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

lmstr_r() void lmstr_r ( int  m, int  n, double  x[], double  fvec[], int  ldfjac, double  fjac[], double  ftol, double  xtol, double  gtol, int  maxfev, double  diag[], int  mode, double  factor, int  nprint, int *  nfev, int *  njev, int  ipvt[], double  work[], int  lwork, int *  info, double  xx[], double  yy[], double  yypr[], int *  irev  ) Nonlinear least squares approximation by Levenberg-Marquardt method (limited storage version) (reverse communication version) Purpose lmstr_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 and the Jacobian (row-by-row) according to irev. 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.   irev >= 60: The abscissa where the Jacobian shoule be evaluated. [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 two dimensional array fjac[]. (ldfjac >= m) [out] fjac[][] Array fjac[lfjac][ldfjac] (lfjac >= n) irev = 0: 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,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 or 2. [out] njev Number of Jacobian evaluations with irev >= 60. [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 >= 3*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 <= 0) = -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) = -11: The argument diag had an illegal value (diag[i] <= 0 when mode = 2) = -13: 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 or 2 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 or 2, 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 or 2, the function value fi(xx[]) (i = 1 to m) should be given in yy[] in the next call. [in] yypr[] Array yypr[lyypr] (lyypr >= n) When returned with irev >= 60, the (irev-60+1)-th row of Jacobian (dfi/dxj) (i = irev-60+1, j = 1 to n) should be given in yypr[] 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 or 2: 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. >= 60: User should set the (irev-60+1)-th row of Jacobian at x[] in yypr[]. Do not alter any variables other than yypr[]. Reference netlib/minpack