! F12AEF Example Program Text ! Mark 24 Release. NAG Copyright 2012. Module f12aefe_mod ! F12AEF 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 :: three = 3.0_nag_wp Real (Kind=nag_wp), Parameter :: two = 2.0_nag_wp Real (Kind=nag_wp), Parameter :: zero = 0.0_nag_wp Integer, Parameter :: 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]. ! .. Scalar Arguments .. Integer, Intent (In) :: n ! .. Array Arguments .. Real (Kind=nag_wp), Intent (Inout) :: v(n) ! .. Local Scalars .. Real (Kind=nag_wp) :: vm1, vv Integer :: j ! .. Executable Statements .. vm1 = v(1) v(1) = four*v(1) + v(2) Do j = 2, n - 1 vv = v(j) v(j) = vm1 + four*vv + v(j+1) vm1 = vv End Do v(n) = vm1 + four*v(n) Return End Subroutine mv Subroutine av(n,v,w) ! .. 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 .. Integer :: j ! .. Executable Statements .. w(1) = two*v(1) + three*v(2) Do j = 2, n - 1 w(j) = -two*v(j-1) + two*v(j) + three*v(j+1) End Do w(n) = -two*v(n-1) + two*v(n) Return End Subroutine av End Module f12aefe_mod Program f12aefe ! F12AEF Example Main Program ! .. Use Statements .. Use nag_library, Only: ddot, dnrm2, f06bnf, f12aaf, f12abf, f12acf, & f12adf, f12aef, nag_wp, zgttrf, zgttrs Use f12aefe_mod, Only: av, four, mv, nin, nout, three, two, zero ! .. Implicit None Statement .. Implicit None ! .. Local Scalars .. Complex (Kind=nag_wp) :: c1, c2, c3, csig Real (Kind=nag_wp) :: deni, denr, nev_nrm, numi, numr, & sigmai, sigmar Integer :: ifail, ifail1, info, irevcm, j, & lcomm, ldv, licomm, n, nconv, & ncv, nev, niter, nshift Logical :: first ! .. Local Arrays .. Complex (Kind=nag_wp), Allocatable :: cdd(:), cdl(:), cdu(:), cdu2(:), & ctemp(:) Real (Kind=nag_wp), Allocatable :: ax(:), comm(:), d(:,:), mx(:), & resid(:), v(:,:), x(:) Integer, Allocatable :: icomm(:), ipiv(:) ! .. Intrinsic Procedures .. Intrinsic :: cmplx, real ! .. Executable Statements .. Write (nout,*) 'F12AEF Example Program Results' Write (nout,*) ! Skip heading in data file Read (nin,*) Read (nin,*) n, nev, ncv, sigmar, sigmai ldv = n licomm = 140 lcomm = 3*n + 3*ncv*ncv + 6*ncv + 60 Allocate (cdd(n),cdl(n),cdu(n),cdu2(n),ctemp(n),ax(n),comm(lcomm), & d(ncv,3),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. ifail = 0 Call f12adf('SHIFTED REAL',icomm,comm,ifail) ! Set problem type Call f12adf('GENERALIZED',icomm,comm,ifail) ! Solve A*x = lambda*B*x in shift-invert mode. ! The shift, sigma, is a complex number (sigmar, sigmai). ! OP = Real_Part{inv[A-(SIGMAR,SIGMAI)*M]*M and B = M. csig = cmplx(sigmar,sigmai,kind=nag_wp) c1 = cmplx(-two,kind=nag_wp) - csig c2 = cmplx(two,kind=nag_wp) - cmplx(four,kind=nag_wp)*csig c3 = cmplx(three,kind=nag_wp) - csig cdl(1:n-1) = c1 cdd(1:n-1) = c2 cdu(1:n-1) = c3 cdd(n) = c2 ! The NAG name equivalent of zgttrf is f07crf Call zgttrf(n,cdl,cdd,cdu,cdu2,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) ctemp(1:n) = cmplx(x(1:n),kind=nag_wp) ! The NAG name equivalent of zgttrs is f07csf Call zgttrs('N',n,1,cdl,cdd,cdu,cdu2,ipiv,ctemp,n,info) x(1:n) = real(ctemp(1:n)) Case (1) ! Perform x <--- OP*x = inv[A-SIGMA*M]*M*x, ! M*X stored in MX. ctemp(1:n) = cmplx(mx(1:n),kind=nag_wp) ! The NAG name equivalent of zgttrs is f07csf Call zgttrs('N',n,1,cdl,cdd,cdu,cdu2,ipiv,ctemp,n,info) x(1:n) = real(ctemp(1:n)) Case (2) ! Perform y <--- M*x Call mv(n,x) Case (4) ! Output monitoring information Call f12aef(niter,nconv,d,d(1,2),d(1,3),icomm,comm) ! The NAG name equivalent of dnrm2 is f06ejf nev_nrm = dnrm2(nev,d(1,3),1) Write (6,99999) niter, nconv, nev_nrm 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) first = .True. Do j = 1, nconv ! Use Rayleigh Quotient to recover eigenvalues of the original ! problem. ! The NAG name equivalent of ddot is f06eaf If (d(j,2)==zero) Then ! Ritz value is real. x = v(:,j); eig = x'Ax/x'Mx. Call av(n,v(1,j),ax) numr = ddot(n,v(1,j),1,ax,1) mx(1:n) = v(1:n,j) Call mv(n,mx) denr = ddot(n,v(1,j),1,mx,1) d(j,1) = numr/denr Else If (first) Then ! Ritz value is complex: x = v(:,j) - i v(:,j+1). ! Compute x'(Ax): ! first (xr,xi)'*(A xr) Call av(n,v(1,j),ax) numr = ddot(n,v(1,j),1,ax,1) numi = ddot(n,v(1,j+1),1,ax,1) ! then add (xi,-xr)'*(A xi) Call av(n,v(1,j+1),ax) numr = numr + ddot(n,v(1,j+1),1,ax,1) numi = -numi + ddot(n,v(1,j),1,ax,1) ! Compute x'(Mx) as above using mv in, place of av. mx(1:n) = v(1:n,j) Call mv(n,mx) denr = ddot(n,v(1,j),1,mx,1) deni = ddot(n,v(1,j+1),1,mx,1) mx(1:n) = v(1:n,j+1) Call mv(n,mx) denr = denr + ddot(n,v(1,j+1),1,mx,1) deni = -deni + ddot(n,v(1,j),1,mx,1) ! Rayleigh quotient, d=x'(Ax)/x'(Mx), (complex division). d(j,1) = (numr*denr+numi*deni)/f06bnf(denr,deni) d(j,2) = (numi*denr-numr*deni)/f06bnf(denr,deni) first = .False. Else ! Second of complex conjugate pair. d(j,1) = d(j-1,1) d(j,2) = -d(j-1,2) first = .True. End If End Do ! Print computed eigenvalues. Write (nout,99998) nconv, sigmar, sigmai Write (nout,99997)(j,d(j,1:2),j=1,nconv) End If 99999 Format (1X,'Iteration',1X,I3,', No. converged =',1X,I3,', norm o', & 'f estimates =',E12.4) 99998 Format (1X/' The ',I4,' generalized Ritz values closest to (',F8.4,', ', & F8.4,') are:'/) 99997 Format (1X,I8,5X,'(',F7.4,',',F7.4,')') End Program f12aefe