Provided by: minpack-dev_19961126+dfsg1-5_amd64 bug

NAME

       lmstr_, lmstr1_ - minimize the sum of squares of m nonlinear functions, with user supplied
       Jacobian and minimal storage

SYNOPSIS

       include <minpack.h>

       void lmstr1_ ( void (*fcn) (int *m, int *n, double *x, double *fvec, double *fjrow, int
                                   *iflag),
                      int *m, int * n, double *x, double *fvec, double *fjac, int *ldfjac,
                      double *tol, int *info, int *iwa,
                      double *wa, int *kwa);

       void lmstr_ ( void (*fcn)( int *m, int *n, double *x, double *fvec, double *fjrow, int
                                  *iflag),
                     int *m, int *n, double *x, double *fvec, double *fjac, int *ldfjac,
                     double *ftol, double *xtol, double *gtol,
                     int *maxfev, double *diag, int *mode, double *factor,
                     int *nprint, int *info, int *nfev, int *njev,
                     int *ipvt, double *qtf,
                     double *wa1, double *wa2, double *wa3, double *wa4 );

DESCRIPTION

       The purpose of lmstr_ is to minimize the sum of the squares of m nonlinear functions in  n
       variables  by a modification of the Levenberg-Marquardt algorithm. The user must provide a
       function which calculates the functions and the rows of the Jacobian.

       lmstr1_ performs the same function but has a simplified calling sequence.

       lmder(3) and lmder1(3) perform the same function but do not attempt to minimize storage.

   Language notes
       These functions are written in FORTRAN. If calling from C, keep these points in mind:

       Name mangling.
              With gfortran, all the function names end in an underscore.

       Compile with gfortran.
              Even if your program is all C code, you should link with gfortran so it  will  pull
              in  the  FORTRAN  libraries automatically.  It's easiest just to use gfortran 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]

   User-supplied Function
       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(m,n,x,fvec,fjrow,iflag)
         integer m,n,iflag
         double precision x(n),fvec(m),fjrow(n)
         ----------
         if iflag = 1 calculate the functions at x and
         return this vector in fvec. Do not alter fjac.
         if iflag = i calculate row (i-1) of the
         Jacobian at x and return this vector in fjrow.
         ----------
         return
         end

       In C, fcn should be written as follows:

         void fcn(int *m, int *n, double *x, double *fvec, double *fjrow,
                  int *iflag)
         {
           /* If iflag = 1 calculate the functions at x and return the
              values in fvec[0] through fvec[m-1].  Do not alter fjac.
              If iflag = i calculate row (i-1) of the Jacobian
              at x and return the vector in fjrow. */
         }

       iflag is an input integer which specifies whether a function value or Jacobian row  is  to
       be  calculated.   The value of iflag should not be changed by fcn unless the user wants to
       terminate execution of lmstr_ (or lmstr1_). In this case set iflag to a negative integer.

   Parameters for both lmstr_ and lmstr1_
       m is a positive integer input variable set to the number of functions.

       n is a positive integer input variable set to the number of variables. n must  not  exceed
       m.

       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.

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

       fjrow  is an output array of length n which is set to one row of the Jacobian evaluated at
       x.

       fjac is an output m by n array. The upper n by n  submatrix  of  fjac  contains  an  upper
       triangular matrix r with diagonal elements of nonincreasing magnitude such that

                t     t           t
               p *(jac *jac)*p = r *r,

       where p is a permutation matrix and jac is the final calculated Jacobian. Column j of p is
       column ipvt(j) (see below) of the identity matrix. The  lower  trapezoidal  part  of  fjac
       contains information generated during the computation of r.

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

   Parameters for lmstr1_
       tol is a nonnegative input variable.  Termination  occurs  when  the  algorithm  estimates
       either  that  the relative error in the sum of squares is at most tol or 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 in the sum of squares is at most
       tol.

         info = 2  algorithm estimates that the relative error between x and the solution  is  at
       most tol.

         info = 3  conditions for info = 1 and info = 2 both hold.

         info = 4  fvec is orthogonal to the columns of the Jacobian to machine precision.

         info = 5  number of calls to fcn has reached or exceeded 100*(n+1).

         info = 6  tol is too small. no further reduction in the sum of squares is possible.

         info  =  7   tol  is  too small. no further improvement in the approximate solution x is
       possible.

       wa is a work array of length lwa.

       lwa is an integer input variable not less than m*n + 5*n + m  for  lmder1,  or  5*n+m  for
       lmstr1_.

   Parameters for lmstr_
       ftol  is  a  nonnegative  input  variable.  Termination  occurs  when  both the actual and
       predicted relative reductions in the sum of squares are at  most  ftol.   Therefore,  ftol
       measures the relative error desired in the sum of squares.

       xtol  is  a nonnegative input variable. Termination occurs when the relative error between
       two consecutive iterates is at most xtol. Therefore,  xtol  measures  the  relative  error
       desired in the approximate solution.

       gtol  is  a  nonnegative  input  variable. Termination occurs when the cosine of the angle
       between fvec and any column of the Jacobian is at most gtol in absolute value.  Therefore,
       gtol measures the orthogonality desired between the function vector and the columns of the
       Jacobian.

       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 the latter is 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   both  actual and predicted relative reductions in the sum of squares are at
       most ftol.

         info = 2  relative error between two consecutive iterates is at most xtol.

         info = 3  conditions for info = 1 and info = 2 both hold.

         info = 4  the cosine of the angle between fvec and any column of the Jacobian is at most
       gtol in absolute value.

         info = 5  number of calls to fcn has reached or exceeded maxfev.

         info = 6  ftol is too small. No further reduction in the sum of squares is possible.

         info  =  7   xtol  is too small. No further improvement in the approximate solution x is
       possible.

         info = 8 gtol is too small. fvec is orthogonal to the columns of the Jacobian to machine
       precision.

       nfev is an integer output variable set to the number of calls to fcn with iflag = 1.

       njev is an integer output variable set to the number of calls to fcn with iflag = 2.

       ipvt is an integer output array of length n. ipvt defines a permutation matrix p such that
       jac*p = q*r, where jac is the final calculated Jacobian, q is orthogonal (not stored), and
       r is upper triangular with diagonal elements of nonincreasing magnitude.  Column j of p is
       column ipvt(j) of the identity matrix.

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

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

       wa4 is a work array of length m.

SEE ALSO

       lmdif(3), lmdif1(3), lmder(3), lmder1(3).

AUTHORS

       Jorge  More',  Burt Garbow, and Ken Hillstrom at Argonne National Laboratory.  This manual
       page was written by Jim Van Zandt <jrv@debian.org>, for the Debian GNU/Linux  system  (but
       may be used by others).