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Multiple equation solver for the HP-28C (program)
Message #1 Posted by Mike Ingle on 20 Mar 2007, 3:24 p.m.

RPL calculators never had a simultaneous equation solver until the
MSLV function on the 49 series. Recently I got an HP-28C and decided
to write one small enough to run on it. I wrote the code on the 48GX
and then keyed it in on the HP-28C. The 28C has some annoying
limitations like no storage arithmetic or GET/PUT on local
variables. 

I changed to using stack storage rather than local variables. Surprisingly, all those ROLL and PICK operations use less memory than local variables even though the text is longer. The program after some optimization is 346 bytes on my 48GX. On the HP-28C I had 1274 bytes free after entering it. The 28C can solve useful systems of nonlinear equations.

The program is also useful on a 48G series machine or a 28S, and is small and simple to use. It runs quite a bit faster on the 48GX than on the 48GII, although the 48GII has a much faster editor.

To enter the program on a 28C, bring up the STACK menu first, because most of the keywords you will need are there. Make sure you enter it correctly. You probably will not be able to edit it. You may want to put a CLMF at the end so the display goes back to normal. On a 48 this is not required.

To use the solver:

Enter your expressions and save them in variables. They should be expressions for which the calculator will find a zero. If you start out with equations, put parens around both sides and change the = to a - sign.

Enter initial guesses and save them in the appropriate variables. All the variables must exist, so the expressions will eval to numbers.

Enter four lines on the stack: List of expressions to solve. List of variables to solve for. Acceptable error, indicating when to stop. Delta (small number which is added to obtain slopes.)

Run the solver. If you saved it as MSLV, enter MSLV CLMF

Example: '2*X^3+Y+7*Z-96' 'E1' STO '3*X+6*Y^3-2*Z-65' 'E2' STO '-6*X+4*Y+2*Z^3-42' 'E3' STO 1 'X' STO 2 'Y' STO 3 'Z' STO { 'E1' 'E2' 'E3' } { 'X' 'Y' 'Z' } 1E-7 1E-7 MSLV CLMF

In 4 FIX: X=3.3161 Y=2.1666 Z=2.9857

After the first iteration, you will see two lines. The first shows the iteration count starting at 1. The second shows the worst residual. The first line will count up and the second will hopefully move toward zero.

If the equations are ill-behaved the program may generate an error. Try a different set of initial guesses.

The program evals each expression at the current guess and at guess + delta for each variable. It fills out a matrix of the slopes and a vector of the values, uses the built-in linear algebra to solve the linear system, subtracts the result from the guesses, and repeats until the worst residual is less than the acceptable error.

%%HP: T(3)A(R)F(.); \<< 4 PICK SIZE DUP IDN DUP2 SWAP 1 \->LIST RDM 0 DUP DO DROP 1 + 0 3 ROLL 1 6 PICK FOR i 9 PICK i GET DUP \->NUM 3 ROLL i 1 \->LIST 3 PICK PUT 3 ROLLD 1 8 PICK FOR j 10 PICK j GET 9 PICK DUP2 STO+ 8 ROLL i j 2 \->LIST 6 PICK \->NUM 6 PICK - 12 PICK / PUT 8 ROLLD STO- NEXT ABS 4 ROLL MAX 3 ROLLD DROP NEXT DUP 5 PICK / 1 7 PICK FOR i 9 PICK i GET OVER i 1 \->LIST GET STO- NEXT DROP 3 ROLLD OVER 1 DISP DUP 2 DISP UNTIL DUP 8 PICK < END 9 ROLLD 8 DROPN \>>

-- END --

      
Re: Multiple equation solver for the HP-28C (program)
Message #2 Posted by Egan Ford on 20 Mar 2007, 4:49 p.m.,
in response to message #1 by Mike Ingle

Quote:
RPL calculators never had a simultaneous equation solver until the
MSLV function on the 49 series. Recently I got an HP-28C and decided
to write one small enough to run on it. I wrote the code on the 48GX
and then keyed it in on the HP-28C. The 28C has some annoying
limitations like no storage arithmetic or GET/PUT on local
variables. 

OT, is there any MES or SES for the 42S?

Edited: 20 Mar 2007, 4:52 p.m.

            
Re: Multiple equation solver for the HP-28C (program)
Message #3 Posted by Thomas Okken on 24 Mar 2007, 3:10 a.m.,
in response to message #2 by Egan Ford

Quote:
OT, is there any MES or SES for the 42S?

