## Gaussian Random Number Distribution

By popular request, the code to generate random numbers in a Gaussian distribution for VB.Net.

Usage:

Code:
`GaussNumDist(Mean, Standard Deviation, Sample Size)`

This will populate GaussNumArray() with the sample of numbers, whose distribution will have the mean and standard deviation specified.

Code:

Code:
```Imports System.Math

Module Module1

Friend GaussNumArray() As Double
Friend intICell As Long

Friend Function GaussNumDist(ByVal Mean As Double, ByVal StdDev As Double, ByVal SampleSize As Integer)

intICell = 1                'Loop variable

ReDim GaussNumArray(SampleSize)

Do While (intICell < (SampleSize + 1))
Call NumDist(Mean, StdDev)
Application.DoEvents()
Loop

End Function

Sub NumDist(ByVal meanin As Double, ByVal sdin As Double)

'---------------------------------------------------------------------------------
'Converts uniform random numbers over the region 0 to 1 into Gaussian distributed
'random numbers using Box-Muller algorithm.
'Adapted from Numerical Recipes in C
'---------------------------------------------------------------------------------

'Defining variables
Dim dblR1 As Double
Dim dblR2 As Double
Dim mean As Double
Dim var As Double
Dim circ As Double
Dim trans As Double
Dim dblY1 As Double
Dim dblY2 As Double
Dim Pi As Double
Pi = 4 * Atan(1)

'Get two random numbers
dblR1 = (2 * UniformRandomNumber()) - 1
dblR2 = (2 * UniformRandomNumber()) - 1

circ = (dblR1 ^ 2) + (dblR2 ^ 2)        'Radius of circle

If circ >= 1 Then       'If outside unit circle, then reject number
Call NumDist(meanin, sdin)
Exit Sub
End If

'Transform to Gaussian
trans = Sqrt(-2 * Log(circ) / circ)

dblY1 = (trans * dblR1 * sdin) + meanin
dblY2 = (trans * dblR2 * sdin) + meanin

GaussNumArray(intICell) = dblY1   'First number

'Increase intICell for next random number
intICell = (intICell + 1)

GaussNumArray(intICell) = dblY2   'Second number

'Increase intICell again ready for next call of ConvertNumberDistribution
intICell = (intICell + 1)

End Sub
Friend Function UniformRandomNumber() As Double

'-----------------------------------------------------------------------------------
'Outputs random numbers with a period of > 2x10^18 in the range 0 to 1 (exclusive)
'Implements a L'Ecuyer generator with Bays-Durham shuffle
'Adapted from Numerical Recipes in C
'-----------------------------------------------------------------------------------

'Defining constants
Const IM1 As Double = 2147483563
Const IM2 As Double = 2147483399
Const AM As Double = (1.0# / IM1)
Const IMM1 As Double = (IM1 - 1.0#)
Const IA1 As Double = 40014
Const IA2 As Double = 40692
Const IQ1 As Double = 53668
Const IQ2 As Double = 52774
Const IR1 As Double = 12211
Const IR2 As Double = 3791
Const NTAB As Double = 32
Const NDIV As Double = (1.0# + IM1 / NTAB)
Const ESP As Double = 0.00000012
Const RNMX As Double = (1.0# - ESP)

Dim iCell As Integer
Dim idum As Double
Dim j As Integer
Dim k As Long
Dim temp As Double

Static idum2 As Long
Static iy As Long
Static iv(NTAB) As Long

idum2 = 123456789
iy = 0

'Seed value required is a negative integer (idum)
Randomize()
idum = (-Rnd() * 1000)

'For loop to generate a sequence of random numbers based on idum
For iCell = 1 To 10
'Initialize generator
If (idum <= 0) Then
'Prevent idum = 0
If (-(idum) < 1) Then
idum = 1
Else
idum = -(idum)
End If
idum2 = idum
For j = (NTAB + 7) To 0
k = ((idum) / IQ1)
idum = ((IA1 * (idum - (k * IQ1))) - (k * IR1))
If (idum < 0) Then
idum = (idum + IM1)
End If
If (j < NTAB) Then
iv(j) = idum
End If
Next j
iy = iv(0)
End If

'Start here when not initializing
k = (idum / IQ1)
idum = ((IA1 * (idum - (k * IQ1))) - (k * IR1))
If (idum < 0) Then
idum = (idum + IM1)
End If
k = (idum2 / IQ2)
idum2 = ((IA2 * (idum2 - (k * IQ2))) - (k * IR2))
If (idum2 < 0) Then
idum2 = idum2 + IM2
End If
j = (iy / NDIV)
iy = (iv(j) - idum2)
iv(j) = idum
If (iy < 1) Then
iy = (iy + IMM1)
End If
temp = AM * iy
If (temp <= RNMX) Then
'Return the value of the random number
UniformRandomNumber = temp
End If
Next iCell
End Function
End Module```

zaza