Lambert W functions on WP 34s



#2

It is impressive to see the Lambert W functions included in WP 34s.

However, the W-1 function give incorrect results. Example:

x ex = -0.2 has two solutions

-0.259171

-2.542641

On the emulator W(-0.2) correctly returns the first solution.

But W-1(-0.2), which is expected to give the second solution,

instead returns -0.163746


#3

FYI, W^-1 represents the inverse of W in the WP 34S.


#4

I see. What I thought was the Lambert W-1 function is

actually the inverse of the Lambert W0 function. Which
could also be easily calculated as x ex.


W-1 is not so easily calculated. So would be more useful
to have on the calc.


#5

With the next software build, you'll find both branches on the WP 34S: Wp for the principal branch and Wm=W-1 for the lower branch. The latter is calculated by an XROM routine, so it may not be as accurate as Wp.


#6

Great!

#7

Easily done on the HP-12C:

01 CHS               
02 1/x
03 STO 0
04 STO 1
05 LN
06 RCL 0
07 *
08 RCL 1
09 x<>y
10 -
11 x=0
12 GTO 15
13 LST x
14 GTO 04
15 LST x
16 RCL 0
17 /
18 CHS
19 GTO 00

-0.2 R/S -> -2.542641358

http://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum/archv019.cgi?read=159032

Edited: 25 Nov 2011, 10:54 a.m.


#8

It would be easy enough to include a user code programme to calculate this branch of the W function in the device -- for real arguments only. I'd guess 100 or so bytes of precious flash.

Alternatively, use this program:

	01  LBL'W[sub-1]'
02 LocR 02
03 STO .02
04 +/-
05 1/x
06 STO .00
07 STO .01
08 LN
09 RCL[times] .00
10 RCL .01
11 x[<->] Y
12 -
13 x=0?
14 SKIP 03
15 DROP
16 RCL L
17 BACK 10
18 DROP
19 RCL L
20 RCL/ .00
21 +/-
22 x[<->] .02
23 STO L
24 x[<->] .02
25 RTN

Store it in one of the flash segments and you've got the W-1 function. It behaves like a keyboard command in that Last X is set properly and the stack is not damaged. The argument range is not correctly validated however.


- Pauli


#9

Pauli, [sub-1] ??


#10

Yeah, [sub-1] which displays as 1. We don't have a subscript minus or minus 1. All our codes for subscripts are [sub-X].

The other convention I've seen is Wm and Wp for w-1 and W0 respectively.


- Pauli


#11

Exactly. And we feature [sub-m] and [sub-p] ... :-)


#12

I know that was why I mentioned them ;-)


- Pauli

#13

Just in case it's useful, functions WL1 and WL0 are available in the SandMath-II module for the HP-41, both implemented in MCODE.

The module is available at TOS for V41 and i41CX usage - also possible to burn into Clonix, MLDL2k, etc. of course.

Cheers,
ÁM

Edited: 25 Nov 2011, 10:49 a.m.


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