Here's a quick-and-dirty port of Mike's program to the HP-42S. It could use some work to give it a nice user interface -- entering the vectors with the function and parameter names is pretty awkward right now. See the TEST program for how to initialize the parameters etc.; it's basically identical to Mike's RPL program.
In case you want to run it on an emulator, save yourself the trouble of typing and load mes.raw instead; it contains all the five programs listed below.

- Thomas

00 { 221-Byte Prgm }
01>LBL "MES"
02 CF 21
03 STO 00
04 Rv
05 STO 01
06 Rv
07 STO "VARS"
08 Rv
09 STO "EQS"
10 STO "RES"
11 DIM?
12 Rv
13 ENTER
14 ENTER
15 NEWMAT
16 STO "DER"
17 Rv
18 1E3
19 ÷
20 1
21 +
22 STO 04
23 CLX
24 STO 02
25>LBL 00
26 1
27 STO+ 02
28 CLX
29 STO 03
30 RCL 04
31 STO 05
32>LBL 01
33 INDEX "EQS"
34 RCL 05
35 1
36 STOIJ
37 RCLEL
38 STO 07
39 INDEX "RES"
40 RCL 05
41 1
42 STOIJ
43 XEQ IND 07
44 STOEL
45 ABS
46 RCL 03
47 X<>Y
48 X>Y?
49 STO 03
50 RCL 04
51 STO 06
52>LBL 02
53 INDEX "VARS"
54 RCL 06
55 1
56 STOIJ
57 RCLEL
58 STO 08
59 RCL 00
60 STO+ IND 08
61 XEQ IND 07
62 RCL 00
63 STO- IND 08
64 INDEX "RES"
65 RCL 05
66 1
67 STOIJ
68 R^
69 RCLEL
70 -
71 RCL÷ 00
72 INDEX "DER"
73 RCL 05
74 RCL 06
75 STOIJ
76 Rv
77 Rv
78 STOEL
79 ISG 06
80 GTO 02
81 ISG 05
82 GTO 01
83 RCL "DER"
84 STO÷ "RES"
85 RCL 04
86 STO 05
87>LBL 03
88 INDEX "RES"
89 RCL 05
90 1
91 STOIJ
92 RCLEL
93 INDEX "VARS"
94 RCL 05
95 1
96 STOIJ
97 RCLEL
98 R^
99 STO- IND ST Y
100 ISG 05
101 GTO 03
102 CLA
103 RCL 02
104 AIP
105 |-"\LF"
106 ARCL 03
107 AVIEW
108 RCL 01
109 RCL 03
110 X>=Y?
111 GTO 00
112 CLD
113 END

00 { 37-Byte Prgm } 01>LBL "E1" 02 MVAR "X" 03 MVAR "Y" 04 MVAR "Z" 05 2 06 RCL "X" 07 3 08 Y^X 09 × 10 RCL+ "Y" 11 7 12 RCL× "Z" 13 + 14 96 15 - 16 END

00 { 40-Byte Prgm } 01>LBL "E2" 02 MVAR "X" 03 MVAR "Y" 04 MVAR "Z" 05 3 06 RCL× "X" 07 6 08 RCL "Y" 09 3 10 Y^X 11 × 12 + 13 2 14 RCL× "Z" 15 - 16 65 17 - 18 END

00 { 41-Byte Prgm } 01>LBL "E3" 02 MVAR "X" 03 MVAR "Y" 04 MVAR "Z" 05 -6 06 RCL× "X" 07 4 08 RCL× "Y" 09 + 10 2 11 RCL "Z" 12 3 13 Y^X 14 × 15 + 16 42 17 - 18 END

00 { 89-Byte Prgm } 01>LBL "TEST" 02 1 03 STO "X" 04 2 05 STO "Y" 06 3 07 STO "Z" 08 3 09 1 10 NEWMAT 11 ENTER 12 EDIT 13 "E1" 14 ASTO ST X 15 -> 16 "E2" 17 ASTO ST X 18 -> 19 "E3" 20 ASTO ST X 21 EXITALL 22 X<>Y 23 EDIT 24 "X" 25 ASTO ST X 26 -> 27 "Y" 28 ASTO ST X 29 -> 30 "Z" 31 ASTO ST X 32 EXITALL 33 1E-7 34 1E-7 35 XEQ "MES" 36 .END.

Edited: 24 Mar 2007, 3:29 a.m.

                  
Re: Multiple equation solver for the HP-28C (program)
Message #4 Posted by Egan Ford on 24 Mar 2007, 11:33 a.m.,
in response to message #3 by Thomas Okken

Thanks! I will give this a try.

