```!   E04NGA Example Program Text
!   Mark 26.2 Release. NAG Copyright 2017.

Module e04ngae_mod

!     E04NGA 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                           :: qphess
!     .. Parameters ..
Integer, Parameter, Public       :: iset = 1, lcwsav = 1, liwsav = 610,  &
llwsav = 120, lrwsav = 475, nin = 5, &
ninopt = 7, nout = 6
Contains
Subroutine qphess(n,jthcol,h,ldh,x,hx,iuser,ruser,iwsav)
!       In this version of QPHESS, the lower triangle of matrix H is
!       stored in packed form (by columns) in array H.
!       More precisely, the lower triangle of matrix H must be stored with
!       matrix element H(i,j) in array element H(i+(2*N-j)*(j-1)/2,1),
!       for i .ge. j.
!       Note that storing the lower triangle of matrix H in packed form (by
!       columns) is equivalent to storing the upper triangle of matrix H in
!       packed form (by rows).
!       Note also that LDH is used to define the size of array H, and
!       must therefore be at least N*(N+1)/2.

!       .. Scalar Arguments ..
Integer, Intent (In)           :: jthcol, ldh, n
!       .. Array Arguments ..
Real (Kind=nag_wp), Intent (In) :: h(ldh,*), x(n)
Real (Kind=nag_wp), Intent (Out) :: hx(n)
Real (Kind=nag_wp), Intent (Inout) :: ruser(*)
Integer, Intent (Inout)        :: iuser(*), iwsav(610)
!       .. Local Scalars ..
Real (Kind=nag_wp)             :: s
Integer                        :: i, inc, j, l, lp1
!       .. Executable Statements ..
If (jthcol/=0) Then

!         Special case -- extract one column of  H.

l = jthcol
inc = n

Do i = 1, jthcol
hx(i) = h(l,1)
inc = inc - 1
l = l + inc
End Do

l = l - inc + 1

If (jthcol<n) Then
lp1 = l

Do i = jthcol + 1, n
hx(i) = h(lp1,1)
lp1 = lp1 + 1
End Do

End If

Else

!         Normal case.

l = 0

Do i = 1, n
s = 0.0E0_nag_wp

Do j = i, n
l = l + 1
s = s + h(l,1)*x(j)
End Do

hx(i) = s
End Do

l = 0

Do j = 1, n - 1
l = l + 1

Do i = j + 1, n
l = l + 1
hx(i) = hx(i) + h(l,1)*x(j)
End Do

End Do

End If

Return

End Subroutine qphess
End Module e04ngae_mod
Program e04ngae

!     E04NGA Example Main Program

!     .. Use Statements ..
Use e04ngae_mod, Only: iset, lcwsav, liwsav, llwsav, lrwsav, nin,        &
ninopt, nout, qphess
Use nag_library, Only: e04nfa, e04nga, e04nha, e04wbf, nag_wp, x04abf,   &
x04acf, x04baf
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Character (*), Parameter         :: fname = 'e04ngae.opt'
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: obj
Integer                          :: i, ifail, inform, iter, j, lda, ldh, &
liwork, lwork, mode, n, nclin,       &
outchn, sda
Character (80)                   :: rec
Character (1)                    :: uplo
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: a(:,:), ax(:), bl(:), bu(:),         &
clamda(:), cvec(:), h(:,:), work(:), &
x(:)
Real (Kind=nag_wp)               :: ruser(1), rwsav(lrwsav)
Integer, Allocatable             :: istate(:), iwork(:)
Integer                          :: iuser(1), iwsav(liwsav)
Logical                          :: lwsav(llwsav)
Character (80)                   :: cwsav(lcwsav)
!     .. Intrinsic Procedures ..
Intrinsic                        :: max
!     .. Executable Statements ..
