Program f08yxfe
! F08YXF Example Program Text
! Mark 29.2 Release. NAG Copyright 2023.
! .. Use Statements ..
Use nag_library, Only: dznrm2, f06tff, f06thf, m01daf, m01edf, nag_wp, &
x04dbf, zgeqrf, zggbak, zggbal, zgghrd, zhgeqz, &
ztgevc, zungqr, zunmqr
! .. Implicit None Statement ..
Implicit None
! .. Parameters ..
Complex (Kind=nag_wp), Parameter :: cone = (1.0E0_nag_wp,0.0E0_nag_wp)
Complex (Kind=nag_wp), Parameter :: czero = (0.0E0_nag_wp,0.0E0_nag_wp)
Integer, Parameter :: nin = 5, nout = 6
Logical, Parameter :: prbal = .False., prhess = .False.
! .. Local Scalars ..
Complex (Kind=nag_wp) :: scal
Integer :: i, icols, ifail, ihi, ilo, info, &
irows, j, jwork, k, lda, ldb, ldvl, &
ldvr, lwork, m, n
Logical :: ileft, iright
Character (1) :: compq, compz, howmny, job, side
! .. Local Arrays ..
Complex (Kind=nag_wp), Allocatable :: a(:,:), alpha(:), b(:,:), beta(:), &
tau(:), v(:,:), vl(:,:), vr(:,:), &
work(:), zwork(:)
Real (Kind=nag_wp), Allocatable :: lscale(:), rscale(:), rwork(:)
Integer, Allocatable :: irank(:)
Logical, Allocatable :: select(:)
Character (1) :: clabs(1), rlabs(1)
! .. Intrinsic Procedures ..
Intrinsic :: abs, aimag, all, cmplx, conjg, &
maxloc, nint, real
! .. Executable Statements ..
Write (nout,*) 'F08YXF Example Program Results'
Flush (nout)
! ileft is TRUE if left eigenvectors are required
! iright is TRUE if right eigenvectors are required
ileft = .True.
iright = .True.
! Skip heading in data file
Read (nin,*)
Read (nin,*) n
lda = n
ldb = n
ldvl = n
ldvr = n
lwork = 6*n
Allocate (a(lda,n),alpha(n),b(ldb,n),beta(n),tau(n),vl(ldvl,ldvl), &
vr(ldvr,ldvr),work(lwork),lscale(n),rscale(n),rwork(6*n),select(n), &
irank(n),v(n,n))
! READ matrix A from data file
Read (nin,*)(a(i,1:n),i=1,n)
! READ matrix B from data file
Read (nin,*)(b(i,1:n),i=1,n)
! Balance matrix pair (A,B)
job = 'B'
! The NAG name equivalent of zggbal is f08wvf
Call zggbal(job,n,a,lda,b,ldb,ilo,ihi,lscale,rscale,rwork,info)
If (prbal) Then
! Matrix A after balancing
! ifail: behaviour on error exit
! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call x04dbf('General',' ',n,n,a,lda,'Bracketed','F7.4', &
'Matrix A after balancing','Integer',rlabs,'Integer',clabs,80,0, &
ifail)
Write (nout,*)
Flush (nout)
! Matrix B after balancing
ifail = 0
Call x04dbf('General',' ',n,n,b,ldb,'Bracketed','F7.4', &
'Matrix B after balancing','Integer',rlabs,'Integer',clabs,80,0, &
ifail)
Write (nout,*)
Flush (nout)
End If
! Reduce B to triangular form using QR
irows = ihi + 1 - ilo
icols = n + 1 - ilo
! The NAG name equivalent of zgeqrf is f08asf
Call zgeqrf(irows,icols,b(ilo,ilo),ldb,tau,work,lwork,info)
! Apply the orthogonal transformation to A
! The NAG name equivalent of zunmqr is f08auf
Call zunmqr('L','C',irows,icols,irows,b(ilo,ilo),ldb,tau,a(ilo,ilo),lda, &
work,lwork,info)
! Initialize VL (for left eigenvectors)
If (ileft) Then
Call f06thf('General',n,n,czero,cone,vl,ldvl)
Call f06tff('Lower',irows-1,irows-1,b(ilo+1,ilo),ldb,vl(ilo+1,ilo), &
ldvl)
! The NAG name equivalent of zungqr is f08atf
Call zungqr(irows,irows,irows,vl(ilo,ilo),ldvl,tau,work,lwork,info)
End If
! Initialize VR for right eigenvectors
If (iright) Then
Call f06thf('General',n,n,czero,cone,vr,ldvr)
End If
! Compute the generalized Hessenberg form of (A,B)
