Program f08sqfe
! F08SQF Example Program Text
! Mark 30.1 Release. NAG Copyright 2024.
! .. Use Statements ..
Use nag_library, Only: ddisna, nag_wp, x02ajf, x04daf, zhegvd, &
zlanhe => f06ucf, ztrcon
! .. Implicit None Statement ..
Implicit None
! .. Parameters ..
Real (Kind=nag_wp), Parameter :: one = 1.0E+0_nag_wp
Integer, Parameter :: nb = 64, nin = 5, nout = 6
! .. Local Scalars ..
Complex (Kind=nag_wp) :: scal
Real (Kind=nag_wp) :: anorm, bnorm, eps, rcond, rcondb, &
t1, t2
Integer :: i, ifail, info, k, lda, ldb, liwork, &
lrwork, lwork, n
! .. Local Arrays ..
Complex (Kind=nag_wp), Allocatable :: a(:,:), b(:,:), work(:)
Complex (Kind=nag_wp) :: cdum(1)
Real (Kind=nag_wp), Allocatable :: eerbnd(:), rcondz(:), rwork(:), &
w(:), zerbnd(:)
Real (Kind=nag_wp) :: rdum(1)
Integer :: idum(1)
Integer, Allocatable :: iwork(:)
! .. Intrinsic Procedures ..
Intrinsic :: abs, conjg, max, maxloc, nint, real
! .. Executable Statements ..
Write (nout,*) 'F08SQF Example Program Results'
Write (nout,*)
! Skip heading in data file
Read (nin,*)
Read (nin,*) n
lda = n
ldb = n
Allocate (a(lda,n),b(ldb,n),eerbnd(n),rcondz(n),w(n),zerbnd(n))
! Use routine workspace query to get optimal workspace.
lwork = -1
liwork = -1
lrwork = -1
! The NAG name equivalent of zhegvd is f08sqf
Call zhegvd(2,'Vectors','Upper',n,a,lda,b,ldb,w,cdum,lwork,rdum,lrwork, &
idum,liwork,info)
! Make sure that there is enough workspace for block size nb.
lwork = max((nb+2+n)*n,nint(real(cdum(1))))
lrwork = max(1+(5+2*n)*n,nint(rdum(1)))
liwork = max(3+5*n,idum(1))
Allocate (work(lwork),rwork(lrwork),iwork(liwork))
! Read the upper triangular parts of the matrices A and B
Read (nin,*)(a(i,i:n),i=1,n)
Read (nin,*)(b(i,i:n),i=1,n)
! Compute the one-norms of the symmetric matrices A and B
! f06ucf is the NAG name equivalent of the LAPACK auxiliary zlanhe
anorm = zlanhe('One norm','Upper',n,a,lda,rwork)
bnorm = zlanhe('One norm','Upper',n,b,ldb,rwork)
! Solve the generalized Hermitian eigenvalue problem
! A*B*x = lambda*x (itype = 2)
! The NAG name equivalent of zhegvd is f08sqf
Call zhegvd(2,'Vectors','Upper',n,a,lda,b,ldb,w,work,lwork,rwork,lrwork, &
iwork,liwork,info)
If (info==0) Then
! Print solution
Write (nout,*) 'Eigenvalues'
Write (nout,99999) w(1:n)
Flush (nout)
! Normalize the eigenvectors, largest element real
Do i = 1, n
rwork(1:n) = abs(a(1:n,i))
k = maxloc(rwork(1:n),1)
scal = conjg(a(k,i))/abs(a(k,i))
a(1:n,i) = a(1:n,i)*scal
End Do
! ifail: behaviour on error exit
! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call x04daf('General',' ',n,n,a,lda,'Eigenvectors',ifail)
! Call ZTRCON (F07TUF) to estimate the reciprocal condition
! number of the Cholesky factor of B. Note that:
! cond(B) = 1/rcond**2
Call ztrcon('One norm','Upper','Non-unit',n,b,ldb,rcond,work,rwork, &
info)
! Print the reciprocal condition number of B
rcondb = rcond**2
Write (nout,*)
Write (nout,*) 'Estimate of reciprocal condition number for B'
Write (nout,99998) rcondb
Flush (nout)
! Get the machine precision, eps, and if rcondb is not less
! than eps**2, compute error estimates for the eigenvalues and
! eigenvectors
eps = x02ajf()
If (rcond>=eps) Then
! Call DDISNA (F08FLF) to estimate reciprocal condition
! numbers for the eigenvectors of (A*B - lambda*I)
Call ddisna('Eigenvectors',n,n,w,rcondz,info)
! Compute the error estimates for the eigenvalues and
! eigenvectors
t1 = one/rcond
t2 = anorm*bnorm
Do i = 1, n
eerbnd(i) = (t2+abs(w(i))/rcondb)
zerbnd(i) = t1*(t2/rcondz(i)+t1)
End Do
! Print the approximate error bounds for the eigenvalues
! and vectors
Write (nout,*)
Write (nout,*) 'Error estimates (relative to machine precision)'
Write (nout,*) 'for the eigenvalues:'
Write (nout,99998) eerbnd(1:n)
Write (nout,*)
Write (nout,*) 'for the eigenvectors:'
Write (nout,99998) zerbnd(1:n)
Else
Write (nout,*)
Write (nout,*) 'B is very ill-conditioned, error ', &
'estimates have not been computed'
End If
Else If (info>n) Then
i = info - n
Write (nout,99997) 'The leading minor of order ', i, &
' of B is not positive definite'
Else
Write (nout,99996) 'Failure in ZHEGVD. INFO =', info
End If
99999 Format (3X,(6F11.4))
99998 Format (4X,1P,6E11.1)
99997 Format (1X,A,I4,A)
99996 Format (1X,A,I4)
End Program f08sqfe