SUBROUTINE OPTIF9(NR,N,X,FCN,D1FCN,D2FCN,TYPSIZ,FSCALE,
     +     METHOD,IEXP,MSG,NDIGIT,ITNLIM,IAGFLG,IAHFLG,IPR,
     +     DLT,GRADTL,STEPMX,STEPTL,XPLS,FPLS,GPLS,ITRMCD,A,WRK)
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
C
C PURPOSE
C -------
C PROVIDE COMPLETE INTERFACE TO MINIMIZATION PACKAGE.
C USER HAS FULL CONTROL OVER OPTIONS.
C
C OPTIF9 is designed to solve the unconstrained nonlinear optimization
C problem.  This problem involves finding the minimums of a twice
C continuously differentiable real-valued function f of n variables
C from a given start point x(0).
C
C
C PARAMETERS
C ----------
C NR         --> Row dimension of matrix.
C                A positive integer specifying the row dimension of the
C                matrices A and WRK in the user's calling program.  NR
C                must satisfy the relation NR >= N (see N).  The provision
C                of this variable allows the user the flexibility of
C                solving several problems of different order N one after
C                the other.
C
C N          --> Dimension of problem.  A positive integer specifying
C                the order or dimension of the problem.  The program will
C                abort if N <= 0.  The program is inefficient for the
C                one-dimensional case (N=1); the user is advised to find
C                more efficient software.  The package will abort for
C                N=1 unless the parameter MSG is appropriately set; in
C                this instance the interface OPTIF9 must be utilized.
C
C X(N)       --> ON ENTRY: Estimate to a root of FCN
C
C FCN        --> The name of a user supplied subroutine that evaluates
C                the optimization function at an arbitrary vector X.
C                The subroutine must be declared EXTERNAL in the user's
C                calling program and must conform to the usage:
C
C                     CALL FCN (N,X,F)
C
C                where X is a vector of length N.  The subroutine must
C                not alter the values of X or N.  On return F is the
C                value of the optimization function at X.
C
C D1FCN      --> (OPTIONAL) Name of subroutine to evaluate gradient
C                of FCN.  Must be declared external in calling routine
C
C D2FCN      --> (OPTIONAL) Name of subroutine to evaluate Hessian of
C                of FCN.  Must be declared external in calling routine
C
C TYPSIZ(N)  --> Typical size for each component of X
C
C FSCALE     --> Estimate of scale of objective function
C
C METHOD     --> Algorithm to use to solve minimization problem
C                  =1 LINE SEARCH
C                  =2 DOUBLE DOGLEG
C                  =3 MORE-HEBDON
C
C IEXP       --> =1 If optimization function FCN is expensive to
C                evaluate, =0 Otherwise.  If set then Hessian will
C                be evaluated by secant update instead of
C                analytically or by finite differences
C
C MSG       <--> ON INPUT:  (.GT.0) message to inhibit certain
C                  automatic checks
C                ON OUTPUT: (.LT.0) error code; =0 No error
C
C NDIGIT     --> Number of good digits in optimization function FCN
C
C ITNLIM     --> Maximum number of allowable iterations
C
C IAGFLG     --> =1 If analytic gradient supplied
C IAHFLG     --> =1 If analytic Hessian supplied
                 =0  Otherwise.
C IPR        --> Device to which to send output
C
C DLT        --> Trust region radius
C
C GRADTL     --> Tolerance at which gradient considered close
C                enough to zero to terminate algorithm
C
C STEPMX     --> Maximum allowable step size
C
C STEPTL     --> Relative step size at which succesive iterates
C                considered close enough to terminate algorithm.
C
C
C XPLS(N)   <--  Local minimum
C
C FPLS      <--  Funtion value at local minimum XPLS
C
C GPLS(N)   <--  Gradient at local minimum XPLS
C ITRMCD    <--  Termination code
C                = 0  Erroneous input detected
C                = 1  Relative gradient is close to zero.  Current
C                     iterate is probably solution.
C                = 2  Successive iterates within tolerance.  Current
C                     iterate is probably solution.
C                = 3  Last global step failed to locate a point lower
C                     than XPLS.  Either XPLS is an approximate local
C                     minimum of the function, the function is too
C                     non-linear for this algorithm, or STEPTL is too
C                     large.
C                = 4  Iteration limit exceeded.
C                = 5  Maximum step size STEPMX exceeded five consecutive
C                     times.  Either the functon is unbounded below,
C                     becomes asymtotic to a finite value from above
C                     in some direction, or STEPMX is too small.
C
C
C A(N,N)     --> Workspace. A real matrix array which is used to store
C                the Hessian and its Cholesky decomposition.
C WRK(N,8)   --> Workspace required by the program.
C
C For a more detailed description of the parameters, see:
C
C  AN UNCONSTRAINED NON-LINEAR OPTIMIZATION SOLVER: A USER'S GUIDE
C
C available through Richard Jackson, Operations Research Division,
C National Bureau of Standards, Washington, DC  (301)921-3855.