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Namespace MathEx.SysLin
Public Class rsolve
'/*************************************************************************
' Solving a system of linear equations with a system matrix given by its
' LU decomposition.
' The algorithm solves a system of linear equations whose matrix is given by
' its LU decomposition. In case of a singular matrix, the algorithm returns
' False.
' The algorithm solves systems with a square matrix only.
' Input parameters:
' A - LU decomposition of a system matrix in compact form (the
' result of the RMatrixLU subroutine).
' Pivots - row permutation table (the result of a
' RMatrixLU subroutine).
' B - right side of a system.
' Array whose index ranges within [0..N-1].
' N - size of matrix A.
' Output parameters:
' X - solution of a system.
' Array whose index ranges within [0..N-1].
' Result:
' True, if the matrix is not singular.
' False, if the matrux is singular. In this case, X doesn't contain a
' solution.
' -- ALGLIB --
' Copyright 2005-2008 by Bochkanov Sergey
'*************************************************************************/
' Methods
Public Shared Function rmatrixlusolve(ByRef a As Double(,), ByRef pivots As Integer(), ByVal b As Double(), ByVal n As Integer, ByRef x As Double()) As Boolean
Dim result As Boolean = False
Dim y As Double() = New Double(0) {}
Dim i As Integer = 0
Dim v As Double = 0
Dim i_ As Integer = 0
b = DirectCast(b.Clone, Double())
y = New Double(((n - 1) + 1)) {}
x = New Double(((n - 1) + 1)) {}
result = True
i = 0
Do While (i <= (n - 1))
If (a(i, i) = 0) Then
Return False
End If
i += 1
Loop
i = 0
Do While (i <= (n - 1))
If (pivots(i) <> i) Then
v = b(i)
b(i) = b(pivots(i))
b(pivots(i)) = v
End If
i += 1
Loop
y(0) = b(0)
i = 1
Do While (i <= (n - 1))
v = 0
i_ = 0
Do While (i_ <= (i - 1))
v = (v + (a(i, i_) * y(i_)))
i_ += 1
Loop
y(i) = (b(i) - v)
i += 1
Loop
x((n - 1)) = (y((n - 1)) / a((n - 1), (n - 1)))
i = (n - 2)
Do While (i >= 0)
v = 0
i_ = (i + 1)
Do While (i_ <= (n - 1))
v = (v + (a(i, i_) * x(i_)))
i_ += 1
Loop
x(i) = ((y(i) - v) / a(i, i))
i -= 1
Loop
Return result
End Function
'/*************************************************************************
' Solving a system of linear equations.
' The algorithm solves a system of linear equations by using the
' LU decomposition. The algorithm solves systems with a square matrix only.
' Input parameters:
' A - system matrix.
' Array whose indexes range within [0..N-1, 0..N-1].
' B - right side of a system.
' Array whose indexes range within [0..N-1].
' N - size of matrix A.
' Output parameters:
' X - solution of a system.
' Array whose index ranges within [0..N-1].
' Result:
' True, if the matrix is not singular.
' False, if the matrix is singular. In this case, X doesn't contain a
' solution.
' -- ALGLIB --
' Copyright 2005-2008 by Bochkanov Sergey
'*************************************************************************/
Public Shared Function rmatrixsolve(ByVal a As Double(,), ByVal b As Double(), ByVal n As Integer, ByRef x As Double()) As Boolean
Dim pivots As Integer() = New Integer(0) {}
a = DirectCast(a.Clone, Double(,))
b = DirectCast(b.Clone, Double())
lu.rmatrixlu(a, n, n, pivots)
Return rsolve.rmatrixlusolve(a, pivots, b, n, x)
End Function
Public Shared Function solvesystem(ByVal a As Double(,), ByVal b As Double(), ByVal n As Integer, ByRef x As Double()) As Boolean
Dim pivots As Integer() = New Integer(0) {}
a = DirectCast(a.Clone, Double(,))
b = DirectCast(b.Clone, Double())
lu.ludecomposition(a, n, n, pivots)
Return rsolve.solvesystemlu(a, pivots, b, n, x)
End Function
Public Shared Function solvesystemlu(ByRef a As Double(,), ByRef pivots As Integer(), ByVal b As Double(), ByVal n As Integer, ByRef x As Double()) As Boolean
Dim result As Boolean = False
Dim y As Double() = New Double(0) {}
Dim i As Integer = 0
Dim v As Double = 0
Dim ip1 As Integer = 0
Dim im1 As Integer = 0
Dim i_ As Integer = 0
b = DirectCast(b.Clone, Double())
y = New Double(n + 1) {}
x = New Double(n + 1) {}
result = True
i = 1
Do While (i <= n)
If (a(i, i) = 0) Then
Return False
End If
i += 1
Loop
i = 1
Do While (i <= n)
If (pivots(i) <> i) Then
v = b(i)
b(i) = b(pivots(i))
b(pivots(i)) = v
End If
i += 1
Loop
y(1) = b(1)
i = 2
Do While (i <= n)
im1 = (i - 1)
v = 0
i_ = 1
Do While (i_ <= im1)
v = (v + (a(i, i_) * y(i_)))
i_ += 1
Loop
y(i) = (b(i) - v)
i += 1
Loop
x(n) = (y(n) / a(n, n))
i = (n - 1)
Do While (i >= 1)
ip1 = (i + 1)
v = 0
i_ = ip1
Do While (i_ <= n)
v = (v + (a(i, i_) * x(i_)))
i_ += 1
Loop
x(i) = ((y(i) - v) / a(i, i))
i -= 1
Loop
Return result
End Function
End Class
Public Class lu
'/*************************************************************************
' LU decomposition of a general matrix of size MxN
' The subroutine calculates the LU decomposition of a rectangular general
' matrix with partial pivoting (with row permutations).
' Input parameters:
' A - matrix A whose indexes range within [0..M-1, 0..N-1].
' M - number of rows in matrix A.
' N - number of columns in matrix A.
' Output parameters:
' A - matrices L and U in compact form (see below).
' Array whose indexes range within [0..M-1, 0..N-1].
' Pivots - permutation matrix in compact form (see below).
' Array whose index ranges within [0..Min(M-1,N-1)].
' Matrix A is represented as A = P * L * U, where P is a permutation matrix,
' matrix L - lower triangular (or lower trapezoid, if M>N) matrix,
' U - upper triangular (or upper trapezoid, if M<N) matrix.
' Let M be equal to 4 and N be equal to 3:
' ( 1 ) ( U11 U12 U13 )
' A = P1 * P2 * P3 * ( L21 1 ) * ( U22 U23 )
' ( L31 L32 1 ) ( U33 )
' ( L41 L42 L43 )
' Matrix L has size MxMin(M,N), matrix U has size Min(M,N)xN, matrix P(i) is
' a permutation of the identity matrix of size MxM with numbers I and Pivots[I].
' The algorithm returns array Pivots and the following matrix which replaces
' matrix A and contains matrices L and U in compact form (the example applies
' to M=4, N=3).
' ( U11 U12 U13 )
' ( L21 U22 U23 )
' ( L31 L32 U33 )
' ( L41 L42 L43 )
' As we can see, the unit diagonal isn't stored.
