Emulate BETADIST function

[mark14]

Hi everyone,

I have another application that I'm developing in Oracle Application Express using Oracle 10g. I developed a 'prototype' of the Oracle application in Excel and used the BETADIST function in this prototype. However, Oracle doesn't have this function, and I basically need to re-write it.

I've read all the documentation on the BETADIST function and how to use it in Excel, so I have a pretty good handle on that. I understand that you provide your x, alpha, beta, and optionally, lower and upper bounds, and the function returns the cumulative beta probability density function.

For example, =BETADIST(0.2,1.57,2) gives me 0.1803.

The problem is, I'm no statistician, and have no idea what it is doing behind the scenes to get the 0.1803 value in order to recreate it. I've checked the Wikipedia pages, among others, and all of those formulas are greek to me.

Can anyone help break down this function for me and explain how that value is logically derived in my example above, using those numbers? That will greatly help me figure out how to rewrite it.

Thanks in advance!
Mark

 

[shg]

OK, this works better, but not great.

On entry, it computes a scale factor used in the subsequent calls to Func. Func itself is computed in log space, and then the scale factor is added before it's exponentiated.

=BETADIST(0.3, 401, 1001, 0, 1) returns 0.8761, as you noted.

=BetaDist1(0.3, 401, 1001, 0, 1) with nInt set to 500 returns 0.8725. With nInt set to 10000, it returns 0.8759, but is noticeably slow.

Option Explicit
 
' Number of double-intervals; increase for accuracy, decrease for speed
Const nInt          As Long = 10000
 
'======================= B e t a D i s t  E x a m p l e  =======================
' shg 2010-1223
 
' Beta distribution parameters
Public mAlpha       As Double
Public mBeta        As Double
Public miScale      As Long
 
Function Func(x As Double) As Double
    ' The evaluated function for BetaDist
 
    ' computed as a log and then scaled by Exp(miScale)
    ' to accommodate numerical precision
 
    If x = 0 Then
        Func = 0
    ElseIf x = 1 Then
        Func = 1
    Else
        Func = (mAlpha - 1) * Log(x) + (mBeta - 1) * Log(1 - x)
        Func = Exp(Func + miScale)
    End If
 
    'Func = x ^ (mAlpha - 1) * (1 - x) ^ (mBeta - 1)
End Function
 
' The UDF/VBA function itself
Function BetaDist1(ByVal x As Double, _
                   alpha As Double, beta As Double, _
                   Optional A As Double = 0#, Optional B As Double = 1#) As Variant
 
    ' shg 2008/2011
 
    ' For arguments, see Excel Help for BETADIST
 
    Dim d1          As Double   ' result of left-side integration
    Dim d2          As Double   ' result of right-side integration
 
    If alpha <= 0# Or beta <= 0# Or _
       x < A Or x > B Or _
       A = B Then
        BetaDist1 = CVErr(xlErrNum)
 
    Else
        mAlpha = alpha
        mBeta = beta
        x = (x - A) / (B - A)           ' scale x to interval
 
        ' set the scale factor for Func
        miScale = 300 - (mBeta - 1) * Log(1 - (1 - x) / nInt)
 
        d1 = SimpsonInt(0#, x, nInt)    ' get left-side integral
        d2 = SimpsonInt(x, 1#, nInt)    ' get right-side integral
        BetaDist1 = d1 / (d1 + d2)      ' compute ratio of left side to total
    End If
End Function
 
'============= G e n e r a l   S i m p s o n   I n t e g r a t o r =============
Private Function SimpsonInt(xi As Double, xf As Double, ByVal n As Long) As Double
    ' shg 2006
 
    ' Returns the integral of Func (specific to problem) over the interval xi to xf
    ' using the Composite Simpson's Rule over n intervals
 
    Dim i           As Double  ' index
    Dim dH          As Double  ' step size
    Dim dF          As Double   ' cumulative integration of f
 
    If n < 1 Then Exit Function
    n = n * 2
    dH = (xf - xi) / n
 
    dF = Func(xi)                          ' initial value
 
    For i = 1 To n - 1 Step 2
        dF = dF + 4 * Func(xi + i * dH) ' odd values
    Next i
 
    For i = 2 To n - 2 Step 2
        dF = dF + 2 * Func(xi + i * dH) ' even values
    Next i
 
    dF = dF + Func(xi)                  ' final value
 
    SimpsonInt = dF * dH / 3
End Function

Side note: there is an online calculator for BetaDist at http://www.solvemymath.com/online_m...cs/continuous_distributions/beta/cdf_beta.php

Plug those numbers in, and you get (drum roll) ... a divide by zero error. I'm not alone

 

[shg]

Well that had a hideous mistake. This is much better behaved, and converges much faster.

