chkder hybrd hybrd1 hybrd1_r hybrd_r hybrj hybrj1 hybrj1_r hybrj_r sos sos_r

hybrj_r() void hybrj_r ( 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, double  xx[], double  yy[], int  ldyypd, double  yypd[], int *  irev  ) Solution of a system of nonlinear equations by Powell hybrid method (reverse communication version) Purpose hybrj_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 the calculated function values and the Jacobian according to irev. 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] irev = 0: The obtained solution vector.   irev = 30: The abscissa where the Jacobian shoule be evaluated.   irev = 50, 51: Recent approximation of the solution vector. [out] fvec[] Array fvec[lfvec] (lfvec >= n) 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] 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 function evaluations with irev = 1 or 2 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: To return 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: Not to return for printing intermediate result. [out] nfev Number of function evaluations with irev = 1 or 2. [out] njev Number of Jacobian evaluation with irev = 30. [out] work[] Array work[lwork] Work array. [in] lwork The length of work[]. (lwork >= n*(n + 11)/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) = -5: The argument maxfev had an illegal value (maxfev <= 0) = -6: The argument diag had an illegal value (diag[i] <= 0 when mode = 2) = -8: The argument factor had an illegal value (factor <= 0) = -13: The argument lwork had an illegal value (lwork too small) = -17: The argument ldyypd had an illegal value (ldyypd < n) = 1: Number of function evaluations with irev=1 or 2 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 [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 >= n) When returned with irev = 1 or 2, the function value fi(xx[]) (i = 0 to n-1) should be given in yy[] in the next call. [in] ldyypd The leading dimension of the array yypd[][]. (ldyypd >= n) [in,out] yypd[][] Array yypd[lyypd][ldyypd] (lyypd >= n) [in] irev = 30: Jacobian(dfi/dxj) at x[] should be given in yypd[][] in the next call. [out] irev = 0: The orthogonal matrix Q produced by the QR factorization of the final approximate Jacobian [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 yypd[][]. Do not alter any variables other than yypd[][]. = 50 or 51: Display the intermediate result (x[], fvec[], etc.) (in the case of nprint > 0). Do not alter any variables. Reference netlib/minpack