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Perform Gaussian Elimination to solve a system of linear equations on n-variables, having n-number

Perform Gaussian Elimination to solve a system of linear equations on n-variables, having n-number of equations, with partial pivoting.

API Declarations


' Solve a system of linear equations by GaussElimination with PartialPivoting
' Accuracy upto five-decimal dizits of N linear equations on N variables
' Programmed by Dipankar Bose on November 30, 2006. Updated : February 2007.



Rate Perform Gaussian Elimination to solve a system of linear equations on n-variables, having n-number

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(1(1 Vote))

Private mat()                    As Single
Private NoOfVariableEquations    As Integer


Private Sub BkSubst()       '   BackSubstitution

Dim i      As Integer
Dim j      As Integer
Dim mBound As Integer
Dim sSum   As Single
Dim msgStr As String

    mBound = NoOfVariableEquations - 1
    ReDim reslt(mBound) As Single
    reslt(mBound) = FormatNumber(mat(mBound, mBound + 1) / mat(mBound, mBound), 5)
    For i = mBound - 1 To 0 Step -1
        sSum = 0
        For j = i + 1 To mBound
            sSum = sSum + mat(i, j) * reslt(j)
        Next j
        reslt(i) = FormatNumber((mat(i, mBound + 1) - sSum) / mat(i, i), 5)
    Next i
    For i = 0 To mBound
        msgStr = msgStr + vbNewLine & "X" & i + 1 & vbTab & reslt(i)
    Next i
    MsgBox msgStr, , "Result"
    Print "Solution of Equations" & msgStr

End Sub

Private Sub Command1_Click()        ' Input Matrix data

Dim mBound As Integer
Dim i      As Integer
Dim j      As Integer

    NoOfVariableEquations = Val(InputBox("Number of variables", "Equations", 3))
    If Not NoOfVariableEquations <= 0 Then
        mBound = NoOfVariableEquations - 1
        If mBound > 1 Then
            ReDim mat(mBound, mBound + 1)
        End If
        For i = 0 To mBound
            For j = 0 To mBound
mat(i, j) = InputBox("Enter Element co-eff value" & vbNewLine & "Element [" & i & "," & j & "]", "Input Data Element")
            Next j
mat(i, mBound + 1) = InputBox("Enter Element Value" & vbNewLine & "Value [" & i & "," & mBound + 1 & "]", "Input Equation Value")
        Next i
        Print "Matrix representation of the linear Equations"
        DisplayMatrixData
        UpperTriangular
        Print "converted to Upper Triangular form"
        DisplayMatrixData
        BkSubst
    End If

End Sub

Private Sub DisplayMatrixData()

Dim i   As Integer
Dim j   As Integer
Dim res As String

    For i = 0 To NoOfVariableEquations - 1
        For j = 0 To NoOfVariableEquations
            res = res & vbTab & mat(i, j)
        Next j
        res = res & vbNewLine
    Next i
    MsgBox res
    Print res & vbNewLine

End Sub

Private Sub swapRowMat(ByVal r1 As Integer, _
                       ByVal r2 As Integer)

Dim i    As Integer
Dim mB   As Integer
Dim dVal As Single

    mB = NoOfVariableEquations
    For i = 0 To mB
        dVal = mat(r1, i)
        mat(r1, i) = mat(r2, i)
        mat(r2, i) = dVal
    Next i

End Sub

Private Sub UpperTriangular()       ' Matrix to Echelon form

Dim i      As Integer
Dim j      As Integer
Dim k      As Integer
Dim mBound As Integer
Dim df     As Single
Dim pTerms As Integer

    mBound = NoOfVariableEquations - 1
    For k = 0 To mBound - 1
        For i = k + 1 To mBound
            For pTerms = i To mBound
                If Abs(mat(k, k)) < Abs(mat(pTerms, k)) Then
                    swapRowMat pTerms, k
                End If
            Next pTerms
            df = mat(i, k) / mat(k, k)
            For j = k To 3
                mat(i, j) = FormatNumber(mat(i, j) - mat(k, j) * df, 6)
            Next j
        Next i
    Next k

End Sub