! F12ADF Example Program Text ! Mark 23 Release. NAG Copyright 2011. 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 ! .. Implicit None Statement .. IMPLICIT NONE ! .. 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 Functions .. 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 USE f12adfe_mod, ONLY : four, imon, mv, nag_wp, 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 Functions .. 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