' -- LAPACK routine (version 3.0) --
' Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
' Courant Institute, Argonne National Lab, and Rice University
' June 30, 1992
' *************************************************************************/
' Methods
Public Shared Sub ludecomposition(ByRef a As Double(,), ByVal m As Integer, ByVal n As Integer, ByRef pivots As Integer())
Dim i As Integer = 0
Dim j As Integer = 0
Dim jp As Integer = 0
Dim t1 As Double() = New Double(0) {}
Dim s As Double = 0
Dim i_ As Integer = 0
pivots = New Integer((Math.Min(m, n) + 1)) {}
t1 = New Double((Math.Max(m, n) + 1)) {}
If Not ((m = 0) Or (n = 0)) Then
j = 1
Do While (j <= Math.Min(m, n))
jp = j
i = (j + 1)
Do While (i <= m)
If (Math.Abs(a(i, j)) > Math.Abs(a(jp, j))) Then
jp = i
End If
i += 1
Loop
pivots(j) = jp
If (a(jp, j) <> 0) Then
If (jp <> j) Then
i_ = 1
Do While (i_ <= n)
t1(i_) = a(j, i_)
i_ += 1
Loop
i_ = 1
Do While (i_ <= n)
a(j, i_) = a(jp, i_)
i_ += 1
Loop
i_ = 1
Do While (i_ <= n)
a(jp, i_) = t1(i_)
i_ += 1
Loop
End If
If (j < m) Then
jp = (j + 1)
s = (1 / a(j, j))
i_ = jp
Do While (i_ <= m)
a(i_, j) = (s * a(i_, j))
i_ += 1
Loop
End If
End If
If (j < Math.Min(m, n)) Then
jp = (j + 1)
i = (j + 1)
Do While (i <= m)
s = a(i, j)
i_ = jp
Do While (i_ <= n)
a(i, i_) = (a(i, i_) - (s * a(j, i_)))
i_ += 1
Loop
i += 1
Loop
End If
j += 1
Loop
End If
End Sub
Public Shared Sub ludecompositionunpacked(ByVal a As Double(,), ByVal m As Integer, ByVal n As Integer, ByRef l As Double(,), ByRef u As Double(,), ByRef pivots As Integer())
Dim i As Integer = 0
Dim j As Integer = 0
Dim minmn As Integer = 0
a = DirectCast(a.Clone, Double(,))
If Not ((m = 0) Or (n = 0)) Then
minmn = Math.Min(m, n)
l = New Double((m + 1), (minmn + 1)) {}
u = New Double((minmn + 1), (n + 1)) {}
lu.ludecomposition(a, m, n, pivots)
i = 1
Do While (i <= m)
j = 1
Do While (j <= minmn)
If (j > i) Then
l(i, j) = 0
End If
If (j = i) Then
l(i, j) = 1
End If
If (j < i) Then
l(i, j) = a(i, j)
End If
j += 1
Loop
i += 1
Loop
i = 1
Do While (i <= minmn)
j = 1
Do While (j <= n)
If (j < i) Then
u(i, j) = 0
End If
If (j >= i) Then
u(i, j) = a(i, j)
End If
j += 1
Loop
i += 1
Loop
End If
End Sub
Public Shared Sub rmatrixlu(ByRef a As Double(,), ByVal m As Integer, ByVal n As Integer, ByRef pivots As Integer())
Dim b(,) As Double = New Double(0, 0) {}
Dim t As Double() = New Double(0) {}
Dim bp As Integer() = New Integer(0) {}
Dim minmn As Integer = 0
Dim i As Integer = 0
Dim ip As Integer = 0
Dim j As Integer = 0
Dim j1 As Integer = 0
Dim j2 As Integer = 0
Dim cb As Integer = 0
Dim nb As Integer = 0
Dim v As Double = 0
Dim i_ As Integer = 0
Dim i1_ As Integer = 0
nb = 8
If (((n <= 1) Or (Math.Min(m, n) <= nb)) Or (nb = 1)) Then
lu.rmatrixlu2(a, m, n, pivots)
Else
b = New Double(((m - 1) + 1), ((nb - 1) + 1)) {}
t = New Double(((n - 1) + 1)) {}
pivots = New Integer(((Math.Min(m, n) - 1) + 1)) {}
minmn = Math.Min(m, n)
j1 = 0
j2 = (Math.Min(minmn, nb) - 1)
Do While (j1 < minmn)
cb = ((j2 - j1) + 1)
i = j1
Do While (i <= (m - 1))
i1_ = j1
i_ = 0
Do While (i_ <= (cb - 1))
b((i - j1), i_) = a(i, (i_ + i1_))
i_ += 1
Loop
i += 1
Loop
lu.rmatrixlu2(b, (m - j1), cb, bp)
i = j1
Do While (i <= (m - 1))
i1_ = -j1
i_ = j1
Do While (i_ <= j2)
a(i, i_) = b((i - j1), (i_ + i1_))
i_ += 1
Loop
i += 1
Loop
i = 0
Do While (i <= (cb - 1))
ip = bp(i)
pivots((j1 + i)) = (j1 + ip)
If (bp(i) <> i) Then
If (j1 <> 0) Then
i_ = 0
Do While (i_ <= (j1 - 1))
t(i_) = a((j1 + i), i_)
i_ += 1
Loop
i_ = 0
Do While (i_ <= (j1 - 1))
a((j1 + i), i_) = a((j1 + ip), i_)
i_ += 1
Loop
i_ = 0
Do While (i_ <= (j1 - 1))
a((j1 + ip), i_) = t(i_)
i_ += 1
Loop
End If
If (j2 < (n - 1)) Then
i_ = (j2 + 1)
Do While (i_ <= (n - 1))
t(i_) = a((j1 + i), i_)
i_ += 1
Loop
i_ = (j2 + 1)
Do While (i_ <= (n - 1))
a((j1 + i), i_) = a((j1 + ip), i_)
i_ += 1
Loop
i_ = (j2 + 1)
Do While (i_ <= (n - 1))
a((j1 + ip), i_) = t(i_)
i_ += 1
Loop
End If
End If
i += 1
Loop
If (j2 < (n - 1)) Then
i = (j1 + 1)
Do While (i <= j2)
j = j1
Do While (j <= (i - 1))
v = a(i, j)
i_ = (j2 + 1)
Do While (i_ <= (n - 1))
a(i, i_) = (a(i, i_) - (v * a(j, i_)))
i_ += 1
Loop
j += 1
Loop
i += 1
Loop
End If
If (j2 < (n - 1)) Then
i = (j2 + 1)
Do While (i <= (m - 1))
j = j1
Do While (j <= j2)
v = a(i, j)
i_ = (j2 + 1)
Do While (i_ <= (n - 1))
a(i, i_) = (a(i, i_) - (v * a(j, i_)))
i_ += 1
Loop
j += 1
Loop
i += 1
Loop
End If
j1 = (j2 + 1)
