NAG Library Manual, Mark 29.3
Interfaces:  FL   CL   CPP   AD
```!   F12FCF Example Program Text
!   Mark 29.3 Release. NAG Copyright 2023.

Module f12fcfe_mod

!     F12FCF 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                           :: av, 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 :: zero = 0.0_nag_wp
Real (Kind=nag_wp), Parameter    :: two = 2.0_nag_wp
Integer, Parameter, Public       :: imon = 0, licomm = 140, nin = 5,     &
nout = 6
Contains
Subroutine mv(n,v,w)

!       .. Use Statements ..
Use nag_library, Only: dscal
!       .. Scalar Arguments ..
Integer, Intent (In)           :: n
!       .. Array Arguments ..
Real (Kind=nag_wp), Intent (In) :: v(n)
Real (Kind=nag_wp), Intent (Out) :: w(n)
!       .. Local Scalars ..
Real (Kind=nag_wp)             :: h
Integer                        :: j
!       .. Intrinsic Procedures ..
Intrinsic                      :: real
!       .. Executable Statements ..
h = one/(real(n+1,kind=nag_wp)*six)
w(1) = four*v(1) + v(2)
Do j = 2, n - 1
w(j) = v(j-1) + four*v(j) + v(j+1)
End Do
j = n
w(j) = v(j-1) + four*v(j)
!       The NAG name equivalent of dscal is f06edf
Call dscal(n,h,w,1)
Return
End Subroutine mv

Subroutine av(n,v,w)

!       .. Use Statements ..
Use nag_library, Only: dscal
!       .. Scalar Arguments ..
Integer, Intent (In)           :: n
!       .. Array Arguments ..
Real (Kind=nag_wp), Intent (In) :: v(n)
Real (Kind=nag_wp), Intent (Out) :: w(n)
!       .. Local Scalars ..
Real (Kind=nag_wp)             :: h
Integer                        :: j
!       .. Intrinsic Procedures ..
Intrinsic                      :: real
!       .. Executable Statements ..
h = one/real(n+1,kind=nag_wp)
w(1) = two*v(1) - v(2)
Do j = 2, n - 1
w(j) = -v(j-1) + two*v(j) - v(j+1)
End Do
j = n
w(j) = -v(j-1) + two*v(j)
!       The NAG name equivalent of dscal is f06edf
Call dscal(n,one/h,w,1)
Return
End Subroutine av
End Module f12fcfe_mod
Program f12fcfe

!     F12FCF Example Main Program

!     .. Use Statements ..
Use f12fcfe_mod, Only: av, four, imon, licomm, mv, nin, nout, one, six,  &
zero
Use nag_library, Only: dgttrf, dgttrs, dnrm2, f12faf, f12fbf, f12fcf,    &
f12fdf, f12fef, nag_wp
!     .. Implicit None Statement ..
Implicit None
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: h, r1, r2, sigma
Integer                          :: ifail, info, irevcm, j, lcomm, ldv,  &
n, nconv, ncv, nev, niter, nshift
!     .. Local Arrays ..
comm(:), d(:,:), mx(:), resid(:),    &
v(:,:), x(:)
Integer                          :: icomm(licomm)
Integer, Allocatable             :: ipiv(:)
!     .. Intrinsic Procedures ..
Intrinsic                        :: real
!     .. Executable Statements ..
Write (nout,*) 'F12FCF Example Program Results'
Write (nout,*)
!     Skip heading in data file
Read (nin,*) n, nev, ncv

lcomm = 3*n + ncv*ncv + 8*ncv + 60
ldv = n
resid(n),v(ldv,ncv),x(n),ipiv(n))

ifail = 0
Call f12faf(n,nev,ncv,icomm,licomm,comm,lcomm,ifail)

!     We are solving a generalized problem
ifail = 0
Call f12fdf('GENERALIZED',icomm,comm,ifail)

h = one/real(n+1,kind=nag_wp)
r1 = (four/six)*h
r2 = (one/six)*h
!     The NAG name equivalent of dgttrf is f07cdf

irevcm = 0
ifail = -1
revcm: Do
Call f12fbf(irevcm,resid,v,ldv,x,mx,nshift,comm,icomm,ifail)
If (irevcm==5) Then
Exit revcm
Else If (irevcm==-1 .Or. irevcm==1) Then
!         Perform  X <--- OP*x = inv[M]*A*x.
Call av(n,x,mx)
x(1:n) = mx(1:n)
!         The NAG name equivalent of dgttrs is f07cef
Else If (irevcm==2) Then
!         Perform  MX <--- M*x.
Call mv(n,x,mx)
Else If (irevcm==4 .And. imon/=0) Then
!         Output monitoring information
Call f12fef(niter,nconv,d,d(1,2),icomm,comm)
!         The NAG name equivalent of dnrm2 is f06ejf
Write (6,99999) niter, nconv, dnrm2(nev,d(1,2),1)
End If
End Do revcm

If (ifail==0) Then
!       Post-Process using F12FCF to compute eigenvalues/vectors.
sigma = zero
ifail = 0
Call f12fcf(nconv,d,v,ldv,sigma,resid,v,ldv,comm,icomm,ifail)
Write (nout,99998) nconv
Write (nout,99997)(j,d(j,1),j=1,nconv)
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 of largest magn',      &
'itude are:',/)
99997 Format (1X,I8,5X,F9.1)
End Program f12fcfe
```