行列式(三)：n階行列式

標籤：

  1.數學定義

　   n階行列式定義如下:

 

  2.演算法實現

　　函數名: GetValue()

　　功能:返回一個行列式的值

    Private Function GetValue()        Dim gValue As Double        Dim tempResultList As New List(Of Array)        Dim tempNumArray(RankLength - 1) As Integer ‘要進行全排列的序列        For i = 0 To RankLength - 1            tempNumArray(i) = i        Next        GetFullPerm(tempNumArray, 0, tempResultList)        Dim temp As Double        Dim tempData() As Integer        For i = 0 To tempResultList.Count - 1            temp = 1            tempData = tempResultList(i)            For j = 0 To RankLength - 1                temp = temp * TableData(j, tempData(j))            Next            temp = Math.Pow(-1, GetInverseNum(tempData)) * temp            gValue += temp        Next        Return gValue    End Function

3.完整的行列式類(determinant)

　　使用樣本:

Dim d As New Determinant(3)
d.Item(1, 1) = 1
d.Item(2, 2) = 2
d.Item(3, 3) = 4
Console.write(d.value)

Public Class Determinant    Private TableData(,) As Double    Private RankLength As Integer    ‘行列式的階    Public ReadOnly Property Rank()        Get            Return RankLength        End Get    End Property    ‘行列式第iRow行第iCol列的元素        Public Property Item(ByVal iRow As Integer, ByVal iCol As Integer)            Get                Return TableData(iRow - 1, iCol - 1)            End Get            Set(ByVal value)                TableData(iRow - 1, iCol - 1) = value            End Set        End Property    Public ReadOnly Property value()        Get            Return GetValue()        End Get    End Property    Public Sub New(ByVal nRank As Integer)        Dim tempArray(nRank - 1, nRank - 1) As Double        TableData = tempArray        RankLength = nRank    End Sub    ‘求行列式的值    Private Function GetValue()        Dim gValue As Double        Dim tempResultList As New List(Of Array)        Dim tempNumArray(RankLength - 1) As Integer ‘要進行全排列的序列        For i = 0 To RankLength - 1            tempNumArray(i) = i        Next        GetFullPerm(tempNumArray, 0, tempResultList)        Dim temp As Double        Dim tempData() As Integer        For i = 0 To tempResultList.Count - 1            temp = 1            tempData = tempResultList(i)            For j = 0 To RankLength - 1                temp = temp * TableData(j, tempData(j))            Next            temp = Math.Pow(-1, GetInverseNum(tempData)) * temp            gValue += temp        Next        Return gValue    End Function    ‘全排列    Private Sub GetFullPerm(ByVal NumArray() As Integer, ByVal LeftIndex As Integer, ByRef Result As List(Of Array))        Dim temp As Integer        If LeftIndex = NumArray.Length - 1 Then            Dim tempArray(NumArray.Length - 1) As Integer            NumArray.CopyTo(tempArray, 0)            Result.Add(tempArray)        Else            temp = NumArray(LeftIndex)            For i = LeftIndex To NumArray.Length - 1                NumArray(LeftIndex) = NumArray(i)                NumArray(i) = temp ‘對換                GetFullPerm(NumArray, LeftIndex + 1, Result)                NumArray(i) = NumArray(LeftIndex)                NumArray(LeftIndex) = temp ‘還原對換            Next        End If    End Sub    ‘逆序數    Private Function GetInverseNum(ByVal NumArray() As Integer)        Dim Num As Integer = 0        For i = 0 To NumArray.Length - 1            For j = i To NumArray.Length - 1                If NumArray(i) > NumArray(j) Then Num += 1            Next        Next        Return Num    End FunctionEnd Class

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行列式(三)：n階行列式