j2 = (Math.Min(minmn, (j1 + nb)) - 1)
Loop
End If
End Sub
Private Shared Sub rmatrixlu2(ByRef a As Double(,), ByVal m As Integer, ByVal n As Integer, ByRef pivots As Integer())
Dim i As Integer = 0
Dim j As Integer = 0
Dim jp As Integer = 0
Dim t1 As Double() = New Double(0) {}
Dim s As Double = 0
Dim i_ As Integer = 0
pivots = New Integer((Math.Min(Convert.ToInt32((m - 1)), Convert.ToInt32((n - 1))) + 1)) {}
t1 = New Double((Math.Max(Convert.ToInt32((m - 1)), Convert.ToInt32((n - 1))) + 1)) {}
If Not ((m = 0) Or (n = 0)) Then
j = 0
Do While (j <= Math.Min(Convert.ToInt32((m - 1)), Convert.ToInt32((n - 1))))
jp = j
i = (j + 1)
Do While (i <= (m - 1))
If (Math.Abs(a(i, j)) > Math.Abs(a(jp, j))) Then
jp = i
End If
i += 1
Loop
pivots(j) = jp
If (a(jp, j) <> 0) Then
If (jp <> j) Then
i_ = 0
Do While (i_ <= (n - 1))
t1(i_) = a(j, i_)
i_ += 1
Loop
i_ = 0
Do While (i_ <= (n - 1))
a(j, i_) = a(jp, i_)
i_ += 1
Loop
i_ = 0
Do While (i_ <= (n - 1))
a(jp, i_) = t1(i_)
i_ += 1
Loop
End If
If (j < m) Then
jp = (j + 1)
s = (1 / a(j, j))
i_ = jp
Do While (i_ <= (m - 1))
a(i_, j) = (s * a(i_, j))
i_ += 1
Loop
End If
End If
If (j < (Math.Min(m, n) - 1)) Then
jp = (j + 1)
i = (j + 1)
Do While (i <= (m - 1))
s = a(i, j)
i_ = jp
Do While (i_ <= (n - 1))
a(i, i_) = (a(i, i_) - (s * a(j, i_)))
i_ += 1
Loop
i += 1
Loop
End If
j += 1
Loop
End If
End Sub
' Fields
Public Const lunb As Integer = 8
End Class
Public Class yves
'Author: Yves Vander Haeghen (Yves.VanderHaeghen@UGent.be)
'Version: 1.0
'VersionDate": 13 june 2003
'Class of helper functions for simple algebra operations on 1 and 2 dimensional single arrays
'Although speed is not essential, we try to avoid recreating and reallocating output arrays
'on every call as this could slow things down a lot. This means that usually the output arrays MUST
'be allocated and passed to the functions, except when they are passed on by reference.
'All matrices are supposedly ordered ROW x COLUMN
'August 2003: Added non-linear optimization (Nelder-Mead simplex algorithm)
Enum NormOrder As Integer
AbsoluteValue = 1
Euclidean = 2
Max = 16
End Enum
'Defines for NMS algorithm
Private Const NMSMAX = 30000
Private Const NMSTINY = 0.000000001
Private Const NMSTOL = 1.0E-23 'Machine precision?
'Helper function for NMS algorithm
Private Shared Sub Swap(ByRef sA As Single, ByRef sB As Single)
Dim sTemp As Single
sTemp = sA
sA = sB
sB = sTemp
End Sub
'Prototype for the function to be optimized
Delegate Function SolveNonLinearError(ByVal sX() As Single) As Single
Public Shared Function SolveNonLinear(ByVal sX(,) As Single, _
ByVal sY() As Single, _
ByVal lNrIterations As Long, _
ByVal ErrorFunction As SolveNonLinearError) As Boolean
'Minimize a function of iNrDim dimensions using the Nelder-Mead
'simplex algorythm (NMS). sX is a (iNrDim + 1) by iNrDim matrix
'initialized with a starting simplex. sY is a iNrDim vector with
'function values at the simplex points.
Dim iNrDims As Integer
Dim iNrPts As Integer, iLo As Integer, iHi As Integer
Dim i As Integer, j As Integer, iNHi As Integer
Dim sSum() As Single, sYSave As Single, sYTry As Single
Dim sRTol As Single, iDisplayCounter As Integer
SolveNonLinear = False
iNrDims = sX.GetUpperBound(1) + 1
iNrPts = iNrDims + 1
ReDim sSum(iNrDims - 1)
lNrIterations = 0
iDisplayCounter = 0
Sum(sX, sSum)
Do
'Rank vertices of simplex by function value
iLo = 0
If sY(0) > sY(1) Then
iNHi = 1
iHi = 0
Else
iNHi = 0
iHi = 1
End If
For i = 0 To iNrPts - 1
If sY(i) <= sY(iLo) Then iLo = i
If sY(i) > sY(iHi) Then
iNHi = iHi
iHi = i
ElseIf (sY(i) > sY(iNHi)) And (i <> iHi) Then
iNHi = i
End If
Next i
'TEST
'Debug.Print "Highest vertex: " & iHi & ", next " & iNHi
'Debug.Print "Lowest vertex: " & iLo
iDisplayCounter = iDisplayCounter + 1
sRTol = 2.0# * Math.Abs(sY(iHi) - sY(iLo)) / (Math.Abs(sY(iHi)) + Math.Abs(sY(iLo)) + NMSTINY)
If iDisplayCounter Mod 200 = 0 Then
Console.WriteLine("Iteration " & lNrIterations & ", best solution has error: " & sY(iLo))
End If
'Convergence criterium
If sRTol < NMSTOL Then
Swap(sY(0), sY(iLo))
For i = 0 To iNrDims - 1
Swap(sX(0, i), sX(iLo, i))
Next i
Dim sCoef(iNrDims - 1) As Single
Console.WriteLine("Convergence after " & lNrIterations & " iterations, with error " & sY(iLo))
GetMatrixRow(sX, sCoef, iLo)
Console.WriteLine("Parameters are " & ToString(sCoef))
Exit Do
End If
If lNrIterations > NMSMAX Then
'Do not raise error, result is useful most of the time!