compq = 'V'
compz = 'V'
! The NAG name equivalent of zgghrd is f08wsf
Call zgghrd(compq,compz,n,ilo,ihi,a,lda,b,ldb,vl,ldvl,vr,ldvr,info)
If (prhess) Then
! Matrix A in generalized Hessenberg form
ifail = 0
Call x04dbf('General',' ',n,n,a,lda,'Bracketed','F7.3', &
'Matrix A in Hessenberg form','Integer',rlabs,'Integer',clabs,80,0, &
ifail)
Write (nout,*)
Flush (nout)
! Matrix B in generalized Hessenberg form
ifail = 0
Call x04dbf('General',' ',n,n,b,ldb,'Bracketed','F7.3', &
'Matrix B in Hessenberg form','Integer',rlabs,'Integer',clabs,80,0, &
ifail)
Write (nout,*)
Flush (nout)
End If
! Routine ZHGEQZ
! Workspace query: jwork = -1
jwork = -1
job = 'S'
! The NAG name equivalent of zhgeqz is f08xsf
Call zhgeqz(job,compq,compz,n,ilo,ihi,a,lda,b,ldb,alpha,beta,vl,ldvl,vr, &
ldvr,work,jwork,rwork,info)
lwork = nint(real(work(1)))
Allocate (zwork(lwork))
! Compute the generalized Schur form
! The NAG name equivalent of zhgeqz is f08xsf
Call zhgeqz(job,compq,compz,n,ilo,ihi,a,lda,b,ldb,alpha,beta,vl,ldvl,vr, &
ldvr,zwork,lwork,rwork,info)
! Sort and print generalized eigenvalues if none are infinite.
If (all(real(beta(1:n))>0.0_nag_wp)) Then
! Store absolute values of eigenvalues for ranking
work(1:n) = alpha(1:n)/beta(1:n)
rwork(1:n) = abs(work(1:n))
! Rank eigenvalues
ifail = 0
Call m01daf(rwork,1,n,'Descending',irank,ifail)
! Sort eigenvalues in work(1:n)
Call m01edf(work,1,n,irank,ifail)
Write (nout,99999)
Do i = 1, n
Write (nout,99998) i, '(', real(work(i)), ',', aimag(work(i)), ')'
End Do
Write (nout,*)
Flush (nout)
Else
irank(1:n) = (/(i,i=1,n)/)
End If
! Compute left and right generalized eigenvectors
! of the balanced matrix
howmny = 'B'
If (ileft .And. iright) Then
side = 'B'
Else If (ileft) Then
side = 'L'
Else If (iright) Then
side = 'R'
End If
! The NAG name equivalent of ztgevc is f08yxf
Call ztgevc(side,howmny,select,n,a,lda,b,ldb,vl,ldvl,vr,ldvr,n,m,work, &
rwork,info)
! Compute right eigenvectors of the original matrix
If (iright) Then
job = 'B'
side = 'R'
! The NAG name equivalent of zggbak is f08wwf
Call zggbak(job,side,n,ilo,ihi,lscale,rscale,n,vr,ldvr,info)
! Normalize the right eigenvectors
Do i = 1, n
j = irank(i)
rwork(1:n) = abs(vr(1:n,i))
k = maxloc(rwork(1:n),1)
scal = conjg(vr(k,i))/abs(vr(k,i))/dznrm2(n,vr(1,i),1)
v(1:n,j) = vr(1:n,i)*scal
v(k,j) = cmplx(real(v(k,j)),kind=nag_wp)
End Do
! Print the right eigenvectors
ifail = 0
Call x04dbf('General',' ',n,n,v,n,'Bracketed','F7.4', &
'Right eigenvectors','Integer',rlabs,'Integer',clabs,80,0,ifail)
Write (nout,*)
Flush (nout)
End If
! Compute left eigenvectors of the original matrix
If (ileft) Then
job = 'B'
side = 'L'
! The NAG name equivalent of zggbak is f08wwf
Call zggbak(job,side,n,ilo,ihi,lscale,rscale,n,vl,ldvl,info)
! Normalize the left eigenvectors
Do i = 1, n
j = irank(i)
rwork(1:n) = abs(vl(1:n,i))
k = maxloc(rwork(1:n),1)
scal = conjg(vl(k,i))/abs(vl(k,i))/dznrm2(n,vl(1,i),1)
v(1:n,j) = vl(1:n,i)*scal
v(k,j) = cmplx(real(v(k,j)),kind=nag_wp)
End Do
! Print the left eigenvectors
ifail = 0
Call x04dbf('General',' ',n,n,v,n,'Bracketed','F7.4', &
'Left eigenvectors','Integer',rlabs,'Integer',clabs,80,0,ifail)
End If
99999 Format (1X,/,1X,'Generalized eigenvalues')
99998 Format (1X,I4,5X,A,F7.3,A,F7.3,A)
End Program f08yxfe