Attribute VB_Name = "INTEGRATION_ASYMPTOTIC_LIBR"

Option Explicit     'Requires that all variables to be declared explicitly.

                            
Option Base 1       'The "Option Base" statement allows to specify 0 or 1 as the
                    'default first index of arrays.

'************************************************************************************
'************************************************************************************
'© Copyright NicoSystem 2009. All rights reserved by Rafael Nicolas Fermin Cota,
'San Francisco, CA. USA  www.rnfc.org
'nfermincota.hba2005@ivey.ca
'************************************************************************************
'************************************************************************************
'FUNCTION      : ASYMPTOTIC_EXPANSION_FUNC

'DESCRIPTION   : Evaluates exponential integral function for special case
'n=1 using formula of asymptotic expansion

'LIBRARY       : INTEGRATION
'GROUP         : ASYMPTOTIC
'ID            : 001
'AUTHOR        : RAFAEL NICOLAS FERMIN COTA
'LAST UPDATE   : 21/01/2009
'************************************************************************************
'************************************************************************************

Function ASYMPTOTIC_EXPANSION_FUNC(ByVal X_VAL As Double, _
Optional ByVal nLOOPS As Long = 100, _
Optional ByVal EPSILON As Double = 2 ^ -52)
  
  Dim i As Long
  
  Dim TEMP_SUM As Double
  Dim TEMP_FACT As Double
  
  Dim TEMP_PROD As Double
  Dim TEMP_PREV As Double
  
  Dim TEMP_RESID As Double
    
  On Error GoTo ERROR_LABEL
  
  If X_VAL <= 0 Then: GoTo ERROR_LABEL
  'Expansion function is not defined for x<0"
  
  TEMP_FACT = (-Log(X_VAL) - 0.5772156649)
  
  TEMP_SUM = 0
  TEMP_PROD = 1
  TEMP_RESID = -1
  TEMP_PREV = 0
  For i = 1 To nLOOPS
    TEMP_SUM = TEMP_SUM + ((-X_VAL) ^ i) / (i * TEMP_PROD)
    TEMP_PROD = TEMP_PROD * (i + 1)
    TEMP_RESID = TEMP_FACT - TEMP_SUM
    If (Abs(TEMP_PREV - TEMP_RESID) < EPSILON) Then
      ASYMPTOTIC_EXPANSION_FUNC = TEMP_RESID
      Exit Function
    End If
    TEMP_PREV = TEMP_RESID
  Next i

Exit Function
ERROR_LABEL:
ASYMPTOTIC_EXPANSION_FUNC = Err.number
End Function