Datasets:

introvoyz041
/

Dwsim

﻿'    Copyright 2020 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.Optimization

    Public Class NewtonSolver

        Public Property Tolerance As Double = 0.0001

        Public Property MaxIterations As Integer = 100

        Public Property EnableDamping As Boolean = True

        Public Property UseBroydenApproximation As Boolean = False

        Public Property ExpandFactor As Double = 1.5

        Public Property MaximumDelta As Double = 0.5

        Public Property Epsilon As Double = Double.NaN

        Private _Iterations As Integer = 0

        Private fxb As Func(Of Double(), Double())

        Private broydengrad As Double(,)

        Private brentsolver As New BrentOpt.BrentMinimize

        Private tmpx As Double(), tmpdx As Double()

        Private _jacobian As Boolean

        Private dfdx As Func(Of Double(), Double(,))

        Private _error As Double

        Private _jac As Double(,)

        Public ReadOnly Property Jacobian As Double(,)
            Get
                Return _jac
            End Get
        End Property

        Public ReadOnly Property BuildingJacobian As Boolean
            Get
                Return _jacobian
            End Get
        End Property

        Public ReadOnly Property Iterations As Integer
            Get
                Return _Iterations
            End Get
        End Property

        Sub New()

            brentsolver.DefineFuncDelegate(AddressOf minimizeerror)

        End Sub

        Public Sub Reset()

            _Iterations = 0
            _error = 0.0

        End Sub

        Public Shared Function FindRoots(functionbody As Func(Of Double(), Double()), vars As Double(),
                                         maxits As Integer, tol As Double) As Double()

            Dim newton As New NewtonSolver
            newton.Tolerance = tol
            newton.MaxIterations = maxits

            Return newton.Solve(functionbody, vars)

        End Function

        ''' <summary>
        ''' Solves a system of non-linear equations [f(x) = 0] using newton's method.
        ''' </summary>
        ''' <param name="functionbody">f(x) where x is a vector of double, returns the error values for each x</param>
        ''' <param name="vars">initial values for x</param>
        ''' <returns>vector of variables which solve the equations according to the minimum allowable error value (tolerance).</returns>
        Function Solve(functionbody As Func(Of Double(), Double()), vars As Double()) As Double()

            Dim dfacs As Double() = New Double() {0.1, 0.2, 0.4, 0.6, 0.8, 1.0}
            Dim epsilons As Double() = New Double() {0.000000000001, 0.00000001, 0.0001, 0.001, 0.01, 0.1}

            Dim leave As Boolean = False
            Dim finalx As Double() = vars

            dfdx = Nothing

            If Not Double.IsNaN(Epsilon) Then epsilons = New Double() {Epsilon}

            If EnableDamping Then
                For Each d In dfacs
                    If leave Then Exit For
                    For Each eps In epsilons
                        If leave Then Exit For
                        Try
                            finalx = solve_internal(d, eps, functionbody, vars)
                            leave = True
                        Catch ex As ArgumentException
                            'try next parameters
                        End Try
                    Next
                Next
            Else
                For Each eps In epsilons
                    If leave Then Exit For
                    Try
                        finalx = solve_internal(1.0, eps, functionbody, vars)
                        leave = True
                    Catch ex As ArgumentException
                        'try next parameters
                    End Try
                Next
            End If

            If Not leave Then Throw New Exception("Newton Convergence Error")

            Return finalx

        End Function

        ''' <summary>
        ''' Solves a system of non-linear equations [f(x) = 0] using newton's method.
        ''' </summary>
        ''' <param name="functionbody">f(x) where x is a vector of double, returns the error values for each x</param>
        ''' <param name="vars">initial values for x</param>
        ''' <returns>vector of variables which solve the equations according to the minimum allowable error value (tolerance).</returns>
        Function Solve(functionbody As Func(Of Double(), Double()), functiongradient As Func(Of Double(), Double(,)), vars As Double()) As Double()

            Dim dfacs As Double() = New Double() {0.1, 0.2, 0.4, 0.6, 0.8, 1.0}
            Dim epsilons As Double() = New Double() {0.000000000001, 0.00000001, 0.0001, 0.001, 0.01, 0.1}

