bring attention to the idea and discuss the proper way to do it.EDIT:
This is motivated by the usefulness of such a generic function for the fast and accurate computation of
f(A)*vwithout explicitly computingf(A), which is especially attractive whenAis sparse butf(A)may not be. The one interesting case where this can be applied isexpm, but potentially others as well, such aslogm,sqrtm(see below).Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators, Awad H. Al-Mohy and Nicholas J. Higham, SIAM Journal on Scientific Computing 2011 33:2, 488-511. (preprint)
Computing f(A)b for Matrix Functions f, Philip I. Davies and Nicholas J. Higham. Lecture Notes in Computational Science and Engineering Volume 47, 2005, pp 15-24 (preprint)
Estimating the condition number of f(A)b, Edvin Deadman. Numerical Algorithms December 2014 (article)
An Improved Schur--Padé Algorithm for Fractional Powers of a Matrix and their Fréchet Derivatives, Nicholas J Higham, Lijing Lin, SIAM. J. Matrix Anal. & Appl. 32 1056 2013. (preprint)