[sage-support] Re: create a subdiagonal matrix quickly
Rajeev Singh wrote: I should mention that these methods are all nice for this problem, but they also end up copying an awful lot of zeros. I think it would be way more efficient in general to make a zero matrix, then set the right diagonal by hand using a for loop. Don't you think using a sparse matrix would be a better thing to do in such situations? I think that choice ought to be given to the user, in the usual sparse=True/False option. If I'm doing a bunch of linear algebra on small dense matrices, it slows things down to have one sparse matrix in the mix. I think the sparse option ought to default to False (i.e., default to dense) since that seems to be the current convention. Jason --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: create a subdiagonal matrix quickly
On Jun 20, 10:18 pm, Robert Bradshaw rober...@math.washington.edu wrote: sage: n = 10 sage: m = block_matrix([0, zero_matrix(1,1), identity_matrix(n), 0]) sage: m.subdivide() # get rid of the block divisions sage: m [0 0 0 0 0 0 0 0 0 0 0] [1 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 0] [0 0 0 0 1 0 0 0 0 0 0] [0 0 0 0 0 1 0 0 0 0 0] [0 0 0 0 0 0 1 0 0 0 0] [0 0 0 0 0 0 0 1 0 0 0] [0 0 0 0 0 0 0 0 1 0 0] [0 0 0 0 0 0 0 0 0 1 0] You can also use this to get anything you want on the sub-diagonal (or pretty much anywhere). sage: m = block_matrix([0, zero_matrix(1,1), diagonal_matrix([10, 20, 30, 40]), 0]); m.subdivide(); m [ 0 0 0 0 0] [10 0 0 0 0] [ 0 20 0 0 0] [ 0 0 30 0 0] [ 0 0 0 40 0] Very nice - I didn't know about block_matrix. In addition, it seems block_matrix has an optional argument subdivide. sage: n = 10 sage: m = block_matrix([0, zero_matrix(1,1), identity_matrix(n), 0],subdivide=False) sage: m [0 0 0 0 0 0 0 0 0 0 0] [1 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 0] [0 0 0 0 1 0 0 0 0 0 0] [0 0 0 0 0 1 0 0 0 0 0] [0 0 0 0 0 0 1 0 0 0 0] [0 0 0 0 0 0 0 1 0 0 0] [0 0 0 0 0 0 0 0 1 0 0] [0 0 0 0 0 0 0 0 0 1 0] --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: create a subdiagonal matrix quickly
rickhg12hs wrote: On Jun 20, 10:18 pm, Robert Bradshaw rober...@math.washington.edu wrote: sage: n = 10 sage: m = block_matrix([0, zero_matrix(1,1), identity_matrix(n), 0]) sage: m.subdivide() # get rid of the block divisions sage: m [0 0 0 0 0 0 0 0 0 0 0] [1 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 0] [0 0 0 0 1 0 0 0 0 0 0] [0 0 0 0 0 1 0 0 0 0 0] [0 0 0 0 0 0 1 0 0 0 0] [0 0 0 0 0 0 0 1 0 0 0] [0 0 0 0 0 0 0 0 1 0 0] [0 0 0 0 0 0 0 0 0 1 0] You can also use this to get anything you want on the sub-diagonal (or pretty much anywhere). sage: m = block_matrix([0, zero_matrix(1,1), diagonal_matrix([10, 20, 30, 40]), 0]); m.subdivide(); m [ 0 0 0 0 0] [10 0 0 0 0] [ 0 20 0 0 0] [ 0 0 30 0 0] [ 0 0 0 40 0] Very nice - I didn't know about block_matrix. In addition, it seems block_matrix has an optional argument subdivide. sage: n = 10 sage: m = block_matrix([0, zero_matrix(1,1), identity_matrix(n), 0],subdivide=False) sage: m [0 0 0 0 0 0 0 0 0 0 0] [1 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 0] [0 0 0 0 1 0 0 0 0 0 0] [0 0 0 0 0 1 0 0 0 0 0] [0 0 0 0 0 0 1 0 0 0 0] [0 0 0 0 0 0 0 1 0 0 0] [0 0 0 0 0 0 0 0 1 0 0] [0 0 0 0 0 0 0 0 0 1 0] I should mention that these methods are all nice for this problem, but they also end up copying an awful lot of zeros. I think it would be way more efficient in general to make a zero matrix, then set the right diagonal by hand using a for loop. Jason --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: create a subdiagonal matrix quickly
I should mention that these methods are all nice for this problem, but they also end up copying an awful lot of zeros. I think it would be way more efficient in general to make a zero matrix, then set the right diagonal by hand using a for loop. Don't you think using a sparse matrix would be a better thing to do in such situations? Rajeev --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: create a subdiagonal matrix quickly