            Dim leave As Boolean = False
            Dim finalx As Double() = vars

            dfdx = functiongradient

            If EnableDamping Then
                For Each d In dfacs
                    If leave Then Exit For
                    For Each eps In epsilons
                        If leave Then Exit For
                        Try
                            finalx = solve_internal(d, eps, functionbody, vars)
                            leave = True
                        Catch ex As ArgumentException
                            'try next parameters
                        End Try
                    Next
                Next
            Else
                For Each eps In epsilons
                    If leave Then Exit For
                    Try
                        finalx = solve_internal(1.0, eps, functionbody, vars)
                        leave = True
                    Catch ex As ArgumentException
                        'try next parameters
                    End Try
                Next
            End If

            If Not leave Then Throw New Exception("Newton Convergence Error")

            Return finalx

        End Function


        Private Function solve_internal(mindamp As Double, epsilon As Double, functionbody As Func(Of Double(), Double()), vars As Double()) As Double()

            fxb = functionbody

            Dim fx(), x(), dx(), dfdx(,), df, fxsum, fxsum0 As Double
            Dim success As Boolean = False

            x = vars.Clone

            dx = x.Clone

            _Iterations = 0

            Do

                If _Iterations = 0 Then
                    fxsum0 = 1.0E+20
                Else
                    fxsum0 = MathEx.Common.SumSqr(fx)
                End If

                _jacobian = False

                fx = fxb.Invoke(x)

                _error = MathEx.Common.SumSqr(fx)
                fxsum = _error

                If fxsum < Tolerance Then
                    Exit Do
                End If

                _jacobian = True

                dfdx = gradient(epsilon, x, fx)

                Dim A = MathNet.Numerics.LinearAlgebra.Matrix(Of Double).Build.DenseOfArray(dfdx)
                Dim B = MathNet.Numerics.LinearAlgebra.Vector(Of Double).Build.DenseOfArray(fx)

                dx = A.Solve(B).ToArray()

                'SysLin.rsolve.rmatrixsolve(dfdx, fx, x.Length, dx)

                'If success Then

                If Common.SumSqr(dx) < Tolerance And _Iterations > MaxIterations / 2 Then
                    Exit Do
                End If

                If EnableDamping Then
                    If _Iterations > 5 Then
                        df = df * ExpandFactor
                        If df > 1.0 Then df = 1.0
                    Else
                        df = mindamp
                    End If
                Else
                    df = 1.0#
                End If

                For i = 0 To x.Length - 1
                    If Math.Abs(x(i)) < 1.0E-20 Then
                        x(i) -= dx(i) * df
                    Else
                        If Math.Abs(dx(i) / x(i)) > MaximumDelta Then
                            dx(i) = Math.Sign(dx(i)) * Math.Abs(x(i)) * MaximumDelta
                        End If
                        x(i) -= dx(i) * df
                    End If
                Next

                'Else

                '    For i = 0 To x.Length - 1
                '        x(i) *= 0.999
                '    Next

                'End If

                _Iterations += 1

                If _Iterations > 50 And fxsum > fxsum0 Then
                    Throw New ArgumentException("not converging")
                End If

                If Double.IsNaN(fxsum) Then
                    Throw New ArgumentException("not converging")
                End If

            Loop Until _Iterations > MaxIterations

            If _Iterations > MaxIterations Then
                Throw New ArgumentException("not converged")
            End If

            If dfdx Is Nothing Then dfdx = gradient(epsilon, x, fx)

            _jac = dfdx

            Return x

        End Function

        Private Function gradient(epsilon As Double, ByVal x() As Double, fx() As Double) As Double(,)

            Dim f1(), f2() As Double
            Dim g(x.Length - 1, x.Length - 1), x1(x.Length - 1), x2(x.Length - 1), dx(x.Length - 1), xbr(x.Length - 1), fbr(x.Length - 1) As Double
            Dim i, j, k, n As Integer

            n = x.Length - 1

            If UseBroydenApproximation Then

                If broydengrad Is Nothing Then broydengrad = g.Clone()

                If _Iterations = 0 Then
                    For i = 0 To n
                        For j = 0 To n
                            If i = j Then broydengrad(i, j) = 1.0 Else broydengrad(i, j) = 0.0
                        Next
                    Next
                    Broyden.broydn(n, x, fx, dx, xbr, fbr, broydengrad, 0)
                Else
                    Broyden.broydn(n, x, fx, dx, xbr, fbr, broydengrad, 1)
                End If

                Return broydengrad

            Else

                If dfdx IsNot Nothing Then

                    g = dfdx.Invoke(x)