=BETADIST(0.3, 401, 1001, 0, 1) returns 0.876099

=BetaDist1(0.3, 401, 1001, 0, 1) with nInt set to 100 returns 0.876111, pretty darn close

Option Explicit
 
' Number of double-intervals; increase for accuracy, decrease for speed
Const nInt          As Long = 100
 
'======================= B e t a D i s t  E x a m p l e  =======================
' shg 2010-1223
 
' Beta distribution parameters
Public mAlpha       As Double
Public mBeta        As Double
Public miScale      As Long
 
Function Func(x As Double) As Double
    ' The evaluated function for BetaDist
 
    ' computed as a log and then scaled by Exp(miScale)
    ' to accommodate numerical precision
 
    If x = 0 Or x = 1 Then
        Func = 0
    Else
        Func = (mAlpha - 1) * Log(x) + (mBeta - 1) * Log(1 - x)
        Func = Exp(Func + miScale)
    End If
 
    'Func = x ^ (mAlpha - 1) * (1 - x) ^ (mBeta - 1)
End Function
 
Function BetaDist1(ByVal x As Double, _
                   alpha As Double, beta As Double, _
                   Optional A As Double = 0#, Optional B As Double = 1#) As Variant
    ' shg 2008/2011
    ' For arguments, see Excel Help for BETADIST
 
    Dim d1          As Double   ' result of left-side integration
    Dim d2          As Double   ' result of right-side integration
 
    If alpha <= 0# Or beta <= 0# Or _
       x < A Or x > B Or _
       A = B Then
        BetaDist1 = CVErr(xlErrNum)
 
    Else
        mAlpha = alpha
        mBeta = beta
        x = (x - A) / (B - A)           ' scale x to interval
 
        ' set the scale factor for Func
        miScale = 300 - (mBeta - 1) * Log(1 - (1 - x) / nInt)
 
        d1 = SimpsonInt(0#, x, nInt)    ' get left-side integral
        d2 = SimpsonInt(x, 1#, nInt)    ' get right-side integral
        BetaDist1 = d1 / (d1 + d2)      ' compute ratio of left side to total
    End If
End Function
'============= G e n e r a l   S i m p s o n   I n t e g r a t o r =============
Private Function SimpsonInt(xi As Double, xf As Double, ByVal n As Long) As Double
    ' shg 2006
 
    ' Returns the integral of Func (specific to problem) over the interval xi to xf
    ' using the Composite Simpson's Rule over 2n intervals
 
    Dim i           As Double  ' index
    Dim dH          As Double  ' step size
    Dim dF          As Double   ' cumulative integration of f
 
    If n < 1 Then Exit Function
    n = 2 * n
    dH = (xf - xi) / n
 
    dF = Func(xi)                       ' initial value
 
    For i = 1 To n - 1 Step 2
        dF = dF + 4 * Func(xi + i * dH) ' odd values
    Next i
 
    For i = 2 To n - 2 Step 2
        dF = dF + 2 * Func(xi + i * dH) ' even values
    Next i
 
    dF = dF + Func(xf)                  ' final value
 
    SimpsonInt = dF * dH / 3
End Function

 

[mark14]

ssgh4421,

Once again thank you so much for sticking with me on this and helping with this function. That's too funny that those parameters produced an error on another online calculator . Leave it to me to find the weirdest parameter combinations possible. Although, to my credit, I wasn't the one that came up with those parameters, so I'll blame it on the subject matter experts. I've already asked if they could come up with some different numbers for those cases, but again, if Excel can do it, I need to be able to do it.

Anyway, it looks like you've found a solid solution, so I'll try to incorporate your changes into my Oracle function and see how it works.

