Raul M. & Roger H. have both provided useful verbs that would allow one to enter complex numbers with a zero imaginary part, thus maintaining a complex data type in memory. Thanks! As usual, Roger's solution is quite elegant.
Unfortunately, that's only half the problem. The other half of the issue is how to displaying a complex number such as (1j0) with a zero imaginary part, instead of just the real part. Even if the complex number is stored in memory, J throws the zero away on output. I haven't had much luck coding a zero-imaginary-part-displaying verb, but then I am far from a competent J programmer. If we did have a display verb that could always show the zero-imaginary-part of complex numbers in storage, then we would have to use that verb every time we displayed output that might be complex, if we wanted to see any zero imaginary part. Raul said: "However, when J displays the number, it routinely removes irrelevant information." Relevancy is in the eyes of the beholder. It turns out that J's complex numbers are useful for other things besides complex arithmetic: eg. intervals. Also, I know I've seen complex numbers used for other interesting J applications somewhere, where complex number pairs were used in a novel way, but I can't remember where. Having a native datatype that compactly supports number pairs turns out to be pretty handy for lots of applications besides complex arithmetic. Of course, boxed pairs could likely be used in these applications instead, but this would likely add the requirement for various custom manipulation verbs. Common operations with complex numbers are native in J. In any case, these other applications that use J's complex invariably need to always maintain both parts of the complex number. Hiding imaginary zeros in these applications causes lots of exception-handling. It seems it would be more consistent to simply have the J interpreter not throw away zero imaginary parts when entering *or* displaying complex numbers. J doesn't throw away any other kind of imaginary parts, just zeros. I have always liked J for it's extreme consistency and minimized rule sets. Hiding zero complex parts seems to me to be an arbitrary rule with minimal benefit. Aside from a small increase in storage, what would be the downside of eliminating the "zero discard" feature in J? Complex number arithmetic would be unaffected. Skip Skip Cave Cave Consulting LLC On Thu, Aug 18, 2016 at 6:04 PM, Roger Hui <[email protected]> wrote: > cmpx=: j.&0 > > datatype cmpx 1 0 > complex > datatype cmpx 3 4 > complex > datatype cmpx 5.6 7 > complex > datatype cmpx 3j4 > complex > > (-: cmpx) 1 0 > 1 > (-: cmpx) 3 4 > 1 > (-: cmpx) 5.6 7 > 1 > (-: cmpx) 3j4 > 1 > > > > On Thu, Aug 18, 2016 at 3:53 PM, Raul Miller <[email protected]> > wrote: > > > You could make a verb that converts a number to complex: > > > > interval=: 1j1 - 1j1 - ] > > > > interval 0 > > > > 0 > > > > datatype interval 0 > > > > complex > > > > > > -- > > > > Raul > > > > > > > > On Thu, Aug 18, 2016 at 6:37 PM, Skip Cave <[email protected]> > > wrote: > > > > > Interesting. The vanishing imaginary zero is more than just a display > > > issue though. More like a storage issue: > > > > > > 1j1 + 1j_1 > > > > > > 2 > > > > > > datatype 1j1 + 1j_1 > > > > > > complex > > > > > > > > > 2j0 > > > > > > 2 > > > > > > datatype 2j0 > > > > > > integer > > > > > > > > > Though both 1j1 + 1j_1 and 2j0 are complex numbers, only the