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LBFGS.vb
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Namespace MathEx.LBFGS
Public Class lbfgs
Delegate Sub funcgraddelegate(ByVal x As Double(), ByRef f As Double, ByRef g As Double())
Delegate Sub newiterdelegate(ByRef x As Double(), ByVal f As Double, ByRef g As Double(), ByRef abort As Boolean)
Public fc As funcgraddelegate
Public fc2 As newiterdelegate
Sub New()
End Sub
Sub DefineFuncGradDelegate(ByVal fg As funcgraddelegate)
Me.fc = fg
End Sub
Sub funcgrad(ByVal x As Double(), ByRef f As Double, ByRef g As Double())
fc.Invoke(x, f, g)
End Sub
Sub DefineNewIterDelegate(ByVal fg As newiterdelegate)
Me.fc2 = fg
End Sub
Private Sub lbfgsnewiteration(ByRef x As Double(), ByVal f As Double, ByRef g As Double(), ByRef abort As Boolean)
fc2.Invoke(x, f, g, abort)
End Sub
'/*************************************************************************
' LIMITED MEMORY BFGS METHOD FOR LARGE SCALE OPTIMIZATION
' JORGE NOCEDAL
'The subroutine minimizes function F(x) of N arguments by using a quasi-
'Newton method (LBFGS scheme) which is optimized to use a minimum amount
'of memory.
'The subroutine generates the approximation of an inverse Hessian matrix by
'using information about the last M steps of the algorithm (instead of N).
'It lessens a required amount of memory from a value of order N^2 to a
'value of order 2*N*M.
'This subroutine uses the FuncGrad subroutine which calculates the value of
'the function F and gradient G in point X. The programmer should define the
'FuncGrad subroutine by himself. It should be noted that the subroutine
'doesn't need to waste time for memory allocation of array G, because the
'memory is allocated in calling the subroutine. Setting a dimension of array
'G each time when calling a subroutine will excessively slow down an
'algorithm.
'The programmer could also redefine the LBFGSNewIteration subroutine which
'is called on each new step. The current point X, the function value F and
'the gradient G are passed into this subroutine. It is reasonable to
'redefine the subroutine for better debugging, for example, to visualize
'the solution process.
'Input parameters:
' N - problem dimension. N>0
' M - number of corrections in the BFGS scheme of Hessian
' approximation update. Recommended value: 3<=M<=7. The smaller
' value causes worse convergence, the bigger will not cause a
' considerably better convergence, but will cause a fall in the
' performance. M<=N.
' X - initial solution approximation.
' Array whose index ranges from 1 to N.
' EpsG - positive number which defines a precision of search. The
' subroutine finishes its work if the condition ||G|| < EpsG is
' satisfied, where ||.|| means Euclidian norm, G - gradient, X -
' current approximation.
' EpsF - positive number which defines a precision of search. The
' subroutine finishes its work if on iteration number k+1 the
' condition |F(k+1)-F(k)| <= EpsF*max{|F(k)|, |F(k+1)|, 1} is
' satisfied.
' EpsX - positive number which defines a precision of search. The
' subroutine finishes its work if on iteration number k+1 the
' condition |X(k+1)-X(k)| <= EpsX is fulfilled.
' MaxIts- maximum number of iterations. If MaxIts=0, the number of
' iterations is unlimited.
'Output parameters:
' X - solution approximation. Array whose index ranges from 1 to N.
' Info- a return code:
' * -1 wrong parameters were specified,
' * 0 interrupted by user,
' * 1 relative function decreasing is less or equal to EpsF,
' * 2 step is less or equal EpsX,
' * 4 gradient norm is less or equal to EpsG,
' * 5 number of iterations exceeds MaxIts.
'FuncGrad routine description. User-defined.
'Input parameters:
' X - array whose index ranges from 1 to N.
'Output parameters:
' F - function value at X.
' G - function gradient.
' Array whose index ranges from 1 to N.
'The memory for array G has already been allocated in the calling subroutine,
'and it isn't necessary to allocate it in the FuncGrad subroutine.
