Manpage of HYBRJ_

# HYBRJ_

Section: C Library Functions (3)
Updated: March 8, 2002
Index Return to Main Contents

## NAME

hybrj_, hybrj1_ - find a zero of a system of nonlinear function

## SYNOPSIS

#include <minpack.h>

void hybrj1_ (void (*fcn)(int *n, double *x, double *fvec, double *fjec, int *ldfjac, int *iflag),

  int *n, double *x, double *fvec, double *fjac,
  int *ldfjac,
  double *tol, int *info, double *wa, int *lwa);

void hybrj_ (void (*fcn)(int *n, double *x, double *fvec, double *fjec, int *ldfjac, int *iflag),

  int *n, double *x, double *fvec, double *fjac,
  int *ldfjac,
  double *xtol, int *maxfev, double *diag, int *mode, double *factor, int *nprint, int *info, int *nfev,
  int *njev, double *r, int *lr, double *qtf,
  double *wa1, double *wa2, double *wa3, double *wa4);

## DESCRIPTION

  The purpose of hybrj_ is to find a zero of a system of n nonlinear functions in n variables by a modification of the Powell hybrid method. The user must provide a subroutine which calculates the functions and the Jacobian.

  hybrj1_ serves the same function but has a simplified calling sequence.

  ### Language notes

  hybrj_ and hybrj1_ are written in FORTRAN. If calling from C, keep these points in mind:
  Name mangling.
    With g77 version 2.95 or 3.0, all the function names end in an underscore. This may change with future versions of g77.
  Compile with g77.
    Even if your program is all C code, you should link with g77 so it will pull in the FORTRAN libraries automatically. It's easiest just to use g77 to do all the compiling. (It handles C just fine.)
  Call by reference.
    All function parameters must be pointers.
  Column-major arrays.
    Suppose a function returns an array with 5 rows and 3 columns in an array z and in the call you have declared a leading dimension of 7. The FORTRAN and equivalent C references are:

                z(1,1)          z[0]
                z(2,1)          z[1]
                z(5,1)          z[4]
                z(1,2)          z[7]
                z(1,3)          z[14]
                z(i,j)          z[(i-1) + (j-1)*7]

  ### Parameters for both functions

  fcn is the name of the user-supplied subroutine which calculates the functions. In FORTRAN, fcn must be declared in an external statement in the user calling program, and should be written as follows:

      subroutine fcn(n,x,fvec,fjac,ldfjac,iflag)
      integer n,ldfjac,iflag
      double precision x(n),fvec(n),fjac(ldfjac,n)
      ----------
      if iflag = 1 calculate the functions at x and
      return this vector in fvec. do not alter fjac.
      if iflag = 2 calculate the jacobian at x and
      return this matrix in fjac. do not alter fvec.
      ---------
      return
      end

  In C, fcn should be written as follows:

        void fcn(int n, double *x, double *fvec, double *fjac,
                 int *ldfjac, int *iflag)
        {
        /* if iflag = 1 calculate the functions at x and
           return this vector in fvec. do not alter fjac.
           if iflag = 2 calculate the jacobian at x and
           return this matrix in fjac. do not alter fvec. */
        }

  The value of iflag should not be changed by fcn unless the user wants to terminate execution of hybrj_. In this case set iflag to a negative integer.

  n is a positive integer input variable set to the number of functions and variables.

  x is an array of length n. On input x must contain an initial estimate of the solution vector. On output x contains the final estimate of the solution vector.

  fjac is an output n by n array which contains the orthogonal matrix q produced by the qr factorization of the final approximate jacobian.

  ldfjac is a positive integer input variable not less than n which specifies the leading dimension of the array fjac.

  fvec is an output array of length n which contains the functions evaluated at the output x.

  ### Parameters for hybrj1_

  tol is a nonnegative input variable. Termination occurs when the algorithm estimates that the relative error between x and the solution is at most tol.

  info is an integer output variable. If the user has terminated execution, info is set to the (negative) value of iflag. See description of fcn. Otherwise, info is set as follows.

  info = 0 improper input parameters.

  info = 1 algorithm estimates that the relative error
  between x and the solution is at most tol.

  info = 2 number of calls to fcn has reached or exceeded
  200*(n+1).

  info = 3 tol is too small. No further improvement in
  the approximate solution x is possible.

  info = 4 iteration is not making good progress.

  wa is a work array of length lwa.

  lwa is a positive integer input variable not less than (n*(3*n+13))/2.

  ### Parameters for hybrj_

  xtol is a nonnegative input variable. Termination occurs when the relative error between two consecutive iterates is at most xtol.

  maxfev is a positive integer input variable. Termination occurs when the number of calls to fcn is at least maxfev by the end of an iteration.

  diag is an array of length n. If mode = 1 (see below), diag is internally set. If mode = 2, diag must contain positive entries that serve as multiplicative scale factors for the variables.

  mode is an integer input variable. If mode = 1, the variables will be scaled internally. If mode = 2, the scaling is specified by the input diag. Other values of mode are equivalent to mode = 1.

  factor is a positive input variable 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 (.1,100.). 100. Is a generally recommended value.

  nprint is an integer input variable that enables controlled printing of iterates if it is positive. In this case, fcn is called with iflag = 0 at the beginning of the first iteration and every nprint iterations thereafter and immediately prior to return, with x and fvec available for printing. If nprint is not positive, no special calls of fcn with iflag = 0 are made.

  info is an integer output variable. If the user has terminated execution, info is set to the (negative) value of iflag. See description of fcn. Otherwise, info is set as follows.

  info = 0 improper input parameters.

  info = 1 relative error between two consecutive iterates
  is at most xtol.

  info = 2 number of calls to fcn has reached or exceeded
  maxfev.

  info = 3 xtol is too small. No further improvement in
  the approximate solution x is possible.

  info = 4 iteration is not making good progress, as
  measured by the improvement from the last
  five jacobian evaluations.

  info = 5 iteration is not making good progress, as
  measured by the improvement from the last
  ten iterations.

  nfev is an integer output variable set to the number of calls to fcn.

  fjac is an output n by n array which contains the orthogonal matrix q produced by the qr factorization of the final approximate jacobian.

  ldfjac is a positive integer input variable not less than n which specifies the leading dimension of the array fjac.

  r is an output array of length lr which contains the upper triangular matrix produced by the qr factorization of the final approximate Jacobian, stored rowwise.

  lr is a positive integer input variable not less than (n*(n+1))/2.

  qtf is an output array of length n which contains the vector (q transpose)*fvec.

  wa1, wa2, wa3, and wa4 are work arrays of length n.

  ## SEE ALSO

  hybrd(3), hybrd1(3).

  ## AUTHORS

  Burton S. Garbow, Kenneth E. Hillstrom, Jorge J. More.
  This manual page was written by Jim Van Zandt <jrv@debian.org>, for the Debian GNU/Linux system (but may be used by others).

  ## Index

  NAME
  SYNOPSIS
  DESCRIPTION
    Language notes
    Parameters for both functions
    Parameters for hybrj1_
    Parameters for hybrj_
  SEE ALSO
  AUTHORS

  This document was created by man2html, using the manual pages.
  Time: 10:19:50 GMT, April 20, 2007