Program f08nvfe ! F08NVF Example Program Text ! Mark 24 Release. NAG Copyright 2012. ! .. Use Statements .. Use nag_library, Only: nag_wp, x04dbf, zgebak, zgebal, zgehrd, zhseqr, & ztrevc, zunghr ! .. Implicit None Statement .. Implicit None ! .. Parameters .. Integer, Parameter :: nin = 5, nout = 6 ! .. Local Scalars .. Complex (Kind=nag_wp) :: firstnz Integer :: i, ifail, ihi, ilo, info, j, lda, & ldh, ldvl, ldvr, lwork, m, n ! .. Local Arrays .. Complex (Kind=nag_wp), Allocatable :: a(:,:), h(:,:), tau(:), vl(:,:), & vr(:,:), w(:), work(:) Real (Kind=nag_wp), Allocatable :: rwork(:), scale(:) Logical :: select(1) Character (1) :: clabs(1), rlabs(1) ! .. Intrinsic Procedures .. Intrinsic :: aimag, real ! .. Executable Statements .. Write (nout,*) 'F08NVF Example Program Results' Flush (nout) ! Skip heading in data file Read (nin,*) Read (nin,*) n ldvl = 1 lda = n ldh = n ldvr = n lwork = 64*n Allocate (a(lda,n),h(ldh,n),tau(n),vl(ldvl,1),vr(ldvr,n),w(n), & work(lwork),rwork(n),scale(n)) ! Read A from data file Read (nin,*)(a(i,1:n),i=1,n) ! Balance A ! The NAG name equivalent of zgebal is f08nvf Call zgebal('Both',n,a,lda,ilo,ihi,scale,info) ! Reduce A to upper Hessenberg form H = (Q**H)*A*Q ! The NAG name equivalent of zgehrd is f08nsf Call zgehrd(n,ilo,ihi,a,lda,tau,work,lwork,info) ! Copy A to H and VR h(1:n,1:n) = a(1:n,1:n) vr(1:n,1:n) = a(1:n,1:n) ! Form Q explicitly, storing the result in VR ! The NAG name equivalent of zunghr is f08ntf Call zunghr(n,1,n,vr,ldvr,tau,work,lwork,info) ! Calculate the eigenvalues and Schur factorization of A ! The NAG name equivalent of zhseqr is f08psf Call zhseqr('Schur form','Vectors',n,ilo,ihi,h,ldh,w,vr,ldvr,work,lwork, & info) Write (nout,*) If (info>0) Then Write (nout,*) 'Failure to converge.' Else Write (nout,*) 'Eigenvalues' Write (nout,99999)(' (',real(w(i)),',',aimag(w(i)),')',i=1,n) Flush (nout) ! Calculate the eigenvectors of A, storing the result in VR ! The NAG name equivalent of ztrevc is f08qxf Call ztrevc('Right','Backtransform',select,n,h,ldh,vl,ldvl,vr,ldvr,n, & m,work,rwork,info) ! The NAG name equivalent of zgebak is f08nwf Call zgebak('Both','Right',n,ilo,ihi,scale,m,vr,ldvr,info) ! Print eigenvectors Write (nout,*) Flush (nout) ! Normalize the eigenvectors Do i = 1, m Do j = n, 1, -1 If (vr(j,i)/=(0._nag_wp,0._nag_wp)) Then firstnz = vr(j,i) End If End Do vr(1:n,i) = vr(1:n,i)/firstnz End Do ! ifail: behaviour on error exit ! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft ifail = 0 Call x04dbf('General',' ',n,m,vr,ldvr,'Bracketed','F7.4', & 'Contents of array VR','Integer',rlabs,'Integer',clabs,80,0,ifail) End If 99999 Format ((3X,4(A,F7.4,A,F7.4,A:))) End Program f08nvfe