WP34S solver question

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WP34S solver question
Message #1 Posted by Reth on 12 July 2012, 8:20 a.m.

I noticed strange behaviour of the SLV function. Long story short:
comparing WP34S and (HP15C):
calculator in RAD mode, FIX 9;
formula: 2*R(tan(D) - D) - L = 0

34S: LBL D TAN RCL- L RCL* A 2 * RCL- B END
15C: LBL D TAN LSTx - RCL* 0 2 * RCL- 1 RTN
R = 6,371,000 in r.A(0)
L in r.B(1)
initial guesses: 0 ENTER 0.001;
L = 1; 34S 15C -1.570796327 0.006174837
L = 0.1; 34S 15C -1.570796327 0.002866172
L = 0.01; 34S 15C 1.570796327 0.001330163
L = 0.001; 34S 15C 0.000617487 0.000617410

HP48G (and identically HP35S) and HP42S (Free 42) give similar to 15C, right within accuracy answers.
Am I missing something?
Timing is also interesting. 15C takes almost constant time unlike the 34S.
Edited: 12 July 2012, 8:27 a.m.

Re: WP34S solver question
Message #2 Posted by Walter B on 12 July 2012, 11:00 a.m.,
in response to message #1 by Reth

Not sure you are aware of: L is the LASTx register of the WP 34S.

Re: WP34S solver question
Message #3 Posted by Gerson W. Barbosa on 12 July 2012, 11:35 a.m.,
in response to message #2 by Walter B

The lack of dedicated stack registers is one of the few weaknesses of the WP 34s, IMHO. The user should not worry about not using these forbidden alpha registers for whatever purpose. No problem LastX occupying a position on the keyboard, ./, could gladly go away.

Re: WP34S solver question
Message #4 Posted by Walter B on 12 July 2012, 12:03 p.m.,
in response to message #3 by Gerson W. Barbosa

Easy rule: use numbered registers -- keep off the lettered registers! Unlike many Pioneers, the WP 34S doesn't feature lettered registers beyond the stack and specials. Please see p.23 of the manual.

Re: WP34S solver question
Message #5 Posted by Gerson W. Barbosa on 12 July 2012, 12:39 p.m.,
in response to message #4 by Walter B

Sorry! I'll be patient and wait for the wp43s :-)

Re: WP34S solver question
Message #6 Posted by Marcus von Cube, Germany on 12 July 2012, 2:28 p.m.,
in response to message #2 by Walter B

L is used correctly as lastX here. A and B may only be used as general registers if the stack size is set to 4, not 8. Even if the solver itself runs with the stack size fixed at 4, this is not true for the called function which uses whichever stack size is set by the user.

Re: WP34S solver question
Message #7 Posted by reth on 12 July 2012, 2:58 p.m.,
in response to message #2 by Walter B

Quote:
Not sure you are aware of: L is the LASTx register of the WP 34S.
What makes you think I'm not?

Re: WP34S solver question
Message #8 Posted by Damir on 12 July 2012, 11:19 a.m.,
in response to message #1 by Reth

Initial guess 0.001 is too small.Try 0.01.
Damir

Re: WP34S solver question
Message #9 Posted by reth on 12 July 2012, 2:53 p.m.,
in response to message #8 by Damir

It is good enough for all other mentioned calculators.

Re: WP34S solver question
Message #10 Posted by Paul Dale on 12 July 2012, 6:10 p.m.,
in response to message #1 by Reth

Quote:
comparing WP34S and (HP15C)
Don't. The algorithms used underneath are very different.
In order to get faster convergence, the 34S is using more advanced algorithms than HP's solver. HP's solver is a guarded secant from my understanding whereas the 34S uses this plus quadratic and Ridder's steps.
The 34S is finding a pole rather than a root which is unfortunate but by no means impossible with either solver.
- Pauli

Re: WP34S solver question
Message #11 Posted by fhub on 12 July 2012, 6:30 p.m.,
in response to message #10 by Paul Dale

Quote:
The 34S is finding a pole rather than a root which is unfortunate but by no means impossible with either solver.
So the 34s SLV command is in fact a combined root&pole finder. ;-)
Won't it be possible to check for a pole with the following method:
If for the last iterations xk,xk+1,... the values |f(xk)|,|f(xk+1)|,... are increasing (instead of decreasing), then it must be a pole instead of a root.
Franz

Re: WP34S solver question
Message #12 Posted by Paul Dale on 12 July 2012, 6:55 p.m.,
in response to message #11 by fhub

That might work but leaves the questions:

How to know for sure that there isn't a solution in the interval?
How to sensibly look elsewhere?
The solver is being trapped because f(a) > 0 and f(b) < 0. For a continuous function there must be a root between a and b (by the intermediate value theorem). The solver can't just blindly abandon the search because the absolute value increased or it will miss legitimate roots.
HP's solver can and does get stuck in exactly the same way when it encounters a zero crossing discontinuity.
Still, there seems to be some scope for improvement here.
- Pauli

Re: WP34S solver question
Message #13 Posted by Reth on 12 July 2012, 8:27 p.m.,
in response to message #12 by Paul Dale

Quote:
HP's solver can and does get stuck in exactly the same way when it encounters a zero crossing discontinuity.
Still, there seems to be some scope for improvement here.