'NMSErrorType = NMSTooManyIterations
'GoTo ErrorHandler
Exit Function
End If
lNrIterations = lNrIterations + 2
sYTry = SolveNonLinearAdjustSimplex(sX, sY, sSum, iNrDims, iHi, -1.0#, ErrorFunction)
If sYTry < sY(iLo) Then
sYTry = SolveNonLinearAdjustSimplex(sX, sY, sSum, iNrDims, iHi, 2.0#, ErrorFunction)
ElseIf sYTry > sY(iNHi) Then
sYSave = sY(iHi)
sYTry = SolveNonLinearAdjustSimplex(sX, sY, sSum, iNrDims, iHi, 0.5, ErrorFunction)
If sYTry >= sYSave Then
For i = 0 To iNrPts - 1
If i <> iLo Then
For j = 0 To iNrDims - 1
sX(i, j) = 0.5 * (sX(i, j) + sX(iLo, j))
sSum(j) = sX(i, j)
Next j
sY(i) = ErrorFunction(sSum)
End If
Next i
lNrIterations = lNrIterations + iNrDims
Sum(sX, sSum)
Else
lNrIterations = lNrIterations - 1
End If
End If
Loop While True
SolveNonLinear = True
End Function
Private Shared Function SolveNonLinearAdjustSimplex(ByVal sX(,) As Single, _
ByVal sY() As Single, _
ByVal sSum() As Single, _
ByVal iNrDims As Integer, _
ByVal iHi As Integer, _
ByVal sFactor As Single, _
ByVal ErrorFunction As SolveNonLinearError) As Single
Dim i As Integer, sFactor1 As Single, sFactor2 As Single
Dim sYTry As Single, sXTry(iNrDims - 1) As Single
'Debug.Print "Try adjustment simplex with factor " & sFactor
sFactor1 = (1.0# - sFactor) / iNrDims
sFactor2 = sFactor1 - sFactor
For i = 0 To iNrDims - 1
sXTry(i) = sSum(i) * sFactor1 - sX(iHi, i) * sFactor2
Next i
sYTry = ErrorFunction(sXTry)
'Console.WriteLine("Proposed vertex " & ToString(sXTry) & "Value " & sYTry)
If sYTry < sY(iHi) Then
sY(iHi) = sYTry
For i = 0 To iNrDims - 1
sSum(i) = sSum(i) + sXTry(i) - sX(iHi, i)
sX(iHi, i) = sXTry(i)
Next i
'DisplayMatrix "New simplex", sX()
Else
'Debug.Print "Vertex rejected"
End If
SolveNonLinearAdjustSimplex = sYTry
End Function
Public Shared Sub SolveNonLinearTest(ByVal iNrDims As Integer)
Dim sCoef() As Single, iVertexNr As Integer
Dim sSimplex(,) As Single, iNrVertices As Integer
Dim sSimplexVal() As Single, lNrIterations As Long
Dim i As Integer
Randomize()
iNrVertices = iNrDims + 1
ReDim sCoef(iNrDims - 1)
ReDim sSimplex(iNrVertices - 1, iNrDims - 1)
ReDim sSimplexVal(iNrVertices - 1)
For iVertexNr = 0 To iNrVertices - 1
For i = 0 To iNrDims - 1
If iVertexNr > 0 And i = iVertexNr - 1 Then
sCoef(i) = 1.0 * Rnd()
Else
sCoef(i) = 0.0#
End If
Next i
'Put in simplex and compute function value
SetMatrixRow(sSimplex, sCoef, iVertexNr)
sSimplexVal(iVertexNr) = SolveNonLinearTestError(sCoef)
Next iVertexNr
'Optimize
SolveNonLinear(sSimplex, sSimplexVal, lNrIterations, AddressOf SolveNonLinearTestError)
End Sub
Public Shared Function SolveNonLinearTestError(ByVal sCoef() As Single) As Single
'Return the error
Dim i, iNrDims As Integer, sError As Single = 100
iNrDims = sCoef.GetUpperBound(0) + 1
For i = 0 To iNrDims - 1
If i Mod 2 = 0 Then
sError += sCoef(i) * i
Else
sError -= sCoef(i) * i
End If
Next i
Return Math.Abs(sError)
End Function
Public Overloads Shared Function Solve(ByVal sA(,) As Single, ByVal sX(,) As Single, ByVal sY(,) As Single) As Boolean
'Solve A.X = Y, FOR every column of Y!!!
'This is useful because we only have to decompose A once,
'and then use this decomposition to compute X = inv(A).Y for every column of Y
'The results are stored in the corresponding columns of X
'See overloaded Solve for general explanation about the solver.
Dim sU(,) As Single = New Single(,) {}, sW() As Single = New Single() {}, sV(,) As Single = New Single(,) {}, i As Integer
Dim strError As String = ""
If SVDDecomposition(sA, sU, sW, sV, strError) = False Then
MsgBox("Algebra.Solve: SVD gives error '" & strError & "'", MsgBoxStyle.Critical + MsgBoxStyle.OkOnly)
Return False
End If
SVDRemoveSingularValues(sW, 0.0001)
'Run though every column of sY, compute the result, and store it in the corresponding column of sX.
Dim iNrEquationSets As Integer = sY.GetUpperBound(1) + 1
Dim iNrVariables As Integer = sA.GetUpperBound(1) + 1
Dim iNrEquationsPerSet As Integer = sA.GetUpperBound(0) + 1
Dim sXCol(iNrVariables - 1), sYCol(iNrEquationsPerSet - 1) As Single
For i = 0 To iNrEquationSets - 1
GetMatrixColumn(sY, sYCol, i)
Solve(sA, sXCol, sYCol)
SetMatrixColumn(sX, sXCol, i)
Next
Return False
End Function
Public Overloads Shared Function Solve(ByVal sA(,) As Single, ByVal sX() As Single, ByVal sY() As Single) As Boolean
'Solve the set of linear equations represented by A.x = y.
'The number of equations can be larger than the number of variables (overdetermined):
'i.e. the number of rows in A > number of cols in A. In that case the solution is
'a solution in the least-squares sense.
'This routine uses singular value decomposition, translated from "Numerical recipes in C"
Dim sU(,) As Single = New Single(,) {}, sW() As Single = New Single() {}, sV(,) As Single = New Single(,) {}
Dim strError As String = ""
Console.WriteLine("Solving linear set of equations A.x = y with A" & _
vbNewLine & yves.ToString(sA) & _
vbNewLine & "y" & _
vbNewLine & yves.ToString(sY))
If SVDDecomposition(sA, sU, sW, sV, strError) = False Then
'MsgBox("Algebra.Solve: SVD gives error '" & strError & "'", MsgBoxStyle.Critical + MsgBoxStyle.OkOnly)
Return False
End If
SVDRemoveSingularValues(sW, 0.0001)
'Compute pseudo-inverse multiplied with sY
SVDInvert(sU, sW, sV, sY, sX)
Return True
End Function
Private Shared Sub SVDRemoveSingularValues(ByVal sW() As Single, ByVal sThresholdFactor As Single)
'Set singular values to zero by compairing them to
'the highest value in w.
Dim iNrVariables As Integer = sW.GetUpperBound(0) + 1
Dim i As Integer, sWMax As Single = 0.0
For i = 0 To iNrVariables - 1
If sW(i) > sWMax Then sWMax = sW(i)
Next i
Dim sThreshold As Single = sThresholdFactor * sWMax
For i = 0 To iNrVariables - 1
If sW(i) < sThreshold Then sW(i) = 0.0
Next i
End Sub
Private Shared Sub SVDInvert(ByVal sU(,) As Single, _
ByVal sW() As Single, _
ByVal sV(,) As Single, _
ByVal sY() As Single, _
ByVal sX() As Single)
'Computes Y = inv(A).Y using the SVD decomposition of A = U.W.Vt
Dim jj, j, i, m, n As Integer
Dim s As Single
m = sU.GetUpperBound(0) + 1
n = sU.GetUpperBound(1) + 1
Dim tmp(n - 1) As Single
For j = 1 To n
s = 0.0
If sW(j - 1) <> 0.0 Then
For i = 1 To m
s = s + sU(i - 1, j - 1) * sY(i - 1)
Next i
s = s / sW(j - 1)
End If
tmp(j - 1) = s
Next j
For j = 1 To n
s = 0.0
For jj = 1 To n
s = s + sV(j - 1, jj - 1) * tmp(jj - 1)
Next jj
sX(j - 1) = s
Next j
End Sub
Private Shared Function SVDDecomposition(ByVal sA(,) As Single, _
ByRef sU(,) As Single, _
ByRef sW() As Single, _
ByRef sV(,) As Single, _
ByVal strError As String) As Boolean
'Compute the singular value decomposition of
'an m sx n matrix A: A = U.W.Vt
'None of the byref matrices must be allocated here.
