Program zggevx_example
! ZGGEVX Example Program Text
! Copyright 2017, Numerical Algorithms Group Ltd. http://www.nag.com
! .. Use Statements ..
Use lapack_example_aux, Only: nagf_sort_realvec_rank_rearrange, &
nagf_blas_dpyth, nagf_sort_cmplxvec_rank_rearrange, &
nagf_sort_realvec_rank
Use lapack_interfaces, Only: zggevx
Use lapack_precision, Only: dp
! .. Implicit None Statement ..
Implicit None
! .. Parameters ..
Integer, Parameter :: nb = 64, nin = 5, nout = 6
Logical, Parameter :: verbose = .False.
! .. Local Scalars ..
Complex (Kind=dp) :: eig, scal
Real (Kind=dp) :: abnorm, abnrm, bbnrm, eps, small, tol
Integer :: i, ifail, ihi, ilo, info, j, k, lda, ldb, ldvr, lwork, n
! .. Local Arrays ..
Complex (Kind=dp), Allocatable :: a(:, :), alpha(:), b(:, :), beta(:), &
temp(:), vr(:, :), work(:)
Complex (Kind=dp) :: dummy(1, 1)
Real (Kind=dp), Allocatable :: lscale(:), rconde(:), rcondv(:), &
rscale(:), rwork(:)
Integer, Allocatable :: irank(:), iwork(:)
Logical, Allocatable :: bwork(:)
! .. Intrinsic Procedures ..
Intrinsic :: abs, epsilon, max, maxloc, nint, real, tiny
! .. Executable Statements ..
Write (nout, *) 'ZGGEVX Example Program Results'
! Skip heading in data file
Read (nin, *)
Read (nin, *) n
lda = n
ldb = n
ldvr = n
Allocate (a(lda,n), alpha(n), b(ldb,n), beta(n), vr(ldvr,n), lscale(n), &
rconde(n), rcondv(n), rscale(n), rwork(6*n), iwork(n+2), bwork(n), &
temp(n))
! Use routine workspace query to get optimal workspace.
lwork = -1
Call zggevx('Balance', 'No vectors (left)', 'Vectors (right)', &
'Both reciprocal condition numbers', n, a, lda, b, ldb, alpha, beta, &
dummy, 1, vr, ldvr, ilo, ihi, lscale, rscale, abnrm, bbnrm, rconde, &
rcondv, dummy, lwork, rwork, iwork, bwork, info)
! Make sure that there is enough workspace for block size nb.
lwork = max((nb+2*n)*n, nint(real(dummy(1,1))))
Allocate (work(lwork))
! Read in the matrices A and B
Read (nin, *)(a(i,1:n), i=1, n)
Read (nin, *)(b(i,1:n), i=1, n)
! Solve the generalized eigenvalue problem
Call zggevx('Balance', 'No vectors (left)', 'Vectors (right)', &
'Both reciprocal condition numbers', n, a, lda, b, ldb, alpha, beta, &
dummy, 1, vr, ldvr, ilo, ihi, lscale, rscale, abnrm, bbnrm, rconde, &
rcondv, work, lwork, rwork, iwork, bwork, info)
If (info>0) Then
Write (nout, *)
Write (nout, 100) 'Failure in ZGGEVX. INFO =', info
Else
! Compute the machine precision, the safe range parameter
! SMALL and sqrt(ABNRM**2+BBNRM**2)
eps = epsilon(1.0E0_dp)
small = tiny(1.0E0_dp)
abnorm = nagf_blas_dpyth(abnrm, bbnrm)
tol = eps*abnorm
! Reorder eigenvalues by descending absolute value
rwork(1:n) = abs(alpha(1:n)/beta(1:n))
Allocate (irank(n))
ifail = 0
Call nagf_sort_realvec_rank(rwork, 1, n, 'Descending', irank, ifail)
Call nagf_sort_cmplxvec_rank_rearrange(alpha, 1, n, irank, ifail)
Call nagf_sort_cmplxvec_rank_rearrange(beta, 1, n, irank, ifail)
Call nagf_sort_realvec_rank_rearrange(rconde, 1, n, irank, ifail)
! Reorder eigenvectors accordingly
Do j = 1, n
temp(1:n) = vr(j, 1:n)
Call nagf_sort_cmplxvec_rank_rearrange(temp, 1, n, irank, ifail)
vr(j, 1:n) = temp(1:n)
End Do
Call nagf_sort_realvec_rank_rearrange(rcondv, 1, n, irank, ifail)
! Print out eigenvalues and vectors and associated condition
! number and bounds
Write (nout, *)
Write (nout, *) 'Eigenvalues'
Write (nout, *)
If (verbose) Then
Write (nout, *) ' Eigenvalue rcond error'
Else
Write (nout, *) ' Eigenvalue'
End If
Do j = 1, n
! Print out information on the j-th eigenvalue
If ((abs(alpha(j)))*small>=abs(beta(j))) Then
If (rconde(j)>0.0_dp) Then
If (tol/rconde(j)<500.0_dp*eps) Then
Write (nout, 140) j, rconde(j), '-'
Else
Write (nout, 150) j, rconde(j), tol/rconde(j)
End If
Else
Write (nout, 140) j, rconde(j), 'Inf'
End If
Else
eig = alpha(j)/beta(j)
If (verbose) Then
If (rconde(j)>0.0_dp) Then
If (tol/rconde(j)<500.0_dp*eps) Then
Write (nout, 110) j, eig, rconde(j), '-'
Else
Write (nout, 120) j, eig, rconde(j), tol/rconde(j)
End If
Else
Write (nout, 110) j, eig, rconde(j), 'Inf'
End If
Else
Write (nout, 110) j, eig
End If
End If
End Do
Write (nout, *)
Write (nout, *) 'Eigenvectors'
Write (nout, *)
If (verbose) Then
Write (nout, *) ' Eigenvector rcond error'
Else
Write (nout, *) ' Eigenvector'
End If
Do j = 1, n
! Print information on j-th eigenvector
Write (nout, *)
! Re-normalize eigenvector, largest absolute element real (=1)
rwork(1:n) = abs(vr(1:n,j))
k = maxloc(rwork(1:n), 1)
scal = (1.0_dp, 0.0_dp)/vr(k, j)
vr(1:n, j) = vr(1:n, j)*scal
If (verbose) Then
If (rcondv(j)>0.0_dp) Then
If (tol/rcondv(j)<500.0_dp*eps) Then
Write (nout, 110) j, vr(1, j), rcondv(j), '-'
Else
Write (nout, 120) j, vr(1, j), rcondv(j), tol/rcondv(j)
End If
Else
Write (nout, 110) j, vr(1, j), rcondv(j), 'Inf'
End If
Else
Write (nout, 110) j, vr(1, j)
End If
Write (nout, 130) vr(2:n, j)
End Do
If (verbose) Then
Write (nout, *)
Write (nout, *) &
'Errors below 500*machine precision are not displayed'
End If
End If
100 Format (1X, A, I4)
110 Format (1X, I2, 1X, '(', 1P, E11.4, ',', E11.4, ')', 1X, 0P, F7.4, 4X, &
A)
120 Format (1X, I2, 1X, '(', 1P, E11.4, ',', E11.4, ')', 1X, 0P, F7.4, 1X, &
1P, E8.1)
130 Format (1X, 3X, '(', 1P, E11.4, ',', E11.4, ')')
140 Format (1X, I2, 1X, ' Infinite or undetermined', 1X, 0P, F7.4, 4X, A)
150 Format (1X, I2, 1X, ' Infinite or undetermined', 1X, 0P, F7.4, 1X, 1P, &
E8.1)
End Program