                Else

                    For i = 0 To x.Length - 1
                        For j = 0 To x.Length - 1
                            If i <> j Then
                                x1(j) = x(j)
                                x2(j) = x(j)
                            Else
                                If x(j) = 0.0# Then
                                    x1(j) = epsilon
                                    x2(j) = 2 * epsilon
                                Else
                                    x1(j) = x(j) * (1 - epsilon)
                                    x2(j) = x(j) * (1 + epsilon)
                                End If
                            End If
                        Next
                        f1 = fxb.Invoke(x1)
                        f2 = fxb.Invoke(x2)
                        For k = 0 To x.Length - 1
                            g(k, i) = (f2(k) - f1(k)) / (x2(i) - x1(i))
                        Next
                    Next

                End If

            End If

            Return g

        End Function

        Public Function minimizeerror(ByVal t As Double) As Double

            Dim tmpx0 As Double() = tmpx.Clone

            For i = 0 To tmpx.Length - 1
                tmpx0(i) -= tmpdx(i) * t
            Next

            Dim abssum0 = MathEx.Common.SumSqr(fxb.Invoke(tmpx0))
            If Double.IsNaN(abssum0) Then abssum0 = 1.0E+20
            Return abssum0

        End Function

    End Class

    Public Class NewtonSolver_Old

        Public Property Tolerance As Double = 0.0001

        Public Property MaxIterations As Integer = 1000

        Public Property EnableDamping As Boolean = True

        Private _Iterations As Integer = 0

        Private fxb As Func(Of Double(), Double())

        Private brentsolver As New BrentOpt.BrentMinimize

        Private tmpx As Double(), tmpdx As Double()

        Private _error As Double

        Public ReadOnly Property Iterations
            Get
                Return _Iterations
            End Get
        End Property

        Sub New()

            brentsolver.DefineFuncDelegate(AddressOf minimizeerror)

        End Sub

        ''' <summary>
        ''' Solves a system of non-linear equations [f(x) = 0] using newton's method.
        ''' </summary>
        ''' <param name="functionbody">f(x) where x is a vector of double, returns the error values for each x</param>
        ''' <param name="vars">initial values for x</param>
        ''' <returns>vector of variables which solve the equations according to the minimum allowable error value (tolerance).</returns>
        Function Solve(functionbody As Func(Of Double(), Double()), vars As Double()) As Double()

            Dim minimaldampings As Double() = New Double() {1.0E-20, 0.000000000000001, 0.0000000001, 0.00001, 0.0001, 0.001, 0.01, 0.1}
            Dim epsilons As Double() = New Double() {0.0000000001, 0.000000001, 0.00000001, 0.0000001, 0.000001, 0.00001, 0.0001, 0.001, 0.01, 0.1}

            Dim leave As Boolean = False
            Dim finalx As Double() = vars

            If EnableDamping Then
                For Each mindamp In minimaldampings
                    If leave Then Exit For
                    For Each eps In epsilons
                        If leave Then Exit For
                        Try
                            finalx = solve_internal(mindamp, eps, functionbody, vars)
                            leave = True
                        Catch ex As ArgumentException
                            'try next parameters
                        End Try
                    Next
                Next
            Else
                For Each eps In epsilons
                    If leave Then Exit For
                    Try
                        finalx = solve_internal(1.0, eps, functionbody, vars)
                        leave = True
                    Catch ex As ArgumentException
                        'try next parameters
                    End Try
                Next
            End If

            If Not leave Then Throw New Exception("newton convergence error")

            Return finalx

        End Function

        Private Function solve_internal(mindamp As Double, epsilon As Double, functionbody As Func(Of Double(), Double()), vars As Double()) As Double()

            fxb = functionbody

            Dim fx(), x(), dx(), dfdx(,), df, fxsum, fxsum0 As Double
            Dim success As Boolean = False

            x = vars.Clone

            dx = x.Clone

            _Iterations = 0

            Do

                If _Iterations = 0 Then
                    fxsum0 = 1.0E+20
                Else
                    fxsum0 = MathEx.Common.SumSqr(fx)
                End If

                fx = fxb.Invoke(x)

                _error = MathEx.Common.SumSqr(fx)
                fxsum = _error

                If Common.SumSqr(fx) < Tolerance Then Exit Do

                dfdx = gradient(epsilon, x)

                success = SysLin.rsolve.rmatrixsolve(dfdx, fx, x.Length, dx)

                If success Then

                    'this call to the brent solver calculates the damping factor which minimizes the error (fval).