'If something goes wrong it returns false with a message in strError
Dim Flag As Boolean, i As Integer, its As Integer
Dim j As Integer, jj As Integer, k As Integer
Dim l As Integer, nm As Integer
Dim c As Single, f As Single, h As Single, s As Single
Dim sX As Single, sY As Single, sz As Single, rv1() As Single
Dim anorm As Single, g As Single, hhscale As Single
'Extra variables for VBasic.
Dim sTemp1 As Single, n As Integer, m As Integer
m = sA.GetUpperBound(0) + 1
n = sA.GetUpperBound(1) + 1
If m < n Then
strError = "Not enough rows in A (underdetermined system)"
Return False
End If
ReDim sU(m - 1, n - 1)
ReDim sW(n - 1)
ReDim sV(n - 1, n - 1)
ReDim rv1(n - 1)
'Copy the matrix A in U.
Array.Copy(sA, sU, sA.Length)
'Householder reduction to bidiagonal form
anorm = 0.0#
For i = 1 To n
l = i + 1
rv1(i - 1) = hhscale * g
g = 0.0#
s = 0.0#
hhscale = 0.0#
If i <= m Then
For k = i To m
hhscale = hhscale + Math.Abs(sU(k - 1, i - 1))
Next k
If hhscale <> 0.0# Then
For k = i To m
sU(k - 1, i - 1) = sU(k - 1, i - 1) / hhscale
s = s + sU(k - 1, i - 1) * sU(k - 1, i - 1)
Next k
f = sU(i - 1, i - 1)
If f >= 0 Then
g = -Math.Sqrt(s)
Else
g = Math.Sqrt(s)
End If
h = f * g - s
sU(i - 1, i - 1) = f - g
If i <> n Then
For j = l To n
s = 0.0#
For k = i To m
s = s + sU(k - 1, i - 1) * sU(k - 1, j - 1)
Next k
f = s / h
For k = i To m
sU(k - 1, j - 1) = sU(k - 1, j - 1) + f * sU(k - 1, i - 1)
Next k
Next j
End If
For k = i To m
sU(k - 1, i - 1) = sU(k - 1, i - 1) * hhscale
Next k
End If
End If
sW(i - 1) = hhscale * g
g = 0.0#
s = 0.0#
hhscale = 0.0#
If i <= m And i <> n Then
For k = l To n
hhscale = hhscale + Math.Abs(sU(i - 1, k - 1))
Next k
If hhscale <> 0.0# Then
For k = l To n
sU(i - 1, k - 1) = sU(i - 1, k - 1) / hhscale
s = s + sU(i - 1, k - 1) * sU(i - 1, k - 1)
Next k
f = sU(i - 1, l - 1)
If f >= 0 Then
g = -Math.Sqrt(s)
Else
g = Math.Sqrt(s)
End If
h = f * g - s
sU(i - 1, l - 1) = f - g
For k = l To n
rv1(k - 1) = sU(i - 1, k - 1) / h
Next k
If i <> m Then
For j = l To m
s = 0.0#
For k = l To n
s = s + sU(j - 1, k - 1) * sU(i - 1, k - 1)
Next k
For k = l To n
sU(j - 1, k - 1) = sU(j - 1, k - 1) + s * rv1(k - 1)
Next k
Next j
End If
For k = l To n
sU(i - 1, k - 1) = sU(i - 1, k - 1) * hhscale
Next k
End If
End If
sTemp1 = Math.Abs(sW(i - 1)) + Math.Abs(rv1(i - 1))
If anorm < sTemp1 Then anorm = sTemp1
Next i
'Call DisplayMatrix("Bidiagonal form", a())
'Accumulation of right-hand transformations
For i = n To 1 Step -1
If i < n Then
If g <> 0.0# Then
For j = l To n
sV(j - 1, i - 1) = (sU(i - 1, j - 1) / sU(i - 1, l - 1)) / g
Next j
For j = l To n
s = 0.0#
For k = l To n
s = s + sU(i - 1, k - 1) * sV(k - 1, j - 1)
Next k
For k = l To n
sV(k - 1, j - 1) = sV(k - 1, j - 1) + s * sV(k - 1, i - 1)
Next k
Next j
End If
For j = l To n
sV(i - 1, j - 1) = 0.0#
sV(j - 1, i - 1) = 0.0#
Next j
End If
sV(i - 1, i - 1) = 1.0#
g = rv1(i - 1)
l = i
Next i
'Accumulation of left-hand transformations
For i = n To 1 Step -1
l = i + 1
g = sW(i - 1)
If i < n Then
For j = l To n
sU(i - 1, j - 1) = 0.0#
Next j
End If
If g <> 0.0# Then
g = 1.0# / g
If i <> n Then
For j = l To n
s = 0.0#
For k = l To m
s = s + sU(k - 1, i - 1) * sU(k - 1, j - 1)
Next k
f = (s / sU(i - 1, i - 1)) * g
For k = i To m
sU(k - 1, j - 1) = sU(k - 1, j - 1) + f * sU(k - 1, i - 1)
Next k
Next j
End If
For j = i To m
sU(j - 1, i - 1) = sU(j - 1, i - 1) * g
Next j
Else
For j = i To m
sU(j - 1, i - 1) = 0.0#
Next j
End If
sU(i - 1, i - 1) = sU(i - 1, i - 1) + 1.0#
Next i
'Diagonalization of the bidiagonal form (QR algorythm)
For k = n To 1 Step -1
For its = 1 To 30
'Debug.Print "Iteration " & its
Flag = True
For l = k To 1 Step -1
nm = l - 1
If Math.Abs(rv1(l - 1)) + anorm = anorm Then
Flag = False
Exit For
End If
If Math.Abs(sW(nm - 1)) + anorm = anorm Then
Exit For
End If
Next l
If Flag = True Then
c = 0.0#
s = 1.0#
For i = l To k
f = s * rv1(i - 1)
If (Math.Abs(f) + anorm) <> anorm Then
g = sW(i - 1)
h = Pythagoras(f, g)
sW(i - 1) = h
h = 1.0# / h
c = g * h
s = (-f * h)
For j = 1 To m
sY = sU(j - 1, nm - 1)
sz = sU(j - 1, i - 1)
sU(j - 1, nm - 1) = sY * c + sz * s
sU(j - 1, i - 1) = sz * c - sY * s
Next j
End If
Next i
End If
sz = sW(k - 1)
'Test for convergence
If l = k Then
If sz < 0.0# Then
sW(k - 1) = -sz
For j = 1 To n
sV(j - 1, k - 1) = -sV(j - 1, k - 1)
Next j
End If
Exit For
End If
If its = 30 Then
strError = "Too many iterations"
Return False
End If
sX = sW(l - 1)
nm = k - 1
sY = sW(nm - 1)
g = rv1(nm - 1)
h = rv1(k - 1)
f = ((sY - sz) * (sY + sz) + (g - h) * (g + h)) / (2.0# * h * sY)
g = Pythagoras(f, 1.0#)
If f > 0.0# Then
f = ((sX - sz) * (sX + sz) + h * ((sY / (f + Math.Abs(g))) - h)) / sX
Else
f = ((sX - sz) * (sX + sz) + h * ((sY / (f - Math.Abs(g))) - h)) / sX
End If
c = 1.0#
s = 1.0#
For j = l To nm
i = j + 1
g = rv1(i - 1)
sY = sW(i - 1)
h = s * g
g = c * g
sz = Pythagoras(f, h)