addition > > > process produces a complex result that can be stored. It looks like > that > > > when you input a complex number with a zero imaginary part, J ignores > the > > > complex part, and stores the number as a real number (could be boolean, > > > integer, or floating). Thus J looses the fact that the number was > entered > > > as a complex number. > > > > > > > > > So if you want to maintain a complex datatype, you can't simply > assign a > > > noun with a value that has a zero imaginary part. You must find a way > to > > > compute the value with the zero imaginary part (thus avoiding direct > > > entry), then assign it. > > > > > > > > > In complex arithmetic, 2 & 2j0 are essentially the same, so J dropping > > the > > > imaginary part probably saves storage by making this an integer. This > > won't > > > matter, as long as you are staying in the complex domain. > > > > > > > > > However, when you start using J's complex representation for other uses > > > such as interval bounds (and other uses), this will be an issue. For > > > example, say you want to input an interval such as _0.5j0 to a > > computation > > > in Roger's unum lab. The lab can output intervals this way, you just > > can't > > > input them. You can input the interval 0j0.5 and everything's ok. > > > Unfortunately, not the mirror interval on the negative side. > > > > > > > > > Skip > > > > > > > > > > > > Skip Cave > > > Cave Consulting LLC > > > > > > On Thu, Aug 18, 2016 at 3:49 PM, Raul Miller <[email protected]> > > > wrote: > > > > > > > Actually, J usually stores the number in whatever format it happens > to > > > > be storing it as. > > > > > > > > However, when J displays the number, it routinely removes irrelevant > > > > information. > > > > > > > > Something similar happens when you enter numbers. > > > > > > > > Thus: > > > > > > > > 2j0 > > > > 2 > > > > datatype 2j0 > > > > integer > > > > 1j1 + 1j_1 > > > > 2 > > > > datatype 1j1 + 1j_1 > > > > complex > > > > > > > > Thanks, > > > > > > > > -- > > > > Raul > > > > > > > > > > > > On Thu, Aug 18, 2016 at 1:58 PM, Skip Cave <[email protected]> > > > > wrote: > > > > > Roger, > > > > > > > > > > Ah! the light dawns! J doesn't keep the type of the data as > entered > > by > > > > the > > > > > user. If the imaginary part is zero, J stores the number as real. > If > > > the > > > > > number is one or zero (with or without an imaginary zero part), it > > > stores > > > > > the number as boolean. If the number is not floating and not > > > fractional, > > > > it > > > > > stores the number as integer (again ignoring any zero imaginary > > part). > > > > > > > > > > R1 =. _0.5 > > > > > > > > > > I1 =. _0.5j0 > > > > > > > > > > R1 = I1 > > > > > > > > > > 1 > > > > > > > > > > > > > > > R2 =. 1 > > > > > > > > > > I2 =. 1j0 > > > > > > > > > > R2 = I2 > > > > > > > > > > 1 > > > > > > > > > > > > > > > datatype 0j0 > > > > > > > > > > boolean > > > > > > > > > > datatype _0.5j0 > > > > > > > > > > floating > > > > > > > > > > datatype 1j0 > > > > > > > > > > boolean > > > > > > > > > > datatype 1j1 > > > > > > > > > > complex > > > > > > > > > > datatype 2j0 > > > > > > > > > > integer > > > > > > > > > > Skip Cave > > > > > Cave Consulting LLC > > > > > > > > > > On Thu, Aug 18, 2016 at 3:41 AM, roger stokes < > > > [email protected]> > > > > > wrote: > > > > > > > > > >> Skip, > > > > >> > > > > >> Thanks for your message and thanks for all the trouble