'*************************************************************************/
Private Function lbfgsdotproduct(ByVal n As Integer, ByRef dx As Double(), ByVal sx As Integer, ByRef dy As Double(), ByVal sy As Integer) As Double
Dim num2 As Double = 0
Dim num3 As Integer = 0
Dim index As Integer = 0
Dim num5 As Integer = 0
num3 = ((sx + n) - 1)
num5 = (sy - sx)
num2 = 0
index = sx
Do While (index <= num3)
num2 = (num2 + (dx(index) * dy((index + num5))))
index += 1
Loop
Return num2
End Function
Private Sub lbfgslincomb(ByVal n As Integer, ByVal da As Double, ByRef dx As Double(), ByVal sx As Integer, ByRef dy As Double(), ByVal sy As Integer)
Dim num As Integer = 0
Dim index As Integer = 0
Dim num3 As Integer = 0
num = ((sy + n) - 1)
num3 = (sx - sy)
index = sy
Do While (index <= num)
dy(index) = (dy(index) + (da * dx((index + num3))))
index += 1
Loop
End Sub
Private Sub lbfgsmcsrch(ByVal n As Integer, ByRef x As Double(), ByRef f As Double, ByRef g As Double(), ByRef s As Double(), ByVal sstart As Integer, ByRef stp As Double, ByVal ftol As Double, ByVal xtol As Double, ByVal maxfev As Integer, ByRef info As Integer, ByRef nfev As Integer, ByRef wa As Double(), ByVal gtol As Double, ByVal stpmin As Double, ByVal stpmax As Double)
Dim num As Integer = 0
Dim index As Integer = 0
Dim brackt As Boolean = False
Dim flag2 As Boolean = False
Dim num3 As Double = 0
Dim dp As Double = 0
Dim num5 As Double = 0
Dim num6 As Double = 0
Dim dx As Double = 0
Dim num8 As Double = 0
Dim dy As Double = 0
Dim num10 As Double = 0
Dim num11 As Double = 0
Dim num12 As Double = 0
Dim fp As Double = 0
Dim fx As Double = 0
Dim num15 As Double = 0
Dim fy As Double = 0
Dim num17 As Double = 0
Dim num18 As Double = 0
Dim num19 As Double = 0
Dim stx As Double = 0
Dim sty As Double = 0
Dim stmin As Double = 0
Dim stmax As Double = 0
Dim num24 As Double = 0
Dim num25 As Double = 0
Dim num26 As Double = 0
Dim num27 As Double = 0
Dim num28 As Double = 0
sstart -= 1
num18 = 0.5
num19 = 0.66
num26 = 4
num27 = 0
Me.funcgrad(x, f, g)
num = 1
info = 0
If ((((((((n <= 0) Or (stp <= 0)) Or (ftol < 0)) Or (gtol < num27)) Or (xtol < num27)) Or (stpmin < num27)) Or (stpmax < stpmin)) Or (maxfev <= 0)) Then
Return
End If
num5 = 0
index = 1
Do While (index <= n)
num5 = (num5 + (g(index) * s((index + sstart))))
index += 1
Loop
If (num5 >= 0) Then
Return
End If
brackt = False
flag2 = True
nfev = 0
num11 = f
num6 = (ftol * num5)
num24 = (stpmax - stpmin)
num25 = (num24 / num18)
index = 1
Do While (index <= n)
wa(index) = x(index)
index += 1
Loop
stx = 0
fx = num11
dx = num5
sty = 0
fy = num11
dy = num5
Do While True
If brackt Then
If (stx < sty) Then
stmin = stx
stmax = sty
Else
stmin = sty
stmax = stx
End If
Else
stmin = stx
stmax = (stp + (num26 * (stp - stx)))
End If
If (stp > stpmax) Then
stp = stpmax
End If
If (stp < stpmin) Then
stp = stpmin
End If
If ((((brackt And ((stp <= stmin) Or (stp >= stmax))) Or (nfev >= (maxfev - 1))) Or (num = 0)) Or (brackt And ((stmax - stmin) <= (xtol * stmax)))) Then
stp = stx
End If
index = 1
Do While (index <= n)
x(index) = (wa(index) + (stp * s((index + sstart))))
index += 1
Loop
Me.funcgrad(x, f, g)
info = 0
nfev += 1
num3 = 0
index = 1
Do While (index <= n)
num3 = (num3 + (g(index) * s((index + sstart))))
index += 1
Loop
num12 = (num11 + (stp * num6))
