```!   E04MWF Example Program Text
!   Mark 26.1 Release. NAG Copyright 2017.

Module e04mwfe_mod

!     E04MWF 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
Contains
Subroutine qphx(ncolh,x,hx,nstate,cuser,iuser,ruser)

!       Subroutine to compute H*x.

!       Note: IUSER and RUSER contain the following data:
!       RUSER(1:NNZH) = H(1:NNZH)
!       IUSER(1:NCOLH+1) = ICCOLH(1:NCOLH+1)
!       IUSER(NCOLH+2:NNZH+NCOLH+1) = IROWH(1:NNZH)

!       .. 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(*)
!       .. Local Scalars ..
Integer                        :: icol, idx, iend, irow, istart
!       .. Executable Statements ..
hx(1:ncolh) = 0.0E0_nag_wp

Do icol = 1, ncolh
istart = iuser(icol)
iend = iuser(icol+1) - 1

Do idx = istart, iend
irow = iuser(ncolh+1+idx)
hx(irow) = hx(irow) + x(icol)*ruser(idx)
If (irow/=icol) Then
hx(icol) = hx(icol) + x(irow)*ruser(idx)
End If
End Do
End Do
Return

End Subroutine qphx
End Module e04mwfe_mod

Program e04mwfe

!     E04MWF Example Main Program

!     .. Use Statements ..
Use e04mwfe_mod, Only: qphx
Use nag_library, Only: e04mwf, e04npf, e04nqf, e04ntf, nag_wp, x04acf,   &
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: lencw = 600, leniw = 600,            &
lenrw = 600, nin = 5, nout = 6,      &
outfile = 42
Character (*), Parameter         :: outfile_name = 'e04mwfe.mps'
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: obj, objadd, sinf
Integer                          :: i, icol, ierr, ifail, iobj, jcol,    &
lenc, lintvar, m, minmax, n, ncolh,  &
ne, ninf, nname, nnzh, ns
Logical                          :: verbose_output
Character (1)                    :: istart
Character (8)                    :: prob
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: acol(:), bl(:), bu(:), c(:), h(:),   &
pi(:), rc(:), ruser(:), x(:)
Real (Kind=nag_wp)               :: rw(lenrw)
Integer, Allocatable             :: helast(:), hs(:), iccolh(:),         &
idxc(:), inda(:), intvar(:),         &
irowh(:), iuser(:), loca(:)
Integer                          :: iw(leniw)
Character (8)                    :: cuser(1), cw(lencw), pnames(5)
Character (8), Allocatable       :: names(:)
!     .. Intrinsic Procedures ..
Intrinsic                        :: max
!     .. Executable Statements ..
Write (nout,*) 'E04MWF Example Program Results'

!     Skip heading in data file.

Read (nin,*) ne, iobj, ncolh, nnzh, nname
Allocate (inda(ne),loca(n+1),helast(n+m),hs(n+m),acol(ne),bl(n+m),       &
bu(n+m),x(n+m),pi(m),rc(n+m),names(nname),h(nnzh),irowh(nnzh),         &
iccolh(ncolh+1))

!     Read the matrix ACOL from data file. Set up LOCA.
jcol = 1
loca(jcol) = 1

Do i = 1, ne
!       Element ( INDA( I ), ICOL ) is stored in ACOL( I ).

If (icol<jcol) Then
!         Elements not ordered by increasing column index.
Write (nout,99998) 'Element in column', icol,                        &
' found after element in column', jcol, '. Problem', ' abandoned.'
Go To 100
Else If (icol==jcol+1) Then
!         Index in ACOL of the start of the ICOL-th column equals I.
loca(icol) = i
jcol = icol
Else If (icol>jcol+1) Then
!         Columns JCOL+1,JCOL+2,...,ICOL-1 are empty. Set the
!         corresponding elements of LOCA to I.
loca((jcol+1):icol) = i
jcol = icol
End If
End Do

loca(n+1) = ne + 1

!     Columns N,N-1,...,ICOL+1 are empty. Set the corresponding
!     elements of LOCA accordingly.
Do i = n, icol + 1, -1
loca(i) = loca(i+1)
End Do

!     Read the matrix H from data file. Set up ICCOLH.
jcol = 1
iccolh(1) = 1

Do i = 1, nnzh
!       Element ( IROWH( I ), ICOL ) is stored in H( I ).

If (icol<jcol) Then
!         Elements not ordered by increasing column index
Write (nout,99998) 'Element in column', icol,                        &
' found after element in column', jcol, '. Problem', ' abandoned.'
Go To 100
Else If (icol==jcol+1) Then
!         Index in ICCOLH of the start of the ICOL-th column equals I.
iccolh(icol) = i
jcol = icol
Else If (icol>jcol+1) Then
!         Columns JCOL+1,JCOL+2,...,ICOL-1 are empty. Set the
!         corresponding elements of ICCOLH to I.
iccolh((jcol+1):icol) = i
jcol = icol
End If
End Do

iccolh(ncolh+1) = nnzh + 1

!     Columns N,N-1,...,ICOL+1 are empty. Set the corresponding
!     elements of ICCOLH accordingly.
Do i = n, icol + 1, -1
iccolh(i) = iccolh(i+1)
End Do

!     Read lower and upper bounds

!     Set cold start
istart = 'C'
hs(1:(n+m)) = 0.0_nag_wp

!     Read the initial point x_0

!     Print dimensions of the QP problem
Write (nout,99999) n, m

!     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
!       By default e04nqf does not print monitoring
!       information. Set the print file unit or the summary
!       file unit to get information.
ifail = 0
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 ACOL.
lenc = 0
Allocate (c(max(1,lenc)),iuser(ncolh+1+nnzh),ruser(nnzh))

prob = ' '

!     Do not allow any elastic variables (i.e. they cannot be
!     infeasible). If we'd set optional argument "Elastic mode" to 0,
!     we wouldn't need to set the individual elements of array HELAST.
helast(1:(n+m)) = 0

If (ncolh>0) Then
!       Store the non zeros of H in ruser for use by qphx
ruser(1:nnzh) = h(1:nnzh)

!       Store iccolh and irowh in iuser for use by qphx
iuser(1:ncolh+1) = iccolh(1:ncolh+1)
iuser(ncolh+2:nnzh+ncolh+1) = irowh(1:nnzh)
End If

!     Call e04nqf to solve the problem.
ifail = 0
inda,loca,bl,bu,c,names,helast,hs,x,pi,rc,ns,ninf,sinf,obj,cw,lencw,   &
iw,leniw,rw,lenrw,cuser,iuser,ruser,ifail)

!     Print objective function and optimal x*
Write (nout,*)
Write (nout,99997) obj
Write (nout,99996) x(1:n)

!     Set the rest of inputs for e04mwf. Due to IOBJ > 0, LENC = 0 and
!     C and IDXC will not be referenced.
lintvar = 0
Allocate (idxc(lenc),intvar(lintvar))
c(:) = 0
idxc(:) = 0
intvar(:) = 0
pnames(:) = '        '
pnames(1) = 'USRPNAME'
pnames(2) = 'OBJ.....'
minmax = -1

!     Open data file for writing
ifail = 0
Call x04acf(outfile,outfile_name,1,ifail)

!     Call e04mwf to store the problem in a MPS file with fixed format.
ifail = 0
Call e04mwf(outfile,n,m,lenc,ne,ncolh,nnzh,lintvar,idxc,c,iobj,acol,     &
inda,loca,bl,bu,pnames,nname,names,h,irowh,iccolh,minmax,intvar,ifail)

Write (nout,99995) outfile_name

!     Close data file
ierr = 0