you have > gone > > > to. > > > > >> Let me try to explain the results you are seeing. > > > > >> > > > > >> First, the important thing to note is that J itself displays a > > > complex > > > > >> number with imaginary part zero as looking like a real number. To > > > > >> check this, try entering 0.5j0 _0.5j0 directly into any J session: > > > > >> > > > > >> > > > > >> 0.5j0 _0.5j0 > > > > >> 0.5 _0.5 > > > > >> > > > > >> Second, the result you are seeing is indeed complex: > > > > >> > > > > >> Z =: JNFS SFJN _0.25 > > > > >> > > > > >> datatype Z > > > > >> complex > > > > >> > > > > >> but it looks like a real number (and hence your objection) > > > > >> > > > > >> Z > > > > >> _0.5 > > > > >> > > > > >> but it does have the value that you say it should have > > > > >> > > > > >> Z = _0.5j0 > > > > >> 1 > > > > >> > > > > >> Hope this is useful > > > > >> > > > > >> Regards > > > > >> > > > > >> > > > > >> On Wed, Aug 17, 2016 at 8:35 PM, Skip Cave < > [email protected] > > > > > > > >> wrote: > > > > >> > > > > >> > All, > > > > >> > > > > > >> > I agree that the unum for _0.25 should be "_0.5j0" > > > > >> > My previous statement was wrong in its declaration of what > *should > > > > be*, > > > > >> but > > > > >> > it wasn't wrong about what *is wrong in the lab*. > > > > >> > > > > > >> > I said: "Shouldn't converting _0.25 to a SORN, then back to a > > > > >> > J number produce _0j0.5, NOT _0.5? " > > > > >> > > > > > >> > I should have said: > > > > >> > "Shouldn't converting _0.25 to a SORN, then back to a > > > > >> > J number produce > > > > >> > > > > > >> > > > > > >> > > > > > >> > _0.5j0, NOT _0.5? " > > > > >> > > > > > >> > The key here is the words "NOT _0.5". > > > > >> > > > > > >> > > > > > >> > Here are the lab results copied directly from the session: > > > > >> > > > > > >> > > > > > >> > > > > > >> > JNFS SFJN 0.25 > > > > >> > > > > > >> > 0j0.5 > > > > >> > > > > > >> > > > > > >> > > > > > >> > JNFS SFJN _0.25 > > > > >> > _0.5 > > > > >> > > > > > >> > > > > > >> > So as I tried to state in my previous post: The lab is producing > > > wrong > > > > >> > results for conversions of _0.25 to SORNS and back to J numbers. > > The > > > > lab > > > > >> > should produce " > > > > >> > > > > > >> > _0.5j0 > > > > >> > " for the result of > > > > >> > > > > > >> > JNFS SFJN _0.25 > > > > >> > > > > > >> > For that matter, the lab produces wrong results for the whole > > > interval > > > > >> from > > > > >> > 0 < x < 0.5 > > > > >> > > > > > >> > > > > > >> > > > > > >> > JNFS SFJN _0.25 > > > > >> > > > > > >> > _0.5 > > > > >> > > > > > >> > > > > > >> > JNFS SFJN _0.35 > > > > >> > _0.5 > > > > >> > > > > > >> > > > > > >> > JNFS SFJN _0.1 > > > > >> > > > > > >> > _0.5 > > > > >> > JNFS SFJN _0.499 > > > > >> > > > > > >> > _0.5 > > > > >> > > > > > >> > > > > > >> > JNFS SFJN _0.5 > > > > >> > > > > > >> > _1r2 > > > > >> > > > > > >> > > > > > >> > I believe that all these results should be " > > > > >> > > > > > >> > _0.5j0 > > > > >> > " in the lab. > > > > >> > > > > > >> > Then the lab gets it right again once we cross the _1r2 border > > > > (heading > > > > >> > negatively): > > > > >> > > > > > >> > > > > > >> > > > > > >> > JNFS SFJN _0.6 > > > > >> > > > > > >> > _1j_0.5 > > > > >> > > > > > >> > Skip > > > > >> > > > > > >> > > > > > >> > > > > > >> > Skip Cave > > > > >> > Cave Consulting LLC > > > > >> > > > > > >> > On Wed, Aug 17, 2016 at 10:47 