! F12FDF Example Program Text
! Mark 30.3 Release. nAG Copyright 2024.
Module f12fdfe_mod
! F12FDF 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 ..
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
Real (Kind=nag_wp), Parameter, Public :: zero = 0.0_nag_wp
Integer, Parameter, Public :: imon = 0, ipoint = 1, 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
End Module f12fdfe_mod
Program f12fdfe
! F12FDF Example Main Program
! .. Use Statements ..
Use f12fdfe_mod, Only: four, imon, ipoint, licomm, mv, nin, nout, one, &
six, two, zero
Use nag_library, Only: dcopy, 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 ..
Real (Kind=nag_wp), Allocatable :: ad(:), adl(:), adu(:), adu2(:), &
comm(:), d(:,:), mx(:), resid(:), &
v(:,:), x(:)
Integer :: icomm(licomm)
Integer, Allocatable :: ipiv(:)
! .. Intrinsic Procedures ..
Intrinsic :: real
! .. Executable Statements ..
Write (nout,*) 'F12FDF Example Program Results'
Write (nout,*)
! Skip heading in data file
Read (nin,*)
Read (nin,*) n, nev, ncv
lcomm = 3*n + ncv*ncv + 8*ncv + 60
ldv = n
Allocate (ad(n),adl(n),adu(n),adu2(n),comm(lcomm),d(ncv,2),mx(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)
! Indicate that we are using the shift and invert mode.
Call f12fdf('SHIFTED INVERSE',icomm,comm,ifail)
If (ipoint==1) Then
! Use pointers to Workspace in calculating matrix vector
! products rather than interfacing through the array X
Call f12fdf('POINTERS=YES',icomm,comm,ifail)
End If
h = one/real(n+1,kind=nag_wp)
r1 = (four/six)*h
r2 = (one/six)*h
sigma = zero
ad(1:n) = two/h - sigma*r1
adl(1:n) = -one/h - sigma*r2
adu(1:n) = adl(1:n)
! The NAG name equivalent of dgttrf is f07cdf
Call dgttrf(n,adl,ad,adu,adu2,ipiv,info)
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) Then
! Perform y <--- OP*x = inv[A-SIGMA*M]*M*x
! The NAG name equivalent of dgttrs is f07cef
If (ipoint==0) Then
Call mv(n,x,mx)
x(1:n) = mx(1:n)
Call dgttrs('N',n,1,adl,ad,adu,adu2,ipiv,x,n,info)
Else
Call mv(n,comm(icomm(1)),comm(icomm(2)))
Call dgttrs('N',n,1,adl,ad,adu,adu2,ipiv,comm(icomm(2)),n,info)
End If
Else If (irevcm==1) Then
! Perform y <-- OP*x = inv[A-sigma*M]*M*x
! The NAG name equivalent of dgttrs is f07cef.
! M*x has been saved in COMM(ICOMM(3)) or MX.
If (ipoint==0) Then
x(1:n) = mx(1:n)
Call dgttrs('N',n,1,adl,ad,adu,adu2,ipiv,x,n,info)
Else
! The NAG name equivalent of dcopy is f06eff
Call dcopy(n,comm(icomm(3)),1,comm(icomm(2)),1)
Call dgttrs('N',n,1,adl,ad,adu,adu2,ipiv,comm(icomm(2)),n,info)
End If
Else If (irevcm==2) Then
! Perform y <--- M*x.
If (ipoint==0) Then
Call mv(n,x,mx)
Else
Call mv(n,comm(icomm(1)),comm(icomm(2)))
End If
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/values.
ifail = 0
Call f12fcf(nconv,d,v,ldv,sigma,resid,v,ldv,comm,icomm,ifail)
Write (nout,99998) nconv, sigma
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,' Ritz values of closest to ',F8.4,' are:',/)
99997 Format (1X,I8,5X,F12.4)
End Program f12fdfe