I have been walking through some of the matrix code before adding some enhancements.
A right_kernel() will take the transpose of a matrix and call left_kernel(). left_kernel() (or kernel()) generally takes a transpose before calling some other code to row-reduce the matrix, and so on. It appears that most of the specialized code actually constructs a right kernel: IML for dense integer/rational matrices, PARI for those with entries in number fields and original Sage code for other fields. The effect is that a matrix is often (always?) transposed twice if you are really after a right kernel. I built a 2500 x 2500 matrix and multiplied it by its transpose so I could work on a symmetric matrix (thus a left or right kernel will be identical computations). sage: a=random_matrix(ZZ,2500,x=10) sage: m=a*a.transpose().change_ring(QQ) sage: time m.left_kernel() --> 5.84 seconds sage: time m.right_kernel() --> 8.58 seconds Timings on just a simple transpose of a matrix of this size pretty much account for all of the difference. It should therefore be possible to get a right kernel in this case at around 3 seconds if two transposes were eliminated. Furthermore, I've found all the transposes a bit confusing as I chase my way up and down the class hierarchy. Proposal: Place the guts of kernel computations for each (specialized) class into a right_kernel() method, where it would seem to naturally belong. Mostly these would replace kernel() methods that are computing left kernels. A call to kernel() or left_kernel() should arrive at the top of the hierarchy where it would take a transpose and call the (specialized) right_kernel(). So there wouldn't be a change in behavior in routines currently calling kernel () or left_kernel(), and we would retain Sage's preference for the left by having the vanilla kernel() give back a left kernel. The changes would be more efficient computationally and also make the code more expressive of what is really happening when and where. Comments, suggestions, warnings? --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
