Program f08nufe

!     F08NUF Example Program Text

!     Mark 29.1 Release. NAG Copyright 2023.

!     .. Use Statements ..
      Use nag_library, Only: dznrm2, nag_wp, x04dbf, zgehrd, zhsein, zhseqr,   &
                             zunmhr
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
      Complex (Kind=nag_wp)            :: scal
      Real (Kind=nag_wp)               :: thresh
      Integer                          :: i, ifail, info, k, lda, ldc, ldh,    &
                                          ldvl, ldz, lwork, m, n
!     .. Local Arrays ..
      Complex (Kind=nag_wp), Allocatable :: a(:,:), c(:,:), h(:,:), tau(:),    &
                                          vl(:,:), w(:), work(:), z(:,:)
      Real (Kind=nag_wp), Allocatable  :: rwork(:)
      Integer, Allocatable             :: ifaill(:), ifailr(:)
      Logical, Allocatable             :: select(:)
      Character (1)                    :: clabs(1), rlabs(1)
!     .. Intrinsic Procedures ..
      Intrinsic                        :: abs, aimag, conjg, maxloc, real
!     .. Executable Statements ..
      Write (nout,*) 'F08NUF Example Program Results'
      Flush (nout)
!     Skip heading in data file
      Read (nin,*)
      Read (nin,*) n
      ldz = 1
      lda = n
      ldc = n
      ldh = n
      ldvl = n
      lwork = 64*n
      Allocate (a(lda,n),c(ldc,n),h(ldh,n),tau(n),vl(ldvl,n),w(n),work(lwork), &
        z(ldz,1),rwork(n),ifaill(n),ifailr(n),select(n))

!     Read A from data file
      Read (nin,*)(a(i,1:n),i=1,n)

      Read (nin,*) thresh

!     Reduce A to upper Hessenberg form H = (Q**H)*A*Q
!     The NAG name equivalent of zgehrd is f08nsf
      Call zgehrd(n,1,n,a,lda,tau,work,lwork,info)

!     Copy A to H
      h(1:n,1:n) = a(1:n,1:n)

!     Calculate the eigenvalues of H (same as A)
!     The NAG name equivalent of zhseqr is f08psf
      Call zhseqr('Eigenvalues','No vectors',n,1,n,h,ldh,w,z,ldz,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)

        Do i = 1, n
          select(i) = real(w(i)) < thresh
        End Do

!       Calculate the eigenvectors of H (as specified by SELECT),
!       storing the result in C
!       The NAG name equivalent of zhsein is f08pxf
        Call zhsein('Right','QR','No initial vectors',select,n,a,lda,w,vl,     &
          ldvl,c,ldc,n,m,work,rwork,ifaill,ifailr,info)

!       Calculate the eigenvectors of A = Q * (eigenvectors of H)
!       The NAG name equivalent of zunmhr is f08nuf
        Call zunmhr('Left','No transpose',n,m,1,n,a,lda,tau,c,ldc,work,lwork,  &
          info)

!       Print eigenvectors

        Write (nout,*)
        Flush (nout)

!       Normalize the eigenvectors, largest element real
        Do i = 1, m
          rwork(1:n) = abs(c(1:n,i))
          k = maxloc(rwork(1:n),1)
          scal = conjg(c(k,i))/abs(c(k,i))/dznrm2(n,c(1,i),1)
          c(1:n,i) = c(1:n,i)*scal
        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,c,ldc,'Bracketed','F7.4',                &
          'Contents of array C','Integer',rlabs,'Integer',clabs,80,0,ifail)

      End If

99999 Format ((3X,4(A,F7.4,A,F7.4,A,:)))
    End Program f08nufe