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' Copyright 2008 Daniel Wagner O. de Medeiros
'
' This file is part of DWSIM.
'
' DWSIM is free software: you can redistribute it and/or modify
' it under the terms of the GNU General Public License as published by
' the Free Software Foundation, either version 3 of the License, or
' (at your option) any later version.
'
' DWSIM is distributed in the hope that it will be useful,
' but WITHOUT ANY WARRANTY; without even the implied warranty of
' MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
' GNU General Public License for more details.
'
' You should have received a copy of the GNU General Public License
' along with DWSIM. If not, see <http://www.gnu.org/licenses/>.
Namespace MathEx.BrentOpt
Public Class BrentMinimize
Public fc As funcdelegate
Delegate Function funcdelegate(ByVal x As Double) As Double
Sub New()
End Sub
Sub DefineFuncDelegate(ByVal fg As funcdelegate)
Me.fc = fg
End Sub
Function f(ByVal x As Double) As Double
Return fc.Invoke(x)
End Function
'************************************************************************
' Minimization by the Brent method
'
' Input parameters:
' a - left boundary of an interval to search minimum in.
' b - right boundary of an interval to search minimum in.
' Epsilon � absolute error of the value of the function minimum.
'
' Output parameters:
' XMin - point of minimum.
'
' The result:
' function value at the point of minimum.
' ************************************************************************
Public Function brentoptimize(ByVal a As Double, ByVal b As Double, ByVal epsilon As Double, ByRef xmin As Double) As Double
Dim result As Double = 0
Dim ia As Double = 0
Dim ib As Double = 0
Dim bx As Double = 0
Dim d As Double = 0
Dim e As Double = 0
Dim etemp As Double = 0
Dim fu As Double = 0
Dim fv As Double = 0
Dim fw As Double = 0
Dim fx As Double = 0
Dim iter As Integer = 0
Dim p As Double = 0
Dim q As Double = 0
Dim r As Double = 0
Dim u As Double = 0
Dim v As Double = 0
Dim w As Double = 0
Dim x As Double = 0
Dim xm As Double = 0
Dim cgold As Double = 0
cgold = 0.381966
bx = 0.5 * (a + b)
If a < b Then
ia = a
Else
ia = b
End If
If a > b Then
ib = a
Else
ib = b
End If
v = bx
w = v
x = v
e = 0.0R
fx = f(x)
fv = fx
fw = fx
For iter = 1 To 100
xm = 0.5 * (ia + ib)
If Math.Abs(x - xm) <= epsilon * 2 - 0.5 * (ib - ia) Then
Exit For
End If
If Math.Abs(e) > epsilon Then
r = (x - w) * (fx - fv)
q = (x - v) * (fx - fw)
p = (x - v) * q - (x - w) * r
q = 2 * (q - r)
If q > 0 Then
p = -p
End If
q = Math.Abs(q)
etemp = e
e = d
If Not (Math.Abs(p) >= Math.Abs(0.5 * q * etemp) Or p <= q * (ia - x) Or p >= q * (ib - x)) Then
d = p / q
u = x + d
If u - ia < epsilon * 2 Or ib - u < epsilon * 2 Then
d = mysign(epsilon, xm - x)
End If
Else
If x >= xm Then
e = ia - x
Else
e = ib - x
End If
d = cgold * e
End If
Else
If x >= xm Then
e = ia - x
Else
e = ib - x
End If
d = cgold * e
End If
If Math.Abs(d) >= epsilon Then
u = x + d
Else
u = x + mysign(epsilon, d)
End If
fu = f(u)
If Double.IsNaN(fu) Then Exit For
If fu <= fx Then
If u >= x Then
ia = x
Else
ib = x
End If
v = w
fv = fw
w = x
fw = fx
x = u
fx = fu
Else
If u < x Then
ia = u
Else
ib = u
End If
If fu <= fw Or w = x Then
v = w
fv = fw
w = u
fw = fu
Else
If fu <= fv Or v = x Or v = 2 Then
v = u
fv = fu
End If
End If
End If
Next
xmin = x
result = fx
Return result
End Function
Public Function brentoptimize2(ByVal a As Double, ByVal b As Double, ByVal epsilon As Double, ByVal func As Func(Of Double, Double)) As Double
Dim result As Double = 0
Dim ia As Double = 0
Dim ib As Double = 0
Dim bx As Double = 0
Dim d As Double = 0
Dim e As Double = 0
Dim etemp As Double = 0
Dim fu As Double = 0
Dim fv As Double = 0
Dim fw As Double = 0
Dim fx As Double = 0
Dim iter As Integer = 0
Dim p As Double = 0
Dim q As Double = 0
Dim r As Double = 0
Dim u As Double = 0
Dim v As Double = 0
Dim w As Double = 0
Dim x As Double = 0
Dim xm As Double = 0
Dim cgold As Double = 0
cgold = 0.381966
bx = 0.5 * (a + b)
If a < b Then
ia = a
Else
ia = b
End If
If a > b Then
ib = a
Else
ib = b
End If
v = bx
w = v
x = v
e = 0.0R
fx = func(x)
fv = fx
fw = fx
For iter = 1 To 100
xm = 0.5 * (ia + ib)
If Math.Abs(x - xm) <= epsilon * 2 - 0.5 * (ib - ia) Then
Exit For
End If
If Math.Abs(e) > epsilon Then
r = (x - w) * (fx - fv)
q = (x - v) * (fx - fw)
p = (x - v) * q - (x - w) * r
q = 2 * (q - r)
If q > 0 Then
p = -p
End If
q = Math.Abs(q)
etemp = e
e = d
If Not (Math.Abs(p) >= Math.Abs(0.5 * q * etemp) Or p <= q * (ia - x) Or p >= q * (ib - x)) Then
d = p / q
u = x + d
If u - ia < epsilon * 2 Or ib - u < epsilon * 2 Then
d = mysign(epsilon, xm - x)
End If
Else
If x >= xm Then
e = ia - x
Else
e = ib - x
End If
d = cgold * e
End If
Else
If x >= xm Then
e = ia - x
Else
e = ib - x
End If
d = cgold * e
End If
If Math.Abs(d) >= epsilon Then
u = x + d
Else
u = x + mysign(epsilon, d)
End If
fu = func(u)
If Double.IsNaN(fu) Then Exit For
If fu <= fx Then
If u >= x Then
ia = x
Else
ib = x
End If
v = w
fv = fw
w = x
fw = fx
x = u
fx = fu
Else
If u < x Then
ia = u
Else
ib = u
End If
If fu <= fw Or w = x Then
v = w
fv = fw
w = u
fw = fu
Else
If fu <= fv Or v = x Or v = 2 Then
v = u
fv = fu
End If
End If
End If
Next
Return x
End Function
Private Shared Function mysign(ByVal a As Double, ByVal b As Double) As Double
Dim result As Double = 0
If b > 0 Then
result = Math.Abs(a)
Else
result = -Math.Abs(a)
End If
Return result
End Function
End Class
End Namespace
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