                    If EnableDamping Then

                        tmpx = x.Clone
                        tmpdx = dx.Clone
                        brentsolver.brentoptimize(mindamp, 1.0, mindamp / 10.0#, df)

                    Else

                        df = 1.0#

                    End If

                    For i = 0 To x.Length - 1
                        x(i) -= dx(i) * df
                    Next

                Else

                    For i = 0 To x.Length - 1
                        x(i) *= 0.999
                    Next

                End If

                _Iterations += 1

                If _Iterations > 50 And fxsum > fxsum0 Then
                    Throw New ArgumentException("not converging")
                End If

                If Double.IsNaN(fxsum) Then
                    Throw New ArgumentException("not converging")
                End If

            Loop Until _Iterations > MaxIterations

            If _Iterations > MaxIterations Then
                Throw New ArgumentException("not converged")
            End If

            Return x

        End Function

        Private Function gradient(epsilon As Double, ByVal x() As Double) As Double(,)

            Dim f1(), f2() As Double
            Dim g(x.Length - 1, x.Length - 1), x2(x.Length - 1) As Double
            Dim i, j, k As Integer

            f1 = fxb.Invoke(x)
            For i = 0 To x.Length - 1
                For j = 0 To x.Length - 1
                    If i <> j Then
                        x2(j) = x(j)
                    Else
                        If x(j) = 0.0# Then
                            x2(j) = epsilon
                        Else
                            x2(j) = x(j) * (1 + epsilon)
                        End If
                    End If
                Next
                f2 = fxb.Invoke(x2)
                For k = 0 To x.Length - 1
                    g(k, i) = (f2(k) - f1(k)) / (x2(i) - x(i))
                Next
            Next

            Return g

        End Function

        Public Function minimizeerror(ByVal t As Double) As Double

            Dim tmpx0 As Double() = tmpx.Clone

            For i = 0 To tmpx.Length - 1
                tmpx0(i) -= tmpdx(i) * t
            Next

            Dim abssum0 = MathEx.Common.SumSqr(fxb.Invoke(tmpx0))
            If Double.IsNaN(abssum0) Then abssum0 = 1.0E+20
            Return abssum0

        End Function

    End Class


End Namespace

	' Copyright 2020 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.Optimization

	Public Class NewtonSolver

	Public Property Tolerance As Double = 0.0001

	Public Property MaxIterations As Integer = 100

	Public Property EnableDamping As Boolean = True

	Public Property UseBroydenApproximation As Boolean = False

	Public Property ExpandFactor As Double = 1.5

	Public Property MaximumDelta As Double = 0.5

	Public Property Epsilon As Double = Double.NaN

	Private _Iterations As Integer = 0

	Private fxb As Func(Of Double(), Double())

	Private broydengrad As Double(,)

	Private brentsolver As New BrentOpt.BrentMinimize

	Private tmpx As Double(), tmpdx As Double()

	Private _jacobian As Boolean

	Private dfdx As Func(Of Double(), Double(,))

	Private _error As Double

	Private _jac As Double(,)

	Public ReadOnly Property Jacobian As Double(,)
	Get
	Return _jac
	End Get
	End Property

	Public ReadOnly Property BuildingJacobian As Boolean
	Get
	Return _jacobian
	End Get
	End Property

	Public ReadOnly Property Iterations As Integer
	Get
	Return _Iterations
	End Get
	End Property

	Sub New()

	brentsolver.DefineFuncDelegate(AddressOf minimizeerror)

	End Sub

	Public Sub Reset()

	_Iterations = 0
	_error = 0.0

	End Sub

	Public Shared Function FindRoots(functionbody As Func(Of Double(), Double()), vars As Double(),
	maxits As Integer, tol As Double) As Double()

	Dim newton As New NewtonSolver
	newton.Tolerance = tol
	newton.MaxIterations = maxits

	Return newton.Solve(functionbody, vars)

	End Function

	''' <summary>
	''' Solves a system of non-linear equations [f(x) = 0] using newton's method.
	''' </summary>
	''' <param name="functionbody">f(x) where x is a vector of double, returns the error values for each x</param>
	''' <param name="vars">initial values for x</param>
	''' <returns>vector of variables which solve the equations according to the minimum allowable error value (tolerance).</returns>
	Function Solve(functionbody As Func(Of Double(), Double()), vars As Double()) As Double()