                  
Re: Multiple equation solver for the HP-28C (program)
Message #5 Posted by Les Wright on 24 Mar 2007, 1:48 p.m.,
in response to message #3 by Thomas Okken

Thomas, this is great!

You know, I am embarrassed to say that prior to this I didn't know that alphanumerics could be stored in matrices and vectors on the 42S. I thought you had real matrices and complex matrices, and that was it.

Les

                  
Re: Multiple equation solver for the HP-28C (program)
Message #6 Posted by Les Wright on 24 Mar 2007, 5:01 p.m.,
in response to message #3 by Thomas Okken

Thomas, for my own purposes I added SF 21 and VIEW "X", etc., to the test routine so I could either see or print the solution rather than search it out in my variable directory.

Les

                        
Re: Multiple equation solver for the HP-28C (program)
Message #7 Posted by Thomas Okken on 24 Mar 2007, 9:01 p.m.,
in response to message #6 by Les Wright

Printing the solution is a nice improvement, and there are a few others that come to mind: an easier way to enter the list of functions and parameters, and using a VARMENU to let the user set initial values...
I'll try to find some time to spiff up the MES program a little bit next week.

- Thomas

      
Re: Multiple equation solver for the HP-28C (program)
Message #8 Posted by Gerson W. Barbosa on 20 Mar 2007, 5:34 p.m.,
in response to message #1 by Mike Ingle

This is worth going to the Software Library. So far there's only one 28C/S program there. You might also consider submitting it to hpcalc.org.

Quote:
I changed to using stack storage rather than local variables. Surprisingly, all those ROLL and PICK operations use less memory than local variables even though the text is longer.

This technique also makes for faster programs, as you may have noticed. I used it on this simple prime-factorizer for the HP-28C/S, which lacks it. I initially used global variables, then local variables and finally the stack only. The program is not fast because of the simple algorithm I used, but it would have been even slower otherwise.

Since we're talking about equation solver, I'd like to present a linear equations system solver for the HP-28S. It was written by one of my classmates back in 1987 and it was very useful in Circuit Analysis classes:

%%HP: T(3)A(D)F(.);
DIR
  \183\<-
    \<< VARS 1 OVER
'\183\<-' POS 1 - SUB
PURGE
    \>>
  SYS
    \<< DUP SIZE \-> l
n
      \<< n \->LIST
'EQS' STO 0 n
        FOR i 1 n
          FOR j i j
== 1 0 IFTE l j GET
STO
          NEXT 1 n
          FOR j '
EQS(j)' \->NUM
          NEXT n
\->ARRY i
          IF NOT
          THEN NEG
'VET' STO
          ELSE VET
+ ARRY\-> DROP
          END
        NEXT { n n
} \->ARRY l PURGE TRN
CONJ 'MAT' STO VET
MAT / n 1
        FOR i DUP i
GET l i GET STO -1
        STEP VET
ARRY\-> DROP { n 1 }
\->ARRY 'VET' STO
DROP
      \>>
    \>>
END

Usage and examples in this old thread:

http://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum/archv015.cgi?read=82010

Unfortunately it doesn't work on the HP-49/50G. One possible reason is TRN (transpose) behaves differently on the 28/48 and on the 49/50 calculators. Could anyone please point out other reasons?

Regards,

Gerson.

Edited: 22 Mar 2007, 7:24 a.m.

      
Now 333.5 bytes
Message #9 Posted by Mike Ingle on 21 Mar 2007, 2:32 p.m.,
in response to message #1 by Mike Ingle

Multiple equation solver now down to 333.5 bytes - this is fun!

%%HP: T(3)A(R)F(.);
\<< 4 PICK SIZE DUP IDN
DUP2 SWAP 1 \->LIST RDM
0 DUP DO DROP 1 + 0
ROT 1 6 PICK   
FOR i 9 PICK i GET DUP
\->NUM ROT i 1 \->LIST
3 PICK PUT 3 ROLLD
1 8 PICK FOR j 
10 PICK j GET 9 PICK DUP2
STO+ 8 ROLL i j 2 \->LIST
6 PICK \->NUM 6 PICK - 
12 PICK / PUT 8 ROLLD STO-
NEXT ABS 4 ROLL MAX 3 ROLLD
DROP NEXT 4 PICK / 1 6 PICK
FOR i 8 PICK i GET OVER
i 1 \->LIST GET STO- NEXT
3 ROLLD DUP2 2 DISP 1 DISP
UNTIL DUP 8 PICK < END
9 ROLLD 8 DROPN \>>


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