rv1(j - 1) = sz
c = f / sz
s = h / sz
f = sX * c + g * s
g = g * c - sX * s
h = sY * s
sY = sY * c
For jj = 1 To n
sX = sV(jj - 1, j - 1)
sz = sV(jj - 1, i - 1)
sV(jj - 1, j - 1) = sX * c + sz * s
sV(jj - 1, i - 1) = sz * c - sX * s
Next jj
sz = Pythagoras(f, h)
sW(j - 1) = sz
If sz <> 0.0# Then
sz = 1.0# / sz
c = f * sz
s = h * sz
End If
f = c * g + s * sY
sX = c * sY - s * g
For jj = 1 To m
sY = sU(jj - 1, j - 1)
sz = sU(jj - 1, i - 1)
sU(jj - 1, j - 1) = sY * c + sz * s
sU(jj - 1, i - 1) = sz * c - sY * s
Next jj
Next j
rv1(l - 1) = 0.0#
rv1(k - 1) = f
sW(k - 1) = sX
Next its
Next k
Return True
End Function
Private Shared Function Pythagoras(ByVal a As Single, ByVal b As Single) As Single
Dim at As Single, bt As Single, ct As Single
at = Math.Abs(a)
bt = Math.Abs(b)
If at > bt Then
ct = bt / at
Pythagoras = at * Math.Sqrt(1.0# + ct * ct)
Else
If bt = 0.0# Then
'Means a is also 0
Pythagoras = 0.0#
Else
ct = at / bt
Pythagoras = bt * Math.Sqrt(1.0# + ct * ct)
End If
End If
End Function
Public Overloads Shared Sub Add(ByVal sV1() As Single, ByVal sV2() As Single, ByVal sR() As Single)
Dim i, iHiCol As Integer
iHiCol = sV1.GetUpperBound(0)
For i = 0 To iHiCol
sR(i) = sV1(i) + sV2(i)
Next
End Sub
Public Overloads Shared Sub Add(ByVal sM1(,) As Single, ByVal sM2(,) As Single, ByVal sMR(,) As Single)
Dim i, j, iHiRow, iHiCol As Integer
GetBounds(sM1, iHiRow, iHiCol)
For j = 0 To iHiCol
For i = 0 To iHiRow
sMR(i, j) = sM1(i, j) + sM2(i, j)
Next i
Next j
End Sub
Public Overloads Shared Sub Subtract(ByVal sV1() As Single, ByVal sV2() As Single, ByVal sR() As Single)
Dim i As Integer, iHiCol As Integer
iHiCol = sV1.GetUpperBound(0)
For i = 0 To iHiCol
sR(i) = sV1(i) - sV2(i)
Next
End Sub
Public Overloads Shared Sub Subtract(ByVal sM1(,) As Single, ByVal sM2(,) As Single, ByVal sMR(,) As Single)
Dim i, j, iHiRow, iHiCol As Integer
GetBounds(sM1, iHiRow, iHiCol)
For j = 0 To iHiCol
For i = 0 To iHiRow
sMR(i, j) = sM1(i, j) - sM2(i, j)
Next i
Next j
End Sub
Public Overloads Shared Function Norm(ByVal sV1() As Single) As Single
Return Norm(sV1, NormOrder.Euclidean)
End Function
Public Overloads Shared Function Norm(ByVal sV1() As Single, ByVal iOrder As NormOrder) As Single
'Compute norm of given order
Dim i As Integer, sNorm As Single = 0.0, iHiCol As Integer
iHiCol = sV1.GetUpperBound(0)
Select Case iOrder
Case NormOrder.AbsoluteValue
For i = 0 To iHiCol
sNorm += Math.Abs(sV1(i))
Next
Case NormOrder.Euclidean
For i = 0 To iHiCol
sNorm += sV1(i) ^ 2
Next
sNorm = sNorm ^ 0.5
Case NormOrder.Max
sNorm = 0
For i = 0 To iHiCol
Dim sTemp As Single = Math.Abs(sV1(i))
If sTemp > sNorm Then sNorm = sTemp
Next
End Select
Return sNorm
End Function
Public Overloads Shared Sub Mean(ByVal sM(,) As Single, ByVal sV() As Single)
'Compute columnwise mean
Dim i, iHiCol As Integer
iHiCol = sV.GetUpperBound(0)
Sum(sM, sV)
For i = 0 To iHiCol
sV(i) = sV(i) / (iHiCol + 1)
Next i
End Sub
Public Overloads Shared Function Mean(ByVal sV() As Single) As Single
'Compute average of a vector
Dim sMean As Single
sMean = Sum(sV)
sMean /= sV.GetLength(0)
Return sMean
End Function
Public Overloads Shared Sub Sum(ByVal sM(,) As Single, ByVal sV() As Single)
'Compute columnwise sum of matrix
Dim i, j, iHiRow, iHiCol As Integer
GetBounds(sM, iHiRow, iHiCol)
For j = 0 To iHiCol
sV(j) = 0.0
For i = 0 To iHiRow
sV(j) += sM(i, j)
Next i
Next j
End Sub
Public Overloads Shared Function Sum(ByVal sV() As Single) As Single
'Compute sum of elements of vector
Dim sSum As Single = 0
Dim i, iHiCol As Integer
iHiCol = sV.GetUpperBound(0)
For i = 0 To iHiCol
sSum = sSum + sV(i)
Next i
Return sSum
End Function
Public Overloads Shared Function Max(ByVal sV() As Single, ByRef iPos As Integer) As Single
'Find max of a vector
Dim i As Integer, sMax As Single = 0.0
Dim iHiCol As Integer
iHiCol = sV.GetUpperBound(0)
For i = 0 To iHiCol
If sV(i) > sMax Then
iPos = i
sMax = sV(i)
End If
Next i
Return sMax
End Function
Public Overloads Shared Function Max(ByVal sV() As Single) As Single
Dim iPos As Integer
Return Max(sV, iPos)
End Function
Public Overloads Shared Function Max(ByVal sM(,) As Single) As Single
'Find max of a matrix
Dim i, j As Integer
Return Max(sM, i, j)
End Function
Public Overloads Shared Function Max(ByVal sM(,) As Single, ByRef iCol As Integer, ByRef iRow As Integer) As Single
'Find max of a matrix
Dim sMAx As Single = 0
Dim i, j, iHiRow, iHiCol As Integer
GetBounds(sM, iHiRow, iHiCol)
For j = 0 To iHiCol
For i = 0 To iHiRow
If sM(i, j) > sMAx Then
iCol = j
iRow = i
sMAx = sM(i, j)
End If
Next i
Next j
Return sMAx
End Function
Public Overloads Shared Function Scale(ByVal sX As Single, ByVal sOffset As Single, ByVal sScale As Single) As Single
'Scale a scalar with an offset. For vectors and matrices this would lead to too many
'different versions, so use Subtract to have an offset.
