 
C
C
C                     PACKAGE DNL2SN
C
C
C      A COLLECTION OF ROUTINES FOR SOLVING NONLINEAR LEAST-SQUARES
C PROBLENS (DNL2S1, NL2SN), AND FOR SOLVING GENERAL UNCONSTRAINED
C MINIMIZATIONS PROBLEMS (DSMSNO, DSUMSL, DHUMSL).
C      SUBROUTINES DNL2S1, AND NL2SN SOLVE NONLINEAR LEAST-
C SQUARES PROBLEMS.  MORE SPECIFICALLY, SUPPOSE R(X) IS A VECTOR OF N
C COMPONENTS THAT ARE CONTINUOUSLY DIFFERENTIABLE FUNCTIONS OF X, A
C VECTOR OF P COMPONENTS.  THE PROBLEM IS TO CHOOSE X SO AS TO
C (LOCALLY) MINIMIZE THE SUM OF THE SQUARES OF THE COMPONENTS OF R(X).
C      DNL2S1 REQUIRES TWO SUBROUTINE PARAMETERS, ONE FOR COMPUTING
C R(X), ANOTHER FOR COMPUTING THE PARTIAL DERIVATIVES OF R WITH RESPECT
C TO X.
C      NL2SN IS SIMILAR TO DNL2S1, BUT IT ONLY REQUIRES ONE SUBROUTINE
C PARAMETER, A SUBROUTINE FOR COMPUTING R(X).  NL2SN ESTIMATES THE
C PARTIAL DERIVATIVES OF R BY FINITE DIFFERENCES.
C      FOR MORE INFORMATION ABOUT DNL2S1, AND NL2SN, SEE THE
C COMMENTS AT THE BEGINNINGS OF THESE ROUTINES.  THESE COMMENTS MAY
C OCCASIONALLY REFER TO A SUBROUTINE PACKAGE NL2SOL, WHICH IS
C AN OLDER VERSION AND IS NOT INCLUDED HEREIN. SEE REF. #1.
C
C      SUBROUTINES DSMSNO, DSUMSL, AND DHUMSL
C ARE FOR SOLVING GENERAL UNCONSTRAINED MINIMIZATION PROBLEMS.  MORE
C SPECIFICALLY, SUPPOSE F(X) IS A CONTINUOUSLY DIFFERENTIABLE FUNCTION
C OF X, A VECTOR OF N COMPONENTS.  THESE SUBROUTINES ATTEMPT TO FIND X
C SO AS TO (LOCALLY) MINIMIZE F(X).  THEY ARE INTENDED FOR USE ON
C PROBLEMS WHERE N IS SMALL ENOUGH THAT IT IS REASONABLE TO WORK WITH
C (AN APPROXIMATION TO) THE HESSIAN OF F.
C      DSMSNO REQUIRES A SUBROUTINE PARAMETER FOR COMPUTING F(X).  IT
C USES FINITE DIFFERENCES TO APPROXIMATE THE GRADIENT OF F AND THE BFGS
C UPDATE TO APPROXIMATE THE HESSIAN OF F.
C      DSUMSL REQUIRES TWO SUBROUTINE PARAMETERS, ONE FOR COMPUTING
C F(X), ANOTHER FOR COMPUTING THE GRADIENT OF F.  IT ALSO USES THE BFGS
C UPDATE TO APPROXIMATE THE HESSIAN OF F.
C      DHUMSL ALSO REQUIRES TWO SUBROUTINE PARAMETERS, ONE FOR
C COMPUTING F(X) (AS WITH DSMSNO AND DSUMSL), ANOTHER FOR COMPUTING
C BOTH THE GRADIENT AND HESSIAN OF F.
C      THE LEADING COMMENTS OF DSUMSL GIVE MUCH DETAIL RELEVANT TO ALL
C THE ABOVE SUBROUTINES.  THE LEADING COMMENTS OF THE OTHER ROUTINES
C EXPLAIN HOW THEY DIFFER FROM DSUMSL.  SEE ALSO REF. 2.
C
C *** REFERENCES ***
C
C 1.  J.E. DENNIS, D.M. GAY, AND R.E. WELSCH, ALGORITHM 573 -- NL2SOL,
C           AN ADAPTIVE NONLINEAR LEAST-SQUARES ALGORITHM, ACM TRANS.
C           MATH. SOFTWARE 7 (1981), PP. 369-383.
C 2.  D.M. GAY, SUBROUTINES FOR UNCONSTRAINED MINIMIZATION USING A
C           MODEL/TRUST-REGION APPROACH, DRAFT REVISION OF MIT/CCREMS
C           REPORT TR-18.
 
 
