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Dwsim / data /DWSIM.Math /MatrixOps.vb
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Namespace MathEx.MatrixOps
'/*************************************************************************
'Copyright (c) 1992-2007 The University of Tennessee. All rights reserved.
'Contributors:
' * Sergey Bochkanov (ALGLIB project). Translation from FORTRAN to
' pseudocode.
'See subroutines comments for additional copyrights.
'Redistribution and use in source and binary forms, with or without
'modification, are permitted provided that the following conditions are
'met:
'- Redistributions of source code must retain the above copyright
' notice, this list of conditions and the following disclaimer.
'- Redistributions in binary form must reproduce the above copyright
' notice, this list of conditions and the following disclaimer listed
' in this license in the documentation and/or other materials
' provided with the distribution.
'- Neither the name of the copyright holders nor the names of its
' contributors may be used to endorse or promote products derived from
' this software without specific prior written permission.
'THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
'"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
'LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
'A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
'OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
'SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
'LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
'DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
'THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
'(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
'OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
'*************************************************************************/
Public Class Determinant
'/*************************************************************************
'Calculation of the determinant of a general matrix
'Input parameters:
' A - matrix, array[0..N-1, 0..N-1]
' N - size of matrix A.
'Result: determinant of matrix A.
' -- ALGLIB --
' Copyright 2005 by Bochkanov Sergey
'*************************************************************************/
Public Shared Function rmatrixdet(ByVal a As Double(,), ByVal n As Integer) As Double
Dim pivots As Integer() = New Integer(0) {}
Dim a2 = DirectCast(a.Clone, Double(,))
MathEx.SysLin.lu.rmatrixlu(a2, n, n, pivots)
Return MathEx.MatrixOps.Determinant.rmatrixludet(a2, pivots, n)
End Function
'/*************************************************************************
'Determinant calculation of the matrix given by its LU decomposition.
'Input parameters:
' A - LU decomposition of the matrix (output of
' RMatrixLU subroutine).
' Pivots - table of permutations which were made during
' the LU decomposition.
' Output of RMatrixLU subroutine.
' N - size of matrix A.
'Result: matrix determinant.
' -- ALGLIB --
' Copyright 2005 by Bochkanov Sergey
'*************************************************************************/
Public Shared Function rmatrixludet(ByRef a As Double(,), ByRef pivots As Integer(), ByVal n As Integer) As Double
Dim num As Double = 0
Dim index As Integer = 0
Dim num3 As Integer = 0
num = 1
num3 = 1
index = 0
Do While (index <= (n - 1))
num = (num * a(index, index))
If (pivots(index) <> index) Then
num3 = -num3
End If
index += 1
Loop
Return (num * num3)
End Function
Public Shared Function determinant(ByVal a As Double(,), ByVal n As Integer) As Double
Dim pivots As Integer() = New Integer(0) {}
a = DirectCast(a.Clone, Double(,))
MathEx.SysLin.lu.ludecomposition(a, n, n, pivots)
Return MathEx.MatrixOps.Determinant.determinantlu(a, pivots, n)
End Function
Public Shared Function determinantlu(ByRef a As Double(,), ByRef pivots As Integer(), ByVal n As Integer) As Double
Dim num As Double = 0
Dim index As Integer = 0
Dim num3 As Integer = 0
num = 1
num3 = 1
index = 1
Do While (index <= n)
num = (num * a(index, index))
If (pivots(index) <> index) Then
num3 = -num3
End If
index += 1
Loop
Return (num * num3)
End Function
End Class
Public Class Inverse
'/*************************************************************************
'Inversion of a general matrix.
'Input parameters:
' A - matrix. Array whose indexes range within [0..N-1, 0..N-1].
' N - size of matrix A.
'Output parameters:
' A - inverse of matrix A.
' Array whose indexes range within [0..N-1, 0..N-1].
'Result:
' True, if the matrix is not singular.
' False, if the matrix is singular.
