chkder hybrd hybrd1 hybrd1_r hybrd_r hybrj hybrj1 hybrj1_r hybrj_r sos sos_r

hybrd1_r() void hybrd1_r ( int  n, double  x[], double  fvec[], double  xtol, double  work[], int  lwork, int *  info, double  xx[], double  yy[], int *  irev  ) Solution of a system of nonlinear equations by Powell hybrid method (Jacobian not required) (simple driver) (reverse communication version) Purpose hybrd1_r 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. Since the Jacobian is calculated by a forward difference approximation within the routine, the user is not required to provide the Jacobian. hybrd1_r is the simple driver for standard use, which calls the hybrd_r with default parameters. Parameters [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 + 13)/2) [out] info = 0: Successful exit (relative error between two consecutive iterates is at most xtol) = -1: The argument n had an illegal value (n < 1) = -4: The argument xtol had an illegal value (xtol < 0) = -6: The argument lwork had an illegal value (lwork too small) = 1: Number of function evaluations with irev = 1 to 4 has reached the limit (200*(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 [out] xx[] Array xx[lxx] (lxx >= n) When returned with irev = 1 to 4, xx[] contains the abscissa where the function value should be evaluated and given in the next call. [in] yy[] Array yy[lyy] (lyy >= n) When returned with irev = 1 to 4, the function value fi(xx[]) (i = 1 to n) 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 4: User should set the function values at xx[] in yy[]. Do not alter any variables other than yy[]. Reference netlib/minpack