HP41 Challenge: Double Integrals by INTEG Recursion

05272016, 02:35 PM
(This post was last modified: 05272016 05:33 PM by Ángel Martin.)
Post: #1




HP41 Challenge: Double Integrals by INTEG Recursion
Well folks, it's time to shake all those dormant brain cells and put them to a worthy task... if you'd agree.
Your mission is to write a program to calculate double integrals, i.e. those where the integrand is a function of two variables, say f(x,y), and where each of them is integrated along an interval  say [y1, y2] and [x1,x2] respectively. Furthermore, allow for the possibility that the inner integral limits (x1, x2) could be a function of the outer variable (y). And here is the key requirement: your program must use the INTEG function from the HP41Advantage, and do it in a RECURSIVE manner  yes, what according to the manual is not possible.. oh well. Input: the function name in ALPHA, and the four integration limits in the stack  plus a user program to define the function of course. You can use as many data registers as you want. You can (and will need to) use functions from other modules, such as the AMC_OS/X and (big hint!) the RamPAGE... I'll post my solution in a few days; it does all the work in just 31 program steps (not counting the function definition). Six data registers are used, R00R05. Can you beat that? Happy recursion! ÁM 

05302016, 03:25 PM
(This post was last modified: 05302016 03:25 PM by Ángel Martin.)
Post: #2




RE: HP41 Challenge: Double Integrals by INTEG Recursion
Well, based on the overwhelming response so far (or lack thereof :) I'll post an article with this subject in case somebody is interested at some point in time.
Cheers, ÁM 

05302016, 04:33 PM
Post: #3




RE: HP41 Challenge: Double Integrals by INTEG Recursion
I have not calculated an integral for 35 years, and never even heard of the existence of a double.
Sounds like an interesting programming challenge, I assume you want to swap in and out the buffer of the Advantage module, maintaining more than instance of the buffer. I look forward to your article, maybe I will (as you say) find time to take a stab at it, at some point in the future. Håkan 

05302016, 06:41 PM
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RE: HP41 Challenge: Double Integrals by INTEG Recursion  
05312016, 05:03 AM
Post: #5




RE: HP41 Challenge: Double Integrals by INTEG Recursion
(05302016 04:33 PM)hth Wrote: I have not calculated an integral for 35 years, and never even heard of the existence of a double. I know what you mean, but it gets even stranger: rumor has it there are even triples!! (05302016 04:33 PM)hth Wrote: Sounds like an interesting programming challenge, I assume you want to swap in and out the buffer of the Advantage module, maintaining more than instance of the buffer. I look forward to your article, maybe I will (as you say) find time to take a stab at it, at some point in the future. You're of course on the right track. The trick consists of changing the buffer14 id# that is created by the first call to INTEG, so that when the second call happens it can create another buffer14# and do its job on the second variable (X). Changing buffer id's is what function REIDBF does for a living, so there's a match made in heaven. Timing and sync up are the only details to pay attention to. For instance there cannot be any key assignments (buffer14# is placed BELOW those!)  The solution is simply to save them in XMEM at the beginning , clear them all, and restore them upon completion. Cheers, 'AM 

05312016, 05:06 AM
(This post was last modified: 05312016 05:06 AM by Ángel Martin.)
Post: #6




RE: HP41 Challenge: Double Integrals by INTEG Recursion
(05302016 06:41 PM)Csaba Tizedes Wrote: OK, I'm interested. It is possible to discuss the method on 15C?! afraid not, at least not using this trick. I don't know the insights of the 15C design but the "buffer" idea is surely not implemented in the same way, if used at all. It's more likely that the OS manages the memory directly using some other approach, not accessible to the user? 

05312016, 10:02 AM
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RE: HP41 Challenge: Double Integrals by INTEG Recursion
(05312016 05:06 AM)Ángel Martin Wrote:(05302016 06:41 PM)Csaba Tizedes Wrote: OK, I'm interested. It is possible to discuss the method on 15C?! OK, please post here one or two example what you want to show on HP41 and I can see what kind of multiple integrals you want to calculate. Thank you! Csaba 

05312016, 03:53 PM
(This post was last modified: 05312016 03:57 PM by Ángel Martin.)
Post: #8




RE: HP41 Challenge: Double Integrals by INTEG Recursion
(05312016 10:02 AM)Csaba Tizedes Wrote: OK, please post here one or two example what you want to show on HP41 and I can see what kind of multiple integrals you want to calculate. The PPC article in V8N4p31 includes some simple examples  which I'm glad to say are also solved by the recursive approach. It is embedded in the manual posted below: Solve/Integrate ROM Manual 