' -- ALGLIB --
' Copyright 2005 by Bochkanov Sergey
'*************************************************************************/
Public Shared Function rmatrixinverse(ByRef a As Double(,), ByVal n As Integer) As Boolean
Dim pivots As Integer() = New Integer() {}
MathEx.SysLin.lu.rmatrixlu(a, n, n, pivots)
Return rmatrixluinverse(a, pivots, n)
End Function
'/*************************************************************************
'Inversion of a matrix given by its LU decomposition.
'Input parameters:
' A - LU decomposition of the matrix (output of RMatrixLU subroutine).
' Pivots - table of permutations which were made during the LU decomposition
' (the output of RMatrixLU subroutine).
' N - size of matrix A.
'Output parameters:
' A - inverse of matrix A.
' Array whose indexes range within [0..N-1, 0..N-1].
'Result:
' True, if the matrix is not singular.
' False, if the matrix is singular.
' -- LAPACK routine (version 3.0) --
' Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
' Courant Institute, Argonne National Lab, and Rice University
' February 29, 1992
'*************************************************************************/
Public Shared Function rmatrixluinverse(ByRef a As Double(,), ByRef pivots As Integer(), ByVal n As Integer) As Boolean
Dim flag As Boolean = False
Dim numArray As Double() = New Double() {}
Dim index As Integer = 0
Dim num2 As Integer = 0
Dim num3 As Integer = 0
Dim num4 As Double = 0
Dim num5 As Integer = 0
flag = True
If (n <> 0) Then
numArray = New Double(((n - 1) + 1)) {}
If Not TRInverse.rmatrixtrinverse(a, n, True, False) Then
Return False
End If
num2 = (n - 1)
Do While (num2 >= 0)
index = (num2 + 1)
Do While (index <= (n - 1))
numArray(index) = a(index, num2)
a(index, num2) = 0
index += 1
Loop
If (num2 < (n - 1)) Then
index = 0
Do While (index <= (n - 1))
num4 = 0
num5 = (num2 + 1)
Do While (num5 <= (n - 1))
num4 = (num4 + (a(index, num5) * numArray(num5)))
num5 += 1
Loop
a(index, num2) = (a(index, num2) - num4)
index += 1
Loop
End If
num2 -= 1
Loop
num2 = (n - 2)
Do While (num2 >= 0)
num3 = pivots(num2)
If (num3 <> num2) Then
num5 = 0
Do While (num5 <= (n - 1))
numArray(num5) = a(num5, num2)
num5 += 1
Loop
num5 = 0
Do While (num5 <= (n - 1))
a(num5, num2) = a(num5, num3)
num5 += 1
Loop
num5 = 0
Do While (num5 <= (n - 1))
a(num5, num3) = numArray(num5)
num5 += 1
Loop
End If
num2 -= 1
Loop
End If
Return flag
End Function
Public Shared Function inverse(ByRef a As Double(,), ByVal n As Integer) As Boolean
Dim pivots As Integer() = New Integer() {}
MathEx.SysLin.lu.ludecomposition(a, n, n, pivots)
Return MathEx.MatrixOps.Inverse.inverselu(a, pivots, n)
End Function
Public Shared Function inverselu(ByRef a As Double(,), ByRef pivots As Integer(), ByVal n As Integer) As Boolean
Dim flag As Boolean = False
Dim numArray As Double() = New Double() {}
Dim index As Integer = 0
Dim num2 As Integer = 0
Dim num3 As Integer = 0
Dim num4 As Integer = 0
Dim num5 As Double = 0
Dim num6 As Integer = 0
flag = True
If (n <> 0) Then
numArray = New Double((n + 1)) {}
If Not TRInverse.invtriangular(a, n, True, False) Then
Return False
End If
num2 = n
