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ADAS Subroutine xxycf2

      SUBROUTINE XXYCF2(FCN, M, N, X, FVEC, FJAC, B, C)
C-----------------------------------------------------------------------
C
C ROUTINE: XXYCF2
C
C PURPOSE: CALCULATES AN ESTIMATE OF THE ELEMENTS OF THE VARIANCE-COVARIANCE
C          MATRIX OF THE ESTIMATED REGRESSION COEFFICIENTS FOR A NON-LINEAR
C          LEAST-SQUARES PROBLEM.
C
C          REPLACES NAG ROUTINE E04YCF WHEN CALLED AFTER E04GCF OR ANOTHER
C          ROUTINE THAT USES FIRST DERIVATIVES.
C*****************************************************************************
C          THIS ROUTINE CAN ONLY BE USED WHEN FIRST DERIVATIVES ARE AVAILABLE.
C*****************************************************************************
C          SEE THE DOCUMENTATION OF E04YCF AND THE E04 SERIES FOR MORE
C          INFORMATION ON THE MATHEMATICS OF CALCULATING THE VARIANCE-
C          COVARIANCE MATRIX.
C
C CALLING PROGRAM: GENERAL USE
C
C INPUT:
C    SUBROUTINE FCN - CALCULATES THE FUNCTIONS AND THEIR DERIVATIVES.
C                     IF ONE IS DIRECTLY REPLACING THE NAG ROUTINE THEN
C                     THIS ARGUMENT WILL BE LSFUN2 IN THE CALLING
C                     PROGRAM, AND LSFUN2 WILL HAVE TO BE MODIFIED TO
C                     ACCOMMODATE THE IFLAG VARIABLE. SEE BELOW FOR DETAILS.
C    (I*4)  M       - NUMBER OF FUNCTIONS
C    (I*4)  N       - NUMBER OF VARIABLES, N<=M
C    (R*8)  X       - VECTOR OF THE ESTIMATED SOLUTION
C    (R*8)  FVEC()  - THE FUNCTION EVALUATED AT X
C    (R*8)  FJAC()  - A WORK MATRIX OF DIMENSION (M,N)
C    (R*8)  B()     - A WORK VECTOR OF DIMENSION N
C
C OUTPUT:
C     (R*8)  C(,)     - THE VARIANCE-COVARIANCE MATRIX. DIMENSIONS NxN.
C
C ROUTINES:
C-----------------------------------------------------------------------
C     NAME     SOURCE   PURPOSE
C-----------------------------------------------------------------------
C     XXMINV   ADAS     INVERTS A SQUARE MATRIX
C     FCN      USER     CALCULATES FUNCTIONS AND THEIR FIRST DERIVATIVES
C {
C    SUBROUTINE FCN(M,N,X,FVEC,FJAC,LDFJAC,IFLAG)
C    INTEGER M,N,IFLAG, LDFJAC
C    REAL*8 X(N), FVEC(M), FJAC(LDFJAC,N)
C  INPUT:
C    M,N    - AS ABOVE
C    LDFJAC - FIRST DIMENSION OF FJAC
C    X      - VECTOR AT WHICH THE FUNCTION IS TO BE EVALUATED
C    IFLAG  - 1=> CALCULATE FVEC BUT DON'T CHANGE FJAC
C           - 2=> CALCULATE FJAC BUT DON'T CHANGE FVEC
C  OUTPUT:
C    FVEC   - FUNCTION EVALUATED AT X OR NOT CHANGED
C    FJAC   - JACOBIAN OF FUNCTION EVALUATED AT X OR NOT CHANGED
C }
C-----------------------------------------------------------------------
C
C AUTHOR: WILLIAM OSBORN (TESSELLA SUPPORT SERVICES PLC.)
C
C DATE:   31-05-96
C 
C VERSION 1.1                             DATE: 31-05-96
C MODIFIED: WILLIAM OSBORN
C           - FIRST VERSION
C
C VERSION 1.2                             DATE: 16-05-07
C MODIFIED: ALLAN WHITEFORD
C           - Updated comments as part of subroutine documentation
C             procedure.
C
C-----------------------------------------------------------------------
C-----------------------------------------------------------------------
      INTEGER             M,           N
      REAL*8              B(N),        C(N,N),      FJAC(M,N),   FVEC(M)
      REAL*8              X(N)
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