PROGRAM f08nhfe ! F08NHF Example Program Text ! Mark 23 Release. NAG Copyright 2011. ! .. Use Statements .. USE nag_library, ONLY : dgebak, dgebal, dgehrd, dhseqr, dorghr, dtrevc, & nag_wp, x04caf ! .. Implicit None Statement .. IMPLICIT NONE ! .. Parameters .. INTEGER, PARAMETER :: nin = 5, nout = 6 ! .. Local Scalars .. REAL (KIND=nag_wp) :: firstnz INTEGER :: i, ifail, ihi, ilo, info, j, lda, & ldh, ldvl, ldvr, lwork, m, n ! .. Local Arrays .. REAL (KIND=nag_wp), ALLOCATABLE :: a(:,:), h(:,:), scale(:), tau(:), & vl(:,:), vr(:,:), wi(:), work(:), & wr(:) LOGICAL :: select(1) ! .. Executable Statements .. WRITE (nout,*) 'F08NHF Example Program Results' ! 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),scale(n),tau(n),vl(ldvl,1),vr(ldvr,n), & wi(n),work(lwork),wr(n)) ! Read A from data file READ (nin,*) (a(i,1:n),i=1,n) ! Balance A ! The NAG name equivalent of dgebal is f08nhf CALL dgebal('Both',n,a,lda,ilo,ihi,scale,info) ! Reduce A to upper Hessenberg form H = (Q**T)*A*Q ! The NAG name equivalent of dgehrd is f08nef CALL dgehrd(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 dorghr is f08nff CALL dorghr(n,1,n,vr,ldvr,tau,work,lwork,info) ! Calculate the eigenvalues and Schur factorization of A ! The NAG name equivalent of dhseqr is f08pef CALL dhseqr('Schur form','Vectors',n,ilo,ihi,h,ldh,wr,wi,vr,ldvr,work, & lwork,info) WRITE (nout,*) IF (info>0) THEN WRITE (nout,*) 'Failure to converge.' ELSE WRITE (nout,*) 'Eigenvalues' WRITE (nout,99999) (' (',wr(i),',',wi(i),')',i=1,n) ! Calculate the eigenvectors of A, storing the result in VR ! The NAG name equivalent of dtrevc is f08qkf CALL dtrevc('Right','Backtransform',select,n,h,ldh,vl,ldvl,vr,ldvr, & n,m,work,info) ! The NAG name equivalent of dgebak is f08njf CALL dgebak('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 x04caf('General',' ',n,m,vr,ldvr,'Contents of array VR',ifail) END IF 99999 FORMAT (1X,A,F8.4,A,F8.4,A) END PROGRAM f08nhfe