Program f08jafe
! F08JAF Example Program Text
! Mark 26.1 Release. NAG Copyright 2016.
! .. Use Statements ..
Use nag_library, Only: ddisna, dstev, nag_wp, x02ajf, x04caf
! .. Implicit None Statement ..
Implicit None
! .. Parameters ..
Integer, Parameter :: nin = 5, nout = 6
! .. Local Scalars ..
Real (Kind=nag_wp) :: eerrbd, eps
Integer :: i, ifail, info, ldz, n
! .. Local Arrays ..
Real (Kind=nag_wp), Allocatable :: d(:), e(:), rcondz(:), work(:), &
z(:,:), zerrbd(:)
! .. Intrinsic Procedures ..
Intrinsic :: abs, max
! .. Executable Statements ..
Write (nout,*) 'F08JAF Example Program Results'
Write (nout,*)
! Skip heading in data file
Read (nin,*)
Read (nin,*) n
ldz = n
Allocate (d(n),e(n-1),rcondz(n),work(2*n-2),z(ldz,n),zerrbd(n))
! Read the diagonal and off-diagonal elements of the matrix A
! from data file
Read (nin,*) d(1:n)
Read (nin,*) e(1:n-1)
! Solve the symmetric tridiagonal eigenvalue problem
! The NAG name equivalent of dstev is f08jaf
Call dstev('Vectors',n,d,e,z,ldz,work,info)
If (info==0) Then
! Print solution
Write (nout,*) 'Eigenvalues'
Write (nout,99999) d(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(D(i)) ) = norm(A), and since the
! eigenvalues are returned in ascending order
! max( abs(D(i)) ) = max( abs(D(1)), abs(D(n)))
eps = x02ajf()
eerrbd = eps*max(abs(d(1)),abs(d(n)))
! Call DDISNA (F08FLF) to estimate reciprocal condition
! numbers for the eigenvectors
Call ddisna('Eigenvectors',n,n,d,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 DSTEV. INFO =', info
End If
99999 Format (3X,(8F8.4))
99998 Format (4X,1P,6E11.1)
99997 Format (1X,A,I4)
End Program f08jafe