AM, roger stokes < > > > > [email protected] > > > > >> > > > > > >> > wrote: > > > > >> > > > > > >> > > Typo in my last: "gives 0.5j0" should be "Gives "_0.5j0" > > > > >> > > > > > > >> > > Sorry. > > > > >> > > > > > > >> > > On Wed, Aug 17, 2016 at 4:43 PM, roger stokes < > > > > >> [email protected]> > > > > >> > > wrote: > > > > >> > > > > > > >> > > > Skip, > > > > >> > > > > > > > >> > > > you wrote "Shouldn't converting _0.25 to a SORN, then > back > > > to > > > > a > > > > >> > > > J number produce _0j0.5, NOT _0.5? " > > > > >> > > > I believe the result given is correct, because _0.25 is in > the > > > > >> > > > interval (_0.5 0) in 4-bit precision. > > > > >> > > > > > > > >> > > > A =: SFJN _0.25 > > > > >> > > > > > > > >> > > > > > > > >> > > > (> A) # UNUMS > > > > >> > > > +------+ > > > > >> > > > ¦_1r2 0¦ > > > > >> > > > +------+ > > > > >> > > > > > > > >> > > > Rendering this as a complex number, with real for lower > bound > > > _1r2 > > > > >> > > > and imaginary for upper bound 0 gives 0.5j0 which is > presented > > > by > > > > J > > > > >> > > > as a real number because imag = 0 > > > > >> > > > > > > > >> > > > ] B =: JNFS A > > > > >> > > > _0.5 > > > > >> > > > datatype B > > > > >> > > > complex > > > > >> > > > B = _0.5j0 > > > > >> > > > 1 > > > > >> > > > > > > > >> > > > > > > > >> > > > I rest my case. > > > > >> > > > > > > > >> > > > These conversions are not yet finished nor documented, in > fact > > > the > > > > >> > whole > > > > >> > > > thing is pretty rough. On that subject, let me mention that > > > > until I > > > > >> > get > > > > >> > > it > > > > >> > > > cleaned up, users should avoid one-character lower case > > > variables, > > > > >> > > because > > > > >> > > > of my sloppy style of doing global assigns to what should be > > > > local. > > > > >> > > > > > > > >> > > > I thought it would be best to use rationals for the values, > > > rather > > > > >> than > > > > >> > > > reals, > > > > >> > > > so that the computations for the lookup tables would be > exact. > > > > >> > > > > > > > >> > > > Regards > > > > >> > > > > > > > >> > > > On Wed, Aug 17, 2016 at 3:02 PM, Skip Cave < > > > > [email protected]> > > > > >> > > > wrote: > > > > >> > > > > > > > >> > > >> Playing with 4-bit unums (compact SORNS), I thought I would > > see > > > > how > > > > >> > the > > > > >> > > >> J-to-SORN & SORN-to-J conversions worked: > > > > >> > > >> > > > > >> > > >> JNFS SFJN _3 > > > > >> > > >> > > > > >> > > >> __j_2 > > > > >> > > >> > > > > >> > > >> JNFS SFJN _2.5 > > > > >> > > >> > > > > >> > > >> __j_2 > > > > >> > > >> > > > > >> > > >> JNFS SFJN _2 > > > > >> > > >> > > > > >> > > >> _2 > > > > >> > > >> > > > > >> > > >> JNFS SFJN _1.5 > > > > >> > > >> > > > > >> > > >> _2j_1 > > > > >> > > >> > > > > >> > > >> JNFS SFJN _1 > > > > >> > > >> > > > > >> > > >> _1 > > > > >> > > >> > > > > >> > > >> JNFS SFJN _0.5 > > > > >> > > >> > > > > >> > > >> _1r2 > > > > >> > > >> > > > > >> > > >> JNFS SFJN _0.25 > > > > >> > > >> > > > > >> > > >> _0.5 NB. ?? > > > > >> > > >> > > > > >> > > >> JNFS SFJN _0 > > > > >> > > >> > > > > >> > > >> 0 > > > > >> > > >> > > > > >> > > >> JNFS SFJN 0 > > > > >> > > >> > > > > >> > > >> 0 > > > > >> > > >> > > > > >> > > >> JNFS SFJN 0.25 > > > > >> > > >> > > > > >> > > >> 0j0.5 > > > > >> > > >> > > > > >> > > >> JNFS SFJN 0.5 > > > > >> > > >> > > > > >> > > >> 1r2 > > > > >> > > >> > > > > >> > > >> JNFS