! F12FDF Example Program Text ! Mark 24 Release. NAG Copyright 2012. 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 ! .. Parameters .. Real (Kind=nag_wp), Parameter :: four = 4.0_nag_wp Real (Kind=nag_wp), Parameter :: one = 1.0_nag_wp Real (Kind=nag_wp), Parameter :: six = 6.0_nag_wp Real (Kind=nag_wp), Parameter :: two = 2.0_nag_wp Real (Kind=nag_wp), Parameter :: zero = 0.0_nag_wp Integer, Parameter :: 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 nag_library, Only: dcopy, dgttrf, dgttrs, dnrm2, f12faf, f12fbf, & f12fcf, f12fdf, f12fef, nag_wp Use f12fdfe_mod, Only: four, imon, ipoint, licomm, mv, nin, nout, one, & six, two, zero ! .. 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