Chris, On Wednesday, 17 August 2011 11:37:02 UTC+8, Chris Godsil wrote: [...]
> One big advantage of sage is that one can do numerical calculations > along with > computations in algebra or number theory or graph theory... > For my own work I find myself wanting to do numerical computations on > adjacency matrices > of graphs. For this matlab is not very useful because it is awkward to > generate the graphs > or read them in from a unix pipe. And if I wanted to compute an > automorphism group, I am > entirely lost. So I have been using sage for numerical computations. > The good news is that it works. > > The bad news is that it is a very frustrating experience. To > illustrate with an example, > I wanted to compute spectral decompositions of symmetric real > matrices. This means I need > actually, did you try the built-in functionality for graph eigenvalues? I imagine it would alleviate some of your complaints. E.g. sage: g=graphs.OctahedralGraph() sage: g.eigenspaces() [ (4, Vector space of degree 6 and dimension 1 over Rational Field User basis matrix: [1 1 1 1 1 1]), (-2, Vector space of degree 6 and dimension 2 over Rational Field User basis matrix: [ 1 0 -1 -1 0 1] [ 0 1 -1 -1 1 0]), (0, Vector space of degree 6 and dimension 3 over Rational Field User basis matrix: [ 1 0 0 0 0 -1] [ 0 1 0 0 -1 0] [ 0 0 1 -1 0 0]) ] > the eigenvalues and an orthogonal basis for each eigenspace. I must > use scipy/numpy, > because sage does not recognise that eigenvalues of symmetric matrices > are real. > Now the fun starts. The sort > of incantations needed to load stuff from numpy and scipy are > difficult to sort out. Basically > you make some semi-random trials until the output seems plausible, and > then hope everything > is working. The fact that the syntax for scipy and numpy differs from > that of sage is just > one more nuisance. For documentation, sage punts to the documentation > for scipy and numpy, > which is poor (and does not seem to be written by people who > understand numerical computation). > > A more general issue is that, once I decide I want to work in floating > point, I want to stay > in floating point. I do not really want to deal with stuff like: > > > sage: sin(2.0*pi) > > sin(2.00000000000000*pi) > > And I'd love to see an engineer's face when s/he enters A.kernel() and > gets > back a message about free modules. > > I agree strongly with comments of Pedro and Simon that editor+shell is > superior to the notebook > for this sort of work. > > To finish, a few key points: > 1. When I am doing numerical linear algebra, I'd like code to return > scalars, vectors, matrices. > So A.kernel() should just return either a basis or a matrix, for > example. The default routines > should call LAPACK or an equivalent, and we should have access to as > many of these as possible. > (All actual code should have been written by a professional numerical > analyst.) > > 2. Any computation which contains a floating point number or variable > should return > a floating point variable. > > 3. The syntax and behaviour should be consistent, whether I am doing > numerical linear algebra, > linear programming, semidefinite optimization, numerical > integration,... > > > On Aug 15, 3:58 pm, William Stein <wst...@gmail.com> wrote: > > Hi, > > > > If somebody walked up to *you* and asked: "Is Sage now a viable > > alternative to MATLAB?" what would you say? > > I'm especially interested in what people who do numerical/applied > > computation think. > > > > My answer: "It's very difficult for *me* to answer this question > > myself, because MATLAB is useless for most of my own > > teaching/research/work, but I realize it is very widely used in > > applied mathematics. Based on going to Scipy and the resources I've > > seen online, it appears that the Numpy/Scipy stack is extremely useful > > to actual people doing numerical computation. Maybe I'll try > > asking on sage-devel." > > > > [NOTE: I am interested in people's answers, rather than somebody > > hijacking this thread to try to define "viable alternative" or say > > this isn't a scientific survey or something. Please try not to hijack > > this thread. Thanks!] > > > > -- William > > > > -- > > William Stein > > Professor of Mathematics > > University of Washingtonhttp://wstein.org -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
