NAG Library Manual, Mark 28.5
!   Mark 28.5 Release. NAG Copyright 2022.

!            Parameters and User-defined Routines

!     .. Use Statements ..
Use nag_library, Only: nag_wp
!     .. Implicit None Statement ..
Implicit None
!     .. Accessibility Statements ..
Private
Public                           :: mv
!     .. Parameters ..
Real (Kind=nag_wp), Parameter, Public :: four = 4.0_nag_wp
Real (Kind=nag_wp), Parameter, Public :: one = 1.0_nag_wp
Real (Kind=nag_wp), Parameter, Public :: six = 6.0_nag_wp
Real (Kind=nag_wp), Parameter, Public :: two = 2.0_nag_wp
Integer, Parameter, Public       :: imon = 0, nin = 5, nout = 6
Contains
Subroutine mv(n,v)
!       Compute the in-place matrix vector multiplication X<---M*X,
!       where M is mass matrix formed by using piecewise linear elements
!       on [0,1].

!       .. Use Statements ..
Use nag_library, Only: dscal
!       .. Scalar Arguments ..
Integer, Intent (In)           :: n
!       .. Array Arguments ..
Real (Kind=nag_wp), Intent (Inout) :: v(n)
!       .. Local Scalars ..
Real (Kind=nag_wp)             :: h, vm1, vv
Integer                        :: j
!       .. Intrinsic Procedures ..
Intrinsic                      :: real
!       .. Executable Statements ..
vm1 = v(1)
v(1) = (four*v(1)+v(2))/six
Do j = 2, n - 1
vv = v(j)
v(j) = (vm1+four*vv+v(j+1))/six
vm1 = vv
End Do
v(n) = (vm1+four*v(n))/six

h = one/real(n+1,kind=nag_wp)
!       The NAG name equivalent of dscal is f06edf
Call dscal(n,h,v,1)
Return
End Subroutine mv

!     .. Use Statements ..
Use f12adfe_mod, Only: four, imon, mv, nin, nout, one, six, two
Use nag_library, Only: dgttrf, dgttrs, dnrm2, f12aaf, f12abf, f12acf,    &
!     .. Implicit None Statement ..
Implicit None
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: h, rho, s, s1, s2, s3, sigmai,       &
sigmar
Integer                          :: ifail, ifail1, info, irevcm, j,      &
lcomm, ldv, licomm, n, nconv, ncv,   &
nev, niter, nshift, nx
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: comm(:), d(:,:), dd(:), dl(:),       &
du(:), du2(:), mx(:), resid(:),      &
v(:,:), x(:)
Integer, Allocatable             :: icomm(:), ipiv(:)
!     .. Intrinsic Procedures ..
Intrinsic                        :: real
!     .. Executable Statements ..
Write (nout,*) 'F12ADF Example Program Results'
Write (nout,*)
!     Skip heading in data file
Read (nin,*) nx, nev, ncv, rho, sigmar, sigmai
n = nx*nx
ldv = n
licomm = 140
lcomm = 3*n + 3*ncv*ncv + 6*ncv + 60
Allocate (comm(lcomm),d(ncv,3),dd(n),dl(n),du(n),du2(n),mx(n),resid(n),  &
v(ldv,ncv),x(n),icomm(licomm),ipiv(n))

!     ifail: behaviour on error exit
!             =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call f12aaf(n,nev,ncv,icomm,licomm,comm,lcomm,ifail)

!     Set the mode.
!     Set problem type
ifail = 0
!     Construct C = A - SIGMA*I, and factor C using DGTTRF/F07CDF.
h = one/real(n+1,kind=nag_wp)
s = rho/two
s1 = -one/h - s - sigmar*h/six
s2 = two/h - four*sigmar*h/six
s3 = -one/h + s - sigmar*h/six
dl(1:n-1) = s1
dd(1:n-1) = s2
du(1:n-1) = s3
dd(n) = s2

!     The NAG name equivalent of dgttrf is f07cdf
Call dgttrf(n,dl,dd,du,du2,ipiv,info)

irevcm = 0

ifail = -1
loop: Do
Call f12abf(irevcm,resid,v,ldv,x,mx,nshift,comm,icomm,ifail)

If (irevcm/=5) Then
Select Case (irevcm)
Case (-1)
!           Perform  x <--- OP*x = inv[A-SIGMA*M]*M*x.
Call mv(n,x)
!           The NAG name equivalent of dgttrs is f07cef
Call dgttrs('N',n,1,dl,dd,du,du2,ipiv,x,n,info)
Case (1)
!           Perform  x <--- OP*x = inv[A-SIGMA*M]*M*x.
Call dgttrs('N',n,1,dl,dd,du,du2,ipiv,mx,n,info)
x(1:n) = mx(1:n)
Case (2)
!           Perform  y <--- M*x
Call mv(n,x)
Case (4)
If (imon/=0) Then
!             Output monitoring information
Call f12aef(niter,nconv,d,d(1,2),d(1,3),icomm,comm)
!             The NAG name equivalent of dnrm2 is f06ejf
Write (6,99999) niter, nconv, dnrm2(nev,d(1,3),1)
End If
End Select
Else
Exit loop
End If
End Do loop
If (ifail==0) Then
!       Post-Process using F12ACF to compute eigenvalues/vectors.
ifail1 = 0
Call f12acf(nconv,d,d(1,2),v,ldv,sigmar,sigmai,resid,v,ldv,comm,icomm, &
ifail1)
!       Print computed eigenvalues.
Write (nout,99998) nconv
Do j = 1, nconv
Write (nout,99997) j, d(j,1), d(j,2)
End Do
End If

99999 Format (1X,'Iteration',1X,I3,', No. converged =',1X,I3,', norm o',       &
'f estimates =',E16.8)
99998 Format (1X,/,' The ',I4,' generalized Ritz values closest to ',          &
'unity are:',/)
99997 Format (1X,I8,5X,'( ',F12.4,' , ',F12.4,' )')