chkder hybrd hybrd1 hybrd1_r hybrd_r hybrj hybrj1 hybrj1_r hybrj_r sos sos_r

hybrj1() void hybrj1 ( void(*)(int, double *, double *, int, double *, int *)  fcn, int  n, double  x[], double  fvec[], double  xtol, double  work[], int  lwork, int *  info  ) Solution of a system of nonlinear equations by Powell hybrid method (simple driver) Purpose hybrj1 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. hybrj1 is the simple driver for standard use, which calls the hybrj with default parameters. 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. } 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) [out] work[] Array work[lwork] Work array. [in] lwork The length of work[]. (lwork >= n*(3*n + 17)/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) = -7: The argument lwork had an illegal value (lwork too small) = 1: Number of calls to fcn with iflag = 1 has reached the limit (100*(n + 1)) = 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