! ZGGESX Example Program Text
! Copyright 2017, Numerical Algorithms Group Ltd. http://www.nag.com
Module zggesx_mod
! ZGGESX Example Program Module:
! Parameters and User-defined Routines
! .. Use Statements ..
Use lapack_precision, Only: dp
! .. Implicit None Statement ..
Implicit None
! .. Accessibility Statements ..
Private
Public :: selctg
! .. Parameters ..
Integer, Parameter, Public :: nb = 64, nin = 5, nout = 6
Logical, Parameter, Public :: chkfac = .False., prcond = .False., &
prmat = .False.
Contains
Function selctg(a, b)
! Logical function selctg for use with ZGGESX (ZGGESX)
! Returns the value .TRUE. if the absolute value of the eigenvalue
! a/b < 6.0
! .. Function Return Value ..
Logical :: selctg
! .. Scalar Arguments ..
Complex (Kind=dp), Intent (In) :: a, b
! .. Intrinsic Procedures ..
Intrinsic :: abs
! .. Executable Statements ..
selctg = (abs(a)<6.0_dp*abs(b))
Return
End Function
End Module
Program zggesx_example
! ZGGESX Example Main Program
! .. Use Statements ..
Use blas_interfaces, Only: zgemm
Use zggesx_mod, Only: chkfac, nb, nin, nout, prcond, prmat, selctg
Use lapack_example_aux, Only: nagf_sort_realvec_rank, nagf_blas_dpyth, &
nagf_file_print_matrix_complex_gen_comp, &
nagf_sort_cmplxvec_rank_rearrange
Use lapack_interfaces, Only: zggesx, zlange
Use lapack_precision, Only: dp
! .. Implicit None Statement ..
Implicit None
! .. Local Scalars ..
Complex (Kind=dp) :: alph, bet
Real (Kind=dp) :: abnorm, anorm, bnorm, eps, normd, norme, tol
Integer :: i, ifail, info, lda, ldb, ldc, ldd, lde, ldvsl, ldvsr, &
liwork, lwork, n, sdim
Logical :: factor
! .. Local Arrays ..
Complex (Kind=dp), Allocatable :: a(:, :), alpha(:), b(:, :), beta(:), &
c(:, :), d(:, :), e(:, :), vsl(:, :), vsr(:, :), work(:)
Complex (Kind=dp) :: dummy(1)
Real (Kind=dp) :: rconde(2), rcondv(2)
Real (Kind=dp), Allocatable :: rwork(:)
Integer :: idum(1)
Integer, Allocatable :: iwork(:)
Logical, Allocatable :: bwork(:)
Character (1) :: clabs(1), rlabs(1)
! .. Intrinsic Procedures ..
Intrinsic :: abs, cmplx, epsilon, max, nint, real
! .. Executable Statements ..
Write (nout, *) 'ZGGESX Example Program Results'
Write (nout, *)
Flush (nout)
! Skip heading in data file
Read (nin, *)
Read (nin, *) n
lda = n
ldb = n
ldc = n
ldd = n
lde = n
ldvsl = n
ldvsr = n
Allocate (a(lda,n), alpha(n), b(ldb,n), beta(n), c(ldc,n), d(ldd,n), &
e(lde,n), vsl(ldvsl,n), vsr(ldvsr,n), rwork(8*n), bwork(n))
! Use routine workspace query to get optimal workspace.
lwork = -1
liwork = -1
Call zggesx('Vectors (left)', 'Vectors (right)', 'Sort', selctg, &
'Both reciprocal condition numbers', n, a, lda, b, ldb, sdim, alpha, &
beta, vsl, ldvsl, vsr, ldvsr, rconde, rcondv, dummy, lwork, rwork, &
idum, liwork, bwork, info)
! Make sure that there is enough workspace for block size nb.
lwork = max(n*nb+n*n/2, nint(real(dummy(1))))
liwork = max(n+2, idum(1))
Allocate (work(lwork), iwork(liwork))
! 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)
If (chkfac) Then
! Copy A and B into D and E respectively
d(1:n, 1:n) = a(1:n, 1:n)
e(1:n, 1:n) = b(1:n, 1:n)
End If
! Find the Frobenius norms of A and B
anorm = zlange('Frobenius', n, n, a, lda, rwork)
bnorm = zlange('Frobenius', n, n, b, ldb, rwork)
If (prmat) Then
! Print matrices A and B
! ifail: behaviour on error exit
! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call nagf_file_print_matrix_complex_gen_comp('General', ' ', n, n, a, &
lda, 'Bracketed', 'F8.4', 'Matrix A', 'Integer', rlabs, 'Integer', &
clabs, 80, 0, ifail)
Write (nout, *)
Flush (nout)
ifail = 0
Call nagf_file_print_matrix_complex_gen_comp('General', ' ', n, n, b, &
ldb, 'Bracketed', 'F8.4', 'Matrix B', 'Integer', rlabs, 'Integer', &
clabs, 80, 0, ifail)
Write (nout, *)
Flush (nout)
End If
factor = .True.