I'm not so much into the theory, but I can't remember HP solver getting stuck - for the problems I had to solve, or at least in this way (giving -/+90 degrees). Isn't it possible SLV to give up instead?
Cheers

Re: WP34S solver question
Message #14 Posted by Reth on 12 July 2012, 8:17 p.m.,
in response to message #10 by Paul Dale

Thanks for the explanation, I suspected so... Apparently I got fouled by the way SLV is used as described in the manual and the reference to the HP15C. Never the less, I'd prefer the old working horse, never had such problems with it. Cheers,

Re: WP34S solver question
Message #15 Posted by Paul Dale on 12 July 2012, 8:34 p.m.,
in response to message #14 by Reth

If I had the code for the old solver, I'd likely have just implemented it identically. Unfortunately, HP's code isn't available.
- Pauli

Re: WP34S solver question
Message #16 Posted by Gerson W. Barbosa on 12 July 2012, 9:15 p.m.,
in response to message #15 by Paul Dale

Quote:
Unfortunately, HP's code isn't available.
Sure, but would Prof. Kahan's article help in any way?
Hewlett-Packard Journal December 1979
"Personal Calculator Has Key to Solve Any Equation f(x) = 0" starts at page 20.
Gerson.


Re: WP34S solver question
Message #17 Posted by Paul Dale on 12 July 2012, 9:23 p.m.,
in response to message #16 by Gerson W. Barbosa

I read through that article multiple times :-) It is good and I do do most of what is written about but it isn't quite complete I think.
Regardless, if someone wants to do work on the solver it would be appreciated. The code is: solve.wp34s.
- Pauli

Re: WP34S solver question
Message #18 Posted by Valentin Albillo on 13 July 2012, 7:09 a.m.,
in response to message #16 by Gerson W. Barbosa

. Hi, Gerson:

Quote:
Sure, but would Prof. Kahan's article help in any way?
Hewlett-Packard Journal December 1979
"Personal Calculator Has Key to Solve Any Equation f(x) = 0" starts at page 20.

Forget that old article, it's quite nebulous and incomplete and thus can't be used to re-engineer the original HP Solve code.
I suggest you peruse instead this much more complete, 63-page PDF document, somewhat heavier on the math side but then it's the real thing, not a brief article:
Lecture notes on Real Root-Finding
Have a nice weekend and best regards from V.


Re: WP34S solver question
Message #19 Posted by Paul Dale on 13 July 2012, 6:48 p.m.,
in response to message #18 by Valentin Albillo

Thanks for this far more up to date reference. I hadn't seen it.
I'm not in the least bit scared of a bit of heavy mathematics :-)
Now to try to find some free time....
- Pauli

Re: WP34S solver question
Message #20 Posted by Gerson W. Barbosa on 13 July 2012, 7:34 p.m.,
in response to message #19 by Paul Dale

Quote:
I'm not in the least bit scared of a bit of heavy mathematics :-)
I am. I'm glad Valentin's reference has reached the right audience :-)
Mathematics Written in Sand might also be a good reading.
Gerson.

Re: WP34S solver question
Message #21 Posted by Paul Dale on 13 July 2012, 7:48 p.m.,
in response to message #20 by Gerson W. Barbosa

I know that document well :-)
- Pauli

Re: WP34S solver question
Message #22 Posted by �ngel Martin on 13 July 2012, 10:03 a.m.,
in response to message #15 by Paul Dale

I don't mean to add controversy and this is probably not useful anyway, but the HP code (at least the Advantage's MCODE) *is* available - as long as one doesn't mind a bit of reverse-engineering.
If you remove all the Buffer#14 handling routines it's a sizable but relatively understandable task.
FWIW, feel free to ignore it and persue a new approach. After all it may also flunk with the same example,- I didn't try it but being based ont he 15C I guess it won't.
Cheers, �M
Edited to add: tried the example in question and not surprisingly it yields the same results as the 15C.
Edited: 13 July 2012, 3:10 p.m.

Re: WP34S solver question
Message #23 Posted by Paul Dale on 13 July 2012, 6:55 p.m.,
in response to message #22 by �ngel Martin

I hadn't thought of this possibility, it would give us compatibility. The MATH pack solver is another option I guess.
I'd like to think that there has been some worthwhile progress in automatic solving in the last forty odd years though.
- Pauli

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