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座右铭:
只做有益人类的事
不做有害人类的事

在给定的区间内搜索函数的最大值或最小值及自变量的取值

董占山

该函数具有十分强大的功能，给定任意一个多项式方程，并给定各个自变量的取值区间及步长，就可以自动搜寻多项式方程的极值。函数的用法：
MinMax(n As Integer, X As Object, b As Object, Optional isMax As Boolean = True)
其中，n是自变量的个数,X为各个自变量的取值区间和步长值,b为多项式的系数矩阵,isMax是一个布尔变量，默认值是true,表示计算最大值，如果计算最小值，将其设置为false即可。
函数的返回值是一个一行多列的数组，列数等于自变量个数加1。第一个返回值是函数的极值，其后的数据为自变量在函数极值时的取值。
本文所附的EXCEL文件含有宏命令，当你使用EXCEL打开文件时，请接受宏，这样你就可以运行程序了。

Option Explicit
Option Base 1

' search the minimum or maximum value of an equation in a specific range
Function MinMax(n As Integer, X As Object, b As Object, Optional isMax _
	 As Boolean = True)
' n - the number of variables
' X - is a n-by-3 matrix, first column is the initial values for each variable
'                         second column is the end values for each variables
'                         third column is the step size for each variables
' b - n+1-by-n+1 matrix, the coeficients for polynomial equation
'     column 1 - constant, column 2 - x1, and so on
'     row 1 - constant, row 2 - x1, ans so on
' isMax - a boolean variable to indicate calculate the maximum or minimum
'
' output variable - a row vector with n+1 values
' first value - maximum or minimum value of the equation
' the remaining values - the values for all xs at maximum or minimum of y
'
    Dim i, j, l, y
    ReDim myMinMax(n + 1)
    If isMax Then
        myMinMax(1) = -1E+100
    Else
        myMinMax(1) = 1E+100
    End If
    Dim xtemp, TotalN
    ReDim tempint(n), xn(n), xminmax(n)
    TotalN = 1
    For i = 1 To n
        tempint(i) = 1
    Next
    For i = 1 To n
        xn(i) = Round((X(i, 2) - X(i, 1)) / X(i, 3)) + 1
        TotalN = TotalN * xn(i)
    Next
    For j = 1 To n
        For i = j + 1 To n
            tempint(j) = tempint(j) * xn(j)
        Next
    Next
    ReDim gridx(TotalN, n)
    For i = 1 To TotalN
        j = 1
        Do While j <= n
         gridx(i, j) = X(j, 1) + X(j, 3) * (((i - 1) \ tempint(j)) Mod xn(j))
         j = j + 1
        Loop
    Next
    For l = 1 To TotalN
        y = 0
        For i = 1 To n + 1
            For j = i To n + 1
                If i = 1 Then
                    If j = 1 Then
                        y = y + b(i, j)
                    Else
                        y = y + b(i, j) * gridx(l, j - 1)
                    End If
                Else
                    y = y + b(i, j) * gridx(l, j - 1) * gridx(l, i - 1)
                End If
            Next
        Next
        If isMax Then
            If y > myMinMax(1) Then
                myMinMax(1) = y
                For i = 1 To n
                    myMinMax(i + 1) = gridx(l, i)
                Next
            End If
        Else
            If y < myMinMax(1) Then
                myMinMax(1) = y
                For i = 1 To n
                    myMinMax(i + 1) = gridx(l, i)
                Next
            End If
        End If
    Next
    MinMax = myMinMax
End Function

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