Program f08nufe
! F08NUF Example Program Text
! Mark 29.3 Release. NAG Copyright 2023.
! .. Use Statements ..
Use nag_library, Only: dznrm2, nag_wp, x04dbf, zgehrd, zhsein, zhseqr, &
zunmhr
! .. Implicit None Statement ..
Implicit None
! .. Parameters ..
Integer, Parameter :: nin = 5, nout = 6
! .. Local Scalars ..
Complex (Kind=nag_wp) :: scal
Real (Kind=nag_wp) :: thresh
Integer :: i, ifail, info, k, lda, ldc, ldh, &
ldvl, ldz, lwork, m, n
! .. Local Arrays ..
Complex (Kind=nag_wp), Allocatable :: a(:,:), c(:,:), h(:,:), tau(:), &
vl(:,:), w(:), work(:), z(:,:)
Real (Kind=nag_wp), Allocatable :: rwork(:)
Integer, Allocatable :: ifaill(:), ifailr(:)
Logical, Allocatable :: select(:)
Character (1) :: clabs(1), rlabs(1)
! .. Intrinsic Procedures ..
Intrinsic :: abs, aimag, conjg, maxloc, real
! .. Executable Statements ..
Write (nout,*) 'F08NUF Example Program Results'
Flush (nout)
! Skip heading in data file
Read (nin,*)
Read (nin,*) n
ldz = 1
lda = n
ldc = n
ldh = n
ldvl = n
lwork = 64*n
Allocate (a(lda,n),c(ldc,n),h(ldh,n),tau(n),vl(ldvl,n),w(n),work(lwork), &
z(ldz,1),rwork(n),ifaill(n),ifailr(n),select(n))
! Read A from data file
Read (nin,*)(a(i,1:n),i=1,n)
Read (nin,*) thresh
! Reduce A to upper Hessenberg form H = (Q**H)*A*Q
! The NAG name equivalent of zgehrd is f08nsf
Call zgehrd(n,1,n,a,lda,tau,work,lwork,info)
! Copy A to H
h(1:n,1:n) = a(1:n,1:n)
! Calculate the eigenvalues of H (same as A)
! The NAG name equivalent of zhseqr is f08psf
Call zhseqr('Eigenvalues','No vectors',n,1,n,h,ldh,w,z,ldz,work,lwork, &
info)
Write (nout,*)
If (info>0) Then
Write (nout,*) 'Failure to converge.'
Else
Write (nout,*) 'Eigenvalues'
Write (nout,99999)(' (',real(w(i)),',',aimag(w(i)),')',i=1,n)
Flush (nout)
Do i = 1, n
select(i) = real(w(i)) < thresh
End Do
! Calculate the eigenvectors of H (as specified by SELECT),
! storing the result in C
! The NAG name equivalent of zhsein is f08pxf
Call zhsein('Right','QR','No initial vectors',select,n,a,lda,w,vl, &
ldvl,c,ldc,n,m,work,rwork,ifaill,ifailr,info)
! Calculate the eigenvectors of A = Q * (eigenvectors of H)
! The NAG name equivalent of zunmhr is f08nuf
Call zunmhr('Left','No transpose',n,m,1,n,a,lda,tau,c,ldc,work,lwork, &
info)
! Print eigenvectors
Write (nout,*)
Flush (nout)
! Normalize the eigenvectors, largest element real
Do i = 1, m
rwork(1:n) = abs(c(1:n,i))
k = maxloc(rwork(1:n),1)
scal = conjg(c(k,i))/abs(c(k,i))/dznrm2(n,c(1,i),1)
c(1:n,i) = c(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 x04dbf('General',' ',n,m,c,ldc,'Bracketed','F7.4', &
'Contents of array C','Integer',rlabs,'Integer',clabs,80,0,ifail)
End If
99999 Format ((3X,4(A,F7.4,A,F7.4,A,:)))
End Program f08nufe