	Dim dfacs As Double() = New Double() {0.1, 0.2, 0.4, 0.6, 0.8, 1.0}
	Dim epsilons As Double() = New Double() {0.000000000001, 0.00000001, 0.0001, 0.001, 0.01, 0.1}

	Dim leave As Boolean = False
	Dim finalx As Double() = vars

	dfdx = Nothing

	If Not Double.IsNaN(Epsilon) Then epsilons = New Double() {Epsilon}

	If EnableDamping Then
	For Each d In dfacs
	If leave Then Exit For
	For Each eps In epsilons
	If leave Then Exit For
	Try
	finalx = solve_internal(d, eps, functionbody, vars)
	leave = True
	Catch ex As ArgumentException
	'try next parameters
	End Try
	Next
	Next
	Else
	For Each eps In epsilons
	If leave Then Exit For
	Try
	finalx = solve_internal(1.0, eps, functionbody, vars)
	leave = True
	Catch ex As ArgumentException
	'try next parameters
	End Try
	Next
	End If

	If Not leave Then Throw New Exception("Newton Convergence Error")

	Return finalx

	End Function

	''' <summary>
	''' Solves a system of non-linear equations [f(x) = 0] using newton's method.
	''' </summary>
	''' <param name="functionbody">f(x) where x is a vector of double, returns the error values for each x</param>
	''' <param name="vars">initial values for x</param>
	''' <returns>vector of variables which solve the equations according to the minimum allowable error value (tolerance).</returns>
	Function Solve(functionbody As Func(Of Double(), Double()), functiongradient As Func(Of Double(), Double(,)), vars As Double()) As Double()

	Dim dfacs As Double() = New Double() {0.1, 0.2, 0.4, 0.6, 0.8, 1.0}
	Dim epsilons As Double() = New Double() {0.000000000001, 0.00000001, 0.0001, 0.001, 0.01, 0.1}

	Dim leave As Boolean = False
	Dim finalx As Double() = vars

	dfdx = functiongradient

	If EnableDamping Then
	For Each d In dfacs
	If leave Then Exit For
	For Each eps In epsilons
	If leave Then Exit For
	Try
	finalx = solve_internal(d, eps, functionbody, vars)
	leave = True
	Catch ex As ArgumentException
	'try next parameters
	End Try
	Next
	Next
	Else
	For Each eps In epsilons
	If leave Then Exit For
	Try
	finalx = solve_internal(1.0, eps, functionbody, vars)
	leave = True
	Catch ex As ArgumentException
	'try next parameters
	End Try
	Next
	End If

	If Not leave Then Throw New Exception("Newton Convergence Error")

	Return finalx

	End Function


	Private Function solve_internal(mindamp As Double, epsilon As Double, functionbody As Func(Of Double(), Double()), vars As Double()) As Double()

	fxb = functionbody

	Dim fx(), x(), dx(), dfdx(,), df, fxsum, fxsum0 As Double
	Dim success As Boolean = False

	x = vars.Clone

	dx = x.Clone

	_Iterations = 0

	Do

	If _Iterations = 0 Then
	fxsum0 = 1.0E+20
	Else
	fxsum0 = MathEx.Common.SumSqr(fx)
	End If

	_jacobian = False

	fx = fxb.Invoke(x)

	_error = MathEx.Common.SumSqr(fx)
	fxsum = _error

	If fxsum < Tolerance Then
	Exit Do
	End If

	_jacobian = True

	dfdx = gradient(epsilon, x, fx)

	Dim A = MathNet.Numerics.LinearAlgebra.Matrix(Of Double).Build.DenseOfArray(dfdx)
	Dim B = MathNet.Numerics.LinearAlgebra.Vector(Of Double).Build.DenseOfArray(fx)

	dx = A.Solve(B).ToArray()

	'SysLin.rsolve.rmatrixsolve(dfdx, fx, x.Length, dx)

	'If success Then

	If Common.SumSqr(dx) < Tolerance And _Iterations > MaxIterations / 2 Then
	Exit Do
	End If

	If EnableDamping Then
	If _Iterations > 5 Then
	df = df * ExpandFactor
	If df > 1.0 Then df = 1.0
	Else
	df = mindamp
	End If
	Else
	df = 1.0#
	End If

