41CL Quiz: Determinant of 30x30 antiIdentity matrix

05312018, 03:42 PM
Post: #41




RE: 41CL Quiz: Determinant of 30x30 antiIdentity matrix
The CL Expanded Memory ROM found on TOS. QRG is there.


05312018, 05:39 PM
Post: #42




RE: 41CL Quiz: Determinant of 30x30 antiIdentity matrix
(05312018 03:42 PM)Gene Wrote: The CL Expanded Memory ROM found on TOS. QRG is there. Thx. I have this!! I forgot the YRegisters in the CL are in fact the Expanded memory register set. You know, the halflife of unused knowledge is very short... Bob Prosperi 

05312018, 06:41 PM
(This post was last modified: 06012018 06:04 AM by Ángel Martin.)
Post: #43




RE: 41CL Quiz: Determinant of 30x30 antiIdentity matrix
(05312018 05:39 PM)rprosperi Wrote:(05312018 03:42 PM)Gene Wrote: The CL Expanded Memory ROM found on TOS. QRG is there. Also available at Monte's "Other Docs" page: http://systemyde.com/hp41/documents.html I've finally decided to incorporate the enhancements in the SANDMATRIX module, which has multiple additions over the original Matrix function set. I'm actually amazed to see this working, believe me when i tell you it wasn't trivial... So the SandMatrix now offers the following options to create a matrix, depending on its name in ALPHA: 1. 1st. character "R" => array will be located in the standard registers; R00 to the Rmax. defined by SIZE. 2. 1st. character "Y" => array will be located in the expanded CL YRegisters; Y000 to Y1023 3. any other 1st. character => array will be located in XMemory The new option is obviously #2. All functions in the SandMatrix are fully functional with the three types of arrays. For example, with "R22,Y22" in ALPHA and CLST , calling MMOVE will copy the array from standard registers to expanded registers. Ahh the sweet taste of success... ;) "To live or die by your own sword one must first learn to wield it aptly." 

05312018, 08:09 PM
Post: #44




RE: 41CL Quiz: Determinant of 30x30 antiIdentity matrix
Thanks for the puzzle Ángel. It seems to make sense that the determinate of such a matrix would boil down to a lot of 1*1  1+1 (or zero) terms with a few 0  1*1 terms (1). So, 29 is related to the dimension. I think it's something like norm(30), or 435 terms, most of which are zero.
Anyway, I thought about how this would look as a function of the diagonal value from 0 to 2. Interesting: Outside that range, the numbers get big/small very quickly! Nice how concise such an analysis turns into Python. I'm thinking of writing a python to RPN compiler. Maybe someone here has already done so? 

05312018, 08:19 PM
Post: #45




RE: 41CL Quiz: Determinant of 30x30 antiIdentity matrix
(05312018 08:09 PM)MikeOShea Wrote: I'm thinking of writing a python to RPN compiler. Maybe someone here has already done so? Yes, see here. 

06012018, 01:41 AM
Post: #46




RE: 41CL Quiz: Determinant of 30x30 antiIdentity matrix  
06022018, 11:41 PM
Post: #47




RE: 41CL Quiz: Determinant of 30x30 antiIdentity matrix
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Hi, Ángel: (05312018 07:40 AM)Ángel Martin Wrote: BTW the benchmark with the 30x30 antiidentity matrix is now 16 seconds to calculate its determinant  down from the 11 minutes using the FOCAL program. And the result is 29.000000000 exact to 9 decimal places. Not bad! ;) You can do better ... ;) ... Try this one out instead with your new machinecode functionality: Consider the determinant D(N) = determinant of this NxN matrix: 3 1 1 ... 1 1 4 1 ... 1 1 1 5 ... 1 ... ... ... ... ... 1 1 1 ... N+2 For example, D(3) = 50. Now compute and time D(11), D(13),D(30). If you succeed in getting the correct integer values, see if you can find an exact formula for D(N) (Hint: after a while, D(n) ends with more and more 0's). Congratulations on your costly (in terms of your time and effort) achievement. Regards and have a nice weekend. V. . All My Articles & other Materials here: Valentin Albillo's HP Collection 

