vb 矩阵计算程序（转载）

测量专用 · 发表于 2020-6-2 14:53

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'  模块名：MatrixModule.bas
'  函数名：MSymTri
'  功能：  用豪斯荷尔德变换约化对称矩阵为对称三对角矩阵
'  参数： n - Integer型变量，对称矩阵的阶数。
'       dblA  - Double型二维数组，体积为n x n。存放n阶对称矩阵。
'       dblQ  - Double型二维数组，体积为n x n。返回时存放豪斯荷尔德变换的乘积矩阵Q。
'       dblT - Double型二维数组，体积为n x n。返回时存放对称三对角矩阵T。
'       dblB - Double型一维数组，长度为n。返回时存放对称三对角矩阵T主对角线上的元素。
'       dblC - Double型一维数组，长度为n。返回时前n-1个元素存放对称三对角矩阵T次对角线上的元素。
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Sub MSymTri(n As Integer, dblA() As Double, dblQ() As Double, dblT() As Double, dblB() As Double, dblC() As Double)
Dim i As Integer, j As Integer, k As Integer
Dim h As Double, f As Double, g As Double, h2 As Double

For i = 1 To n
      For j = 1 To n
         dblQ(i, j) = dblA(i, j)
      Next j
Next i

For i = n To 2 Step -1
      h = 0#
      If (i > 2) Then
         For k = 1 To i - 1
            h = h + dblQ(i, k) * dblQ(i, k)
         Next k
      End If

      If (h + 1# = 1#) Then
         dblC(i) = 0#
         If (i = 2) Then dblC(i) = dblQ(i, i - 1)
         dblB(i) = 0#
      Else
         dblC(i) = Sqr(h)

         If (dblQ(i, i - 1) > 0#) Then dblC(i) = -dblC(i)

         h = h - dblQ(i, i - 1) * dblC(i)
         dblQ(i, i - 1) = dblQ(i, i - 1) - dblC(i)
         f = 0#

         For j = 1 To i - 1
            dblQ(j, i) = dblQ(i, j) / h
            g = 0#
            For k = 1 To j
               g = g + dblQ(j, k) * dblQ(i, k)
            Next k

            If (j + 1 <= i - 1) Then
                  For k = j + 1 To i - 1
                     g = g + dblQ(k, j) * dblQ(i, k)
                  Next k
            End If

            dblC(j) = g / h
            f = f + g * dblQ(j, i)
         Next j

         h2 = f / (h + h)
         For j = 1 To i - 1
            f = dblQ(i, j)
            g = dblC(j) - h2 * f
            dblC(j) = g
            For k = 1 To j
                  dblQ(j, k) = dblQ(j, k) - f * dblC(k) - g * dblQ(i, k)
            Next k
         Next j

         dblB(i) = h
      End If
Next i

For i = 1 To n - 1
      dblC(i) = dblC(i + 1)
Next i

dblC(n) = 0#
dblB(1) = 0#
For i = 1 To n
      If ((dblB(i) <> 0#) And (i - 1 >= 0)) Then
      For j = 1 To i - 1
            g = 0#
            For k = 1 To i - 1
                  g = g + dblQ(i, k) * dblQ(k, j)
            Next k
            For k = 1 To i - 1
                  dblQ(k, j) = dblQ(k, j) - g * dblQ(k, i)
            Next k
      Next j
      End If

      dblB(i) = dblQ(i, i)
      dblQ(i, i) = 1#
      If (i - 1 >= 0) Then
         For j = 1 To i - 1
            dblQ(i, j) = 0#
            dblQ(j, i) = 0#
         Next j
      End If
Next i

' 构造对称三对角矩阵
For i = 1 To n
      For j = 1 To n
         dblT(i, j) = 0
         k = i - j
         If k = 0 Then dblT(i, j) = dblB(j)
         If k = 1 Then dblT(i, j) = dblC(j)
         If k = -1 Then dblT(i, j) = dblC(i)
      Next j
Next i

