This will take a while. I"ll see what I can do. --Kip Sent from my iPad
> On Oct 3, 2013, at 1:47 PM, Raul Miller <[email protected]> wrote: > > 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
