```!   E04MZF Example Program Text
!   Mark 26.2 Release. NAG Copyright 2017.
Module e04mzfe_mod

!     E04MZF 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                           :: qphx
!     .. Parameters ..
Real (Kind=nag_wp), Parameter, Public :: xbldef = 0.0_nag_wp
Real (Kind=nag_wp), Parameter, Public :: xbudef = 1.0E+20_nag_wp
Integer, Parameter, Public       :: iset = 1, lencw = 600, leniw = 600,  &
lenrw = 600, maxm = 10000,           &
maxn = 10000, maxnnz = 100000,       &
nindat = 7, nout = 6
Contains
Subroutine qphx(ncolh,x,hx,nstate,cuser,iuser,ruser)

!       Routine to compute H*x. (In this version of QPHX, the Hessian
!       matrix H is not referenced explicitly.)

!       .. Scalar Arguments ..
Integer, Intent (In)           :: ncolh, nstate
!       .. Array Arguments ..
Real (Kind=nag_wp), Intent (Out) :: hx(ncolh)
Real (Kind=nag_wp), Intent (Inout) :: ruser(*)
Real (Kind=nag_wp), Intent (In) :: x(ncolh)
Integer, Intent (Inout)        :: iuser(*)
Character (8), Intent (Inout)  :: cuser(*)
!       .. Executable Statements ..
If (nstate==1) Then

!         First entry. You may perform any required one-time
!         operations here.

End If

hx(1) = 2.0_nag_wp*x(1) + x(2) + x(3) + x(4) + x(5)
hx(2) = x(1) + 2.0_nag_wp*x(2) + x(3) + x(4) + x(5)
hx(3) = x(1) + x(2) + 2.0_nag_wp*x(3) + x(4) + x(5)
hx(4) = x(1) + x(2) + x(3) + 2.0_nag_wp*x(4) + x(5)
hx(5) = x(1) + x(2) + x(3) + x(4) + 2.0_nag_wp*x(5)

If (nstate>=2) Then

!         Final entry. You may perform any required clean up
!         operations here.

End If

Return

End Subroutine qphx
End Module e04mzfe_mod
Program e04mzfe

!     E04MZF Example Main Program

!     .. Use Statements ..
Use e04mzfe_mod, Only: iset, lencw, leniw, lenrw, maxm, maxn, maxnnz,    &
nindat, nout, qphx, xbldef, xbudef
Use nag_library, Only: e04mzf, e04npf, e04nqf, e04ntf, nag_wp, x04abf,   &
x04acf
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Character (*), Parameter         :: fname = 'e04mzfe.opt'
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: obj, objadd, sinf
Integer                          :: i, ifail, infile, iobj, lenc, m,     &
mode, n, ncolh, ninf, nname, nnz,    &
ns, outchn
Logical                          :: mpslst, verbose_output
Character (8)                    :: prob
Character (1)                    :: start
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: a(:), bl(:), bu(:), c(:), pi(:),     &
rc(:), xs(:)
Real (Kind=nag_wp)               :: ruser(1), rw(lenrw)
Integer, Allocatable             :: ha(:), helast(:), istate(:), ka(:)
Integer                          :: iuser(1), iw(leniw)
Character (8), Allocatable       :: crname(:)
Character (8)                    :: cuser(1), cw(lencw), names(5)
!     .. Intrinsic Procedures ..
Intrinsic                        :: max
!     .. Executable Statements ..
Write (nout,*) 'E04MZF Example Program Results'

Allocate (ha(maxnnz),ka(maxn+1),istate(maxn+maxm),a(maxnnz),             &
bl(maxn+maxm),bu(maxn+maxm),xs(maxn+maxm),crname(maxn+maxm))

!     Open the data file for reading

mode = 0

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

!     Initialize parameters.

infile = nindat
mpslst = .False.
names(1:5) = '        '

!     Convert the MPSX data file for use by E04NQF.

Write (nout,99999)

ifail = 0
Call e04mzf(infile,maxn,maxm,maxnnz,xbldef,xbudef,mpslst,n,m,nnz,iobj,   &
ncolh,a,ha,ka,bl,bu,start,names,nname,crname,xs,istate,ifail)

Write (nout,99998) n, m

!     Set the unit number for advisory messages to OUTCHN.

outchn = nout
Call x04abf(iset,outchn)

!     Set the value of NCOLH (the number of columns of the Hessian matrix)

ncolh = 5

!     Call E04NPF to initialize E04NQF.

ifail = 0
Call e04npf(cw,lencw,iw,leniw,rw,lenrw,ifail)

!     Set this to .True. to cause e04nqf to produce intermediate
!     progress output
verbose_output = .False.
If (verbose_output) Then
Call e04ntf('Print file',nout,cw,iw,rw,ifail)
End If

!     We have no explicit objective vector so set LENC = 0; the
!     objective vector is stored in row IOBJ of A.

lenc = 0
Allocate (c(max(1,lenc)),helast(n+m),pi(m),rc(n+m))

prob = ' '

!     Do not allow any elastic variables (i.e. they cannot be
!     infeasible).

helast(1:(n+m)) = 0

Write (nout,99997)
ifail = 0
ka,bl,bu,c,crname,helast,istate,xs,pi,rc,ns,ninf,sinf,obj,cw,lencw,iw, &
leniw,rw,lenrw,cuser,iuser,ruser,ifail)

Write (nout,99996) obj
Write (nout,99995)
Write (nout,99994)(i,xs(i),i=1,n)