End Sub

测量专用 · 发表于 2020-6-2 14:54

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'  模块名：MatrixModule.bas
'  函数名：MSymTriEigenv
'  功能：  用变形QR方法计算对称三对角矩阵的全部特征值和特征向量
'  参数： n - Integer型变量，对称三对角矩阵的阶数。
'       dblB - Double型一维数组，长度为n，存放对称三对角矩阵T主对角线上的元素。返回时，存放全部特征值。
'       dblC - Double型一维数组，长度为n，前n-1个元素存放对称三对角矩阵T次对角线上的元素。
'       dblQ - Double型二维数组，体积为n x n。
'                1）如果存放单位矩阵，则返回n阶对称三对角矩阵的特征向量组。
'                2）如果存放对称矩阵A的豪斯荷尔德变换的乘积矩阵Q（可由函数MSymTri求得），则返回n阶对称矩阵A的特征向量组。
'                   其中dblQ中的第j列为与数组dblB中第j个特征值对应的特征向量。
'       eps  - Double型变量。迭代过程中的控制精度参数。
'       nMaxItNum - Integer。为求得一个特征值所允许的最大迭代次数。
'  返回值： Boolean型。False，失败无解；True, 成功
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Function MSymTriEigenv(n As Integer, dblB() As Double, dblC() As Double, dblQ() As Double, eps As Double, nMaxItNum As Integer) As Boolean
' 局部变量
Dim i As Integer, j As Integer, k As Integer, m As Integer, it As Integer
Dim d As Double, f As Double, h As Double, g As Double, p As Double, r As Double, e As Double, s As Double

dblC(n) = 0#
d = 0#
f = 0#

For j = 1 To n
      it = 0
      h = eps * (Abs(dblB(j)) + Abs(dblC(j)))
      If (h > d) Then d = h
      m = j
      While ((m <= n) And (Abs(dblC(m)) > d))
         m = m + 1
      Wend

      If (m <> j) Then
         Do
            If (it = nMaxItNum) Then
                  MSymTriEigenv = False
                  Exit Function
            End If

            it = it + 1
            g = dblB(j)
            p = (dblB(j + 1) - g) / (2# * dblC(j))
            r = Sqr(p * p + 1#)

            If (p >= 0#) Then
                  dblB(j) = dblC(j) / (p + r)
            Else
                  dblB(j) = dblC(j) / (p - r)
            End If

            h = g - dblB(j)
            For i = j + 1 To n
               dblB(i) = dblB(i) - h
            Next i

            f = f + h
            p = dblB(m)
            e = 1#
            s = 0#

            For i = m - 1 To j Step -1
                  g = e * dblC(i)
                  h = e * p
                  If (Abs(p) >= Abs(dblC(i))) Then
                     e = dblC(i) / p
                     r = Sqr(e * e + 1#)
                     dblC(i + 1) = s * p * r
                     s = e / r
                     e = 1# / r
                  Else
                     e = p / dblC(i)
                     r = Sqr(e * e + 1#)
                     dblC(i + 1) = s * dblC(i) * r
                     s = 1# / r
                     e = e / r
                  End If

                  p = e * dblB(i) - s * g
                  dblB(i + 1) = h + s * (e * g + s * dblB(i))
                  For k = 1 To n
                     h = dblQ(k, i + 1)
                     dblQ(k, i + 1) = s * dblQ(k, i) + e * h
                     dblQ(k, i) = e * dblQ(k, i) - s * h
                  Next k
            Next i

            dblC(j) = s * p
            dblB(j) = e * p

         Loop While (Abs(dblC(j)) > d)

      End If

      dblB(j) = dblB(j) + f

Next j

For i = 1 To n
      k = i
      p = dblB(i)
      If (i + 1 <= n) Then
         j = i + 1
         While ((j <= n) And (dblB(j) <= p))
            k = j
            p = dblB(j)
            j = j + 1
         Wend
      End If

      If (k <> i) Then
         dblB(k) = dblB(i)
         dblB(i) = p

         For j = 1 To n
            p = dblQ(j, i)
            dblQ(j, i) = dblQ(j, k)
            dblQ(j, k) = p
         Next j
      End If
Next i

MSymTriEigenv = True

End Function

测量专用 · 发表于 2020-6-2 14:59

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'  模块名：MatrixModule.bas
'  函数名：MHberg
'  功能：  用初等相似变换约化一般矩阵为赫申伯格（Hessen Berg）矩阵
'  参数： n - Integer型变量，矩阵的阶数。
'       mtxA  - Double型二维数组，体积为n x n。存放n阶矩阵；返回时存放矩阵的H矩阵。
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Sub MHberg(n As Integer, mtxA() As Double)
' 局部变量
Dim i As Integer, j As Integer, k As Integer
Dim d As Double, t As Double

For k = 2 To n - 1
      d = 0#
      For j = k To n
         t = mtxA(j, k - 1)
         If (Abs(t) > Abs(d)) Then
            d = t
            i = j
         End If
      Next j

