Program f08gtfe

!     F08GTF Example Program Text

!     Mark 29.1 Release. NAG Copyright 2023.

!     .. Use Statements ..
      Use nag_library, Only: dznrm2, nag_wp, x04dbf, zhptrd, zsteqr, zupgtr
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
      Complex (Kind=nag_wp)            :: scal
      Integer                          :: i, ifail, info, j, k, ldq, n
      Character (1)                    :: uplo
!     .. Local Arrays ..
      Complex (Kind=nag_wp), Allocatable :: ap(:), q(:,:), tau(:), work(:)
      Real (Kind=nag_wp), Allocatable  :: d(:), e(:), rwork(:)
      Character (1)                    :: clabs(1), rlabs(1)
!     .. Intrinsic Procedures ..
      Intrinsic                        :: abs, conjg, maxloc
!     .. Executable Statements ..
      Write (nout,*) 'F08GTF Example Program Results'
!     Skip heading in data file
      Read (nin,*)
      Read (nin,*) n
      ldq = n
      Allocate (ap(n*(n+1)/2),q(ldq,n),tau(n),work(n-1),d(n),e(n),rwork(2*n-2) &
        )

!     Read A from data file

      Read (nin,*) uplo
      If (uplo=='U') Then
        Read (nin,*)((ap(i+j*(j-1)/2),j=i,n),i=1,n)
      Else If (uplo=='L') Then
        Read (nin,*)((ap(i+(2*n-j)*(j-1)/2),j=1,i),i=1,n)
      End If

!     Reduce A to tridiagonal form T = (Q**H)*A*Q
!     The NAG name equivalent of zhptrd is f08gsf
      Call zhptrd(uplo,n,ap,d,e,tau,info)

!     Form Q explicitly, storing the result in Q
!     The NAG name equivalent of zupgtr is f08gtf
      Call zupgtr(uplo,n,ap,tau,q,ldq,work,info)

!     Calculate all the eigenvalues and eigenvectors of A
!     The NAG name equivalent of zsteqr is f08jsf
      Call zsteqr('V',n,d,e,q,ldq,rwork,info)

      Write (nout,*)
      If (info>0) Then
        Write (nout,*) 'Failure to converge.'
      Else

!       Print eigenvalues and eigenvectors

        Write (nout,*) 'Eigenvalues'
        Write (nout,99999) d(1:n)
        Write (nout,*)
        Flush (nout)

!       Normalize the eigenvectors, largest element real
        Do i = 1, n
          rwork(1:n) = abs(q(1:n,i))
          k = maxloc(rwork(1:n),1)
          scal = conjg(q(k,i))/abs(q(k,i))/dznrm2(n,q(1,i),1)
          q(1:n,i) = q(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,n,q,ldq,'Bracketed','F7.4','Eigenvectors', &
          'Integer',rlabs,'Integer',clabs,80,0,ifail)

      End If

99999 Format (8X,4(F7.4,11X,:))
    End Program f08gtfe