Covar Lmder Lmder1 Lmder1_r Lmder_r Lmdif Lmdif1 Lmdif1_r Lmdif_r Lmstr Lmstr1 Lmstr1_r Lmstr_r N2f N2f1 N2f1_r N2f_r N2g N2g1 N2g1_r N2g_r N2p N2p_r

N2g1_r() Sub N2g1_r ( M As  Long, N As  Long, X() As  Double, Info As  Long, YY() As  Double, YYp() As  Double, IRev As  Long, Optional NFcall As  Long, Optional NFjcall As  Long, Optional Niter As  Long  ) Nonlinear least squares approximation (adaptive algorithm) (reverse communication version) Purpose This routine minimizes the sum of the squares of M nonlinear functions in N variables by the adaptive algorithm which combines and augments a Gauss-Newton, Levenberg-Marquardt and other techniques for better convergence. minimize the sum of fi(x1, x2, ..., xn)^2 (sum for i = 1 to M) The user must provide the function and Jacobian values in accordance with IRev. N2g1_r is equivalent to using N2g_r with setting default parameters. Covariance matrix and regression diagnostic vector are not computed. Parameters [in] M Number of data. (M > 0) [in] N Number of parameters. (0 < N <= M) [in,out] X() Array X(LX - 1) (LX >= N) [in] X must contain an initial estimate of the solution vector. [out] IRev = 0: Solution vector, i.e. best point so far found.   IRev = 1, 2: The abscissa where the function value or derivatives shoule be evaluated. [out] Info = 0: Successful exit. = -1: The argument M had an illegal value. (M < N) = -2: The argument N had an illegal value. (N < 1) = -3: The argument X() is invalid. = -5: The argument YY() is invalid. = -6: The argument YYp() is invalid. = 7: Singular convergence. (Hessian near the current iterate appears to be singular) = 8: False convergence. (Iterate appears to be converging to a noncritical point. Tolerances may be too small) = 9: Function evaluation limit reached. = 10: Iteration limit reached. = 63: F(X) cannot be computed at the initial X. = 65: The gradient could not be computed at X. [in] YY() Array YYp(LYY - 1) (LYY >= M) When returned with IRev = 1, the function value at X() should be given in YY() in the next call. [in] YYp() Array YYp(LYYp1 - 1, LYYp2 - 1) (LYYp1 >= M, LYYp2 >= N) When returned with IRev = 2, Jacobian matrix at X() should be given in YYp() in the next call. [in,out] IRev Control variable for reverse communication. [in] Before first call, IRev should be initialized to zero. On succeeding calls, IRev should not be altered. [out] If IRev is not zero, set the required values to the specified variables or display the intermediate result as follows and call the routine again. = 0: Computation finished. See return code in Info. = 1: User should set the function values at X() in YY(). Do not alter any variables other than YY(). = 2: User should set the derivatives at X() in YYp(). Do not alter any variables other than YYp(). [out] NFcall (Optional) Number of function evaluations with IRev = 1. [out] NFjcall (Optional) Number of Jacobian evaluations with IRev = 2. [out] Niter (Optional) Number of iterations. Reference netlib/port Example Program Approximate the following data with model function f(x) = c1*(1 - exp(-c2*x)). Determine two parameters c1 and c2 by the nonlinear least squares method. f(x) x 10.07 77.6 29.61 239.9 50.76 434.8 81.78 760.0 The initial estimates of the solution are c1 = 500 and c2 = 0.0001. Sub FN2g(M As Long, N As Long, X() As Double, Nf As Long, Fvec() As Double) Dim Xdata(3) As Double, Ydata(3) As Double, I As Long Ydata(0) = 10.07: Xdata(0) = 77.6 Ydata(1) = 29.61: Xdata(1) = 239.9 Ydata(2) = 50.76: Xdata(2) = 434.8 Ydata(3) = 81.78: Xdata(3) = 760 For I = 0 To M - 1 Fvec(I) = Ydata(I) - X(0) * (1 - Exp(-Xdata(I) * X(1))) Next End Sub Sub JN2g(M As Long, N As Long, X() As Double, Nf As Long, Fjac() As Double) Dim Xdata(3) As Double, Ydata(3) As Double, I As Long Ydata(0) = 10.07: Xdata(0) = 77.6 Ydata(1) = 29.61: Xdata(1) = 239.9 Ydata(2) = 50.76: Xdata(2) = 434.8 Ydata(3) = 81.78: Xdata(3) = 760 For I = 0 To M - 1 Fjac(I, 0) = Exp(-Xdata(I) * X(1)) - 1 Fjac(I, 1) = -Xdata(I) * X(0) * Exp(-X(1) * Xdata(I)) Next End Sub Sub Ex_N2g1_r() Const M = 4, N = 2 Dim X(N - 1) As Double, Info As Long Dim YY(M - 1) As Double, YYp(M - 1, N - 1) As Double, IRev As Long X(0) = 500: X(1) = 0.0001 IRev = 0 Do Call N2g1_r(M, N, X(), Info, YY(), YYp(), IRev) If IRev = 1 Then Call FN2g(M, N, X(), 0, YY()) ElseIf IRev = 2 Then Call JN2g(M, N, X(), 0, YYp()) End If Loop While IRev <> 0 Debug.Print "C1, C2 =", X(0), X(1) Debug.Print "Info =", Info End Sub Example Results C1, C2 = 241.084896112856 5.44942234058364E-04 Info = 0