Program f08fafe
! F08FAF Example Program Text
! Mark 30.2 Release. NAG Copyright 2024.
! .. Use Statements ..
Use nag_library, Only: blas_damax_val, ddisna, dsyev, nag_wp, x02ajf, &
x04caf
! .. Implicit None Statement ..
Implicit None
! .. Parameters ..
Real (Kind=nag_wp), Parameter :: zero = 0.0_nag_wp
Integer, Parameter :: nb = 64, nin = 5, nout = 6
! .. Local Scalars ..
Real (Kind=nag_wp) :: eerrbd, eps, r
Integer :: i, ifail, info, k, lda, lwork, n
! .. Local Arrays ..
Real (Kind=nag_wp), Allocatable :: a(:,:), rcondz(:), w(:), work(:), &
zerrbd(:)
Real (Kind=nag_wp) :: dummy(1)
! .. Intrinsic Procedures ..
Intrinsic :: abs, max, nint
! .. Executable Statements ..
Write (nout,*) 'F08FAF Example Program Results'
Write (nout,*)
! Skip heading in data file
Read (nin,*)
Read (nin,*) n
lda = n
Allocate (a(lda,n),rcondz(n),w(n),zerrbd(n))
! Use routine workspace query to get optimal workspace.
! The NAG name equivalent of dsyev is f08faf
lwork = -1
Call dsyev('Vectors','Upper',n,a,lda,w,dummy,lwork,info)
! Make sure that there is enough workspace for block size nb.
lwork = max((nb+2)*n,nint(dummy(1)))
Allocate (work(lwork))
! Read the upper triangular part of the matrix A from data file
Read (nin,*)(a(i,i:n),i=1,n)
! Solve the symmetric eigenvalue problem
! The NAG name equivalent of dsyev is f08faf
Call dsyev('Vectors','Upper',n,a,lda,w,work,lwork,info)
If (info==0) Then
! Print solution
Write (nout,*) 'Eigenvalues'
Write (nout,99999) w(1:n)
Flush (nout)
! Normalize the eigenvectors: largest element positive
Do i = 1, n
Call blas_damax_val(n,a(1,i),1,k,r)
If (a(k,i)<zero) Then
a(1:n,i) = -a(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,a,lda,'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 DSYEV. INFO =', info
End If
99999 Format (3X,(8F8.4))
99998 Format (4X,1P,6E11.1)
99997 Format (1X,A,I4)
End Program f08fafe