<>这程序是用来求解一个线性拟合,先用最小二乘法建立函数,再通过Gasuss-Newton法求解</P>
<>程序如下:</P>
<>Private Sub Command1_Click()<BR>Dim a As Double<BR>Dim re(10), r(10), s(3), x(3), x1(3), f(10) As Double<BR>Dim j(10, 3), j1(3, 10), c(3, 1), d(3, 3) As Double<BR> re(1) = 4658: re(23) = 5820: re(3) = 6525: re(4) = 7400: re(5) = 9045: re(6) = 10350: re(7) = 11050: re(8) = 11820: re(9) = 12850: re(10) = 13840<BR> r(1) = 0.0399: r(2) = 0.0386: r(3) = 0.0368: r(4) = 0.0362: r(5) = 0.0349: r(6) = 0.0339: r(7) = 0.0341: r(8) = 0.0323: r(9) = 0.0324: r(10) = 0.0321<BR> a = 0.001<BR> For i = 1 To 3<BR> x(i) = 0<BR> s(i) = 0.01<BR> Next i<BR> While ((Abs(s(1)) + Abs(s(2)) + Abs(s(3))) > 0.0001)<BR> For i = i To 3<BR> <BR> s(i) = 0<BR> Next i<BR> For i = 1 To 10<BR> j(i, 1) = 2 * Exp(x(2) * Log(re(i))) * (x(1) * Exp(x(2) * Log(re(i))) + x(3) - r(i))<BR> j(i, 2) = 2 * x(1) * Log(re(i)) * Exp(x(2) * Log(re(i))) * (x(1) * Exp(x(2) * Log(re(i))) + x(3) - r(i))<BR> j(i, 3) = 2 * (x(1) * Exp(x(2) * Log(re(i))) + x(3) - r(i))<BR> f(i) = (x(1) * Exp(x(2) * Log(re(i))) + x(3) - r(i)) ^ 2<BR> Next i<BR> Call MTrans(10, 3, j(), j1())<BR> Call MMul(3, 10, 1, j1(), f(), c())<BR> Call MMul(3, 10, 3, j1(), j(), d())<BR> Call MRinv(3, d())<BR> Call MMul(3, 3, 1, d(), c(), s())<BR> For i = 1 To 3<BR> x1(i) = x(i) - a * s(i)<BR> x(i) = x1(i)<BR> Next i<BR> Wend<BR>For i = 1 To 3<BR> Print x(i)<BR> Next i<BR>End Sub<BR>Function MRinv(n As Integer, mtxA() As Double) As Boolean<BR> '求逆矩阵<BR> ReDim nIs(n) As Integer, nJs(n) As Integer<BR> Dim i As Integer, j As Integer, k As Integer<BR> Dim d As Double, p As Double</P>
<P> <BR> For k = 1 To n<BR> d = 0#<BR> For i = k To n<BR> For j = k To n<BR> p = Abs(mtxA(i, j))<BR> If (p > d) Then<BR> d = p<BR> nIs(k) = i<BR> nJs(k) = j<BR> End If<BR> Next j<BR> Next i<BR> <BR> <BR> If (d + 1# = 1#) Then<BR> MRinv = False<BR> Exit Function<BR> End If</P>
<P> If (nIs(k) <> k) Then<BR> For j = 1 To n<BR> p = mtxA(k, j)<BR> mtxA(k, j) = mtxA(nIs(k), j)<BR> mtxA(nIs(k), j) = p<BR> Next j<BR> End If</P>
<P> If (nJs(k) <> k) Then<BR> For i = 1 To n<BR> p = mtxA(i, k)<BR> mtxA(i, k) = mtxA(i, nJs(k))<BR> mtxA(i, nJs(k)) = p<BR> Next i<BR> End If</P>
<P> mtxA(k, k) = 1# / mtxA(k, k)<BR> For j = 1 To n<BR> If (j <> k) Then mtxA(k, j) = mtxA(k, j) * mtxA(k, k)<BR> Next j<BR> For i = 1 To n<BR> If (i <> k) Then<BR> For j = 1 To n<BR> If (j <> k) Then mtxA(i, j) = mtxA(i, j) - mtxA(i, k) * mtxA(k, j)<BR> Next j<BR> End If<BR> Next i<BR> For i = 1 To n<BR> If (i <> k) Then mtxA(i, k) = -mtxA(i, k) * mtxA(k, k)<BR> Next i<BR> Next k</P>
<P> <BR> For k = n To 1 Step -1<BR> If (nJs(k) <> k) Then<BR> For j = 1 To n<BR> p = mtxA(k, j)<BR> mtxA(k, j) = mtxA(nJs(k), j)<BR> mtxA(nJs(k), j) = p<BR> Next j<BR> End If<BR> If (nIs(k) <> k) Then<BR> For i = 1 To n<BR> p = mtxA(i, k)<BR> mtxA(i, k) = mtxA(i, nIs(k))<BR> mtxA(i, nIs(k)) = p<BR> Next i<BR> End If<BR> Next k<BR> <BR> <BR> MRinv = True</P>
<P>End Function<BR>Sub MMul(m As Integer, n As Integer, l As Integer, mtxA() As Double, mtxB() As Double, mtxC() As Double)<BR> Dim i As Integer, j As Integer, k As Integer<BR> '矩阵乘法<BR> For i = 1 To m<BR> For j = 1 To l<BR> mtxC(i, j) = 0#<BR> For k = 1 To n<BR> mtxC(i, j) = mtxC(i, j) + mtxA(i, k) * mtxB(k, j)<BR> Next k<BR> Next j<BR> Next i</P>
<P>End Sub<BR>Sub MTrans(m As Integer, n As Integer, mtxA() As Double, mtxAT() As Double)<BR> Dim i As Integer, j As Integer<BR> '矩阵转置</P>
<P> For i = 1 To m<BR> For j = 1 To n<BR> mtxAT(i, j) = mtxAT(j, i)<BR> Next j<BR> Next i</P>
<P>End Sub<BR>拜托各位拉!!!</P>
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