Lambert W function, or the product logarithm, for LibreOffice and OpenOffice. Original version for Excel from here: http://www.vbforums.com/showthread.php?683003-Lambert-W-function-for-Excel-work-on-real-and-complex-number

LambertW.bas

Attribute VB_Name = "Module1"

Function Complex(a As Double, b As Double) As Any
   Dim svc As Object
   svc = createUnoService("com.sun.star.sheet.FunctionAccess")
   Complex = svc.callFunction("COMPLEX",Array(a,b))
End Function

Function ImProduct(a As Any, b As Any) As Any
   Dim svc As Object
   svc = createUnoService("com.sun.star.sheet.FunctionAccess")
   ImProduct = svc.callFunction("IMPRODUCT",Array(a,b))
End Function

Function ImReal(a As Any) As Double
   Dim svc As Object
   svc = createUnoService("com.sun.star.sheet.FunctionAccess")
   ImReal = svc.callFunction("IMREAL",Array(a))
End Function

Function Imaginary(a As Any) As Double
   Dim svc As Object
   svc = createUnoService("com.sun.star.sheet.FunctionAccess")
   Imaginary = svc.callFunction("IMAGINARY",Array(a))
End Function

Function ImExp(a As Any) As Any
   Dim svc As Object
   svc = createUnoService("com.sun.star.sheet.FunctionAccess")
   ImExp = svc.callFunction("IMEXP",Array(a))
End Function

Function ImSum(a As Any, b As Any) As Any
   Dim svc As Object
   svc = createUnoService("com.sun.star.sheet.FunctionAccess")
   ImSum = svc.callFunction("IMSUM",Array(a, b))
End Function

Function ImSub(a As Any, b As Double) As Any
   Dim svc As Object
   svc = createUnoService("com.sun.star.sheet.FunctionAccess")
   ImSub = svc.callFunction("IMSUB",Array(a, b))
End Function

Function ImSqrt(a As Any) As Any
   Dim svc As Object
   svc = createUnoService("com.sun.star.sheet.FunctionAccess")
   ImSqrt = svc.callFunction("IMSQRT",Array(a))
End Function

Function ImLn(a As Any) As Any
   Dim svc As Object
   svc = createUnoService("com.sun.star.sheet.FunctionAccess")
   ImLn = svc.callFunction("IMLN",Array(a))
End Function

Function ImDiv(a As Any, b As Any) As Any
   Dim svc As Object
   svc = createUnoService("com.sun.star.sheet.FunctionAccess")
   ImDiv = svc.callFunction("IMDIV",Array(a, b))
End Function


Public Function LambertW(x As Double)
  ' Lambert W function for x (real number)
  ' real result, domain: [-1/e , infinity]
  ' complex result, domain: [infinity , infinity]
  ' return: Complex number (in the form a+bi)
    
  LambertW = LambertWc(x, 0)
End Function

Public Function LambertWc(a As Double, b As Double)
  ' Lambert W function for a+bi
  ' real result, domain: [-1/e , infinity]
  ' complex result, domain: [infinity , infinity]
  ' return: Complex number (in the form a+bi)
  Dim z, x, z1, z2, z3, q1
  If a = 0 And b = 0 Then
    z = 0
  Else
    ' complex parameter
    x = Complex(a, b)

    ' approx initial value = sqtr(2*(1+e*x))-1
    z = ImProduct(x, ImExp(1))
    z = ImProduct(2, ImSum(1, z))
    If ImReal(z) = 0 And Imaginary(z) = 0 Then
      z = -1
    Else
      z = ImSub(ImSqrt(z), 1)
      For i = 1 To 100
        ' the comments are right to left evaluation
        ' z1 = 0 sub z sub ln x div z
        z1 = ImSub(z, ImLn(ImDiv(x, z)))
        z1 = ImSub(0, z1)
        ' q1 = 2 mul (1 add z) mul 1 add z add 2 mul z1 div 3
        z2 = ImProduct(2, ImDiv(z1, 3))
        z2 = ImSum(1, ImSum(z, z2))
        z2 = ImProduct(ImSum(z, 1), z2)
        q1 = ImProduct(2, z2)
        ' z1 = z mul 1 add (z1 div 1 add z) mul (q1 sub z1) div q1 sub 2 mul z1
        z2 = ImSub(q1, ImProduct(2, z1))
        z2 = ImDiv(ImSub(q1, z1), z2)
        z3 = ImDiv(z1, ImSum(1, z))
        z2 = ImSum(1, ImProduct(z3, z2))
        z1 = ImProduct(z, z2)
        If z = z1 Then
          Exit For
        Else
          z = z1
        End If
      Next
    End If
  End If
  LambertWc = z
End Function

Sub Main

End Sub