From: Richard Kaye <R.W.Kaye@bham.ac.uk>

Date: Thu, 31 May 2007 13:24:44 +0100

To: Michael Weitzel <michael.weitzel@uni-siegen.de>

Cc: www-math@w3.org

Message-Id: <1180614284.16410.16.camel@mat140.bham.ac.uk>

Date: Thu, 31 May 2007 13:24:44 +0100

To: Michael Weitzel <michael.weitzel@uni-siegen.de>

Cc: www-math@w3.org

Message-Id: <1180614284.16410.16.camel@mat140.bham.ac.uk>

If one or other format is chosen for this, I think it would also be necessary to have a slot to describe the default value, which I guess is <mn>0</mn> or <cn>0</cn> or something like this normally. It may need to be changed if the author prefers to display a blank here, or to display the zero in a different style, or if the author is working in some mathematical context where "zero" is something other than "0". Richard On Thu, 2007-05-31 at 10:53 +0200, Michael Weitzel wrote: > Hi, > > from my point of view (as implementor of a MathML parser and a user of > Content-MathML and sparse matrix algorithms) a sparse matrix > representation should be as general and simple as possible. I personally > don't like implementing logic for many different variants of sparse > matrices (sparse, banded, upper hessenberg, ...). > > Probably the most common storage scheme is the compressed row or column > scheme. Here, a sparse matrix is stored without wasting extra memory > using three arrays: cidx[], ridx[] and data[] > > for example (taken from Octave; a compressed column scheme): > > 1 2 0 0 > 0 0 0 3 > 0 0 0 4 > > int cidx[] = {0,1,2,2,4}; > int ridx[] = {0,0,1,2}; > double data[] = {1,2,3,4}; > > a left-right, top-down enumeration of all non-zero elements works as > follows: > > int i,j; > int nc = 4; > for (j=0; j<nc; j++) > for (i=cidx[j]; i<cidx[j+1]; i++) > printf("(%i,%i) = %i\n", ridx[i],j,data[i]); > > An overview of other common storage schemes can be found here: > http://www.cs.utk.edu/~dongarra/etemplates/node372.html > > The above example is taken from: > http://www.sce.carleton.ca/faculty/adler/publications/2006/bateman-adler-octave2006-sparse-matrix.pdf > > This compressed format represents a reasonable tradeoff between memory > consumption and the overhead for randomly accessing the elements. As a > drawback it is rather hard to read. Since random access performance is > unimportant for a serialized representation MathML should just provide a > representation with minimal storage requirements. > > The OpenMath approaches suggested by Bill and David are surely > reasonable. IMO a scheme which lists rows and within rows non-zero > columns would be favorable (similar to the existing matrix-element), > i.e. something that looks like: > > <smatrix columns="4"> > <smatrixrow> > <smatrixelem col="1"><cn>1</cn></smatrixelem> > <smatrixelem col="2"><cn>2</cn></smatrixelem> > </smatrixrow> > <smatrixrow> > <smatrixelem col="4"><cn>3</cn></smatrixelem> > </smatrixrow> > <smatrixrow> > <smatrixelem col="4"><cn>4</cn></smatrixelem> > </smatrixrow> > </smatrix> > > again, for the above example: > 1 2 0 0 > 0 0 0 3 > 0 0 0 4 > > An empty <smatrixrow/> elements corresponds to a row with zeros. Since > the information about the number of columns is missing it should be > added to the smatrix-Element. > > regards, > > Michael > > Robert Miner wrote: > > Michael, > > > > I'm not knowledgeable about sparse matrix representations. Are there a > > couple "standard" ones that are widely supported, and if so, what are > > they like? If not, what is your view to the "pure OpenMath" approach > > using csymbol that David Carlisle and Bill Naylor are talking about. > > > > --Robert > > > > Robert Miner > > Director, New Product Development > > > > Design Science, Inc. > > 140 Pine Avenue, 4th Floor > > Long Beach, California 90802 > > USA > > Tel: (651) 223-2883 > > Fax: (651) 292-0014 > > robertm@dessci.com > > www.dessci.com > > ~ Makers of MathType, MathFlow, MathPlayer, WebEQ, Equation Editor, > > TexAide ~ > > > > > >> -----Original Message----- > >> From: www-math-request@w3.org [mailto:www-math-request@w3.org] On > > Behalf > >> Of Michael Weitzel > >> Sent: Wednesday, May 30, 2007 5:25 AM > >> To: www-math@w3.org > >> Subject: sparse matrix support in MathML > >> > >> > >> Hi, > >> > >> I definitely miss support for sparse matrices in Content-MathML. > > Loading > >> and saving tons of zeros involves ugly delays for large sparse > > matrices > >> and unnecessarily bloats the XML files. Sadly, MathML version 3 does > > not > >> introduce such a type. Programming environments like Matlab/Octave and > >> Maple support sparse matrices -- MathML should likewise. > >> > >> regards, > >> -- > >> Michael WeitzelReceived on Thursday, 31 May 2007 12:24:50 UTC

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