Thanks again! You. Are. Awesome.
Mark

 

[mark14]

Hi shg4421,

In the =BetaDist1(0.3, 401, 1001) example, I'm getting an unexpected number when stepping through the VBA code for miScale at this line:

' set the scale factor for Func
  miScale = 300 - (mBeta - 1) * Log(1 - (1 - x) / nInt)

Which ends up being...

' set the scale factor for Func
  miScale = 300 - (1001 - 1) * Log(1 - (1 - 0.3) / 100)

After stepping into that line, the code is saying miScale = 307. However, when I type in (what I think is) the same formula below into an Excel cell, it gives me 303.0508.

=300 - (1001 - 1) * LOG(1 - (1 - 0.3) / 100)

Any idea why there is a difference?

Thanks!
Mark

 

[shg]

You're welcome, but this is much less robust because of the log evaluation. I'm sure a more rigorous solution is possible. Use with caution.

 

[mark14]

http://www.techonthenet.com/excel/formulas/log.php

Looks like, in VBA, the log function returns the natural log of a number, which is why it's 307, instead of the logarithm of 303.0508.

That's weird that the same-named (LOG) function does two entirely different things between Excel and VBA.

So, LN() in Excel actually equals LOG() in VBA.

Oh well... is natural log what we want?

 

[shg]

It doesn't matter what base you use -- the purpose is just to eliminate overflow errors (run-time errors) and minimize underflow (lose significant data).

 

[Dango]

Hi guys

Would you be able to post your SQL implementation of the beta code? I'm trying to implement something too, where i need to return a probability for all records in a table, each of which have different beta parameters contained in separate fields and a couple of general parameters which don't change on each process run. Any help gratefully appreciated...

Cheers

 

[mark14]

Hi Dango, I ended up finding out about a Java library that already had the betadist function defined. So, I loaded that library and am now calling the Java function. It works perfectly. See the solution for this approach from MichaelS in this thread:

https://forums.oracle.com/forums/thread.jspa?messageID=9240804&#9240804

But, thanks to shg, I was originally able to derive the following PL/SQL code, which helped me understand the function much more. I haven't looked at it in awhile, and I'm not sure if I ever got it 100% correct, although it was really close. Sorry, the formatting didn't quite remain intact.

