NAG Library Manual, Mark 27.2
Interfaces:  FL   CL   CPP   AD
```!   F12ARF Example Program Text
!   Mark 27.2 Release. NAG Copyright 2021.

Module f12arfe_mod

!     F12ARF 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                           :: mv
!     .. Parameters ..
Complex (Kind=nag_wp), Parameter, Public :: four = (4.0_nag_wp,          &
0.0_nag_wp)
Complex (Kind=nag_wp), Parameter, Public :: one = (1.0_nag_wp,0.0_nag_wp &
)
Complex (Kind=nag_wp), Parameter, Public :: six = (6.0_nag_wp,0.0_nag_wp &
)
Complex (Kind=nag_wp), Parameter, Public :: two = (2.0_nag_wp,0.0_nag_wp &
)
Integer, Parameter, Public       :: imon = 0, licomm = 140, nerr = 6,    &
nin = 5, nout = 6
Contains
Subroutine mv(nx,v,w)
!       Compute the out-of--place matrix vector multiplication Y<---M*X,
!       where M is mass matrix formed by using piecewise linear elements
!       on [0,1].

!       .. Use Statements ..
Use nag_library, Only: zscal
!       .. Scalar Arguments ..
Integer, Intent (In)           :: nx
!       .. Array Arguments ..
Complex (Kind=nag_wp), Intent (In) :: v(nx*nx)
Complex (Kind=nag_wp), Intent (Out) :: w(nx*nx)
!       .. Local Scalars ..
Complex (Kind=nag_wp)          :: h
Integer                        :: j, n
!       .. Intrinsic Procedures ..
Intrinsic                      :: cmplx
!       .. Executable Statements ..
n = nx*nx
w(1) = (four*v(1)+v(2))/six
Do j = 2, n - 1
w(j) = (v(j-1)+four*v(j)+v(j+1))/six
End Do
w(n) = (v(n-1)+four*v(n))/six

h = one/cmplx(n+1,kind=nag_wp)
!       The NAG name equivalent of zscal is f06gdf
Call zscal(n,h,w,1)
Return
End Subroutine mv
End Module f12arfe_mod
Program f12arfe

!     F12ARF Example Main Program

!     .. Use Statements ..
Use f12arfe_mod, Only: four, imon, licomm, mv, nerr, nin, nout, one,     &
six, two
Use nag_library, Only: dznrm2, f12anf, f12apf, f12aqf, f12arf, f12asf,   &
nag_wp, zgttrf, zgttrs
!     .. Implicit None Statement ..
Implicit None
!     .. Local Scalars ..
Complex (Kind=nag_wp)            :: h, rho, s, s1, s2, s3, sigma
Integer                          :: ifail, ifail1, info, irevcm, j,      &
lcomm, ldv, n, nconv, ncv, nev,      &
niter, nshift, nx
!     .. Local Arrays ..
Complex (Kind=nag_wp), Allocatable :: ax(:), comm(:), d(:,:), dd(:),     &
dl(:), du(:), du2(:), mx(:),         &
resid(:), v(:,:), x(:)
Integer                          :: icomm(licomm)
Integer, Allocatable             :: ipiv(:)
!     .. Intrinsic Procedures ..
Intrinsic                        :: cmplx
!     .. Executable Statements ..
Write (nout,*) 'F12ARF Example Program Results'
Write (nout,*)
!     Skip heading in data file
Read (nin,*)
Read (nin,*) nx, nev, ncv

n = nx*nx
lcomm = 3*n + 3*ncv*ncv + 5*ncv + 60
ldv = n
Allocate (comm(lcomm),ax(n),d(ncv,2),dd(n),dl(n),du(n),du2(n),mx(n),     &
resid(n),v(ldv,ncv),x(n),ipiv(n))

ifail = 0
Call f12anf(n,nev,ncv,icomm,licomm,comm,lcomm,ifail)

!     Set the mode.
ifail = 0
Call f12arf('SHIFTED INVERSE',icomm,comm,ifail)
!     Set problem type.
Call f12arf('GENERALIZED',icomm,comm,ifail)
sigma = (500.0_nag_wp,0.0_nag_wp)
rho = (10.0_nag_wp,0.0_nag_wp)
h = one/cmplx(n+1,kind=nag_wp)
s = rho/two
s1 = -one/h - s - sigma*h/six
s2 = two/h - four*sigma*h/six
s3 = -one/h + s - sigma*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 zgttrf is f07crf
Call zgttrf(n,dl,dd,du,du2,ipiv,info)
If (info/=0) Then
Write (nerr,99999) info
Go To 100
End If

irevcm = 0
ifail = -1
revcm: Do
Call f12apf(irevcm,resid,v,ldv,x,mx,nshift,comm,icomm,ifail)
If (irevcm==5) Then
Exit revcm
Else If (irevcm==-1) Then
!         Perform  x <--- OP*x = inv[A-SIGMA*M]*M*x
Call mv(nx,x,ax)
x(1:n) = ax(1:n)
!         The NAG name equivalent of zgttrs is f07csf
Call zgttrs('N',n,1,dl,dd,du,du2,ipiv,x,n,info)
If (info/=0) Then
Write (nerr,99998) info
Exit revcm
End If
Else If (irevcm==1) Then
!         Perform  x <--- OP*x = inv[A-SIGMA*M]*M*x,
!         MX stored in COMM from location IPNTR(3)
!         The NAG name equivalent of zgttrs is f07csf
Call zgttrs('N',n,1,dl,dd,du,du2,ipiv,mx,n,info)
x(1:n) = mx(1:n)
If (info/=0) Then
Write (nerr,99998) info
Exit revcm
End If
Else If (irevcm==2) Then
!         Perform  y <--- M*x
Call mv(nx,x,ax)
x(1:n) = ax(1:n)
Else If (irevcm==4 .And. imon/=0) Then
!         Output monitoring information
Call f12asf(niter,nconv,d,d(1,2),icomm,comm)
!         The NAG name equivalent of dznrm2 is f06jjf
Write (6,99997) niter, nconv, dznrm2(nev,d(1,2),1)
End If
End Do revcm

If (ifail==0 .And. info==0) Then
!       Post-Process using F12AQF to compute eigenvalues/vectors.
ifail1 = 0
Call f12aqf(nconv,d,v,ldv,sigma,resid,v,ldv,comm,icomm,ifail1)
Write (nout,99996) nconv, sigma
Write (nout,99995)(j,d(j,1),j=1,nconv)
End If
100   Continue

99999 Format (1X,'** Error status returned by ZGTTRF, INFO =',I12)
99998 Format (1X,'** Error status returned by ZGTTRS, INFO =',I12)
99997 Format (1X,'Iteration',1X,I3,', No. converged =',1X,I3,', norm o',       &
'f estimates =',E16.8)
99996 Format (1X,/,' The ',I4,' generalized Ritz values closest to (',F7.3,    &
',',F7.3,') are:',/)
99995 Format (1X,I8,5X,'( ',F10.4,' , ',F10.4,' )')
End Program f12arfe
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