06032018, 03:56 AM
Post: #48




RE: 41CL Quiz: Determinant of 30x30 antiIdentity matrix
(06022018 11:41 PM)Valentin Albillo Wrote: Consider the determinant D(N) = determinant of this NxN matrix: On my HP 50g: D11 = 1486442880. D13 = 283465647360. D30 = 3.31153874629E34 « → n « '(n+1)!*(Psi(n+2)Psi(1))' EVAL » » Probably not the formula you have in mind, but that’s what I could get so far. D(n) = (n + 1)!*Hn+1 Regards, Gerson. 

06032018, 05:36 AM
(This post was last modified: 06032018 05:36 AM by Gerson W. Barbosa.)
Post: #49




RE: 41CL Quiz: Determinant of 30x30 antiIdentity matrix  
06042018, 10:04 PM
Post: #50




RE: 41CL Quiz: Determinant of 30x30 antiIdentity matrix
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Hi, Gerson: (06032018 03:56 AM)Gerson W. Barbosa Wrote: On my HP 50g: All Ok, of course. Quote:Probably not the formula you have in mind, but that’s what I could get so far. Exactly the formula I had in mind: D(N) = (N+1)!*(1+1/2+1/3+...1/(N+1)) = (N+1)!*H(N+1) where H(N) is the sum of the first N terms of the Harmonic series. For example: D(10) = FACT(11)*(1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11) = 120543840 The sum of the Harmonic series is thus: H(N) = D(N1)/FACT(N) which surely would be one of the most inefficient ways to compute the sum. :D ... For example H(11) = D(10)/FACT(11) = 120543840/39916800 = 3.01987734488 = 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11 = 3.01987734488 This 2line HP71B program will create and display the NxN matrix, then compute and display its determinant for arbitrary N: 1 DESTROY ALL @ OPTION BASE 1 @ INPUT N @ DIM A(N,N) @ MAT A=CON 2 FOR I=1 TO N @ A(I,I)=I+2 @ NEXT I @ MAT DISP A; @ DISP @ DISP DET(A) >RUN ? 11 3 1 1 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 1 1 1 1 5 1 1 1 1 1 1 1 1 1 1 1 6 1 1 1 1 1 1 1 1 1 1 1 7 1 1 1 1 1 1 1 1 1 1 1 8 1 1 1 1 1 1 1 1 1 1 1 9 1 1 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 12 1 1 1 1 1 1 1 1 1 1 1 13 1486442880 Still, the idea was that Ángel would use these determinants to check his new microcoded matrix handling functions to see what timings and accuracy they would achieve. Let's hope he sees these posts and obligues. Are you listening, Ángel ? :D Thanks, Gerson, and regards. V. . All My Articles & other Materials here: Valentin Albillo's HP Collection 

06052018, 07:42 AM
(This post was last modified: 06052018 07:52 AM by Ángel Martin.)
Post: #51




