Program f08npfe
! F08NPF Example Program Text
! Mark 30.2 Release. NAG Copyright 2024.
! .. Use Statements ..
Use nag_library, Only: nag_wp, x02ajf, zgeevx
! .. Implicit None Statement ..
Implicit None
! .. Parameters ..
Integer, Parameter :: nb = 64, nin = 5, nout = 6
! .. Local Scalars ..
Real (Kind=nag_wp) :: abnrm, eps, tol
Integer :: i, ihi, ilo, info, j, lda, ldvl, &
ldvr, lwork, n
! .. Local Arrays ..
Complex (Kind=nag_wp), Allocatable :: a(:,:), vl(:,:), vr(:,:), w(:), &
work(:)
Complex (Kind=nag_wp) :: dummy(1)
Real (Kind=nag_wp), Allocatable :: rconde(:), rcondv(:), rwork(:), &
scale(:)
! .. Intrinsic Procedures ..
Intrinsic :: max, nint, real
! .. Executable Statements ..
Write (nout,*) 'F08NPF Example Program Results'
! Skip heading in data file
Read (nin,*)
Read (nin,*) n
lda = n
ldvl = n
ldvr = n
Allocate (a(lda,n),vl(ldvl,n),vr(ldvr,n),w(n),rconde(n),rcondv(n), &
rwork(2*n),scale(n))
! Use routine workspace query to get optimal workspace.
lwork = -1
! The NAG name equivalent of zgeevx is f08npf
Call zgeevx('Balance','Vectors (left)','Vectors (right)', &
'Both reciprocal condition numbers',n,a,lda,w,vl,ldvl,vr,ldvr,ilo,ihi, &
scale,abnrm,rconde,rcondv,dummy,lwork,rwork,info)
! Make sure that there is enough workspace for block size nb.
lwork = max((nb+1)*n,nint(real(dummy(1))))
Allocate (work(lwork))
! Read the matrix A from data file
Read (nin,*)(a(i,1:n),i=1,n)
! Solve the eigenvalue problem
! The NAG name equivalent of zgeevx is f08npf
Call zgeevx('Balance','Vectors (left)','Vectors (right)', &
'Both reciprocal condition numbers',n,a,lda,w,vl,ldvl,vr,ldvr,ilo,ihi, &
scale,abnrm,rconde,rcondv,work,lwork,rwork,info)
If (info==0) Then
! Compute the machine precision
eps = x02ajf()
tol = eps*abnrm
! Print the eigenvalues and vectors, and associated condition
! number and bounds
Write (nout,*)
Write (nout,*) 'Eigenvalues'
Write (nout,*)
Write (nout,*) ' Eigenvalue rcond error'
Do j = 1, n
! Print information on j-th eigenvalue
If (rconde(j)>0.0_nag_wp) Then
If (tol/rconde(j)<10.0_nag_wp*eps) Then
Write (nout,99999) j, w(j), rconde(j), '-'
Else
Write (nout,99998) j, w(j), rconde(j), tol/rconde(j)
End If
Else
Write (nout,99999) j, w(j), rconde(j), 'Inf'
End If
End Do
Write (nout,*)
Write (nout,*) 'Eigenvectors'
Write (nout,*)
Write (nout,*) ' Eigenvector rcond error'
Do j = 1, n
! Print information on j-th eigenvector
Write (nout,*)
! Make first real part component be positive
If (real(vr(1,j))<0.0_nag_wp) Then
vr(1:n,j) = -vr(1:n,j)
End If
If (rcondv(j)>0.0_nag_wp) Then
If (tol/rcondv(j)<10.0_nag_wp*eps) Then
Write (nout,99999) j, vr(1,j), rcondv(j), '-'
Else
Write (nout,99998) j, vr(1,j), rcondv(j), tol/rcondv(j)
End If
Else
Write (nout,99999) j, vr(1,j), rcondv(j), 'Inf'
End If
Write (nout,99997) vr(2:n,j)
End Do
Write (nout,*)
Write (nout,*) 'Errors below 10*machine precision are not displayed'
Else
Write (nout,*)
Write (nout,99996) 'Failure in ZGEEVX. INFO =', info
End If
99999 Format (1X,I2,1X,'(',1P,E11.4,',',E11.4,')',1X,0P,F7.4,4X,A)
99998 Format (1X,I2,1X,'(',1P,E11.4,',',E11.4,')',1X,0P,F7.4,1X,1P,E8.1)
99997 Format (1X,3X,'(',1P,E11.4,',',E11.4,')')
99996 Format (1X,A,I4)
End Program f08npfe