```    Program f08wafe

!     F08WAF Example Program Text

!     Mark 26.2 Release. NAG Copyright 2018.

!     .. Use Statements ..
Use nag_library, Only: dggev, dnrm2, m01def, m01eaf, nag_wp, x02ajf,     &
x02amf
!     .. 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 ..
Complex (Kind=nag_wp)            :: eig
Real (Kind=nag_wp)               :: d, scal_i, scal_r, small
Integer                          :: i, ifail, info, j, k, lda, ldb,      &
ldvr, lwork, n
Logical                          :: pair
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: a(:,:), alphai(:), alphar(:),        &
b(:,:), beta(:), vr(:,:), vr_row(:), &
work(:)
Real (Kind=nag_wp)               :: dummy(1,1)
Integer, Allocatable             :: irank(:)
!     .. Intrinsic Procedures ..
Intrinsic                        :: abs, all, cmplx, max, maxloc, nint,  &
sqrt
!     .. Executable Statements ..
Write (nout,*) 'F08WAF Example Program Results'
!     Skip heading in data file
lda = n
ldb = n
ldvr = n
Allocate (a(lda,n),alphai(n),alphar(n),b(ldb,n),beta(n),vr(ldvr,n),      &
irank(n))

!     Use routine workspace query to get optimal workspace.
lwork = -1
!     The NAG name equivalent of dggev is f08waf
Call dggev('No left vectors','Vectors (right)',n,a,lda,b,ldb,alphar,     &
alphai,beta,dummy,1,vr,ldvr,dummy,lwork,info)

!     Make sure that there is enough workspace for block size nb.
lwork = max((nb+7)*n,nint(dummy(1,1)))
Allocate (work(lwork))

!     Read in the matrices A and B

!     Solve the generalized eigenvalue problem

!     The NAG name equivalent of dggev is f08waf
Call dggev('No left vectors','Vectors (right)',n,a,lda,b,ldb,alphar,     &
alphai,beta,dummy,1,vr,ldvr,work,lwork,info)

If (info>0) Then
Write (nout,*)
Write (nout,99999) 'Failure in DGGEV. INFO =', info
Else
!       If beta(:) > eps, Order eigenvalues by ascending real parts
!       and then by ascending imaginary parts
If (all(abs(beta(1:n))>x02ajf())) Then
!         Make sure real parts of conjugate pair are exactly equal
j = 0
Do While (j<n)
j = j + 1
If (alphai(j)/=zero) Then
alphar(j+1) = alphar(j)
alphai(j+1) = -alphai(j)
beta(j+1) = beta(j)
j = j + 1
End If
End Do
work(1:n) = alphar(1:n)/beta(1:n)
work(n+1:2*n) = alphai(1:n)/beta(1:n)
ifail = 0
Call m01def(work,n,1,n,1,2,'Ascending',irank,ifail)
Call m01eaf(alphar,1,n,irank,ifail)
Call m01eaf(alphai,1,n,irank,ifail)
Call m01eaf(beta,1,n,irank,ifail)
!         Order the eigenvectors in the same way
Allocate (vr_row(n))
Do j = 1, n
vr_row(1:n) = vr(j,1:n)
Call m01eaf(vr_row,1,n,irank,ifail)
vr(j,1:n) = vr_row(1:n)
End Do
Deallocate (vr_row)
End If
small = x02amf()
pair = .False.
Do j = 1, n
Write (nout,*)
If ((abs(alphar(j))+abs(alphai(j)))*small>=abs(beta(j))) Then
Write (nout,99998) 'Eigenvalue(', j, ')',                          &
' is numerically infinite or undetermined', 'ALPHAR(', j,        &
') = ', alphar(j), ', ALPHAI(', j, ') = ', alphai(j), ', BETA(', &
j, ') = ', beta(j)
Else
If (alphai(j)==zero) Then
Write (nout,99997) 'Eigenvalue(', j, ') = ', alphar(j)/beta(j)
Else
eig = cmplx(alphar(j),alphai(j),kind=nag_wp)/                    &
cmplx(beta(j),kind=nag_wp)
Write (nout,99996) 'Eigenvalue(', j, ') = ', eig
End If
End If
Write (nout,*)
Write (nout,99995) 'Eigenvector(', j, ')'
If (alphai(j)==zero) Then
!           Let largest element be positive
work(1:n) = abs(vr(1:n,j))
k = maxloc(work(1:n),1)
If (vr(k,j)<zero) Then
vr(1:n,j) = -vr(1:n,j)
End If
d = dnrm2(n,vr(1,j),1)
vr(1:n,j) = vr(1:n,j)/d
Write (nout,99994)(vr(i,j),i=1,n)
Else
If (pair) Then
Write (nout,99993)(vr(i,j-1),-vr(i,j),i=1,n)
Else
!             Let largest element be real (and positive).
work(1:n) = vr(1:n,j)**2 + vr(1:n,j+1)**2
work(1:n) = sqrt(work(1:n))
d = dnrm2(n,work,1)
k = maxloc(work(1:n),1)
scal_r = (vr(k,j)/work(k))/d
scal_i = (-vr(k,j+1)/work(k))/d
work(1:n) = vr(1:n,j)
vr(1:n,j) = scal_r*work(1:n) - scal_i*vr(1:n,j+1)
vr(1:n,j+1) = scal_r*vr(1:n,j+1) + scal_i*work(1:n)
Write (nout,99993)(vr(i,j),vr(i,j+1),i=1,n)
End If
pair = .Not. pair
End If
End Do

End If

99999 Format (1X,A,I4)
99998 Format (1X,A,I2,2A,/,1X,2(A,I2,A,F11.3,3X),A,I2,A,F11.3)
99997 Format (1X,A,I2,A,F11.3)
99996 Format (1X,A,I2,A,'(',F11.3,',',F11.3,')')
99995 Format (1X,A,I2,A)
99994 Format (1X,F11.5)
99993 Format (1X,'(',F11.5,',',F11.5,')')
End Program f08wafe
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