Attribute VB_Name = "modMethod"
'多項式回歸
Option Explicit
'全主元高斯-約當消去法求逆矩陣
'A(1 To m, 1 To m)：開始存放欲求逆的矩陣，最終存求逆的結果矩陣，m是自變量個數
Public Sub Invert(a() As Double)
    Dim N As Integer, ep As Double
    Dim I As Integer, J As Integer, K As Integer
    Dim I0 As Integer, J0 As Integer
    Dim w As Double, z As Double
    Dim b(1 To 100) As Double, c(1 To 100) As Double
    Dim p(1 To 100) As Double, Q(1 To 100) As Double
    N = UBound(a, 1)
    ep = 0.0000000001
    For K = 1 To N
        w = 0#
        For I = K To N
            For J = K To N
                If Abs(a(I, J)) > Abs(w) Then
                    w = a(I, J): I0 = I: J0 = J
                End If
            Next J
        Next I
        If Abs(w) < ep Then
            MsgBox "全主元素的絕對值小于0.0000000001，矩陣是奇異的！"
            Exit Sub
        End If
        If I0 <> K Then
            For J = 1 To N
                z = a(I0, J): a(I0, J) = a(K, J): a(K, J) = z
            Next J
        End If
        If J0 <> K Then
            For I = 1 To N
                z = a(I, J0): a(I, J0) = a(I, K): a(I, K) = z
            Next I
        End If
        p(K) = I0: Q(K) = J0
        For J = 1 To N
            If J = K Then
                b(J) = 1 / w: c(J) = 1
            Else
                b(J) = -a(K, J) / w: c(J) = a(J, K)
            End If
            a(K, J) = 0#: a(J, K) = 0#
        Next J
        For I = 1 To N
            For J = 1 To N
                a(I, J) = a(I, J) + c(I) * b(J)
            Next J
        Next I
    Next K
    For K = N To 1 Step -1
        I0 = p(K): J0 = Q(K)
        If I0 <> K Then
            For I = 1 To N
                z = a(I, I0): a(I, I0) = a(I, K): a(I, K) = z
            Next I
        End If
        If J0 <> K Then
            For J = 1 To N
                z = a(J0, J): a(J0, J) = a(K, J): a(K, J) = z
            Next J
        End If
    Next K
End Sub

'多元線性回歸
'x(1 To n, 1 To m)：自變量，已知。n是觀測次數，m是自變量的個數
'y(1 To n)：因變量，已知
'a(1 To m, 1 To m)：法方程的系數矩陣，計算結果
'b(0 To m)：回歸系數，計算結果
'F：F檢驗值，計算結果
't(1 To m)：各變量的t檢驗值，計算結果
Public Sub Multi(x() As Double, y() As Double, _
                a() As Double, b() As Single, F As Double, t() As Single)
    Dim I As Integer, J As Integer, K As Integer
    Dim M As Integer, N As Integer
    Dim Xa(1 To 100) As Double, Ya As Double, S2 As Double
    Dim Smm(1 To 100, 1 To 100) As Double, Sy(1 To 100) As Double
    Dim Syy As Double                               '離差平方和
    Dim Q As Double, U As Double                    'Q是殘差平方和，U是回歸平方和
    N = UBound(x, 1)                                'N是觀測數據的組數
    M = UBound(x, 2)                                'M是自變量的個數
    For I = 1 To M
        For K = 1 To N
            Xa(I) = Xa(I) + x(K, I)
        Next K
        Xa(I) = Xa(I) / N                           '自變量的平均值
    Next I
    For K = 1 To N
        Ya = Ya + y(K)
    Next K
    Ya = Ya / N                                     '因變量的平均值
'建立法方程
    For I = 1 To M
        For J = 1 To M
            For K = 1 To N
                Smm(I, J) = Smm(I, J) + (x(K, I) - Xa(I)) * (x(K, J) - Xa(J))
            Next K
        Next J
    Next I
    For I = 1 To M
        For K = 1 To N
            Sy(I) = Sy(I) + (x(K, I) - Xa(I)) * (y(K) - Ya)
        Next K
    Next I
    For I = 1 To M
        For J = 1 To M
            a(I, J) = Smm(I, J)                     'a（）是法方程的系數矩陣
        Next J
    Next I
    Invert a                                        '求法方程系數矩陣的逆矩陣
'求多元線性回歸系數b（）
    For I = 1 To M
        For J = 1 To M
            b(I) = b(I) + a(I, J) * Sy(J)
        Next J
    Next I
    b(0) = Ya
    For I = 1 To M
        b(0) = b(0) - b(I) * Xa(I)
    Next I
'Syy是離差平方和
    For K = 1 To N
        Syy = Syy + (y(K) - Ya) ^ 2
    Next K
'U是回歸平方和
    For I = 1 To M
        U = U + b(I) * Sy(I)
    Next I
'Q是殘差平方和
    Q = Syy - U
    S2 = Q / (N - M - 1)
    F = (U / M) / S2                                'F檢驗值
'求t檢驗值
    S2 = Sqr(S2)
    For I = 1 To M
        t(I) = Abs(b(I) / S2 / Sqr(a(I, I)))
    Next I
End Sub