05312016, 04:52 PM
Post: #9




RE: HP41 Challenge: Double Integrals by INTEG Recursion
Yes, there are triple, quadruple, even quintuple integral examples available on the net. There is no end to the order of integrals, as there is in theory no end to the number of dimensions one can mathematically describe (physically there may be, but then again string / loop theory seems to have come up with quite a few)...
I would like to see the integral program enhanced to do Norder integrals, and would suggest the following quintuple integral be used as a test (since it has been discussed at http://mathfaculty.fullerton.edu/mathews...nk_15.html and they suggest several methods for the solution... With f(x,y,z,u,w) = sqrt(6x^2y^2z^2u^2w^2) evaluate integ(0,0.7) [ integ(0,0.8) [ integ(0,0.9) [ integ(0,1.0) [ integ(0,1.1) f(x,y,z,u,w) dw ] du ] dz ] dy ] dx. The answer seems to lie around 1.189. Greg 

06012016, 04:12 AM
Post: #10




RE: HP41 Challenge: Double Integrals by INTEG Recursion
(05312016 04:52 PM)gjmcclure Wrote: I would like to see the integral program enhanced to do Norder integrals, and would suggest the following quintuple integral be used as a test (since it has been discussed at http://mathfaculty.fullerton.edu/mathews...nk_15.html and they suggest several methods for the solution... This quintuple integral is easy as pie for the HP71B w/Math ROM using straight outofthebox code with no fancy programming or buffer juggling needed. Assorted results for increasing precision (1E1, 1E2, ..., 1E5) are as follows: >LIST 10 DEF FNF(X,Y,Z,U,W)=SQR(6X*XY*YZ*ZU*UW*W) 20 DEF FNG(X,Y,Z,U)=INTEGRAL(0,1.1,K,FNF(X,Y,Z,U,IVAR)) 30 DEF FNH(X,Y,Z)=INTEGRAL(0,1,K,FNG(X,Y,Z,IVAR)) 40 DEF FNI(X,Y)=INTEGRAL(0,.9,K,FNH(X,Y,IVAR)) 50 DEF FNJ(X)=INTEGRAL(0,.8,K,FNI(X,IVAR)) 60 FOR I=1 TO 5 @ K=1/10^I @ DISP K,INTEGRAL(0,.7,K,FNJ(IVAR)) @ NEXT I >DESTROY ALL >RUN .1 1.18887862667 .01 1.18887862667 .001 1.18882510429 .0001 1.18878513051 .00001 1.18878333625 so we get from 5 to 8 correct digits give or take a couple ulps, as compared to Mathematica's 1.18878359. Regards. V. . Find All My HPrelated Materials here: Valentin Albillo's HP Collection 

06012016, 05:32 AM
(This post was last modified: 06012016 05:32 AM by Ángel Martin.)
Post: #11




RE: HP41 Challenge: Double Integrals by INTEG Recursion
(06012016 04:12 AM)Valentin Albillo Wrote:(05312016 04:52 PM)gjmcclure Wrote: With f(x,y,z,u,w) = sqrt(6x^2y^2z^2u^2w^2) evaluate Glad this thread pulled you in from your greener pastures Valentín, always a pleasure to read your comments. Sure enough the 71B/MathPac is a vastly superior engine and the recursion functionality there is impressive  yet for a much humbler platform like the 41's the "buffer juggling" is a very elegant workaround  notwithstanding its inherent design limitations of course. Saludos, ÁM 

06012016, 05:35 AM
(This post was last modified: 06012016 05:38 AM by Ángel Martin.)
Post: #12




RE: HP41 Challenge: Double Integrals by INTEG Recursion
FOCAL code shown below. Includes 6 program steps to preserve and restore the Key assignments so they'll be unmodified at the end of the calculations.
Code:


06012016, 06:51 PM
Post: #13




RE: HP41 Challenge: Double Integrals by INTEG Recursion
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Hola, Ángel: (06012016 05:32 AM)Ángel Martin Wrote: Glad this thread pulled you in from your greener pastures Valentín, always a pleasure to read your comments. Thanks for your interest & kind comment, Ángel. Matter of fact I do read the forum from time to time and still use my HP calculators (mostly HP71B and HP15C) and write code for them. Alas, sharing it is a different matter as I'm still looking for an adequate venue for my many unpublished articles, routines, tips, challenges and assorted stuff. Quote:yet for a much humbler platform like the 41's the "buffer juggling" is a very elegant workaround Indeed it is. I hope you didn't take my comment as somewhat derogatory or unappreciative, far from it, I was just stating the raw fact that the HP71B w/Math ROM makes computing multiple integrals a cinch. I've seen your 41C w/enhancements solution to your own challenge and I think it's as elegant and short as possible, given the limitations you mention. Congratulations. For the record, this is the HP71B code to compute the quintuple integral using a MonteCarlo approach, a straightforward 3line affair with no Math ROM needed. >LIST 10 DESTROY ALL @ RANDOMIZE 1 @ B=.7*.8*.9*1.1 @ FOR K=1 TO 4 @ N=10^K 20 S=0 @ FOR I=1 TO N @ X=RND*.7 @ Y=RND*.8 @ Z=RND*.9 @ U=RND @ W=RND*1.1 30 S=S+SQR(6X*XY*YZ*ZU*UW*W) @ NEXT I @ DISP N,S*B/N @ NEXT K >RUN 10 1.17631976176 100 1.19138525241 1000 1.18851295632 10000 1.18896583878 The output are the results for 10, 100, 1000 and 10000 random samples, the last having 5 correct digits (save one ulp) and about as fast as the INTEGRAL approach. Best regards. V. Find All My HPrelated Materials here: Valentin Albillo's HP Collection 