If ((brackt And ((stp <= stmin) Or (stp >= stmax))) Or (num = 0)) Then
info = 6
End If
If (((stp = stpmax) And (f <= num12)) And (num3 <= num6)) Then
info = 5
End If
If ((stp = stpmin) And ((f > num12) Or (num3 >= num6))) Then
info = 4
End If
If (nfev >= maxfev) Then
info = 3
End If
If (brackt And ((stmax - stmin) <= (xtol * stmax))) Then
info = 2
End If
If ((f <= num12) And (Math.Abs(num3) <= -(gtol * num5))) Then
info = 1
End If
If (Not info = 0) Then
Return
End If
num28 = ftol
If (gtol < ftol) Then
num28 = gtol
End If
If ((flag2 And (f <= num12)) And (num3 >= (num28 * num5))) Then
flag2 = False
End If
If ((flag2 And (f <= fx)) And (f > num12)) Then
fp = (f - (stp * num6))
num15 = (fx - (stx * num6))
num17 = (fy - (sty * num6))
dp = (num3 - num6)
num8 = (dx - num6)
num10 = (dy - num6)
Me.lbfgsmcstep(stx, num15, num8, sty, num17, num10, stp, fp, dp, brackt, stmin, stmax, num)
fx = (num15 + (stx * num6))
fy = (num17 + (sty * num6))
dx = (num8 + num6)
dy = (num10 + num6)
Else
Me.lbfgsmcstep(stx, fx, dx, sty, fy, dy, stp, f, num3, brackt, stmin, stmax, num)
End If
If brackt Then
If (Math.Abs(Convert.ToDouble((sty - stx))) >= (num19 * num25)) Then
stp = (stx + (num18 * (sty - stx)))
End If
num25 = num24
num24 = Math.Abs(Convert.ToDouble((sty - stx)))
End If
Loop
End Sub
Private Sub lbfgsmcstep(ByRef stx As Double, ByRef fx As Double, ByRef dx As Double, ByRef sty As Double, ByRef fy As Double, ByRef dy As Double, ByRef stp As Double, ByVal fp As Double, ByVal dp As Double, ByRef brackt As Boolean, ByVal stmin As Double, ByVal stmax As Double, ByRef info As Integer)
Dim flag As Boolean = False
Dim num As Double = 0
Dim num2 As Double = 0
Dim num3 As Double = 0
Dim num4 As Double = 0
Dim num5 As Double = 0
Dim num6 As Double = 0
Dim num7 As Double = 0
Dim num8 As Double = 0
Dim num9 As Double = 0
Dim num10 As Double = 0
info = 0
If Not (((brackt And ((stp <= Math.Min(stx, sty)) Or (stp >= Math.Max(stx, sty)))) Or ((dx * (stp - stx)) >= 0)) Or (stmax < stmin)) Then
num6 = (dp * (dx / Math.Abs(dx)))
If (fp > fx) Then
info = 1
flag = True
num10 = ((((3 * (fx - fp)) / (stp - stx)) + dx) + dp)
num5 = Math.Max(Math.Abs(num10), Math.Max(Math.Abs(dx), Math.Abs(dp)))
num = (num5 * Math.Sqrt((Math.Sqrt((num10 / num5)) - ((dx / num5) * (dp / num5)))))
If (stp < stx) Then
num = -num
End If
num2 = ((num - dx) + num10)
num3 = (((num - dx) + num) + dp)
num4 = (num2 / num3)
num7 = (stx + (num4 * (stp - stx)))
num9 = (stx + (((dx / (((fx - fp) / (stp - stx)) + dx)) / 2) * (stp - stx)))
If (Math.Abs(Convert.ToDouble((num7 - stx))) < Math.Abs(Convert.ToDouble((num9 - stx)))) Then
num8 = num7
Else
num8 = (num7 + ((num9 - num7) / 2))
End If
brackt = True
ElseIf (num6 < 0) Then
info = 2
flag = False
num10 = ((((3 * (fx - fp)) / (stp - stx)) + dx) + dp)
num5 = Math.Max(Math.Abs(num10), Math.Max(Math.Abs(dx), Math.Abs(dp)))
num = (num5 * Math.Sqrt((Math.Sqrt((num10 / num5)) - ((dx / num5) * (dp / num5)))))
If (stp > stx) Then
num = -num
End If
num2 = ((num - dp) + num10)
num3 = (((num - dp) + num) + dx)
num4 = (num2 / num3)
num7 = (stp + (num4 * (stx - stp)))
num9 = (stp + ((dp / (dp - dx)) * (stx - stp)))
If (Math.Abs(Convert.ToDouble((num7 - stp))) > Math.Abs(Convert.ToDouble((num9 - stp)))) Then
num8 = num7
Else
num8 = num9
End If
brackt = True