SFJN 0.75 > > > > >> > > >> > > > > >> > > >> 0.5j1 > > > > >> > > >> > > > > >> > > >> JNFS SFJN 1 > > > > >> > > >> > > > > >> > > >> 1 > > > > >> > > >> > > > > >> > > >> JNFS SFJN 1.5 > > > > >> > > >> > > > > >> > > >> 1j2 > > > > >> > > >> > > > > >> > > >> JNFS SFJN 1.75 > > > > >> > > >> > > > > >> > > >> 1j2 > > > > >> > > >> > > > > >> > > >> JNFS SFJN 2 > > > > >> > > >> > > > > >> > > >> 2 > > > > >> > > >> > > > > >> > > >> JNFS SFJN 2.5 > > > > >> > > >> > > > > >> > > >> 2j_ > > > > >> > > >> > > > > >> > > >> JNFS SFJN 3 > > > > >> > > >> > > > > >> > > >> 2j_ > > > > >> > > >> > > > > >> > > >> JNFS SFJN _ > > > > >> > > >> > > > > >> > > >> 2j_ > > > > >> > > >> > > > > >> > > >> JNFS SFJN __ > > > > >> > > >> > > > > >> > > >> __ > > > > >> > > >> > > > > >> > > >> > > > > >> > > >> This would have been easier if JNFS and SFJN could handle > > > > vectors. > > > > >> In > > > > >> > > any > > > > >> > > >> case, everything looked good, once I understood how Roger > was > > > > >> > > representing > > > > >> > > >> intervals in J as complex numbers, EXCEPT converting _0.25. > > > > >> Shouldn't > > > > >> > > >> converting _0.25 to a SORN, then back to a J number produce > > > > _0j0.5, > > > > >> > NOT > > > > >> > > >> _0.5? > > > > >> > > >> > > > > >> > > >> > > > > >> > > >> Skip > > > > >> > > >> > > > > >> > > >> > > > > >> > > >> Skip Cave > > > > >> > > >> Cave Consulting LLC > > > > >> > > >> > > > > >> > > >> On Wed, Aug 17, 2016 at 7:21 AM, Skip Cave < > > > > [email protected] > > > > >> > > > > > >> > > >> wrote: > > > > >> > > >> > > > > >> > > >> > Is there a way for the unum lab to discover where it was > > > > started > > > > >> > from, > > > > >> > > >> and > > > > >> > > >> > then set the working directory to that location, rather > > than > > > > >> having > > > > >> > > the > > > > >> > > >> > user have to set the directory? > > > > >> > > >> > > > > > >> > > >> > Skip > > > > >> > > >> > > > > > >> > > >> > Skip Cave > > > > >> > > >> > Cave Consulting LLC > > > > >> > > >> > > > > > >> > > >> > On Wed, Aug 17, 2016 at 6:47 AM, roger stokes < > > > > >> > > [email protected] > > > > >> > > >> > > > > > >> > > >> > wrote: > > > > >> > > >> > > > > > >> > > >> >> Dear All, > > > > >> > > >> >> > > > > >> > > >> >> Please accept my apologies for wasting your time, and my > > > > thanks > > > > >> > > >> >> for your patience, persistence and help. > > > > >> > > >> >> > > > > >> > > >> >> Skip, Raul, Vijay, you are quite right about 1 !: 44 . > > > > >> > > >> >> Instead of cd .... I should have said > > > > >> > > >> >> > > > > >> > > >> >> 1 !: 44 'yourdirectory' NB. full pathname is > > > > >> recommended > > > > >> > > >> >> > > > > >> > > >> >> > > > > >> > > >> >> Vijay, I made a correction following your mention of > > > > >> > > >> general/misc/fndef . > > > > >> > > >> >> This file should not be needed. > > > > >> > > >> >> > > > > >> > > >> >> > > > > >> > > >> >> Bob, thanks for the suggestion - it's a good way to > get > > > the > > > > lab > > > > >> > > >> started > > > > >> > > >> >> but there is still the need to find the other scripts. I > > > will > > > > >> > ponder > > > > >> > > >> this > > > > >> > > >> >> and see if there is a better way than as it is. > > > > >> > > >> >> > > > > >> > > >> >> Bill, thanks for the information about jconsole - I > didn't > > > > know > > > > >> > this > > > > >> > > >> >> and am very glad