'求正態分布的分位數
'Q：上側概率
'x：分位數
Public Sub PNorm(Q, x)
    Dim p As Double, y As Double, z As Double
    Dim b0 As Double, b1 As Double, b2 As Double
    Dim b3 As Double, b4 As Double, b5 As Double
    Dim b6 As Double, b7 As Double, b8 As Double
    Dim b9 As Double, b10 As Double, b As Double
    b0 = 1.570796288: b1 = 0.03706987906
    b2 = -0.0008364353589: b3 = -0.0002250947176
    b4 = 0.000006841218299: b5 = 0.000005824238515
    b6 = -0.00000104527497: b7 = 8.360937017E-08
    b8 = -3.231081277E-09: b9 = 3.657763036E-11
    b10 = 6.936233982E-13
    If Q = 0.5 Then
        x = 0: GoTo PN01
    End If
    If Q > 0.5 Then p = 1 - Q Else p = Q
    y = -Log(4 * p * (1 - p))
    b = y * (b9 + y * b10)
    b = y * (b8 + b): b = y * (b7 + b)
    b = y * (b6 + b): b = y * (b5 + b)
    b = y * (b4 + b): b = y * (b3 + b)
    b = y * (b2 + b): b = y * (b1 + b)
    z = y * (b0 + b): x = Sqr(z)
    If Q > 0.5 Then x = -x
PN01:
End Sub

'計算F分布的分布函數
'n1：自由度，已知
'n2：自由度，已知
'F：F值，已知
'p：下側概率，所求
'd：概率密度，所求
Public Sub F_DIST(n1 As Integer, n2 As Integer, F As Double, _
            p As Double, d As Double)
    Dim x As Double, U As Double, Lu As Double
    Dim IAI As Integer, IBI As Integer, nn1 As Integer, nn2 As Integer
    Dim I As Integer
    Const PI As Double = 3.14159265359
    If F = 0 Then
        p = 0: d = 0: Exit Sub
    End If
    x = n1 * F / (n2 + n1 * F)
    If (n1 \ 2) * 2 = n1 Then
        If (n2 \ 2) * 2 = n2 Then
            U = x * (1 - x): p = x: IAI = 2: IBI = 2
        Else
            U = x * Sqr(1 - x) / 2: p = 1 - Sqr(1 - x): IAI = 2: IBI = 1
        End If
    Else
        If (n2 \ 2) * 2 = n2 Then
            p = Sqr(x): U = p * (1 - x) / 2: IAI = 1: IBI = 2
        Else
            U = Sqr(x * (1 - x)) / PI
            p = 1 - 2 * Atn(Sqr((1 - x) / x)) / PI: IAI = 1: IBI = 1
        End If
    End If
    nn1 = n1 - 2: nn2 = n2 - 2
    If U = 0 Then
        d = U / F
        Exit Sub
    Else
        Lu = Log(U)
    End If
    If IAI = n1 Then GoTo LL1
    For I = IAI To nn1 Step 2
        p = p - 2 * U / I
        Lu = Lu + Log((1 + IBI / I) * x)
        U = Exp(Lu)
    Next I
LL1:
    If IBI = n2 Then
        d = U / F: Exit Sub
    End If
    For I = IBI To nn2 Step 2
        p = p + 2 * U / I
        Lu = Lu + Log((1 + n1 / I) * (1 - x))
        U = Exp(Lu)
    Next I
    d = U / F
End Sub

'計算F分布的分位數
'n1：自由度，已知
'n2：自由度，已知
'Q：上側概率，已知
'F：分位數，所求
Public Sub PF_DIST(n1 As Integer, n2 As Integer, _
                Q As Double, F As Double)
    Dim DF12 As Double, DF22 As Double, a As Double, b As Double
    Dim A1 As Double, b1 As Double, p As Double, YQ As Double
    Dim E As Double, FO As Double, pp As Double, d As Double
    Dim GA1 As Double, GA2 As Double, GA3 As Double
    Dim K As Integer
    DF12 = n1 / 2: DF22 = n2 / 2
    a = 2 / (9 * n1): A1 = 1 - a
    b = 2 / (9 * n2): b1 = 1 - b
    p = 1 - Q: PNorm Q, YQ
    E = b1 * b1 - b * YQ * YQ
    If E > 0.8 Then
        FO = ((A1 * b1 + YQ * Sqr(A1 * A1 * b + a * E)) / E) ^ 3
    Else
        lnGamma DF12 + DF22, GA1
        lnGamma DF12, GA2
        lnGamma DF22, GA3
        FO = (2 / n2) * (GA1 - GA2 - GA3 + 0.69315 + (DF22 - 1) * Log(n2) _
            - DF22 * Log(n1) - Log(Q))
        FO = Exp(FO)
    End If
    For K = 1 To 30
        F_DIST n1, n2, FO, pp, d
        If d = 0 Then
            F = FO: Exit Sub
        End If
        F = FO - (pp - p) / d
        If Abs(FO - F) < 0.000001 * Abs(F) Then Exit Sub Else FO = F
    Next K
End Sub

