```!   E04MZF Example Program Text
!   Mark 25 Release. NAG Copyright 2014.
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.

Write (nout,*)
Write (nout,99999) ncolh
Flush (nout)
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.

Write (nout,*)
Write (nout,99998)
Flush (nout)
End If

Return

99999   Format (1X,' This is the E04MZF example.   NCOLH =',I4,'.')
99998   Format (1X,' Finished the E04MZF example.')
End Subroutine qphx
End Module e04mzfe_mod
Program e04mzfe

!     E04MZF Example Main Program

!     .. Use Statements ..
Use nag_library, Only: e04mzf, e04npf, e04nqf, e04ntf, nag_wp, x04abf,   &
x04acf
Use e04mzfe_mod, Only: iset, lencw, leniw, lenrw, maxm, maxn, maxnnz,    &
nindat, nout, qphx, xbldef, xbudef
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Character (*), Parameter             :: fname = 'e04mzfe.opt'
!     .. Local Scalars ..
Real (Kind=nag_wp)                   :: obj, objadd, sinf
Integer                              :: ifail, infile, iobj, lenc, m,    &
mode, n, ncolh, ninf, nname,     &
nnz, ns, outchn
Logical                              :: mpslst
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,99999) 'E04MZF Example Program Results'
Flush (nout)

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.

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)

!     Set the unit number for advisory messages to OUTCHN.

outchn = nout
Call x04abf(iset,outchn)

!     Reset the value of NCOLH.

ncolh = 5

!     Call E04NPF to initialise E04NQF.

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

Call e04ntf('Print file',nout,cw,iw,rw,ifail)

!     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

!     Solve the QP problem.

ifail = 0