      If (Abs(d) + 1# <> 1#) Then
         If (i <> k) Then
            For j = k - 1 To n
                  t = mtxA(i, j)
                  mtxA(i, j) = mtxA(k, j)
                  mtxA(k, j) = t
            Next j
            For j = 1 To n
                  t = mtxA(j, i)
                  mtxA(j, i) = mtxA(j, k)
                  mtxA(j, k) = t
            Next j
         End If

         For i = k + 1 To n
            t = mtxA(i, k - 1) / d
            mtxA(i, k - 1) = 0#

            For j = k To n
                  mtxA(i, j) = mtxA(i, j) - t * mtxA(k, j)
            Next j

            For j = 1 To n
                  mtxA(j, k) = mtxA(j, k) + t * mtxA(j, i)
            Next j
         Next i
      End If
Next k

End Sub

测量专用 · 发表于 2020-6-2 15:01

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'  模块名：MatrixModule.bas
'  函数名：MHbergEigenv
'  功能：  用QR方法计算赫申伯格（Hessen Berg）矩阵的全部特征值
'  参数： n - Integer型变量，赫申伯格矩阵的阶数。
'       dblA - Double型二维数组，体积为n x n。存放赫申伯格矩阵。
'       dblUR - Double型一维数组，长度为n，存放n个特征值的实部。
'       dblUI - Double型一维数组，长度为n，存放n个特征值的虚部。。
'       eps  - Double型变量。迭代过程中的控制精度参数。
'       nMaxItNum - Integer。为求得一个特征值所允许的最大迭代次数。
'  返回值： Boolean型。False，失败无解；True, 成功
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Function MHbergEigenv(n As Integer, dblA() As Double, dblUR() As Double, dblUI() As Double, eps As Double, nMaxItNum As Integer) As Boolean
' 局部变量
Dim i As Integer, j As Integer, k As Integer, l As Integer, m As Integer, it As Integer
Dim b As Double, c As Double, w As Double, g As Double, xy As Double, p As Double, q As Double
Dim r As Double, x As Double, s As Double, e As Double, f As Double, z As Double, y As Double

it = 0
m = n + 1

While (m <> 1)
      l = m - 1
      While ((l > 1) And (Abs(dblA(l, l - 1)) > eps * (Abs(dblA(l - 1, l - 1)) + Abs(dblA(l, l)))))
         l = l - 1
      Wend

      If (l = m - 1) Then
         dblUR(m - 1) = dblA(m - 1, m - 1)
         dblUI(m - 1) = 0#
         m = m - 1
         it = 0
      Else
         If (l = m - 2) Then
            b = -(dblA(m - 1, m - 1) + dblA(m - 2, m - 2))
            c = dblA(m - 1, m - 1) * dblA(m - 2, m - 2) - dblA(m - 1, m - 2) * dblA(m - 2, m - 1)
            w = b * b - 4# * c
            y = Sqr(Abs(w))

            If (w > 0#) Then
                  xy = 1#
                  If (b < 0#) Then xy = -1#
                  dblUR(m - 1) = (-b - xy * y) / 2#
                  dblUR(m - 2) = c / dblUR(m - 1)
                  dblUI(m - 1) = 0#
                  dblUI(m - 2) = 0#
            Else
                  dblUR(m - 1) = -b / 2#
                  dblUR(m - 2) = dblUR(m - 1)
                  dblUI(m - 1) = y / 2#
                  dblUI(m - 2) = -dblUI(m - 1)
            End If

            m = m - 2
            it = 0
         Else
            If (it >= nMaxItNum) Then
                  MHbergEigenv = False
                  Exit Function
            End If

            it = it + 1
            For j = l + 2 To m - 1
               dblA(j, j - 2) = 0#
            Next j

            For j = l + 3 To m - 1
               dblA(j, j - 3) = 0#
            Next j

            For k = l To m - 2
                  If (k <> l) Then
                     p = dblA(k, k - 1)
                     q = dblA(k + 1, k - 1)
                     r = 0#
                     If (k <> m - 2) Then r = dblA(k + 2, k - 1)
                  Else
                     x = dblA(m - 1, m - 1) + dblA(m - 2, m - 2)
                     y = dblA(m - 2, m - 2) * dblA(m - 1, m - 1) - dblA(m - 2, m - 1) * dblA(m - 1, m - 2)

                     p = dblA(l, l) * (dblA(l, l) - x) + dblA(l, l + 1) * dblA(l + 1, l) + y
                     q = dblA(l + 1, l) * (dblA(l, l) + dblA(l + 1, l + 1) - x)
                     r = dblA(l + 1, l) * dblA(l + 2, l + 1)
                  End If

