! F12ADF Example Program Text ! Mark 24 Release. NAG Copyright 2012. Module f12adfe_mod ! F12ADF 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 Integer, Parameter :: 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 End Module f12adfe_mod Program f12adfe ! F12ADF Example Main Program ! .. Use Statements .. Use nag_library, Only: dgttrf, dgttrs, dnrm2, f12aaf, f12abf, f12acf, & f12adf, f12aef, nag_wp Use f12adfe_mod, Only: four, imon, mv, nin, nout, one, six, two ! .. 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,*) 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. Call f12adf('SHIFTED REAL',icomm,comm,ifail) ! Set problem type ifail = 0 Call f12adf('GENERALIZED',icomm,comm,ifail) ! 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,' )') End Program f12adfe