Hope this helps!
Mark

[FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]CREATE [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]OR [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]REPLACE [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]FUNCTION[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] EV_370[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff].[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#808000][FONT=Courier][SIZE=2][COLOR=#808000][FONT=Courier][SIZE=2][COLOR=#808000]F_BETADIST[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]([/COLOR][/SIZE][/FONT]
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[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]i_alpha [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]IN [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000]BINARY_DOUBLE[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff],[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]i_beta [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]IN [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000]BINARY_DOUBLE[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff],[/COLOR][/SIZE][/FONT]
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[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]i_b [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]IN [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000]BINARY_DOUBLE [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]DEFAULT [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]1[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]) [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]RETURN [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000]BINARY_DOUBLE[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]IS[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_x [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000]BINARY_DOUBLE[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- Reassignment variable for i_x[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_alpha [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000]BINARY_DOUBLE[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- Beta distribution parameter[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_beta [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000]BINARY_DOUBLE[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- Beta distribution parameter[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_d1 [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000]BINARY_DOUBLE[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- Result of left-side integration[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_d2 [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000]BINARY_DOUBLE[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- Result of right-side integration[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_scale [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000]BINARY_DOUBLE[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- Sets the scale factor for F_CALC_FUNC[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]r_f_betadist [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000]BINARY_DOUBLE[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- Return value [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]c_interval [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]CONSTANT [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000]BINARY_DOUBLE [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]:=[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]200[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- Number of double-intervals; Increase for accuracy, decrease for speed[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]c_zero [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]CONSTANT [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000]BINARY_DOUBLE [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]:=[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]0[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- For binary comparison[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]c_one [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]CONSTANT [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000]BINARY_DOUBLE [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]:=[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]1[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- For binary comparison[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT]
[I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]/*******************************************************************************************************************[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[SIZE=2][FONT=Courier][COLOR=#008000][I][SIZE=2][FONT=Courier][COLOR=#008000]Function Name: F_CALC_FUNC[/COLOR][/FONT][/SIZE][/I]
[I][SIZE=2][FONT=Courier][COLOR=#008000]Function Desc: The evaluated function for F_BETADIST[/COLOR][/FONT][/SIZE][/I]
[I][SIZE=2][FONT=Courier][COLOR=#008000]Computed as a log and then scaled by Exp(miScale) to accommodate numerical precision[/COLOR][/FONT][/SIZE][/I]
[I][SIZE=2][FONT=Courier][COLOR=#008000]********************************************************************************************************************/[/COLOR][/FONT][/SIZE][/I][/COLOR][/FONT][/SIZE][/COLOR][/SIZE][/FONT]
[FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]FUNCTION[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] F_CALC[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]([/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]i_calc_val [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]IN [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000]BINARY_DOUBLE[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]) [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]RETURN [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000]BINARY_DOUBLE[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]IS[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]r_f_calc [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000]BINARY_DOUBLE[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT]
[FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]BEGIN[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT]
[FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]IF[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]([/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]i_calc_val [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]=[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]0 [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]OR[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] i_calc_val [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]=[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]1[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]) [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]THEN[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]r_f_calc [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]:=[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]0[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]RETURN[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] r_f_calc[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT]
[FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]ELSE[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]r_f_calc [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]:= [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]([/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_alpha [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]-[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]1[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff])[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] * [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]LN([/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]i_calc_val[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff])[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]+[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]([/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_beta [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]-[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]1[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff])[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] * [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]LN([/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]1[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]-[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] i_calc_val[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]);[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]r_f_calc [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]:= [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]EXP([/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]r_f_calc [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]+[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] v_scale[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]);[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]RETURN[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] r_f_calc[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT]
[FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]END [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]IF;[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT]
[FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]END[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] F_CALC[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]/**************************************************************************************************[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[SIZE=2][FONT=Courier][COLOR=#008000][I][SIZE=2][FONT=Courier][COLOR=#008000]Function Name: F_SIMPSON[/COLOR][/FONT][/SIZE][/I]
[I][SIZE=2][FONT=Courier][COLOR=#008000]Function Desc: General Simpson Integrator[/COLOR][/FONT][/SIZE][/I]
[I][SIZE=2][FONT=Courier][COLOR=#008000]Returns the integral of Func (specific to problem) over the interval xi to xf[/COLOR][/FONT][/SIZE][/I]
[I][SIZE=2][FONT=Courier][COLOR=#008000]using the Composite Simpson's Rule over 2n intervals[/COLOR][/FONT][/SIZE][/I]
[I][SIZE=2][FONT=Courier][COLOR=#008000]***************************************************************************************************/[/COLOR][/FONT][/SIZE][/I][/COLOR][/FONT][/SIZE][/COLOR][/SIZE][/FONT]
[FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]FUNCTION[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] F_SIMPSON[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]([/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]i_xi [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]IN [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000]BINARY_DOUBLE[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff],[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]i_xf [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]IN [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000]BINARY_DOUBLE[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff],[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]i_n [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]IN [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000]BINARY_DOUBLE[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]) [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]RETURN [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000]BINARY_DOUBLE[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]IS[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT]
[SIZE=2][FONT=Courier][SIZE=2][FONT=Courier]v_i [/FONT][/SIZE][/FONT][/SIZE][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000]BINARY_DOUBLE[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- index[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_i_val [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000]BINARY_DOUBLE[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- reassignement variable for v_i[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_n [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000]BINARY_DOUBLE[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- reassignment variable for i_n[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_dh [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000]BINARY_DOUBLE[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- step size[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_df [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000]BINARY_DOUBLE[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- cumulative integration of f[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]r_f_simpson [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000]BINARY_DOUBLE [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]:=[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]0[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- Return value[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT]
[FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]BEGIN[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT]
[FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]IF[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] i_n [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]>= [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]1 [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]THEN[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_n [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]:= [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]2[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] * i_n[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_dh [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]:= [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]([/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]i_xf [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]-[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] i_xi[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff])[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]/[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] v_n[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- Initial value[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_df [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]:=[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] F_CALC[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]([/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]i_xi[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]);[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT]