ElseIf (Math.Abs(dp) < Math.Abs(dx)) Then
info = 3
flag = True
num10 = ((((3 * (fx - fp)) / (stp - stx)) + dx) + dp)
num5 = Math.Max(Math.Abs(num10), Math.Max(Math.Abs(dx), Math.Abs(dp)))
num = (num5 * Math.Sqrt(Math.Max(Convert.ToDouble(0), Convert.ToDouble((Math.Sqrt((num10 / num5)) - ((dx / num5) * (dp / num5)))))))
If (stp > stx) Then
num = -num
End If
num2 = ((num - dp) + num10)
num3 = ((num + (dx - dp)) + num)
num4 = (num2 / num3)
If ((num4 < 0) And (num <> 0)) Then
num7 = (stp + (num4 * (stx - stp)))
ElseIf (stp > stx) Then
num7 = stmax
Else
num7 = stmin
End If
num9 = (stp + ((dp / (dp - dx)) * (stx - stp)))
If brackt Then
If (Math.Abs(Convert.ToDouble((stp - num7))) < Math.Abs(Convert.ToDouble((stp - num9)))) Then
num8 = num7
Else
num8 = num9
End If
ElseIf (Math.Abs(Convert.ToDouble((stp - num7))) > Math.Abs(Convert.ToDouble((stp - num9)))) Then
num8 = num7
Else
num8 = num9
End If
Else
info = 4
flag = False
If brackt Then
num10 = ((((3 * (fp - fy)) / (sty - stp)) + dy) + dp)
num5 = Math.Max(Math.Abs(num10), Math.Max(Math.Abs(dy), Math.Abs(dp)))
num = (num5 * Math.Sqrt((Math.Sqrt((num10 / num5)) - ((dy / num5) * (dp / num5)))))
If (stp > sty) Then
num = -num
End If
num2 = ((num - dp) + num10)
num3 = (((num - dp) + num) + dy)
num4 = (num2 / num3)
num7 = (stp + (num4 * (sty - stp)))
num8 = num7
ElseIf (stp > stx) Then
num8 = stmax
Else
num8 = stmin
End If
End If
If (fp > fx) Then
sty = stp
fy = fp
dy = dp
Else
If (num6 < 0) Then
sty = stx
fy = fx
dy = dx
End If
stx = stp
fx = fp
dx = dp
End If
num8 = Math.Min(stmax, num8)
num8 = Math.Max(stmin, num8)
stp = num8
If (brackt And flag) Then
If (sty > stx) Then
stp = Math.Min((stx + (0.66 * (sty - stx))), stp)
Else
stp = Math.Max((stx + (0.66 * (sty - stx))), stp)
End If
End If
End If
End Sub
Public Sub lbfgsminimize(ByVal n As Integer, ByVal m As Integer, ByRef x As Double(), ByVal epsg As Double, ByVal epsf As Double, ByVal epsx As Double, ByVal maxits As Integer, ByRef info As Integer)
Dim dx As Double() = New Double(0 - 1) {}
Dim abort As Boolean = False
Dim f As Double = 0
Dim num2 As Double = 0
Dim num3 As Double = 0
Dim num4 As Double = 0
Dim numArray2 As Double()
Dim numArray3 As Double()
Dim g As Double()
Dim wa As Double()
Dim num6 As Double = 0
Dim num7 As Double = 0
Dim ftol As Double = 0
Dim stp As Double = 0
Dim num10 As Double = 0
Dim num11 As Double = 0
Dim num12 As Double = 0
Dim num13 As Double = 0
Dim da As Double = 0
Dim num16 As Integer = 0
Dim num17 As Integer = 0
Dim num18 As Integer = 0
Dim num19 As Integer = 0
Dim num20 As Integer = 0
Dim maxfev As Integer = 0
Dim num22 As Integer = 0
Dim num23 As Integer = 0
Dim num24 As Integer = 0
Dim index As Integer = 0
Dim nfev As Integer = 0
Dim num27 As Integer = 0
Dim num28 As Integer = 0
Dim num29 As Integer = 0
Dim xtol As Double = 0
Dim gtol As Double = 0
Dim stpmin As Double = 0
Dim stpmax As Double = 0
Dim num34 As Integer = 0
dx = New Double((((n * ((2 * m) + 1)) + (2 * m)) + 1) - 1) {}
g = New Double((n + 1) - 1) {}
numArray2 = New Double((n + 1) - 1) {}
numArray3 = New Double((n + 1) - 1) {}
wa = New Double((n + 1) - 1) {}
Me.funcgrad(x, f, g)
num2 = f
num16 = 0
info = 0
If (((((((n <= 0) Or (m <= 0)) Or (m > n)) Or (epsg < 0)) Or (epsf < 0)) Or (epsx < 0)) Or (maxits < 0)) Then
info = -1
Return
End If
num17 = 1
num18 = 0