06022016, 08:59 AM
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RE: HP41 Challenge: Double Integrals by INTEG Recursion
(06012016 06:51 PM)Valentin Albillo Wrote: For the record, this is the HP71B code to compute the quintuple integral using a MonteCarlo approach, a straightforward 3line affair with no Math ROM needed. Clear and elegant; sometimes I wonder why I bother with RPN and FOCAL  so cumbersome in comparison... Cheers, ÁM 

06022016, 12:14 PM
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RE: HP41 Challenge: Double Integrals by INTEG Recursion
(06022016 08:59 AM)Ángel Martin Wrote: Clear and elegant; sometimes I wonder why I bother with RPN and FOCAL  so cumbersome in comparison... Remember these JFK words: "We choose to go to the moon in this decade and do the other things, not because they are easy, but because they are hard, because that goal will serve to organize and measure the best of our energies and skills, because that challenge is one that we are willing to accept, one we are unwilling to postpone, and one which we intend to win, and the others, too." In a way, this sometimes also applies to FOCAL programming. ;) Dieter 

06032016, 03:02 AM
Post: #16




RE: HP41 Challenge: Double Integrals by INTEG Recursion
Well, this is not the solution I want, but it will work. It is based on comments above on using a Monte Carlo approach. For the HP41, this approach takes a lot of time, unless you have a 50x speed simulator! I am not satisfied with the immense time vs. lack of precision it yields. I could convert it to MCODE, but I feer that would not be worth the effort.
Nevertheless, here is my program for Ndimension Monte Carlo integration, it requires the AMC OS/X module (E3/E+, SEEDT and RAND) and my GJMV2 module (X/E3, which simply divides X by 1000): Code:
You can see from the results that Monte Carlo integration on an HP41 is not ideal, but it does seem to work. Greg. 

06032016, 01:32 PM
(This post was last modified: 06032016 01:34 PM by Namir.)
Post: #17




RE: HP41 Challenge: Double Integrals by INTEG Recursion
Valentin,
Your use of Monte Carlo integration method is ingenious! The BASIC code can be translated to other BASIC dialects, calculator programming code, and even other PC programming languages!! Hats off to you!!! Namir PS: I think I am adding your Monte Carlo solution to my list of tricks for HHC 2016. 

06032016, 02:46 PM
Post: #18




RE: HP41 Challenge: Double Integrals by INTEG Recursion
Agreed! Both Valentin's solutions are simple and elegant solutions! Actually, his 2nd solution is what lead to my HP41 solution! I just wish it was faster on the HP41.
Oh, I remember reading that some integrator solutions use what is called "QuasiMonte Carlo Integration" (Mathematica is one). Anyone know a practical way to implement that? It has to do with what random numbers are chosen (random number sets in multiple dimentions don't always yield an even distribution sample)... Greg 

06032016, 07:26 PM
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RE: HP41 Challenge: Double Integrals by INTEG Recursion
[quote='Valentin Albillo' pid='56627' dateline='1464807065']
Alas, sharing it is a different matter as I'm still looking for an adequate venue for my many unpublished articles, routines, tips, challenges and assorted stuff. [quote] I don't mean to be controversial here, but is the HPCC Datafile still off limits? Thanks, Jake 

06032016, 10:22 PM
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RE: HP41 Challenge: Double Integrals by INTEG Recursion
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Hi, Namir: (06032016 01:32 PM)Namir Wrote: Valentin, Thanks for your continued appreciation of my humble efforts, Namir, I'm glad you like them and all the better if you find further uses for them. Quote:PS: I think I am adding your Monte Carlo solution to my list of tricks for HHC 2016. You're welcome to add it as you please, I'm sure your HHC 2016 talks will be as deservedly successful as they've been on previous years. Best regards. V. . Find All My HPrelated Materials here: Valentin Albillo's HP Collection 

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