[I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- Odd values[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]FOR[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] v_i [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]IN [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]1[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]..[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] v_n [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]-[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]1[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]LOOP[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]IF [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]MOD([/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_i[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff],[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]2[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]) [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]=[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]0 [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]THEN[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- v_i is even[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]NULL;[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]ELSE[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- v_i is odd[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_df [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]:=[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] v_df [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]+[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]4[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] * F_CALC[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]([/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]i_xi [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]+[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] v_i * v_dh[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]);[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]END [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]IF;[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]END [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]LOOP;[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT]
[I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- Even values[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]FOR[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] v_i [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]IN [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]1[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]..[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] v_n [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]-[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]2[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]LOOP[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]IF [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]MOD([/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_i[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff],[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]2[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]) [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]=[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]0 [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]THEN[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- v_i is even [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_df [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]:=[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] v_df [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]+[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]2[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] * F_CALC[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]([/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]i_xi [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]+[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] v_i * v_dh[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]);[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]ELSE[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- v_i is odd[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]NULL;[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]END [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]IF;[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT]
[FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]END [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]LOOP;[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT]
[I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- Final value[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_df [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]:=[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] v_df [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]+[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] F_CALC[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]([/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]i_xf[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]);[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]r_f_simpson [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]:=[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] v_df * v_dh [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]/[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]3[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]RETURN[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] r_f_simpson[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT]
[FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]ELSE[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]RETURN [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]0[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]END [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]IF;[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]END[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] F_SIMPSON[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT]
[FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]BEGIN[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]IF[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] i_alpha [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]<=[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] c_zero [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]OR[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] i_beta [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]<=[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] c_zero [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]OR[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] i_x [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]<[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] i_a [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]OR[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] i_x [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]>[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] i_b [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]OR[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] i_a [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]=[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] i_b [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]THEN[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]RAISE_APPLICATION_ERROR[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff](-[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]20000[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff],[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000][FONT=Courier][SIZE=2][COLOR=#ff0000]'Invalid beta distribution parameters'[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]);[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT]
[FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]ELSE[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_alpha [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]:=[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] i_alpha[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_beta [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]:=[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] i_beta[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_x [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]:=[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] i_x[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_x [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]:=[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]([/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]i_x [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]-[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] i_a[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff])[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]/[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]([/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]i_b [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]-[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] i_a[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]);[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- scale to intervalb[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_scale [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]:=[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]300[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]-[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]([/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_beta [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]-[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]1[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff])[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] * [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]LN([/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]1[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]-[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]([/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000][FONT=Courier][SIZE=2][COLOR=#800000]1[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]-[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] v_x[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff])[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]/[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] c_interval[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]);[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_d1 [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]:=[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] F_SIMPSON[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]([/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]c_zero[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff],[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] v_x[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff],[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] c_interval[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]);[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- get left-side integral[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_d2 [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]:=[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] F_SIMPSON[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]([/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_x[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff],[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] c_one[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff],[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] c_interval[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]);[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- get right-side integral[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT]
[I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- When v_d1 + v_d2 = 0, then the function will produce an error because you can't divide by zero.[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT][I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- To get around this, I return a binary_double data type, which return NAN in these cases.[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT][I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- Then, using NVL, I can substitute zero for these values.[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]r_f_betadist [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]:=[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] v_d1 [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]/[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]([/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2]v_d1 [/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]+[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] v_d2[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]);[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][I][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000][FONT=Courier][SIZE=2][COLOR=#008000]-- compute ratio of left side to total[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/I][FONT=Courier][SIZE=2][COLOR=#008000]
[/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]RETURN[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][FONT=Courier][SIZE=2] r_f_betadist[/SIZE][/FONT][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]END [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]IF;[/COLOR][/SIZE][/FONT]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff]END [/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#808000][FONT=Courier][SIZE=2][COLOR=#808000][FONT=Courier][SIZE=2][COLOR=#808000]F_BETADIST[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff][FONT=Courier][SIZE=2][COLOR=#0000ff];[/COLOR][/SIZE][/FONT]
[SIZE=2][FONT=Courier][COLOR=#0000ff]/[/COLOR][/FONT][/SIZE]
[/COLOR][/SIZE][/FONT][/COLOR][/SIZE][/FONT]

 

[Dango]

Thanks Mark

I'm using Microsoft SQL 2008 so if i can't find some pre-existing code, i'll try and figure out a way to implement it there. In the meantime, thanks for your help!

Dango