index = 1
Do While (index <= n)
wa(index) = 1
index += 1
Loop
xtol = 0.00000000000005
gtol = 0.9
stpmin = Math.Pow(10, -20)
stpmax = Math.Pow(10, 20)
num19 = (n + (2 * m))
num20 = (num19 + (n * m))
index = 1
Do While (index <= n)
dx((num19 + index)) = -(g(index) * wa(index))
index += 1
Loop
num6 = Math.Sqrt(Me.lbfgsdotproduct(n, g, 1, g, 1))
num7 = (1 / num6)
ftol = 0.0001
maxfev = 20
Label_0289:
num34 = 1
Do While (num34 <= n)
numArray2(num34) = x(num34)
num34 += 1
Loop
num16 += 1
info = 0
num22 = (num16 - 1)
If (num16 <> 1) Then
If (num16 > m) Then
num22 = m
End If
num10 = Me.lbfgsdotproduct(n, dx, ((num20 + num23) + 1), dx, ((num19 + num23) + 1))
num11 = Me.lbfgsdotproduct(n, dx, ((num20 + num23) + 1), dx, ((num20 + num23) + 1))
index = 1
Do While (index <= n)
wa(index) = (num10 / num11)
index += 1
Loop
num24 = num18
If (num18 = 0) Then
num24 = m
End If
dx((n + num24)) = (1 / num10)
index = 1
Do While (index <= n)
dx(index) = -g(index)
index += 1
Loop
num24 = num18
index = 1
Do While (index <= num22)
num24 -= 1
If (num24 = -1) Then
num24 = (m - 1)
End If
num12 = Me.lbfgsdotproduct(n, dx, ((num19 + (num24 * n)) + 1), dx, 1)
num27 = (((n + m) + num24) + 1)
num28 = (num20 + (num24 * n))
dx(num27) = (dx(((n + num24) + 1)) * num12)
Me.lbfgslincomb(n, -dx(num27), dx, (num28 + 1), dx, 1)
index += 1
Loop
index = 1
Do While (index <= n)
dx(index) = (wa(index) * dx(index))
index += 1
Loop
index = 1
Do While (index <= num22)
num13 = Me.lbfgsdotproduct(n, dx, ((num20 + (num24 * n)) + 1), dx, 1)
da = (dx(((n + num24) + 1)) * num13)
num27 = (((n + m) + num24) + 1)
da = (dx(num27) - da)
num29 = (num19 + (num24 * n))
Me.lbfgslincomb(n, da, dx, (num29 + 1), dx, 1)
num24 += 1
If (num24 = m) Then
num24 = 0
End If
index += 1
Loop
index = 1
Do While (index <= n)
dx(((num19 + (num18 * n)) + index)) = dx(index)
index += 1
Loop
End If
nfev = 0
stp = 1
If (num16 = 1) Then
stp = num7
End If
index = 1
Do While (index <= n)
dx(index) = g(index)
index += 1
Loop
Me.lbfgsmcsrch(n, x, f, g, dx, ((num19 + (num18 * n)) + 1), stp, ftol, xtol, maxfev, info, nfev, wa, gtol, stpmin, stpmax)
If ((Not info = 1) AndAlso (info = 0)) Then
info = -1
Else
num17 = (num17 + nfev)
num23 = (num18 * n)
index = 1
Do While (index <= n)
dx(((num19 + num23) + index)) = (stp * dx(((num19 + num23) + index)))
dx(((num20 + num23) + index)) = (g(index) - dx(index))
index += 1
Loop
num18 += 1
If (num18 = m) Then
num18 = 0
End If
If ((num16 > maxits) And (maxits > 0)) Then
info = 5
Else
Me.lbfgsnewiteration(x, f, g, abort)
If abort Then Exit Sub
If (Math.Sqrt(Me.lbfgsdotproduct(n, g, 1, g, 1)) <= epsg) Then
info = 4
Else
num3 = Math.Max(Math.Abs(num2), Math.Max(Math.Abs(f), 1))
If ((num2 - f) <= (epsf * num3)) Then
info = 1
Else
num34 = 1
Do While (num34 <= n)
numArray3(num34) = numArray2(num34)
num34 += 1
Loop
num34 = 1
Do While (num34 <= n)
numArray3(num34) = (numArray3(num34) - x(num34))
num34 += 1
Loop
num4 = Math.Max(Math.Max(Math.Sqrt(Me.lbfgsdotproduct(n, x, 1, x, 1)), Math.Sqrt(Me.lbfgsdotproduct(n, numArray2, 1, numArray2, 1))), 1)
If (Math.Sqrt(Me.lbfgsdotproduct(n, numArray3, 1, numArray3, 1)) <= epsx) Then
info = 2
Else
num2 = f
num34 = 1
Do While (num34 <= n)
numArray2(num34) = x(num34)
num34 += 1
Loop
GoTo Label_0289
End If
End If
End If
End If
End If
End Sub
End Class
End Namespace