1.数学定义
n阶行列式定义如下:
2.算法实现
函数名: GetValue()
功能:返回一个行列式的值
Private Function GetValue() Dim gValue As Double Dim tempResultList As New List(Of Array) ) As Integer '要进行全排列的序列 tempNumArray(i) = i Next GetFullPerm(tempNumArray, , tempResultList) Dim temp As Double Dim tempData() As Integer temp = tempData = tempResultList(i) temp = temp * TableData(j, tempData(j)) Next temp = Math.Pow(-, GetInverseNum(tempData)) * temp gValue += temp Next Return gValue End Function
3.完整的行列式类(determinant)
使用示例:
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 '行列式的阶 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 , iCol - ) End Get Set(ByVal value) TableData(iRow - , iCol - ) = value End Set End Property Public ReadOnly Property value() Get Return GetValue() End Get End Property Public Sub New(ByVal nRank As Integer) , nRank - ) 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) ) As Integer '要进行全排列的序列 tempNumArray(i) = i Next GetFullPerm(tempNumArray, , tempResultList) Dim temp As Double Dim tempData() As Integer temp = tempData = tempResultList(i) temp = temp * TableData(j, tempData(j)) Next temp = Math.Pow(-, 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 Then ) As Integer NumArray.CopyTo(tempArray, ) Result.Add(tempArray) Else temp = NumArray(LeftIndex) NumArray(LeftIndex) = NumArray(i) NumArray(i) = temp '对换 GetFullPerm(NumArray, LeftIndex + , Result) NumArray(i) = NumArray(LeftIndex) NumArray(LeftIndex) = temp '还原对换 Next End If End Sub '逆序数 Private Function GetInverseNum(ByVal NumArray() As Integer) Next Next Return Num End Function End Class