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| | ==a starter== |
| ...just experimenting with subpages, more info on [[http://en.wikipedia.org/wiki/Wikipedia:User_pages wikipedia]] | | ...just experimenting with subpages, more info on [[http://en.wikipedia.org/wiki/Wikipedia:User_pages wikipedia]] |
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| | After this little holiday (Holy Week), I am back to work on gsoc. As Philip Nienhuis noted on the [http://octave.1599824.n4.nabble.com/Re-Query-for-project-on-improving-matrix-functions-td4669292.html#a4669297 mailing list] there is a fair amount of work done on Matrix Functions by Higham himself. Nonetheless, it was made to work with matlab so the first issue to tack is making Gnu Octave work with it, changing it where necessary. Starting from there, then new algorithms should be introduced to the system. |
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| After this little holiday, I am back to work on gsoc. As Philip Nienhuis noted on the [http://octave.1599824.n4.nabble.com/Re-Query-for-project-on-improving-matrix-functions-td4669292.html#a4669297 mailing list] there is a fair amount of work done on Matrix Functions by Higham himself. Nonetheless, it was made to work with matlab so the first issue to tack is making Gnu Octave work with it, changing it where necessary. Starting from there, then new algorithms should be introduced to the system.
| | ==a note== |
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| ==note== | |
| First of all, I am still interested in going on with the project. | | First of all, I am still interested in going on with the project. |
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| [5] N. J. Higham and L. Lin (2011). "A Schur-Parlett Algorithm for Fractional Powers of a Matrix". Manchester Institute for Mathematical Sciences, School of Mathematics, University of Manchester. <http://eprints.ma.man.ac.uk/1677/01/covered/MIMS_ep2010_91.pdf> | | [5] N. J. Higham and L. Lin (2011). "A Schur-Parlett Algorithm for Fractional Powers of a Matrix". Manchester Institute for Mathematical Sciences, School of Mathematics, University of Manchester. <http://eprints.ma.man.ac.uk/1677/01/covered/MIMS_ep2010_91.pdf> |
| Leave a comment | | Leave a comment |
| | ---- |
| | ==updated task outline== |
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| | ...moved the definitive version to my wiki, User:Antonio_Pino |
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| '''Update:'''
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| Part of the work is already done by Prof. N.J. Higham and is available under a GPLv3+ license: [http://www.ma.man.ac.uk/~higham/mftoolbox/ The Matrix Function Toolbox][3] which is closely related to the book by the same author[4]. A [http://www.ma.man.ac.uk/~higham/mctoolbox toolbox for matrix computations][4] (The Matrix Computation Toolbox) is also provided by the same author, under the same license. Finally, a funm function is provided in the page of the NAMF project under GPLv3+. One might suggest that there is still room for improvement; because as Marco Caliari noted the toolboxes are from 2008. A review of the literature needs to be done in order to use more recent algorithms when writing the new functions.
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| '''TENTATIVE TIMELINE'''
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| '''weeks 1-2'''
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| The start should be soft for I am having the finals in this period. At this point the list of algorithms to be used must be completely defined; that is, a final review of the literature is to be done.
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| Work on the toolboxes starts here.
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| '''weeks 3-4'''
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| ''Milestone 0'': the toolboxes are working and packaged.
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| '''weeks 4-7'''
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| funm
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| ''Milestone 1'': general purpose funm based on a Schur-Parlett algorithm)
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| '''weeks 8-9'''
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| expm and logm
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| '''weeks 10-11'''
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| sqrtm
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| p-th roots (p = integer) algorithm [?]
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| ''Milestone 2'': logm, sqrtm, funm
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| '''week 12'''
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| implement trigonometric functions (I submitted a snippet of cosm [http://octave.1599824.n4.nabble.com/GSoC-2015-improving-matrix-funtcions-td4669227.html to the mailing list], [http://agora.octave.org/snippet/tqUQ/ updated])
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| '''weeks 13-14'''
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| Pencils down. Run tests on the Matrix Functions and write/review their documentation.
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| <!-- references
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| these feel like I have just one source, and I am citing it over and over again...
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| --->
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| [1] N.J. Higham. A New sqrtm for MATLAB. Numerical Analysis Report No. 336, Manchester Centre for Computational Mathematics, Manchester, England, January 1999.
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| [2] G.H. Golub and C.F. Van Loan. Matrix Computations, 4th Edition. The Johns Hopkins University Press, Baltimore, USA, 2013.
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| [3] N. J. Higham. The Matrix Function Toolbox. http://www.ma.man.ac.uk/~higham/mftoolbox
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| [4] N. J. Higham, Functions of Matrices: Theory and Computation, Society for Industrial and Applied Mathematics, Philadelphia, USA, 2008.
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| [5] N. J. Higham. The Matrix Computation Toolbox. http://www.ma.man.ac.uk/~higham/mctoolbox
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| [6] M. I. Smith (2003). [http://www.maths.manchester.ac.uk/~higham/narep/narep392.ps.gz A Schur Algorithm For Computing Matrix Pth Roots], SIAM J. MATRIX ANAL. APPL. 24, 4, 971-989.
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