Do While (num2 >= 1)
index = (num2 + 1)
Do While (index <= n)
numArray(index) = a(index, num2)
a(index, num2) = 0
index += 1
Loop
If (num2 < n) Then
num4 = (num2 + 1)
index = 1
Do While (index <= n)
num5 = 0
num6 = num4
Do While (num6 <= n)
num5 = (num5 + (a(index, num6) * numArray(num6)))
num6 += 1
Loop
a(index, num2) = (a(index, num2) - num5)
index += 1
Loop
End If
num2 -= 1
Loop
num2 = (n - 1)
Do While (num2 >= 1)
num3 = pivots(num2)
If (num3 <> num2) Then
num6 = 1
Do While (num6 <= n)
numArray(num6) = a(num6, num2)
num6 += 1
Loop
num6 = 1
Do While (num6 <= n)
a(num6, num2) = a(num6, num3)
num6 += 1
Loop
num6 = 1
Do While (num6 <= n)
a(num6, num3) = numArray(num6)
num6 += 1
Loop
End If
num2 -= 1
Loop
End If
Return flag
End Function
End Class
Public Class TRInverse
'/*************************************************************************
' Triangular matrix inversion
' The subroutine inverts the following types of matrices:
' * upper triangular
' * upper triangular with unit diagonal
' * lower triangular
' * lower triangular with unit diagonal
' In case of an upper (lower) triangular matrix, the inverse matrix will
' also be upper (lower) triangular, and after the end of the algorithm, the
' inverse matrix replaces the source matrix. The elements below (above) the
' main diagonal are not changed by the algorithm.
' If the matrix has a unit diagonal, the inverse matrix also has a unit
' diagonal, and the diagonal elements are not passed to the algorithm.
' Input parameters:
' A - matrix.
' Array whose indexes range within [0..N-1, 0..N-1].
' N - size of matrix A.
' IsUpper - True, if the matrix is upper triangular.
' IsUnitTriangular
' - True, if the matrix has a unit diagonal.
' Output parameters:
' A - inverse matrix (if the problem is not degenerate).
' Result:
' True, if the matrix is not singular.
' False, if the matrix is singular.
' -- LAPACK routine (version 3.0) --
' Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
' Courant Institute, Argonne National Lab, and Rice University
' February 29, 1992
' *************************************************************************/
Public Shared Function rmatrixtrinverse(ByRef a As Double(,), ByVal n As Integer, ByVal isupper As Boolean, ByVal isunittriangular As Boolean) As Boolean
Dim flag As Boolean = False
Dim flag2 As Boolean = False
Dim index As Integer = 0
Dim num2 As Integer = 0
Dim num3 As Double = 0
Dim num4 As Double = 0
Dim numArray As Double() = New Double() {}
Dim num5 As Integer = 0
flag = True
numArray = New Double(((n - 1) + 1)) {}
flag2 = Not isunittriangular
If isupper Then
num2 = 0
Do While (num2 <= (n - 1))
If flag2 Then
If (a(num2, num2) = 0) Then
Return False
End If
a(num2, num2) = (1 / a(num2, num2))
num4 = -a(num2, num2)
Else
num4 = -1
End If
If (num2 > 0) Then
num5 = 0
Do While (num5 <= (num2 - 1))
numArray(num5) = a(num5, num2)
num5 += 1
Loop
index = 0
Do While (index <= (num2 - 1))
If (index < (num2 - 1)) Then
num3 = 0
num5 = (index + 1)
Do While (num5 <= (num2 - 1))
num3 = (num3 + (a(index, num5) * numArray(num5)))
num5 += 1
Loop
Else
num3 = 0
End If
If flag2 Then