you mentioned it. > > > > >> > > >> >> > > > > >> > > >> >> I have now uploaded a corrected version to > > > > >> > > >> www.learningj.com/unumslab.zip > > > > >> > > >> >> . > > > > >> > > >> >> However, I hope, I believe, that the VERSION YOU ALREADY > > > HAVE > > > > >> > should > > > > >> > > >> run > > > > >> > > >> >> OK by doing this: > > > > >> > > >> >> > > > > >> > > >> >> 1 !: 44 'yourdirectory' > > > > >> > > >> >> > > > > >> > > >> >> first =: {. NB. workaround for Vijay's > > issues > > > > >> > > >> >> snd =: 1 & { > > > > >> > > >> >> > > > > >> > > >> >> load 'labs/labs' > > > > >> > > >> >> > > > > >> > > >> >> lab_jlab_ 'unums.ijt' > > > > >> > > >> >> > > > > >> > > >> >> > > > > >> > > >> >> Thanks again, everyone > > > > >> > > >> >> > > > > >> > > >> >> On Wed, Aug 17, 2016 at 4:12 AM, bill lam < > > > > [email protected]> > > > > >> > > wrote: > > > > >> > > >> >> > > > > >> > > >> >> > In the readme, it said > > > > >> > > >> >> > ... jconsole doesn't support labs > > > > >> > > >> >> > > > > > >> > > >> >> > This is incorrect. One can run labs on jconsole > > > > >> > > >> >> > and type labrun_jlab_ '' (and up arrow to recall) > > > > >> > > >> >> > to advance. > > > > >> > > >> >> > > > > > >> > > >> >> > Вт, 16 авг 2016, roger stokes написал(а): > > > > >> > > >> >> > > Dear All, > > > > >> > > >> >> > > > > > > >> > > >> >> > > I've heard it said that you don't understand a > subject > > > > >> > > >> >> > > unless you can explain it to a computer. With that > in > > > mind > > > > >> > > >> >> > > I've attempted a software implementation of > > Gustafson's > > > > Unums > > > > >> > 2.0 > > > > >> > > >> >> > > > > > > >> > > >> >> > > ( http://www.johngustafson.net/ > > > > presentations/Unums2.0.pdf > > > > >> ). > > > > >> > > >> >> > > > > > > >> > > >> >> > > If anyone is interested, there is a demo available > in > > > the > > > > >> > > >> >> > > form of a J lab. To run the lab > > > > >> > > >> >> > > > > > > >> > > >> >> > > Download www.learningj.com/unumslab.zip > > > > >> > > >> >> > > > > > > >> > > >> >> > > Unzip into any convenient directory > > > > >> > > >> >> > > > > > > >> > > >> >> > > Follow directions in the readme file > > > > >> > > >> >> > > > > > > >> > > >> >> > > Comments and criticisms appreciated. > > > > >> > > >> >> > > > > > > >> > > >> >> > > Regards > > > > >> > > >> >> > > ------------------------------ > > > > ------------------------------ > > > > >> > > >> >> ---------- > > > > >> > > >> >> > > For information about J forums see > > > > >> > > http://www.jsoftware.com/forum > > > > >> > > >> >> s.htm > > > > >> > > >> >> > > > > > >> > > >> >> > -- > > > > >> > > >> >> > regards, > > > > >> > > >> >> > ==================================================== > > > > >> > > >> >> > GPG key 1024D/4434BAB3 2008-08-24 > > > > >> > > >> >> > gpg --keyserver subkeys.pgp.net --recv-keys 4434BAB3 > > > > >> > > >> >> > gpg --keyserver subkeys.pgp.net --armor --export > > 4434BAB3 > > > > >> > > >> >> > ------------------------------ > > > > ------------------------------ > > > > >> > > >> ---------- > > > > >> > > >> >> > For information about J forums see > > > > >> > http://www.jsoftware.com/forum > > > > >> > > >> s.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 > > > > >> > > > > > ------------------------------------------------------------ > > ---------- > > > > > 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
