covar lmder lmder1 lmder1_r lmder_r lmdif lmdif1 lmdif1_r lmdif_r lmstr lmstr1 lmstr1_r lmstr_r n2f n2f_r n2g n2g_r n2p n2p_r

lmdif_r() void lmdif_r ( int  m, int  n, double  x[], double  fvec[], int  ldfjac, double  fjac[], double  ftol, double  xtol, double  gtol, int  maxfev, double  epsfcn, double  diag[], int  mode, double  factor, int  nprint, int *  nfev, int  ipvt[], double  work[], int  lwork, int *  info, double  xx[], double  yy[], int *  irev  ) Nonlinear least squares approximation by Levenberg-Marquardt method (Jacobian not required) (reverse communication version) Purpose lmdif_r minimizes the sum of the squares of m nonlinear functions in n variables by a modification of the Levenberg-Marquardt algorithm. minimize the sum of fi(x1, x2, ..., xn)^2 (sum for i = 1 to m) The user must provide the calculated function values according to irev. Since the Jacobian is calculated by finite difference approximation within the routine, the user is not required to calculate the Jacobian. Parameters [in] m Number of functions. (m > 0) [in] n Number of variables. (0 < n <= m) [in,out] x[] Array x[lx] (lx >= n) [in] An initial estimate of the solution vector. [out] irev = 0: The obtained solution vector.   irev = 50, 51: Recent approximation of the solution vector. [out] fvec[] Array fvec[lfvec] (lfvec >= m) irev = 0: The function values evaluated at the solution vector x[]. irev = 50, 51: The function values evaluated at the recent approximation of the solution vector. [in] ldfjac Leading dimension of the two dimensional array fjac[][]. (ldfjac >= m) [out] fjac[][] Array fjac[lfjac][ldfjac] (lfjac >= n) The upper n x n submatrix contains an upper triangular matrix R with diagonal elements of nonincreasing magnitude such that   P^T * (J^T * J)*P = R^T * R where P is a permutation matrix and J is the final calculated Jacobian. [in] ftol Relative error desired in the sum of squares. Termination occurs when both the actual and predicted relative reductions in the sum of squares are at most ftol. (ftol >= 0) [in] xtol Relative error desired in the approximate solution. Termination occurs when the relative error between two consecutive iterates is at most xtol. (xtol >= 0) [in] gtol Orthogonality desired between the function vector and the columns of the Jacobian. Termination occurs when the cosine of the angle between fvec[] and any column of the jacobian is at most gtol in absolute value. (gtol >= 0) [in] maxfev Termination occurs when the number of function evaluations with irev = 1 to 3 has reached this value (maxfev > 0) [in] epsfcn Used in determining a suitable step length for the forward-difference approximation. This approximation assumes that the relative errors in the functions are of the order of epsfcn. If epsfcn is less than the machine precision, it is assumed that the relative errors in the functions are of the order of the machine precision [in,out] diag[] Array diag[ldiag] (ldiag >= n) [in] If mode = 2, diag must contain positive entries that serve as multiplicative scale factors for the variables. (diag[i] > 0) [out] If mode = 1, diag[] is set by the subroutine. [in] mode = 1: The variables will be automatically scaled by the subroutine. = 2: The scaling is specified by the input diag[]. (For other values, mode = 1 is assumed.) [in] factor Used in determining the initial step bound. This bound is set to the product of factor and the Euclidean norm of diag*x if nonzero, or else to factor itself. In most cases factor should lie in the interval (0.1, 100). 100 is a generally recommended value. (factor > 0) [in] nprint > 0: Returns with irev = 50 or 51 at the beginning of the first iteration and every nprint iterations thereafter and at the end of last iteration for printing intermediate result. <= 0: Does not return for printing intermediate result. [out] nfev Number of function evaluations with irev = 1 to 3. [out] ipvt[] Array ipvt[lipvt] (lipvt >= n) The pivot indices that define the permutation matrix P. [out] work[] Array work[lwork] Work array. On return with info = 0, sub-code is set to work[0]. = 1: Both actual and predicted relative reductions in the sum of squares are at most ftol. = 2: Relative error between two consecutive iterates is at most xtol. = 3: Both of above are satisfied. = 4: The cosine of the angle between fvec and any column of the Jacobian is at most gtol in absolute value. [in] lwork The length of work[]. (lwork >= 4*n + m) [out] info = 0: Successful exit (sub-code is set to work[0]) = -1: The argument m had an illegal value (m < n) = -2: The argument n had an illegal value (n < 1) = -5: The argument ldfjac had an illegal value (ldfjac < m) = -7: The argument ftol had an illegal value (ftol < 0) = -8: The argument xtol had an illegal value (xtol < 0) = -9: The argument gtol had an illegal value (gtol < 0) = -10: The argument maxfev had an illegal value (maxfev <= 0) = -12: The argument diag had an illegal value (diag[i] <= 0 when mode = 2) = -14: The argument factor had an illegal value (factor <= 0) = -19: The argument lwork had an illegal value (lwork too small) = 1: Number of function evaluations with irev = 1 to 3 has reached maxfev = 2: ftol is too small. No further reduction in the sum of squares is possible = 3: xtol is too small. No further improvement in the approximate solution x is possible = 4: gtol is too small. fvec is orthogonal to the columns of the Jacobian to machine precision [out] xx[] Array xx[lxx] (lxx >= n) When returned with irev = 1 to 3, xx[] contains the abscissa where the function value should be evaluated and given in the next call. [in] yy[] Array yy[lyy] (lyy >= m) When returned with irev = 1 to 3, the function value fi(xx[]) (i = 1 to m) 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, complete the following process and call this routine again. = 0: Computation finished. See return code in info. = 1 to 3: User should set the function values at xx[] in yy[]. Do not alter any variables other than yy[]. = 50 or 51: Display the intermediate result (x[], fvec[], etc.) (in the case of nprint > 0). Do not alter any variables. Reference netlib/minpack