                  If ((Abs(p) + Abs(q) + Abs(r)) <> 0#) Then
                     xy = 1#
                     If (p < 0#) Then xy = -1#

                     s = xy * Sqr(p * p + q * q + r * r)
                     If (k <> l) Then dblA(k, k - 1) = -s
                     e = -q / s
                     f = -r / s
                     x = -p / s
                     y = -x - f * r / (p + s)
                     g = e * r / (p + s)
                     z = -x - e * q / (p + s)
                     For j = k To m - 1
                        p = x * dblA(k, j) + e * dblA(k + 1, j)
                        q = e * dblA(k, j) + y * dblA(k + 1, j)
                        r = f * dblA(k, j) + g * dblA(k + 1, j)

                        If (k <> m - 2) Then
                              p = p + f * dblA(k + 2, j)
                              q = q + g * dblA(k + 2, j)
                              r = r + z * dblA(k + 2, j)
                              dblA(k + 2, j) = r
                        End If

                        dblA(k + 1, j) = q
                        dblA(k, j) = p
                     Next j

                     j = k + 3
                     If (j >= m - 1) Then j = m - 1

                     For i = l To j
                        p = x * dblA(i, k) + e * dblA(i, k + 1)
                        q = e * dblA(i, k) + y * dblA(i, k + 1)
                        r = f * dblA(i, k) + g * dblA(i, k + 1)

                        If (k <> m - 2) Then
                              p = p + f * dblA(i, k + 2)
                              q = q + g * dblA(i, k + 2)
                              r = r + z * dblA(i, k + 2)
                              dblA(i, k + 2) = r
                        End If

                        dblA(i, k + 1) = q
                        dblA(i, k) = p
                     Next i
                  End If
            Next k
         End If
      End If
Wend

MHbergEigenv = True

End Function

测量专用 · 发表于 2020-6-2 15:03

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'  模块名：MatrixModule.bas
'  函数名：MJacobiEigenv
'  功能：  用雅可比法（Jacobi）计算对称矩阵的特征值和特征向量
'  参数： n - Integer型变量，对称矩阵的阶数。
'       dblA - Double型二维数组，体积为n x n。存放对称矩阵；返回时，对角线上存放求得的n个特征值。
'       dblV - Double型二维数组，体积为n x n。返回n个特征向量，其中第i列为第i个特征值dblA(i,i)对应的特征向量。
'       eps  - Double型变量。迭代过程中的控制精度参数。
'       nMaxItNum - Integer。为求得一个特征值所允许的最大迭代次数。
'  返回值： Boolean型。False，失败无解；True, 成功
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Function MJacobiEigenv(n As Integer, dblA() As Double, dblV() As Double, eps As Double, nMaxItNum As Integer) As Boolean
' 局部变量
Dim i As Integer, j As Integer, p As Integer, q As Integer, l As Integer
Dim fm As Double, cn As Double, sn As Double, omega As Double, x As Double, y As Double, d As Double

l = 1
For i = 1 To n
      dblV(i, i) = 1#
      For j = 1 To n
      If (i <> j) Then dblV(i, j) = 0#
      Next j
Next i

While (True)
      fm = 0#
      For i = 2 To n
         For j = 1 To i - 1
            d = Abs(dblA(i, j))
            If ((i <> j) And (d > fm)) Then
                  fm = d
                  p = i
                  q = j
            End If
         Next j
      Next i

      If (fm < eps) Then
         MJacobiEigenv = True
         Exit Function
      End If

      If (l > nMaxItNum) Then
         MJacobiEigenv = False
         Exit Function
      End If

      l = l + 1
      x = -dblA(p, q)
      y = (dblA(q, q) - dblA(p, p)) / 2#
      omega = x / Sqr(x * x + y * y)
      If (y < 0#) Then omega = -omega
      sn = 1# + Sqr(1# - omega * omega)
      sn = omega / Sqr(2# * sn)
      cn = Sqr(1# - sn * sn)
      fm = dblA(p, p)
      dblA(p, p) = fm * cn * cn + dblA(q, q) * sn * sn + dblA(p, q) * omega
      dblA(q, q) = fm * sn * sn + dblA(q, q) * cn * cn - dblA(p, q) * omega
      dblA(p, q) = 0#
      dblA(q, p) = 0#

