Program f08hafe

!     F08HAF Example Program Text

!     Mark 30.2 Release. NAG Copyright 2024.

!     .. Use Statements ..
      Use nag_library, Only: ddisna, dsbev, nag_wp, x02ajf, x04caf
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Integer, Parameter               :: nin = 5, nout = 6
      Character (1), Parameter         :: uplo = 'U'
!     .. Local Scalars ..
      Real (Kind=nag_wp)               :: eerrbd, eps
      Integer                          :: i, ifail, info, j, kd, ldab, ldz, n
!     .. Local Arrays ..
      Real (Kind=nag_wp), Allocatable  :: ab(:,:), rcondz(:), w(:), work(:),   &
                                          z(:,:), zerrbd(:)
!     .. Intrinsic Procedures ..
      Intrinsic                        :: abs, max, min
!     .. Executable Statements ..
      Write (nout,*) 'F08HAF Example Program Results'
      Write (nout,*)
!     Skip heading in data file
      Read (nin,*)
      Read (nin,*) n, kd
      ldab = kd + 1
      ldz = n
      Allocate (ab(ldab,n),rcondz(n),w(n),work(3*n-2),z(ldz,n),zerrbd(n))

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

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

!     Solve the band symmetric eigenvalue problem

!     The NAG name equivalent of dsbev is f08haf
      Call dsbev('Vectors',uplo,n,kd,ab,ldab,w,z,ldz,work,info)

      If (info==0) Then

!       Print solution

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

!       Get the machine precision, EPS and compute the approximate
!       error bound for the computed eigenvalues.  Note that for
!       the 2-norm, max( abs(W(i)) ) = norm(A), and since the
!       eigenvalues are returned in ascending order
!       max( abs(W(i)) ) = max( abs(W(1)), abs(W(n)))

        eps = x02ajf()
        eerrbd = eps*max(abs(w(1)),abs(w(n)))

!       Call DDISNA (F08FLF) to estimate reciprocal condition
!       numbers for the eigenvectors
        Call ddisna('Eigenvectors',n,n,w,rcondz,info)

!       Compute the error estimates for the eigenvectors

        Do i = 1, n
          zerrbd(i) = eerrbd/rcondz(i)
        End Do

!       Print the approximate error bounds for the eigenvalues
!       and vectors

        Write (nout,*)
        Write (nout,*) 'Error estimate for the eigenvalues'
        Write (nout,99998) eerrbd
        Write (nout,*)
        Write (nout,*) 'Error estimates for the eigenvectors'
        Write (nout,99998) zerrbd(1:n)
      Else
        Write (nout,99997) 'Failure in DSBEV. INFO =', info
      End If

99999 Format (3X,(8F8.4))
99998 Format (4X,1P,6E11.1)
99997 Format (1X,A,I4)
    End Program f08hafe