Lambert W function for Excel, work on real and complex number

The Lambert W function (very efficient, fast)

See, LambertW.bas to get the VB module (attach)

Input: real or complex values from -infinity to +infinity
You can verify the results with

=IMSUM(IMPRODUCT(LambertW(COMPLEX(-100,0)),IMEXP(LambertWc(-100,0))),-1)
return:
-100.999999999999+8.5265128291212E-14i

OR

=IMPRODUCT(LambertW(-0.1),IMEXP(LambertW(-0.1)))
return:
-0.1

Lots of testing, no error found :D

Thank you! That has saved me a lot of work!

:bigyello::bigyello::bigyello:

Martin/

Thank you also.

One minor quibble: there seems to be an issue with the results that come from input values between 0 and -0.0212. As soon as it hits -0.0212 it's like hitting a wall, beyond that the results are wildly off:

-0.0218 > -0.02229
-0.0217 > -0.02219
-0.0216 > -0.02208
-0.0215 > -0.02198
-0.0214 > -0.02187
-0.0213 > -0.02177
-0.0212 > -5.51714
-0.0211 > -5.57716
...and so on, all input values from there to zero are similarly off.


Can anyone see why? Unfortunately I just lack the coding skills to pick it apart - gave it a go, but just no experience there whatsoever :-(

Any help much appreciated.

See: http://www.had2know.com/academics/la...alculator.html

"If x is within the sub interval (-1/e, 0), the calculator returns two values."

And for x = -0.0211, the calculator returns -5.577162 and -0.02156, both values are valid.
In Excel, the function return only 1 of them, I will check if i can return the more suitable one.

Aha, that all makes sense. Thank you.

Please don't spend any more time on my account - now the dual correct answers are apparent I can work with that.

Thanks again.

I searched high and low for access top a vba routine for Lambert W.

This was the best - BUT it sometimes gives the -ve branch solutions instead of the +ve.

It is also complex which i do not need.

For others I will post my solution here.

It returns the +ve branch solution only, is accurate to 9dp for most of the useful space and is reasoanbly faast

Here it is and hope others find it useful.

Bob J.

Code:

---

Public Function myLambertW(x As Double) As Double
      '
      '      Function provided on the web  seems to have starting problems and uses complex Nos where I only need real
      '      This version solves for the upper branch of the solution only
      '
      '      It uses standard Newton iteration
      '
      '      The starting value is log(x+1) which is within 40% of target from -0.33 < x < 10^100
      '
      '      Results are accurate to about 9dp from -0.3678 < x < 10^100
      '
      '      Values for second Branch are not computed ie -0.36788... < x < 0, W(x) < -1
      '
      '      There is some potential to reduce iterations for smaller +ve x values
      '      but may need to increase as x approaches -1
      '
      '                          RB Jordan 3/2/2015
      '
   
      Dim xTry As Double
      Dim Iter As Integer
     
      If x < -Exp(-1) Then
              myLambert = CVErr(xlErrValue)
              Exit Function
      End If
   
      xTry = Log(1 + x)
      For Iter = 1 To 9
          xTry = xTry - (xTry - x / Exp(xTry)) / (1 + xTry)
      Next Iter
     
      myLambertW = xTry
   
End Function

---

All:

There is a very nice presentation of the Lambert's W function (W0) and a method to calculate it based upon Halley's method in MATLAB at http://blogs.mathworks.com/cleve/201...e-1773193df571. (Google: The Lambert W Function Cleve Moler if link inactive).

Adapted VBA Code is attached

This is a very old thread, but there's some great code in it! However, all these formulae apparently work on the principal branch. I need a formula that will work on the -1 branch (as well as the principal branch). Is there such a thing?

Updated with Principal and Lower Branch...
Validated:
LambertW(-0.271,-1)=-2.00
LambertW(-0.366,-1)=-1.10
LambertW(-0.368,0)=-1.00
LambertW(-0.366,)=-0.90
LambertW(-0.090,0)=-0.10
LambertW(0,0)=0
LambertW(0.111,0)=0.10
LambertW(2.178,0)=1.00
...
LambertW(89.472,0)=3.30

Doesn't Work above y=100
LambertW(101.78,0)=5.719 --> Actually should be 3.40Attachment 194434