      For j = 1 To n
         If ((j <> p) And (j <> q)) Then
            fm = dblA(p, j)
            dblA(p, j) = fm * cn + dblA(q, j) * sn
            dblA(q, j) = -fm * sn + dblA(q, j) * cn
         End If
      Next j

      For i = 1 To n
      If ((i <> p) And (i <> q)) Then
            fm = dblA(i, p)
            dblA(i, p) = fm * cn + dblA(i, q) * sn
            dblA(i, q) = -fm * sn + dblA(i, q) * cn
      End If
      Next i

      For i = 1 To n
         fm = dblV(i, p)
         dblV(i, p) = fm * cn + dblV(i, q) * sn
         dblV(i, q) = -fm * sn + dblV(i, q) * cn
      Next i
Wend

End Function

测量专用 · 发表于 2020-6-2 15:05

''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''
'  模块名：MatrixModule.bas
'  函数名：MJacobiEigenv2
'  功能：  用雅可比（Jacobi）过关法计算对称矩阵的特征值和特征向量
'  参数： n - Integer型变量，对称矩阵的阶数。
'       dblA - Double型二维数组，体积为n x n。存放对称矩阵；返回时，对角线上存放求得的n个特征值。
'       dblV - Double型二维数组，体积为n x n。返回n个特征向量，其中第i列为第i个特征值dblA(i,i)对应的特征向量。
'       eps  - Double型变量。迭代过程中的控制精度参数。
''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''
Sub MJacobiEigenv2(n As Integer, dblA() As Double, dblV() As Double, eps As Double)
' 局部变量
Dim i As Integer, j As Integer, p As Integer, q As Integer
Dim ff As Double, fm As Double, cn As Double, sn As Double, omega As Double, x As Double, y As Double, d As Double

For i = 1 To n
      dblV(i, i) = 1#
      For j = 1 To n
      If (i <> j) Then dblV(i, j) = 0#
      Next j
Next i

ff = 0#
For i = 2 To n
      For j = 1 To i
         d = dblA(i, j)
         ff = ff + d * d
      Next j
Next i

ff = Sqr(2# * ff)

loop_0:

ff = ff / (1# * n)

loop_1:

For i = 2 To n
      For j = 1 To i - 1
         d = Abs(dblA(i, j))
         If (d > ff) Then
            p = i
            q = j
            GoTo loop_2
         End If
      Next j
Next i

' 计算已达到精度要求，返回
If (ff < eps) Then Exit Sub

GoTo loop_0

loop_2:

   x = -dblA(p, q)
   y = (dblA(q, q) - dblA(p, p)) / 2#
   omega = x / Sqr(x * x + y * y)
   If (y < 0#) Then omega = -omega
   sn = 1# + Sqr(1# - omega * omega)
   sn = omega / Sqr(2# * sn)
   cn = Sqr(1# - sn * sn)
   fm = dblA(p, p)
   dblA(p, p) = fm * cn * cn + dblA(q, q) * sn * sn + dblA(p, q) * omega
   dblA(q, q) = fm * sn * sn + dblA(q, q) * cn * cn - dblA(p, q) * omega
   dblA(p, q) = 0#
   dblA(q, p) = 0#

   For j = 1 To n
      If ((j <> p) And (j <> q)) Then
         fm = dblA(p, j)
         dblA(p, j) = fm * cn + dblA(q, j) * sn
         dblA(q, j) = -fm * sn + dblA(q, j) * cn
      End If
   Next j

   For i = 1 To n
   If ((i <> p) And (i <> q)) Then
         fm = dblA(i, p)
         dblA(i, p) = fm * cn + dblA(i, q) * sn
         dblA(i, q) = -fm * sn + dblA(i, q) * cn
   End If
   Next i

   For i = 1 To n
      fm = dblV(i, p)
      dblV(i, p) = fm * cn + dblV(i, q) * sn
      dblV(i, q) = -fm * sn + dblV(i, q) * cn
   Next i

GoTo loop_1

End Sub

测量专用 · 发表于 2020-6-2 15:06

传完收工

FOB_FN_L · 发表于 2020-6-2 20:29

从哪弄来的，这些东东

测量专用 · 发表于 2020-6-2 22:26

FOB_FN_L 发表于 2020-6-2 20:29
从哪弄来的，这些东东

其他地方找的

FOB_FN_L · 发表于 2020-6-2 22:36

测量专用发表于 2020-6-2 22:26
其他地方找的

什么地方，来个地址，我也去转转看看还有什么好东东

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