'計算GAMMA函數
'x：自變量
'z：GAMMA函數值
Public Sub GAMMA(x As Double, z As Double)
    Dim H As Double, y As Double, y1 As Double
    H = 1: y = x
LL1:
    If y = 2 Then
        z = H
        Exit Sub
    ElseIf y < 2 Then
        H = H / y: y = y + 1: GoTo LL1
    ElseIf y >= 3 Then
        y = y - 1: H = H * y: GoTo LL1
    End If
    y = y - 2
    y1 = y * (0.005159 + y * 0.001606)
    y1 = y * (0.004451 + y1)
    y1 = y * (0.07211 + y1)
    y1 = y * (0.082112 + y1)
    y1 = y * (0.41174 + y1)
    y1 = y * (0.422787 + y1)
    H = H * (0.999999 + y1)
    z = H
End Sub

'求Gamma函數的對數LogGamma(x)
'x：自變量
'G：Gamma函數的對數
Public Sub lnGamma(x As Double, G As Double)
    Dim y As Double, z As Double, a As Double
    Dim b As Double, b1 As Double, N As Integer
    Dim I As Integer
    If x < 8 Then
        y = x + 8: N = -1
    Else
        y = x: N = 1
    End If
    z = 1 / (y * y)
    a = (y - 0.5) * Log(y) - y + 0.9189385
    b1 = (0.0007663452 * z - 0.0005940956) * z
    b1 = (b1 + 0.0007936431) * z
    b1 = (b1 - 0.002777778) * z
    b = (b1 + 0.0833333) / y
    G = a + b
    If N >= 0 Then Exit Sub
    y = y - 1: a = y
    For I = 1 To 7
        a = a * (y - I)
    Next I
    G = G - Log(a)
End Sub

'計算t分布的分布函數
'n：自由度，已知
'T：t值，已知
'pp：下側概率，所求
'dd：概率密度，所求
Public Sub T_Dist(N As Integer, t As Double, pp As Double, dd As Double)
    Dim Sign As Integer, TT As Double, x As Double
    Dim p As Double, U As Double, GA1 As Double, GA2 As Double
    Dim IBI As Integer, n2 As Integer, I As Integer
    Const PI As Double = 3.14159265359
    If t = 0 Then
        Call GAMMA(N / 2, GA1): Call GAMMA(N / 2 + 0.5, GA2): pp = 0.5
        dd = GA2 / (Sqr(N * PI) * GA1): Exit Sub
    End If
    If t < 0 Then Sign = -1 Else Sign = 1
    TT = t * t: x = TT / (N + TT)
    If (N \ 2) * 2 = N Then                 'n為偶數
        p = Sqr(x): U = p * (1 - x) / 2
        IBI = 2
    Else                                    'n為奇數
        U = Sqr(x * (1 - x)) / PI
        p = 1 - 2 * Atn(Sqr((1 - x) / x)) / PI
        IBI = 1
    End If
    If IBI = N Then GoTo LL1 Else n2 = N - 2
    For I = IBI To n2 Step 2
        p = p + 2 * U / I
        U = U * (1 + I) / I * (1 - x)
    Next I
LL1:
    dd = U / Abs(t)
    pp = 0.5 + Sign * p / 2
End Sub

'求t分布的分位數
'n：自由度，已知
'Q：上側概率（<=0.5），已知
'T：分位數，所求
Public Sub PT_DIST(N As Integer, Q As Double, t As Double)
    Dim PIS As Double, DFR2 As Double, c As Double
    Dim Q2 As Double, p As Double, YQ As Double, E As Double
    Dim GA1 As Double, GA2 As Double, GA3 As Double
    Dim T0 As Double, pp As Double, d As Double
    Dim K As Integer
    Const PI As Double = 3.14159265359
    PIS = Sqr(PI): DFR2 = N / 2
    If N = 1 Then
        t = Tan(PI * (0.5 - Q)): Exit Sub
    End If
    If N = 2 Then
        If Q > 0.5 Then c = -1 Else c = 1
        Q2 = (1 - 2 * Q) ^ 2
        t = Sqr(2 * Q2 / (1 - Q2)) * c
        Exit Sub
    End If
    p = 1 - Q: PNorm Q, YQ              '正態分布分位數
    E = (1 - 1 / (4 * N)) ^ 2 - YQ * YQ / (2 * N)
    If E > 0.5 Then
        T0 = YQ / Sqr(E)
    Else
        lnGamma DFR2, GA1: lnGamma DFR2 + 0.5, GA2
        GA3 = Exp((GA1 - GA2) / N)
        T0 = Sqr(N) / (PIS * Q * N) ^ (1 / N) / GA3
    End If
    For K = 1 To 30
        T_Dist N, T0, pp, d
        If d = 0 Then
            t = T0: Exit Sub
        End If
        t = T0 - (pp - p) / d
        If Abs(T0 - t) < 0.000001 * Abs(t) Then _
            Exit Sub Else T0 = t
    Next K
End Sub