Return (sX - sOffset) * sScale
End Function
Public Overloads Shared Sub Scale(ByVal sScale As Single, _
ByVal sV2() As Single, _
ByVal sY() As Single)
'Scale elements of vector V2 using the scalar sScale
Dim i As Integer, iHiRow As Integer
iHiRow = UBound(sV2)
For i = 0 To iHiRow
sY(i) = sScale * sV2(i)
Next i
End Sub
Public Overloads Shared Sub Scale(ByVal sV1() As Single, _
ByVal sV2() As Single, _
ByVal sY() As Single)
'Scale elements of vector V2 using the elements of V1
Dim i As Integer, iHiRow As Integer
iHiRow = UBound(sV2)
For i = 0 To iHiRow
sY(i) = sV1(i) * sV2(i)
Next i
End Sub
Public Overloads Shared Sub Scale(ByVal sScale As Single, _
ByVal sB(,) As Single, _
ByVal sY(,) As Single)
'Scale elements of matrix sB using sScale
Dim i, j, iHiRow, iHiCol As Integer
GetBounds(sB, iHiRow, iHiCol)
For i = 0 To iHiRow
For j = 0 To iHiCol
sY(i, j) = sScale * sB(i, j)
Next j
Next i
End Sub
Public Overloads Shared Sub Scale(ByVal sA(,) As Single, _
ByVal sB(,) As Single, _
ByVal sY(,) As Single)
'Scale elements of matrix sB using the corresponding elements of sA
Dim i, j, iHiRow, iHiCol As Integer
GetBounds(sB, iHiRow, iHiCol)
For i = 0 To iHiRow
For j = 0 To iHiCol
sY(i, j) = sA(i, j) * sB(i, j)
Next j
Next i
End Sub
Public Overloads Shared Sub Scale(ByVal sRowScales() As Single, _
ByVal sB(,) As Single, _
ByVal sY(,) As Single)
'Scale elements of matrix sB using the corresponding elements of sRowScales, per ROW
Dim i, j, iHiRow, iHiCol As Integer
GetBounds(sB, iHiRow, iHiCol)
For i = 0 To iHiRow
For j = 0 To iHiCol
sY(i, j) = sRowScales(i) * sB(i, j)
Next j
Next i
End Sub
Public Overloads Shared Sub Scale(ByVal sB(,) As Single, _
ByVal sColScales() As Single, _
ByVal sY(,) As Single)
'Scale elements of matrix sB using the corresponding elements of sColScales, per col
Dim i, j, iHiRow, iHiCol As Integer
GetBounds(sB, iHiRow, iHiCol)
For i = 0 To iHiRow
For j = 0 To iHiCol
sY(i, j) = sColScales(j) * sB(i, j)
Next j
Next i
End Sub
Public Overloads Shared Sub Product(ByVal sA(,) As Single, _
ByVal sB(,) As Single, _
ByVal sC(,) As Single)
'Compute A * B and store in C.
'Raise a fatal run-time error if any errors (no return value)!
Dim i, j, k, iAHiRow, iAHiCol As Integer
GetBounds(sA, iAHiRow, iAHiCol)
Dim iBHiRow, iBHiCol As Integer
GetBounds(sB, iBHiRow, iBHiCol)
Dim iCHiRow, iCHiCol As Integer
GetBounds(sC, iCHiRow, iCHiCol)
If (((iAHiCol) <> (iBHiRow)) Or _
((iAHiRow) <> (iCHiRow)) Or _
((iBHiCol) <> (iCHiCol))) Then
MsgBox("Algebra.Product: Incompatible matrix dimensions", MsgBoxStyle.OkOnly + MsgBoxStyle.Critical)
End If
For i = 0 To iCHiRow
For j = 0 To iCHiCol
sC(i, j) = 0.0
For k = 0 To iAHiCol
sC(i, j) += sA(i, k) * sB(k, j)
Next k
Next j
Next i
End Sub
Public Overloads Shared Function Product(ByVal sV1() As Single, ByVal sV2() As Single) As Single
'Return the scalar product of two vectors.
Dim i As Integer, iHiRow As Integer, sResult As Single
iHiRow = UBound(sV1)
For i = 0 To iHiRow
sResult = sResult + sV1(i) * sV2(i)
Next i
Return sResult
End Function
Public Overloads Shared Sub Product(ByVal sM() As Single, _
ByVal sX() As Single, _
ByVal sY(,) As Single)
'Multiply a vector times a vector (Y = M.Y), by interpreting the vector M as a columnmatrix,
'and X as a rowmatrix. Result is a matrix
Dim sA(0, sM.GetUpperBound(0)) As Single, sB(sX.GetUpperBound(0), 0) As Single
SetMatrixColumn(sA, sM, 0)
SetMatrixRow(sB, sX, 0)
Product(sA, sB, sY)
End Sub
Public Overloads Shared Sub Product(ByVal sM(,) As Single, _
ByVal sX() As Single, _
ByVal sY() As Single)
'Multiply a matrix times a vector (y = M.x), by interpreting the vector X as a columnmatrix.
Dim sB(sX.GetUpperBound(0), 0), sC(sM.GetUpperBound(0), 0) As Single
SetMatrixColumn(sB, sX, 0)
Product(sM, sB, sC)
GetMatrixColumn(sC, sY, 0)
End Sub
Public Overloads Shared Sub Product(ByVal sX() As Single, _
ByVal sM(,) As Single, _
ByVal sY() As Single)
'Multiply a vector with a matrix (y = x.M), by interpreting the vector X as a rowmatrix.
Dim iHiCol As Integer = sX.GetUpperBound(0)
Dim sB(0, iHiCol), sC(0, iHiCol) As Single
SetMatrixRow(sB, sX, 0)
Product(sM, sB, sC)
GetMatrixRow(sC, sY, 0)
End Sub
Public Shared Sub SubMatrix(ByVal sA(,) As Single, _
ByVal sB(,) As Single, _
ByVal iRow As Integer, _
ByVal iCol As Integer)
'Extract submatrix of the dimensions of B using row and col
'as start values in sA. sA and sB can be mixed one and zero-
'based, but iRow and iCol are interpreted according to sA
Dim i, j, iHiRow, iHiCol As Integer
GetBounds(sB, iHiRow, iHiCol)
For i = 0 To iHiRow
For j = 0 To iHiCol
sB(i, j) = sA(i + iRow, j + iCol)
Next j
Next i
End Sub
Public Overloads Shared Sub GetMatrixColumn(ByVal sM(,) As Single, _
ByVal sV() As Single, _
ByVal iCol As Integer)
GetMatrixColumn(sM, sV, iCol, 0)
End Sub
Public Overloads Shared Sub GetMatrixColumn(ByVal sM(,) As Single, _
ByVal sV() As Single, _
ByVal iCol As Integer, _
ByVal iStartRow As Integer)
'Fill vector with matrix col
Dim i, iHiCol As Integer
iHiCol = sV.GetUpperBound(0)
For i = 0 To iHiCol
sV(i) = sM(i + iStartRow, iCol)
Next i
End Sub
Public Overloads Shared Sub GetMatrixRow(ByVal sM(,) As Single, _
ByVal sV() As Single, _
ByVal iRow As Integer)
GetMatrixRow(sM, sV, iRow, 0)
End Sub
Public Overloads Shared Sub GetMatrixRow(ByVal sM(,) As Single, _
ByVal sV() As Single, _
ByVal iRow As Integer, _
ByVal iStartCol As Integer)
'Fill vector with matrix row.