a(index, num2) = (num3 + (a(index, index) * numArray(index)))
Else
a(index, num2) = (num3 + numArray(index))
End If
index += 1
Loop
num5 = 0
Do While (num5 <= (num2 - 1))
a(num5, num2) = (num4 * a(num5, num2))
num5 += 1
Loop
End If
num2 += 1
Loop
Return flag
End If
num2 = (n - 1)
Do While (num2 >= 0)
If flag2 Then
If (a(num2, num2) = 0) Then
Return False
End If
a(num2, num2) = (1 / a(num2, num2))
num4 = -a(num2, num2)
Else
num4 = -1
End If
If (num2 < (n - 1)) Then
num5 = (num2 + 1)
Do While (num5 <= (n - 1))
numArray(num5) = a(num5, num2)
num5 += 1
Loop
index = (num2 + 1)
Do While (index <= (n - 1))
If (index > (num2 + 1)) Then
num3 = 0
num5 = (num2 + 1)
Do While (num5 <= (index - 1))
num3 = (num3 + (a(index, num5) * numArray(num5)))
num5 += 1
Loop
Else
num3 = 0
End If
If flag2 Then
a(index, num2) = (num3 + (a(index, index) * numArray(index)))
Else
a(index, num2) = (num3 + numArray(index))
End If
index += 1
Loop
num5 = (num2 + 1)
Do While (num5 <= (n - 1))
a(num5, num2) = (num4 * a(num5, num2))
num5 += 1
Loop
End If
num2 -= 1
Loop
Return flag
End Function
Public Shared Function invtriangular(ByRef a As Double(,), ByVal n As Integer, ByVal isupper As Boolean, ByVal isunittriangular As Boolean) As Boolean
Dim flag As Boolean = False
Dim flag2 As Boolean = False
Dim index As Integer = 0
Dim num2 As Integer = 0
Dim num3 As Integer = 0
Dim num4 As Integer = 0
Dim num5 As Double = 0
Dim num6 As Double = 0
Dim numArray As Double() = New Double() {}
Dim num7 As Integer = 0
flag = True
numArray = New Double((n + 1)) {}
flag2 = Not isunittriangular
If isupper Then
num2 = 1
Do While (num2 <= n)
If flag2 Then
If (a(num2, num2) = 0) Then
Return False
End If
a(num2, num2) = (1 / a(num2, num2))
num6 = -a(num2, num2)
Else
num6 = -1
End If
If (num2 > 1) Then
num3 = (num2 - 1)
num7 = 1
Do While (num7 <= num3)
numArray(num7) = a(num7, num2)
num7 += 1
Loop
index = 1
Do While (index <= (num2 - 1))
If (index < (num2 - 1)) Then
num5 = 0
num7 = (index + 1)
Do While (num7 <= num3)
num5 = (num5 + (a(index, num7) * numArray(num7)))
num7 += 1
Loop
Else
num5 = 0
End If
If flag2 Then
a(index, num2) = (num5 + (a(index, index) * numArray(index)))
Else
a(index, num2) = (num5 + numArray(index))
End If
index += 1
Loop
num7 = 1
Do While (num7 <= num3)
a(num7, num2) = (num6 * a(num7, num2))
num7 += 1
Loop
End If
num2 += 1
Loop
Return flag
End If
num2 = n
Do While (num2 >= 1)
If flag2 Then
If (a(num2, num2) = 0) Then
Return False
End If
a(num2, num2) = (1 / a(num2, num2))
num6 = -a(num2, num2)
Else
num6 = -1
End If
If (num2 < n) Then
num4 = (num2 + 1)
num7 = num4
Do While (num7 <= n)
numArray(num7) = a(num7, num2)
num7 += 1
Loop
index = (num2 + 1)
Do While (index <= n)
If (index > (num2 + 1)) Then
num5 = 0
num7 = num4
Do While (num7 <= (index - 1))
num5 = (num5 + (a(index, num7) * numArray(num7)))
num7 += 1
Loop
Else
num5 = 0
End If
If flag2 Then
a(index, num2) = (num5 + (a(index, index) * numArray(index)))
Else
a(index, num2) = (num5 + numArray(index))
End If
index += 1
Loop
num7 = num4
Do While (num7 <= n)
a(num7, num2) = (num6 * a(num7, num2))
num7 += 1
Loop
End If
num2 -= 1
Loop
Return flag
End Function
End Class
End Namespace