NAG Library Manual, Mark 29.3
```!   E04YCF Example Program Text
!   Mark 29.3 Release. NAG Copyright 2023.

Module e04ycfe_mod

!     E04YCF 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                           :: lsfun1
!     .. Parameters ..
Integer, Parameter, Public       :: mdec = 15, ndec = 3, nin = 5,        &
nout = 6
Integer, Parameter, Public       :: lwork = 7*ndec + ndec*ndec + 2*mdec* &
ndec + 3*mdec + ndec*(ndec-1)/2
!     .. Local Arrays ..
Real (Kind=nag_wp), Public, Save :: t(mdec,ndec), y(mdec)
Contains
Subroutine lsfun1(m,n,xc,fvec,iuser,ruser)
!       Routine to evaluate the residuals

!       .. Scalar Arguments ..
Integer, Intent (In)           :: m, n
!       .. Array Arguments ..
Real (Kind=nag_wp), Intent (Out) :: fvec(m)
Real (Kind=nag_wp), Intent (Inout) :: ruser(*)
Real (Kind=nag_wp), Intent (In) :: xc(n)
Integer, Intent (Inout)        :: iuser(*)
!       .. Executable Statements ..
fvec(1:m) = xc(1) + t(1:m,1)/(xc(2)*t(1:m,2)+xc(3)*t(1:m,3)) - y(1:m)

Return

End Subroutine lsfun1
End Module e04ycfe_mod
Program e04ycfe

!     E04YCF Example Main Program

!     .. Use Statements ..
Use e04ycfe_mod, Only: lsfun1, lwork, mdec, ndec, nin, nout, t, y
Use nag_library, Only: e04fyf, e04ycf, nag_wp
!     .. Implicit None Statement ..
Implicit None
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: fsumsq
Integer                          :: i, ifail, job, ldv, m, n, ns, nv
!     .. Local Arrays ..
Real (Kind=nag_wp)               :: cj(ndec), ruser(1), work(lwork),     &
x(ndec)
Integer                          :: iuser(1)
!     .. Intrinsic Procedures ..
Intrinsic                        :: max
!     .. Executable Statements ..
Write (nout,*) 'E04YCF Example Program Results'

!     Skip heading in data file

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
End Do

x(1:n) = (/0.5E0_nag_wp,1.0E0_nag_wp,1.5E0_nag_wp/)

ifail = -1
Call e04fyf(m,n,lsfun1,x,fsumsq,work,lwork,iuser,ruser,ifail)

Select Case (ifail)
Case (0,2:)
Write (nout,*)
Write (nout,99999) 'On exit, the sum of squares is', fsumsq
Write (nout,*) 'at the point'
Write (nout,99998) x(1:n)

!       Compute estimates of the variances of the sample regression
!       coefficients at the final point.
!       Since NS is greater than N we can use the first N elements
!       of the array WORK for the dummy argument WORK.

ns = 6*n + 2*m + m*n + 1 + max(1,(n*(n-1))/2)
nv = ns + n
job = 0
ldv = n

ifail = -1
Call e04ycf(job,m,n,fsumsq,work(ns),work(nv),ldv,cj,work,ifail)

Select Case (ifail)
Case (0,3:)
Write (nout,*)
Write (nout,*) 'and estimates of the variances of the sample'
Write (nout,*) 'regression coefficients are'
Write (nout,99998) cj(1:n)
End Select

End Select

99999 Format (1X,A,F12.4)
99998 Format (1X,3F12.4)
End Program e04ycfe
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