!   E04YBF Example Program Text
!   Mark 27.3 Release. NAG Copyright 2021.

    Module e04ybfe_mod

!     E04YBF Example Program Module:
!            Parameters and User-defined Routines

!     .. Use Statements ..
      Use nag_library, Only: nag_wp
!     .. Implicit None Statement ..
      Implicit None
!     .. Accessibility Statements ..
      Private
      Public                           :: lsqfun, lsqhes
!     .. Parameters ..
      Integer, Parameter, Public       :: liw = 1, mdec = 15, ndec = 3,        &
                                          nin = 5, nout = 6
      Integer, Parameter, Public       :: lb = ndec*(ndec+1)/2
      Integer, Parameter, Public       :: ldfjac = mdec
      Integer, Parameter, Public       :: lw = 5*ndec + mdec + mdec*ndec +     &
                                          ndec*(ndec-1)/2
!     .. Local Arrays ..
      Real (Kind=nag_wp), Public, Save :: t(mdec,ndec), y(mdec)
    Contains
      Subroutine lsqfun(iflag,m,n,xc,fvec,fjac,ldfjac,iw,liw,w,lw)

!       Routine to evaluate the residuals and their 1st derivatives

!       .. Scalar Arguments ..
        Integer, Intent (Inout)        :: iflag
        Integer, Intent (In)           :: ldfjac, liw, lw, m, n
!       .. Array Arguments ..
        Real (Kind=nag_wp), Intent (Inout) :: fjac(ldfjac,n), w(lw)
        Real (Kind=nag_wp), Intent (Out) :: fvec(m)
        Real (Kind=nag_wp), Intent (In) :: xc(n)
        Integer, Intent (Inout)        :: iw(liw)
!       .. Local Scalars ..
        Real (Kind=nag_wp)             :: denom, dummy
        Integer                        :: i
!       .. Executable Statements ..
        Do i = 1, m
          denom = xc(2)*t(i,2) + xc(3)*t(i,3)
          fvec(i) = xc(1) + t(i,1)/denom - y(i)
          fjac(i,1) = 1.0E0_nag_wp
          dummy = -1.0E0_nag_wp/(denom*denom)
          fjac(i,2) = t(i,1)*t(i,2)*dummy
          fjac(i,3) = t(i,1)*t(i,3)*dummy
        End Do

        Return

      End Subroutine lsqfun
      Subroutine lsqhes(iflag,m,n,fvec,xc,b,lb,iw,liw,w,lw)

!       Routine to compute the lower triangle of the matrix B
!       (stored by rows in the array B)

!       .. Scalar Arguments ..
        Integer, Intent (Inout)        :: iflag
        Integer, Intent (In)           :: lb, liw, lw, m, n
!       .. Array Arguments ..
        Real (Kind=nag_wp), Intent (Out) :: b(lb)
        Real (Kind=nag_wp), Intent (In) :: fvec(m), xc(n)
        Real (Kind=nag_wp), Intent (Inout) :: w(lw)
        Integer, Intent (Inout)        :: iw(liw)
!       .. Local Scalars ..
        Real (Kind=nag_wp)             :: dummy, sum22, sum32, sum33
        Integer                        :: i
!       .. Executable Statements ..
        b(1) = 0.0E0_nag_wp
        b(2) = 0.0E0_nag_wp
        sum22 = 0.0E0_nag_wp
        sum32 = 0.0E0_nag_wp
        sum33 = 0.0E0_nag_wp

        Do i = 1, m
          dummy = 2.0E0_nag_wp*t(i,1)/(xc(2)*t(i,2)+xc(3)*t(i,3))**3
          sum22 = sum22 + fvec(i)*dummy*t(i,2)**2
          sum32 = sum32 + fvec(i)*dummy*t(i,2)*t(i,3)
          sum33 = sum33 + fvec(i)*dummy*t(i,3)**2
        End Do

        b(3) = sum22
        b(4) = 0.0E0_nag_wp
        b(5) = sum32
        b(6) = sum33

        Return

      End Subroutine lsqhes
    End Module e04ybfe_mod
    Program e04ybfe

!     E04YBF Example Main Program

!     .. Use Statements ..
      Use e04ybfe_mod, Only: lb, ldfjac, liw, lsqfun, lsqhes, lw, mdec, ndec,  &
                             nin, nout, t, y
      Use nag_library, Only: e04yaf, e04ybf, nag_wp
!     .. Implicit None Statement ..
      Implicit None
!     .. Local Scalars ..
      Integer                          :: i, ifail, k, m, n
!     .. Local Arrays ..
      Real (Kind=nag_wp)               :: b(lb), fjac(ldfjac,ndec),            &
                                          fvec(mdec), w(lw), x(ndec)
      Integer                          :: iw(liw)
!     .. Executable Statements ..
      Write (nout,*) 'E04YBF Example Program Results'

!     Skip heading in data file
      Read (nin,*)

      m = mdec
      n = ndec

!     Observations of TJ (J = 1, 2, ..., n) are held in T(I, J)
!     (I = 1, 2, ..., m)

      Do i = 1, m
        Read (nin,*) y(i), t(i,1:n)
      End Do

!     Set up an arbitrary point at which to check the derivatives

      x(1:n) = (/0.19E0_nag_wp,-1.34E0_nag_wp,0.88E0_nag_wp/)

!     Check the 1st derivatives

      ifail = 0
      Call e04yaf(m,n,lsqfun,x,fvec,fjac,ldfjac,iw,liw,w,lw,ifail)

      Write (nout,*)
      Write (nout,*) 'The test point is'
      Write (nout,99999) x(1:n)

!     Check the evaluation of B

      ifail = -1
      Call e04ybf(m,n,lsqfun,lsqhes,x,fvec,fjac,ldfjac,b,lb,iw,liw,w,lw,ifail)

      If (ifail>=0 .And. ifail/=1) Then

        Select Case (ifail)
        Case (0)
          Write (nout,*)
          Write (nout,*) 'The matrix B is consistent with 1st derivatives'
        Case (2)
          Write (nout,*)
          Write (nout,*) 'Probable error in calculation of the matrix B'
        End Select

        Write (nout,*)
        Write (nout,*) 'At the test point, LSQFUN gives'
        Write (nout,*)
        Write (nout,*) '      Residuals                   1st derivatives'
        Write (nout,99998)(fvec(i),fjac(i,1:n),i=1,m)
        Write (nout,*)
        Write (nout,*) 'and LSQHES gives the lower triangle of the matrix B'
        Write (nout,*)

        k = 1

        Do i = 1, n
          Write (nout,99998) b(k:(k+i-1))
          k = k + i
        End Do

      End If

99999 Format (1X,4F10.5)
99998 Format (1X,1P,4E15.3)
    End Program e04ybfe