chkder hybrd hybrd1 hybrd1_r hybrd_r hybrj hybrj1 hybrj1_r hybrj_r sos sos_r

hybrj() void hybrj ( void(*)(int, double *, double *, int, double *, int *)  fcn, int  n, double  x[], double  fvec[], double  xtol, int  maxfev, double  diag[], int  mode, double  factor, int  nprint, int *  nfev, int *  njev, double  work[], int  lwork, int *  info  ) Solution of a system of nonlinear equations by Powell hybrid method Purpose hybrj finds a zero of a system of n nonlinear functions in n variables fi(x1, x2, ..., xn) = 0 (i = 1 to n) by a modification of the Powell hybrid method. The user must provide a subroutine which calculates the functions and the Jacobian. Parameters [in] fcn User supplied subroutine which calculates the functions fi(x) and the Jacobian defined as follows. void fcn(int n, double x[], double fvec[], int ldfjac, double fjac[][ldfjac], int *iflag) { If iflag = 1: Calculate the function values fi(x) at x[] and return in fvec[i] (i = 0 to n-1). Other variables should not be changed. If iflag = 2: Calculate the Jacobian matrix (dfi/dxj) and return in fjac[j][i] (i = 0 to n-1, j = 0 to n-1). Other variables should not be changed. ldfjac is the leading dimension of the two dimensional array. If iflag = 0: If nprint is set to positive value, fcn is called every nprint iterations with iflag = 0 for outputting intermediate result x[] and fvec[]. Any variables should not be changed. } The value of iflag should not be changed unless the user wants to terminate the execution. In this case, set iflag to a negative integer. [in] n Number of functions and variables. (n > 0) [in,out] x[] Array x[lx] (lx >= n) [in] An initial estimate of the solution vector. [out] The obtained solution vector. [out] fvec[] Array fvec[lfvec] (lfvec >= n) The function values evaluated at the solution vector x[]. [in] xtol Target relative tolerance. Termination occurs when the relative error between two consecutive iterations is at most xtol. (xtol >= 0) [in] maxfev Termination occurs when the number of calls to fcn with iflag = 1 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: fcn is called with iflag = 0 at the beginning of the first iteration and every nprint iterations thereafter and at the end of last iteration for printing intermediate result. <= 0: No special calls of fcn for printing intermediate results are made. [out] nfev Number of function evaluations (number of calls to fcn with iflag = 1). [out] njev Number of Jacobian evaluations (number of calls to fcn with iflag = 2). [out] work[] Array work[lwork] Work array. [in] lwork The length of work[]. (lwork >= n*(3*n + 15)/2) [out] info = 0: Successful exit (relative error between two consecutive iterates is at most xtol) = -2: The argument n had an illegal value (n < 1) = -5: The argument xtol had an illegal value (xtol < 0) = -6: The argument maxfev had an illegal value (maxfev <= 0) = -7: The argument diag had an illegal value (diag[i] <= 0 when mode = 2) = -9: The argument factor had an illegal value (factor <= 0) = -14: The argument lwork had an illegal value (lwork too small) = 1: Number of calls to fcn with iflag = 1 has reached maxfev = 2: xtol is too small. No further improvement in the approximate solution x is possible = 3: Iteration is not making good progress, as measured by the improvement from the last five Jacobian evaluations = 4: Iteration is not making good progress, as measured by the improvement from the last ten iterations = 5: User imposed termination (returned from fcn with iflag < 0) Reference netlib/minpack