	For i = 0 To x.Length - 1
	If Math.Abs(x(i)) < 1.0E-20 Then
	x(i) -= dx(i) * df
	Else
	If Math.Abs(dx(i) / x(i)) > MaximumDelta Then
	dx(i) = Math.Sign(dx(i)) * Math.Abs(x(i)) * MaximumDelta
	End If
	x(i) -= dx(i) * df
	End If
	Next

	'Else

	' For i = 0 To x.Length - 1
	' x(i) *= 0.999
	' Next

	'End If

	_Iterations += 1

	If _Iterations > 50 And fxsum > fxsum0 Then
	Throw New ArgumentException("not converging")
	End If

	If Double.IsNaN(fxsum) Then
	Throw New ArgumentException("not converging")
	End If

	Loop Until _Iterations > MaxIterations

	If _Iterations > MaxIterations Then
	Throw New ArgumentException("not converged")
	End If

	If dfdx Is Nothing Then dfdx = gradient(epsilon, x, fx)

	_jac = dfdx

	Return x

	End Function

	Private Function gradient(epsilon As Double, ByVal x() As Double, fx() As Double) As Double(,)

	Dim f1(), f2() As Double
	Dim g(x.Length - 1, x.Length - 1), x1(x.Length - 1), x2(x.Length - 1), dx(x.Length - 1), xbr(x.Length - 1), fbr(x.Length - 1) As Double
	Dim i, j, k, n As Integer

	n = x.Length - 1

	If UseBroydenApproximation Then

	If broydengrad Is Nothing Then broydengrad = g.Clone()

	If _Iterations = 0 Then
	For i = 0 To n
	For j = 0 To n
	If i = j Then broydengrad(i, j) = 1.0 Else broydengrad(i, j) = 0.0
	Next
	Next
	Broyden.broydn(n, x, fx, dx, xbr, fbr, broydengrad, 0)
	Else
	Broyden.broydn(n, x, fx, dx, xbr, fbr, broydengrad, 1)
	End If

	Return broydengrad

	Else

	If dfdx IsNot Nothing Then

	g = dfdx.Invoke(x)

	Else

	For i = 0 To x.Length - 1
	For j = 0 To x.Length - 1
	If i <> j Then
	x1(j) = x(j)
	x2(j) = x(j)
	Else
	If x(j) = 0.0# Then
	x1(j) = epsilon
	x2(j) = 2 * epsilon
	Else
	x1(j) = x(j) * (1 - epsilon)
	x2(j) = x(j) * (1 + epsilon)
	End If
	End If
	Next
	f1 = fxb.Invoke(x1)
	f2 = fxb.Invoke(x2)
	For k = 0 To x.Length - 1
	g(k, i) = (f2(k) - f1(k)) / (x2(i) - x1(i))
	Next
	Next

	End If

	End If

	Return g

	End Function

	Public Function minimizeerror(ByVal t As Double) As Double

	Dim tmpx0 As Double() = tmpx.Clone

	For i = 0 To tmpx.Length - 1
	tmpx0(i) -= tmpdx(i) * t
	Next

	Dim abssum0 = MathEx.Common.SumSqr(fxb.Invoke(tmpx0))
	If Double.IsNaN(abssum0) Then abssum0 = 1.0E+20
	Return abssum0

	End Function

	End Class

	Public Class NewtonSolver_Old

	Public Property Tolerance As Double = 0.0001

	Public Property MaxIterations As Integer = 1000

	Public Property EnableDamping As Boolean = True

	Private _Iterations As Integer = 0

	Private fxb As Func(Of Double(), Double())

	Private brentsolver As New BrentOpt.BrentMinimize

	Private tmpx As Double(), tmpdx As Double()

	Private _error As Double

	Public ReadOnly Property Iterations
	Get
	Return _Iterations
	End Get
	End Property

	Sub New()

	brentsolver.DefineFuncDelegate(AddressOf minimizeerror)

	End Sub

	''' <summary>
	''' Solves a system of non-linear equations [f(x) = 0] using newton's method.
	''' </summary>
	''' <param name="functionbody">f(x) where x is a vector of double, returns the error values for each x</param>
	''' <param name="vars">initial values for x</param>
	''' <returns>vector of variables which solve the equations according to the minimum allowable error value (tolerance).</returns>
	Function Solve(functionbody As Func(Of Double(), Double()), vars As Double()) As Double()