On Jun 20, 2009, at 3:08 AM, Pierre wrote: Of course, there are a lot of different pieces of software in the background. One strength of Sage is that it provides a uniform way of communicating with all these pieces of software, namely via Python/ Cython. This is like a good travel agent: You say that you want to go from London to Liverpool, and the travel agent gives you the cheapest or fastest or most comfortable connection: You don't need to worry that there are various train companies in the background. (Also you don't need to go via Paris if you want to travel from Strasbourg to Calais -- sorry, I couldn't resist to mention a detail that I found odd when traveling in France :) that's about what i told him. Mind you the traveling metaphor is quite apt : indeed a good travel agency will get you all the tickets for different rides with different companies, but what if one train is late ? of course the next train, operated by another company, is not going to wait. (Been to england anyone ?) Then suddenly you have to worry about companies. That sort of thing can happen with sage : when one functionality isn't perfect yet, you can usually get around it by knowing that there are several ways of doing things, several pieces of software at work. Which means all needs to be perfect if we want to avoid the criticism... well, none of this is too serious of course, and i'll take care of that colleague personally! but i thought it was interesting to point out somebody's first impression on sage, albeit a curious one. That is a very interesting first impression. For the most part, Sage seamlessly uses the many components underneath, and things are moving even more in this direction. Numerics, however, is one area where there is already a vibrant community around the SciPy/NumPy way of doing things, so exposing (rather than completely wrapping) lots of NumPy does have value. - Robert --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: create a subdiagonal matrix quickly
On Fri, Jun 19, 2009 at 1:55 PM, Harald Schillyharald.schi...@gmail.com wrote: On Jun 19, 12:50 pm, Pierre pierre.guil...@gmail.com wrote: i know numpy does it, so is it there for sage matrices also ? i don't think so, how is the numpy syntax? I think this should be an enhancement to Sage's sage.matrix.constructor.diagonal_matrix function, introducing an offset parameter. If A is a numpy array, you can do matrix(A) to get a Sage matrix. William --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: create a subdiagonal matrix quickly
Harald Schilly wrote: On Jun 19, 12:50 pm, Pierre pierre.guil...@gmail.com wrote: i know numpy does it, so is it there for sage matrices also ? i don't think so, how is the numpy syntax? I think this should be an enhancement to Sage's sage.matrix.constructor.diagonal_matrix function, introducing an offset parameter. +1. That would make it more consistent with matlab too: diag (diagonal, offset). The same syntax works for numpy. I think William's solution is the easiest for now, unless you just want to write the short function to do it. If someone wants to modify diagonal_matrix, and wants a little more ambitious project, they might work on #5110, which is basically pointing to a rewrite of diagonal_matrix at #3704 that languished and was never applied. Jason --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: create a subdiagonal matrix quickly
Hi! On 19 Jun., 18:50, Pierre pierre.guil...@gmail.com wrote: thanks for this. You might be amused by what my colleague said about SAGE, when we were talking about whether or not using numpy: SAGE is like the British train system: you have to worry about which company to use. Correct me if I'm wrong, but isn't Sage's mission creating a UNIFORM viable alternative to Ma*? Then I think this critique is something that needs to be taken very serious: It shows that there are potential users that have the impression that Sage is not uniform at all. I believe it is a wrong impression. A possible reply to your colleague: Of course, there are a lot of different pieces of software in the background. One strength of Sage is that it provides a uniform way of communicating with all these pieces of software, namely via Python/ Cython. This is like a good travel agent: You say that you want to go from London to Liverpool, and the travel agent gives you the cheapest or fastest or most comfortable connection: You don't need to worry that there are various train companies in the background. (Also you don't need to go via Paris if you want to travel from Strasbourg to Calais -- sorry, I couldn't resist to mention a detail that I found odd when traveling in France :) Also of course, Sage isn't a perfect travel agent yet. There is some functionality (here: of numpy) that can be used when working with Sage, but the user needs to know where to find the functionality; this is not uniform. If those examples pop up, I guess the natural way is to open a ticket, submit a patch, and then another functionality is available in a uniform way. Best regards, Simon --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
