This would be a lot more readable, to me, if you supplied a J implementation that matched the informal math notation (which is easy to read for people that mostly already know what you were going to say).
Thanks, -- Raul On Thu, Oct 3, 2013 at 10:11 AM, km <[email protected]> wrote: > Cool examples given in Gilbert Strang's Introduction to Linear Algebra are > > > From Section 6.2 -- The solution to u(k+1) = A uk starting from u0 is > > uk = A^k u0 = S Lambda^k S^-1 u0 , so that > > uk = c1 lambda1^k x1 + ... + cn lambdan^k xn provided > > u0 = c1 x1 + ... + cn xn (xk is eigenvector corrresponding to eigenvalue > lamdak) > > Lambda is a diagonal matrix with the eigenvalues of A on the diagonal, and S > is a > square matrix whose columns are the eigenvectors. Strang illustrates with the > Fibonnaci sequence F0 F1 F2 ... , setting uk = ( F(k+1) , Fk ) and u0 = (1 > , 0) . > > > From Section 6.3 -- The solution to u' = A u starting from u(0) is > > u(t) = c1 e^(lambda1 t) x1 + ... + cn e^(lambdan t) xn provided > > u(0) = c1 x1 + ... + cn xn . The solution can be expressed as > > u(t) = e^(A t) u(0) with the matrix exponential e^(A t) . > > Equations involving y'' reduce to u' = A u by combining y' and y into > > u = (y' , y) > > > --Kip Murray > > Sent from my iPad > >> On Oct 3, 2013, at 6:10 AM, Raul Miller <[email protected]> wrote: >> >> I was looking at those the other day and ran into a variety of difficulties. >> >> I'll not bore you with the details, but I'll admit that I would love >> to see some pages devoted to example usages. >> >> I'm not really looking for comprehensive, in-depth documentation - >> that's already available through web searching ... if I can understand >> what terms I need to use to search on. What I'm looking for are cool >> examples - things that probe the possibilities, bits of prose perhaps >> which hint at relevant search terms. Failed attempts might also be >> useful, as stepping stones for finding or writing more better or >> slightly beautiful expositions. >> >> Thanks, >> >> -- >> Raul >> >>> On Wed, Oct 2, 2013 at 12:27 PM, km <[email protected]> wrote: >>> Here is a resource that should be better known. To use it you load >>> ~addons/math/mt/mt.ijs --Kip Murray >>> >>> >>>>>> On Mon, Apr 8, 2013 at 3:17 AM, Kip Murray <[email protected]> wrote: >>>>> >>>>> Igor Zhuravlof provides j routines that model LAPACK routines for >>>>> eigenvalues and eigenvectors. See "matrix toolbox" >>>>> >>>>> ~addons/math/mt >>>>> >>>>> with contents summarized in >>>>> >>>>> ~addons/math/mt/mt.ijs >>>>> >>>>> I have not tried them but would expect them to run in j701JHS. >>> >>> Sent from my iPad >>> >>>> On Oct 2, 2013, at 9:21 AM, Raul Miller <[email protected]> wrote: >>>> >>>> J's support for mechanisms to compute eigenvalues has been rather >>>> messy. And, by messy I mean that it looks like we rarely exercise >>>> these mechanisms - we don't have unit tests on the entry points to be >>>> run before uploading library updates, we don't have particularly good >>>> documentation on the code we have and there are other problems. >>>> >>>> Here's an example I stumbled over today: >>>> >>>> docs_jlapack_'' >>>> |value error: dirs >>>> | dirs jpathsep path,'doc/*.lap' >>>> require'dirs' >>>> not found: /Users/rdmiller/Applications/j64-801/bin/dirs >>>> |file name error: script >>>> | 0!:0 y[4!:55<'y' >>>> require 'dir' >>>> docs_jlapack_'' >>>> |value error: dirs >>>> | dirs jpathsep path,'doc/*.lap' >>>> getscripts_j_ 'dir' >>>> >>>> >>>> So here's a question: does anyone have the time and energy to put into >>>> this mess? >>>> >>>> Thanks, >>>> >>>> -- >>>> Raul >>>> ---------------------------------------------------------------------- >>>> For information about J forums see http://www.jsoftware.com/forums.htm >>> ---------------------------------------------------------------------- >>> For information about J forums see http://www.jsoftware.com/forums.htm >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