Dim i, iHiCol As Integer
iHiCol = sV.GetUpperBound(0)
For i = 0 To iHiCol
sV(i) = sM(iRow, i + iStartCol)
Next i
End Sub
Public Overloads Shared Sub SetMatrixColumn(ByVal sM(,) As Single, _
ByVal sV() As Single, _
ByVal iCol As Integer, _
ByVal iStartRow As Integer)
'Fill matrix col with vector
Dim i, iHiCol As Integer
iHiCol = sV.GetUpperBound(0)
For i = 0 To iHiCol
sM(i + iStartRow, iCol) = sV(i)
Next i
End Sub
Public Overloads Shared Sub SetMatrixColumn(ByVal sM(,) As Single, _
ByVal sV() As Single, _
ByVal iCol As Integer)
SetMatrixColumn(sM, sV, iCol, 0)
End Sub
Public Overloads Shared Sub SetMatrixRow(ByVal sM(,) As Single, _
ByVal sV() As Single, _
ByVal iRow As Integer)
SetMatrixRow(sM, sV, iRow, 0)
End Sub
Public Overloads Shared Sub SetMatrixRow(ByVal sM(,) As Single, _
ByVal sV() As Single, _
ByVal iRow As Integer, _
ByVal iStartCol As Integer)
Dim i, iHiCol As Integer
iHiCol = sV.GetUpperBound(0)
For i = 0 To iHiCol
sM(iRow, i + iStartCol) = sV(i)
Next i
End Sub
Public Shared Sub MatrixToVector(ByVal sM(,) As Single, _
ByVal sV() As Single)
'Put all elements of a matrix into a vector
Dim i, j, iHiRow, iHiCol, k As Integer
GetBounds(sM, iHiRow, iHiCol)
k = 0
For i = 0 To iHiRow
For j = 0 To iHiCol
sV(k) = sM(i, j)
k += 1
Next
Next
End Sub
Public Shared Sub VectorToMatrix(ByVal sV() As Single, _
ByVal sM(,) As Single)
'Put all elements of a vector into a vector. Use the shape of the matrix
Dim i, j, iHiRow, iHiCol, k As Integer
GetBounds(sM, iHiRow, iHiCol)
k = 0
For i = 0 To iHiRow
For j = 0 To iHiCol
sM(i, j) = sV(k)
k += 1
Next
Next
End Sub
Public Shared Sub Transpose(ByVal sA(,) As Single, ByVal sAt(,) As Single)
'Transpose matrix A and put result in At. Output has
'same base as input. Input arguments must be different!
Dim i, j, iHiRow, iHiCol As Integer
GetBounds(sA, iHiRow, iHiCol)
For i = 0 To iHiRow
For j = 0 To iHiCol
sAt(j, i) = sA(i, j)
Next j
Next i
End Sub
Public Shared Function Load(ByVal strFile As String, ByRef sM(,) As Single) As Boolean
'Read a tex file with a matrix or vector stored separated by spaces and
'newlines. sM will be redimensioned as necessary and must be
'a dynamic array. Redimensioning can only affect the last dimension!
'When a vector is read in the matrix will be of size n x 1, and can easily
'be converted to a vector
Dim iNrCols As Integer
Dim iRowNr As Integer, iColNr As Integer
Dim sMt(,) As Single = New Single(,) {}, strText As String, strTextItems() As String
Try
FileOpen(5, strFile, OpenMode.Input, OpenAccess.Read)
Catch e As Exception
MsgBox("Algebra.Load:" & e.Message, MsgBoxStyle.OkOnly + MsgBoxStyle.Critical)
Return False
End Try
iRowNr = 0
iNrCols = 0
Do While Not EOF(5)
'Read first line to count number of columns
strText = Trim(LineInput(5))
If strText.Length > 0 Then
strText = strText.Replace(" ", " ") 'Make sure no 2 spaces are in the string ...
strText = strText.Replace(" ", " ") 'Make sure no 3 spaces are in the string ...
strTextItems = strText.Split()
'Redimension the array if the nr of cols is known, i.e. after
'reading the first line.
If iRowNr = 0 Then
iNrCols = (strTextItems.GetUpperBound(0) + 1)
ReDim sMt(iNrCols - 1, 0)
Else
ReDim Preserve sMt(iNrCols - 1, iRowNr)
End If
'Read values into transposed matrix
For iColNr = 0 To iNrCols - 1
'sMt(iColNr, iRowNr) = CSng(strTextItems(iColNr))
sMt(iColNr, iRowNr) = Val(strTextItems(iColNr))
Next
iRowNr += 1
End If
Loop
'close file
FileClose(5)
'Transpose matrix to output format
ReDim sM(iRowNr - 1, iNrCols - 1)
Transpose(sMt, sM)
Return True
End Function
Public Overloads Shared Sub Save(ByVal strFile As String, _
ByVal sM(,) As Single)
Save(strFile, sM, 16, 2)
End Sub
Public Overloads Shared Sub Save(ByVal strFile As String, _
ByVal sM(,) As Single, _
ByVal iPrecBeforeDec As Integer, _
ByVal iPrecAfterDec As Integer)
'Save a matrix to file.
Dim strF As String = ""
Dim i, j, iHiRow, iHiCol As Integer
If iPrecAfterDec = -1 Then
strF = "0."
Else
For i = 1 To iPrecAfterDec
strF = strF & "0"
Next
strF = strF & "."
End If
For i = 1 To iPrecBeforeDec
strF = strF & "#"
Next
If System.IO.File.Exists(strFile) Then System.IO.File.Delete(strFile)
Try
FileOpen(5, strFile, OpenMode.Output, OpenAccess.Write)
GetBounds(sM, iHiRow, iHiCol)
For i = 0 To iHiRow
For j = 0 To iHiCol - 1
Print(5, Format(sM(i, j), strF), SPC(1))
Next j
PrintLine(5, SPC(1), Format(sM(i, iHiCol), strF))
Next i
FileClose(5)
Catch e As Exception
MsgBox("Algebra.Save (file = " & strFile & "):" & e.Message, MsgBoxStyle.OkOnly + MsgBoxStyle.Critical)
End Try
End Sub
Private Shared Sub GetBounds(ByVal sM(,) As Single, _
ByRef iHiRow As Integer, _
ByRef iHiCol As Integer)
iHiRow = sM.GetUpperBound(0)
iHiCol = sM.GetUpperBound(1)
End Sub
Public Overloads Shared Function ToString(ByVal sM(,) As Single) As String
Dim strText As String = vbNewLine
Dim i, j, iHiRow, iHiCol As Integer
GetBounds(sM, iHiRow, iHiCol)
For i = 0 To iHiRow
For j = 0 To iHiCol - 1
strText = strText & sM(i, j).ToString & " "
Next j
strText = strText & sM(i, iHiCol).ToString & vbNewLine
Next i
Return strText
End Function
Public Overloads Shared Function ToString(ByVal sV() As Single) As String
Dim strText As String = ""
Dim i, iHiCol As Integer
iHiCol = sV.GetUpperBound(0)
For i = 0 To iHiCol - 1
strText = strText & sV(i).ToString & " "
Next i
strText = vbNewLine & strText & sV(iHiCol).ToString
Return strText
End Function
End Class
End Namespace
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