	Dim minimaldampings As Double() = New Double() {1.0E-20, 0.000000000000001, 0.0000000001, 0.00001, 0.0001, 0.001, 0.01, 0.1}
	Dim epsilons As Double() = New Double() {0.0000000001, 0.000000001, 0.00000001, 0.0000001, 0.000001, 0.00001, 0.0001, 0.001, 0.01, 0.1}

	Dim leave As Boolean = False
	Dim finalx As Double() = vars

	If EnableDamping Then
	For Each mindamp In minimaldampings
	If leave Then Exit For
	For Each eps In epsilons
	If leave Then Exit For
	Try
	finalx = solve_internal(mindamp, eps, functionbody, vars)
	leave = True
	Catch ex As ArgumentException
	'try next parameters
	End Try
	Next
	Next
	Else
	For Each eps In epsilons
	If leave Then Exit For
	Try
	finalx = solve_internal(1.0, eps, functionbody, vars)
	leave = True
	Catch ex As ArgumentException
	'try next parameters
	End Try
	Next
	End If

	If Not leave Then Throw New Exception("newton convergence error")

	Return finalx

	End Function

	Private Function solve_internal(mindamp As Double, epsilon As Double, functionbody As Func(Of Double(), Double()), vars As Double()) As Double()

	fxb = functionbody

	Dim fx(), x(), dx(), dfdx(,), df, fxsum, fxsum0 As Double
	Dim success As Boolean = False

	x = vars.Clone

	dx = x.Clone

	_Iterations = 0

	Do

	If _Iterations = 0 Then
	fxsum0 = 1.0E+20
	Else
	fxsum0 = MathEx.Common.SumSqr(fx)
	End If

	fx = fxb.Invoke(x)

	_error = MathEx.Common.SumSqr(fx)
	fxsum = _error

	If Common.SumSqr(fx) < Tolerance Then Exit Do

	dfdx = gradient(epsilon, x)

	success = SysLin.rsolve.rmatrixsolve(dfdx, fx, x.Length, dx)

	If success Then

	'this call to the brent solver calculates the damping factor which minimizes the error (fval).

	If EnableDamping Then

	tmpx = x.Clone
	tmpdx = dx.Clone
	brentsolver.brentoptimize(mindamp, 1.0, mindamp / 10.0#, df)

	Else

	df = 1.0#

	End If

	For i = 0 To x.Length - 1
	x(i) -= dx(i) * df
	Next

	Else

	For i = 0 To x.Length - 1
	x(i) *= 0.999
	Next

	End If

	_Iterations += 1

	If _Iterations > 50 And fxsum > fxsum0 Then
	Throw New ArgumentException("not converging")
	End If

	If Double.IsNaN(fxsum) Then
	Throw New ArgumentException("not converging")
	End If

	Loop Until _Iterations > MaxIterations

	If _Iterations > MaxIterations Then
	Throw New ArgumentException("not converged")
	End If

	Return x

	End Function

	Private Function gradient(epsilon As Double, ByVal x() As Double) As Double(,)

	Dim f1(), f2() As Double
	Dim g(x.Length - 1, x.Length - 1), x2(x.Length - 1) As Double
	Dim i, j, k As Integer

	f1 = fxb.Invoke(x)
	For i = 0 To x.Length - 1
	For j = 0 To x.Length - 1
	If i <> j Then
	x2(j) = x(j)
	Else
	If x(j) = 0.0# Then
	x2(j) = epsilon
	Else
	x2(j) = x(j) * (1 + epsilon)
	End If
	End If
	Next
	f2 = fxb.Invoke(x2)
	For k = 0 To x.Length - 1
	g(k, i) = (f2(k) - f1(k)) / (x2(i) - x(i))
	Next
	Next

	Return g

	End Function

	Public Function minimizeerror(ByVal t As Double) As Double

	Dim tmpx0 As Double() = tmpx.Clone

	For i = 0 To tmpx.Length - 1
	tmpx0(i) -= tmpdx(i) * t
	Next

	Dim abssum0 = MathEx.Common.SumSqr(fxb.Invoke(tmpx0))
	If Double.IsNaN(abssum0) Then abssum0 = 1.0E+20
	Return abssum0

	End Function

	End Class


	End Namespace