Program f08jhfe

!     F08JHF Example Program Text

!     Mark 30.2 Release. NAG Copyright 2024.

!     .. Use Statements ..
      Use nag_library, Only: dsbtrd, dstedc, nag_wp, x04caf
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Integer, Parameter               :: nin = 5, nout = 6
      Character (1), Parameter         :: uplo = 'U'
!     .. Local Scalars ..
      Integer                          :: i, ifail, info, j, kd, ldab, ldz,    &
                                          lgn, liwork, lwork, n
!     .. Local Arrays ..
      Real (Kind=nag_wp), Allocatable  :: ab(:,:), d(:), e(:), work(:), z(:,:)
      Real (Kind=nag_wp)               :: rdum(1)
      Integer                          :: idum(1)
      Integer, Allocatable             :: iwork(:)
!     .. Intrinsic Procedures ..
      Intrinsic                        :: ceiling, log, max, min, nint, real
!     .. Executable Statements ..
      Write (nout,*) 'F08JHF Example Program Results'
      Write (nout,*)
!     Skip heading in data file
      Read (nin,*)
      Read (nin,*) n, kd
      ldab = kd + 1
      ldz = n
      lgn = ceiling(log(real(n,kind=nag_wp))/log(2.0E0_nag_wp))
      Allocate (ab(ldab,n),d(n),e(n-1),z(ldz,n))

!     Use routine workspace query to get optimal workspace.
      lwork = -1
      liwork = -1
!     The NAG name equivalent of dstedc is f08jhf
      Call dstedc('V',n,d,e,z,ldz,rdum,lwork,idum,liwork,info)

!     Make sure that there is enough workspace.
      lwork = max(1+3*n+2*n*lgn+4*n*n,nint(rdum(1)))
      liwork = max(6+6*n+5*n*lgn,idum(1))
      Allocate (work(lwork),iwork(liwork))

!     Read the upper or lower triangular part of the band matrix A
!     from data file

      If (uplo=='U') Then
        Do i = 1, n
          Read (nin,*)(ab(kd+1+i-j,j),j=i,min(n,i+kd))
        End Do
      Else If (uplo=='L') Then
        Do i = 1, n
          Read (nin,*)(ab(1+i-j,j),j=max(1,i-kd),i)
        End Do
      End If

!     Reduce A to tridiagonal form T = (Z**T)*A*Z, and form Z
!     The NAG name equivalent of dsbtrd is f08hef
      Call dsbtrd('V',uplo,n,kd,ab,ldab,d,e,z,ldz,work,info)

!     Calculate all the eigenvalues and eigenvectors of A,
!     from T and Z
!     The NAG name equivalent of dstedc is f08jhf
      Call dstedc('V',n,d,e,z,ldz,work,lwork,iwork,liwork,info)

      If (info==0) Then

!       Print eigenvalues and eigenvectors

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

        Write (nout,*)
        Flush (nout)

!       Standardize the eigenvectors so that first elements are non-negative.
        Do i = 1, n
          If (z(1,i)<0.0_nag_wp) Then
            z(1:n,i) = -z(1:n,i)
          End If
        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,n,z,ldz,'Eigenvectors',ifail)

      Else
        Write (nout,99998) 'Failure in DSTEDC. INFO = ', info
      End If

99999 Format ((3X,8F8.4))
99998 Format (1X,A,I10)
    End Program f08jhfe