! Find the generalized Schur form
Call zggesx('Vectors (left)', 'Vectors (right)', 'Sort', selctg, &
'Both reciprocal condition numbers', n, a, lda, b, ldb, sdim, alpha, &
beta, vsl, ldvsl, vsr, ldvsr, rconde, rcondv, work, lwork, rwork, &
iwork, liwork, bwork, info)
If (info/=0 .And. info/=(n+2)) Then
Write (nout, 100) 'Failure in ZGGESX. INFO =', info
factor = .False.
Else If (chkfac) Then
! Compute A - Q*S*Z^H from the factorization of (A,B) and store in
! matrix D
alph = cmplx(1, kind=dp)
bet = cmplx(0, kind=dp)
Call zgemm('N', 'N', n, n, n, alph, vsl, ldvsl, a, lda, bet, c, ldc)
alph = cmplx(-1, kind=dp)
bet = cmplx(1, kind=dp)
Call zgemm('N', 'C', n, n, n, alph, c, ldc, vsr, ldvsr, bet, d, ldd)
! Compute B - Q*T*Z^H from the factorization of (A,B) and store in
! matrix E
alph = cmplx(1, kind=dp)
bet = cmplx(0, kind=dp)
Call zgemm('N', 'N', n, n, n, alph, vsl, ldvsl, b, ldb, bet, c, ldc)
alph = cmplx(-1, kind=dp)
bet = cmplx(1, kind=dp)
Call zgemm('N', 'C', n, n, n, alph, c, ldc, vsr, ldvsr, bet, e, lde)
! Find norms of matrices D and E and warn if either is too large
normd = zlange('O', ldd, n, d, ldd, rwork)
If (normd>epsilon(1.0E0_dp)**0.75_dp) Then
Write (nout, *) 'Norm of A-(Q*S*Z^T) is much greater than 0.'
factor = .False.
Write (nout, *) 'Schur factorization has failed.'
End If
norme = zlange('O', lde, n, e, lde, rwork)
If (norme>epsilon(1.0E0_dp)**0.75_dp) Then
Write (nout, *) 'Norm of B-(Q*T*Z^T) is much greater than 0.'
factor = .False.
End If
End If
If (factor) Then
! Print eigenvalue details
Write (nout, 100) 'Number of eigenvalues for which SELCTG is true = ', &
sdim, '(dimension of deflating subspaces)'
Write (nout, *)
! Print selected (finite) generalized eigenvalues
Write (nout, *) 'Selected generalized eigenvalues'
! 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 nagf_sort_realvec_rank(rwork, 1, sdim, 'Descending', iwork, &
ifail)
! Sort eigenvalues in work(1:n)
Call nagf_sort_cmplxvec_rank_rearrange(work, 1, sdim, iwork, ifail)
Do i = 1, sdim
Write (nout, 110) i, work(i)
End Do
If (info==(n+2)) Then
Write (nout, 120) '*** Note that rounding errors mean ', &
'that leading eigenvalues in the', &
'generalized Schur form no longer satisfy SELCTG = .TRUE.'
Write (nout, *)
End If
Flush (nout)
If (prcond) Then
! Compute the machine precision and sqrt(anorm**2+bnorm**2)
eps = epsilon(1.0E0_dp)
abnorm = nagf_blas_dpyth(anorm, bnorm)
tol = eps*abnorm
! Print out the reciprocal condition numbers and error bound for
! selected eigenvalues
Write (nout, *)
Write (nout, 130) &
'Reciprocal condition numbers for the average of the', &
'selected eigenvalues and their asymptotic error bound', &
'rcond-left = ', rconde(1), ', rcond-right = ', rconde(2), &
', error = ', tol/rconde(1)
Write (nout, *)
Write (nout, 130) &
'Reciprocal condition numbers for the deflating subspaces', &
'and their approximate asymptotic error bound', 'rcond-left = ', &
rcondv(1), ', rcond-right = ', rcondv(2), ', error = ', &
tol/rcondv(2)
End If
Else
Write (nout, *) 'Schur factorization has failed.'
End If
100 Format (1X, A, I4, /, 1X, A)
110 Format (1X, I2, 1X, '(', F6.2, ',', F6.2, ')')
120 Format (1X, 2A, /, 1X, A)
130 Format (1X, A, /, 1X, A, /, 1X, 3(A,1P,E8.1))
End Program