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

N2f1_r() Sub N2f1_r ( M As  Long, N As  Long, X() As  Double, Info As  Long, YY() As  Double, IRev As  Long, Optional NFcall As  Long, Optional NFjcall As  Long, Optional Niter As  Long  ) Nonlinear least squares approximation (adaptive algorithm) (Jacobian not required) (simple driver) (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 values in accordance with IRev. Since the Jacobian is calculated by finite difference approximation within the routine, the user is not required to calculate the Jacobian. N2f1_r is equivalent to using N2f_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: The abscissa where the function value 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. = 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,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 \nresult 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(). [out] NFcall (Optional) Number of function evaluations with IRev = 1 excluding those used in computing the Jacobian matrix. [out] NFjcall (Optional) Number of function evaluations with IRev = 1 used in computing the Jacobian matrix. [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 FN2f(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 Ex_N2f1_r() Const M = 4, N = 2 Dim X(N - 1) As Double, Info As Long Dim YY(M - 1) As Double, IRev As Long X(0) = 500: X(1) = 0.0001 IRev = 0 Do Call N2f1_r(M, N, X(), Info, YY(), IRev) If IRev = 1 Then Call FN2f(M, N, X(), 0, YY()) End If Loop While IRev <> 0 Debug.Print "C1, C2 =", X(0), X(1) Debug.Print "Info =", Info End Sub Example Results C1, C2 = 241.084897030993 5.44942231587108E-04 Info = 0