Write (rec,99992) 'E04NGA Example Program Results'
Call x04baf(nout,rec)

!     Skip heading in data file

liwork = 2*n + 3
lda = max(1,nclin)

If (nclin>0) Then
sda = n
Else
sda = 1
End If

!     This particular example problem is of type QP2 with a nondefault QPHESS,
!     so we allocate CVEC(N) and H(LDH,1), and define LDH and LWORK as below

ldh = n*(n+1)/2

If (nclin>0) Then
lwork = 2*n**2 + 8*n + 5*nclin
Else
lwork = n**2 + 8*n
End If

Allocate (istate(n+nclin),ax(max(1,nclin)),iwork(liwork),h(ldh,1),bl(n+  &
nclin),bu(n+nclin),cvec(n),x(n),a(lda,sda),clamda(n+nclin),            &
work(lwork))

If (uplo=='U') Then

!       Read the upper triangle of H

Else If (uplo=='L') Then

!       Read the lower triangle of H

End If

ldh = n*(n+1)/2

!     Set the unit number for advisory messages to OUTCHN

outchn = nout
Call x04abf(iset,outchn)

!     Initialise E04NFA

ifail = 0
Call e04wbf('E04NFA',cwsav,lcwsav,lwsav,llwsav,iwsav,liwsav,rwsav,       &
lrwsav,ifail)

!     Set three options using E04NHA

Call e04nha(' Check Frequency = 10 ',lwsav,iwsav,rwsav,inform)

If (inform==0) Then

Call e04nha(' Crash Tolerance = 0.05 ',lwsav,iwsav,rwsav,inform)

If (inform==0) Then

Call e04nha(' Infinite Bound Size = 1.0D+25 ',lwsav,iwsav,rwsav,     &
inform)

End If

End If

If (inform/=0) Then
Write (rec,99999) 'E04NHA terminated with INFORM = ', inform
Call x04baf(nout,rec)
Go To 100
End If

!     Open the options file for reading

mode = 0

ifail = 0
Call x04acf(ninopt,fname,mode,ifail)

!     Read the options file for the remaining options

Call e04nga(ninopt,lwsav,iwsav,rwsav,inform)

If (inform/=0) Then
Write (rec,99999) 'E04NGA terminated with INFORM =', inform
Call x04baf(nout,rec)
Go To 100
End If

!     Solve the problem

ifail = -1
Call e04nfa(n,nclin,a,lda,bl,bu,cvec,h,ldh,qphess,istate,x,iter,obj,ax,  &
clamda,iwork,liwork,work,lwork,iuser,ruser,lwsav,iwsav,rwsav,ifail)

Select Case (ifail)
Case (0:5,7:)
Write (rec,'()')
Call x04baf(nout,rec)
Write (rec,99998)
Call x04baf(nout,rec)
Write (rec,'()')
Call x04baf(nout,rec)

Do i = 1, n
Write (rec,99997) i, istate(i), x(i), clamda(i)
Call x04baf(nout,rec)
End Do

If (nclin>0) Then
Write (rec,'()')
Call x04baf(nout,rec)
Write (rec,'()')
Call x04baf(nout,rec)
Write (rec,99996)
Call x04baf(nout,rec)
Write (rec,'()')
Call x04baf(nout,rec)

Do i = n + 1, n + nclin
j = i - n
Write (rec,99995) j, istate(i), ax(j), clamda(i)
Call x04baf(nout,rec)
End Do

End If

Write (rec,'()')
Call x04baf(nout,rec)
Write (rec,'()')
Call x04baf(nout,rec)
Write (rec,99994) obj
Call x04baf(nout,rec)
Write (rec,'()')
Call x04baf(nout,rec)
Write (rec,'()')
Call x04baf(nout,rec)
Write (rec,99993) iter
Call x04baf(nout,rec)
End Select

100   Continue

99999 Format (1X,A,I5)
99998 Format (1X,'Varbl',2X,'Istate',3X,'Value',9X,'Lagr Mult')
99997 Format (1X,'V',2(1X,I3),4X,1P,G14.6,2X,1P,G12.4)
99996 Format (1X,'L Con',2X,'Istate',3X,'Value',9X,'Lagr Mult')
99995 Format (1X,'L',2(1X,I3),4X,1P,G14.6,2X,1P,G12.4)
99994 Format (1X,'Final objective value = ',G15.7)
99993 Format (1X,'Exit from problem after',1X,I6,1X,'iterations.')
99992 Format (1X,A)
End Program e04ngae
```