RE: 41CL Quiz: Determinant of 30x30 antiIdentity matrix
Yes, I'm listening :D
in fact I've been busy fixing a few glitches in the MCODE as a result of the beta testing, which this test case has also contributed to... Thanks for the example, it is indeed an interesting one (but of course it *had* to be given its source ;). First off, there's a few remarks to be made:
With those two remarks made, here's how I did it. First, the program used to create the matrices and calculate the determinant: 01 LBL "DDN"  expects n in XReg 02 RCL X 03 E3 04 / 05 + 06 "Y"  matrix will use the YRegisters, starting at Y_001 07 MATDIM 08 1 09 MCON  in the SandMatrix 10 CLX 11 MSIJA 12 2 13 LBL 00 14 1 15 + 16 MSC+ 17 SF 25 18 J+ 19 FS?C 25 20 GTO 00 21 MDET 22 END And these are the results: D(11) = 1,486,442,880.0  in 1.8 seconds D(13) = 2.834656472 E11  in 2.01 seconds D(30) = 3.311538747 E34  in about 11 seconds Not bad again, in fact surprisingly good. Using Gerson's values as the reference, these results are practically as accurate as those obtained using the equivalent formula D(n) = (n+1)!*H(n+1).  which can be easily programmed using the Harmonic function in the SandMath (step #4 in the trivial program below): 01 LBL "DN"  n is expected in X 02 1 03 + 04 HARM 05 LASTX 06 FACT 07 * 08 END which returns respectively (in just a few milliseconds this time): D(11) = 1,486,442,880.0 D(13) = 2.834656474 E11 D(30) = 3.311538746 E34 Thanks for the case study, it's helped with the beta testing and adds another interesting problem to the list. Saludos, Á. "To live or die by your own sword one must first learn to wield it aptly." 

06052018, 01:40 PM
(This post was last modified: 06052018 02:11 PM by Ángel Martin.)
Post: #52




RE: 41CL Quiz: Determinant of 30x30 antiIdentity matrix
ok, let's get crazy and pull all the stops as if we were really playing organ...
why stop at 1,024 registers if there are 3,072 available on the CL for the expanded RAM? You guessed what's coming... ;) Hint: A 55x55 antiIdentity matrix determinant anyone? or rather how about D(40) = ?? Let's try: 40, XEQ "DDN" = (.. and 79.6 seconds later ...)=> 1.439439902 E50 but wait, there's more  n=55 will require 3,025 registers ! 55, XEQ "DDN"= (.. and 1 min 99 secs later ... ) = 3.278748200 E75 he, he... read my lips: it's *working*!! "To live or die by your own sword one must first learn to wield it aptly." 

06052018, 02:51 PM
Post: #53




RE: 41CL Quiz: Determinant of 30x30 antiIdentity matrix
Congrats Ángel!
Well done, as always... (06052018 01:40 PM)Ángel Martin Wrote: 55, XEQ "DDN"= (.. and 1 min 99 secs later ... ) = 3.278748200 E75 Does this translate to 2 min 39 secs, or is it just a typo? Greetings, Massimo +×÷ ↔ left is right and right is wrong 

06052018, 05:24 PM
Post: #54




RE: 41CL Quiz: Determinant of 30x30 antiIdentity matrix
(06052018 01:40 PM)Ángel Martin Wrote: 40, XEQ "DDN" = (.. and 79.6 seconds later ...)=> 1.439439902 E50 On my HP 50g, in Exact mode: 40 « → n « '(n+1)!*((COMB((n+2)!+n+1,n+1)1)/(n+2)!(n+2)*FLOOR((COMB((n+2)!+n+1,n+1)1)/((n+2)*(n+2)!)))' EVAL » » TEVAL > 143943990158833766399457315931645601623572480000000 s: 54.2999 But for a moment I'd forgotten about the KISS principle: 40 « 1 + ! 0 1 LASTARG FOR i i INV + NEXT * EXPAND » TEVAL > 143943990158833766399457315931645601623572480000000 s: 3.1465 

06052018, 09:55 PM
Post: #55




RE: 41CL Quiz: Determinant of 30x30 antiIdentity matrix
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Hi, Ángel: (06052018 01:40 PM)Ángel Martin Wrote: ok, let's get crazy and pull all the stops as if we were really playing organ... why stop at 1,024 registers if there are 3,072 available on the CL for the expanded RAM? See ? I told you in post #47: "You can do better ... ;) And you did ! Quote:but wait, there's more  n=55 will require 3,025 registers ! My most sincere congratulations, truly excellent speed and accuracy. Wish you'd apply your amazing microcoding talents to my beloved HP71B ... perhaps some day ... :D Best regards. V. . All My Articles & other Materials here: Valentin Albillo's HP Collection 

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