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

lmder1_r() void lmder1_r ( int  m, int  n, double  x[], double  fvec[], int  ldfjac, double  fjac[], double  tol, int  ipvt[], double  work[], int  lwork, int *  info, double  xx[], double  yy[], int *  irev  ) Nonlinear least squares approximation by Levenberg-Marquardt method (simple driver) (reverse communication version) Purpose lmder1_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 according to irev. lmder1_r is equivalent to using lmder_r with setting ftol = tol, xtol = tol, gtol = 0, maxfev = 100*(n+1), mode = 1, factor = 100 and nprint = 0. 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 = 30: 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[]. [in] ldfjac Leading dimension of two dimensional array fjac[]. (ldfjac >= m) [in,out] fjac[][] Array fjac[lfjac][ldfjac] (lfjac >= n) [in] irev = 30: Jacobian(dfi/dxj) at x[] should be given in fjac[][] in the next call. [out] 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] tol Relative error desired in the sum of squares and the approximate solution. (tol >= 0) [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. [in] lwork The length of work[]. (lwork >= 5*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 tol had an illegal value (tol < 0) = -10: 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,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[]. = 30: User should set the Jacobian at x[] in fjac[][]. Do not alter any variables other than fjac[][]. Reference netlib/minpack