Module zgges3_mod
! ZGGES3 Example Program Module:
! .. Implicit None Statement ..
Implicit None
! .. Accessibility Statements ..
Private
Public :: selctg
Contains
Function selctg(a, b)
! .. Use Statements ..
Use lapack_precision, Only: dp
! .. Implicit None Statement ..
Implicit None
! .. Function Return Value ..
Logical :: selctg
! .. Scalar Arguments ..
Complex (Kind=dp), Intent (In) :: a, b
! .. Intrinsic Procedures ..
Intrinsic :: abs
! .. Executable Statements ..
Continue
! Dummy function - it is not called by ZGGES3 when sorting is not required.
selctg = (abs(a)<6.0_dp*abs(b))
Return
End Function
End Module
Program zgges3_example
! ZGGES3 Example Program Text
! Copyright 2017, Numerical Algorithms Group Ltd. http://www.nag.com
! .. Use Statements ..
Use blas_interfaces, Only: zgemm
Use lapack_example_aux, Only: nagf_sort_cmplxvec_rank_rearrange, &
nagf_sort_realvec_rank, nagf_file_print_matrix_complex_gen, &
nagf_file_print_matrix_complex_gen_comp
Use lapack_interfaces, Only: zgges3, zlange
Use lapack_precision, Only: dp
Use zgges3_mod, Only: selctg
! .. Implicit None Statement ..
Implicit None
! .. Parameters ..
Integer, Parameter :: nb = 64, nin = 5, nout = 6
! .. Local Scalars ..
Complex (Kind=dp) :: alph, bet
Real (Kind=dp) :: normd, norme
Integer :: i, ifail, info, lda, ldb, ldc, ldd, lde, ldvsl, ldvsr, lwork, &
n, sdim
! .. Local Arrays ..
Complex (Kind=dp), Allocatable :: a(:, :), alpha(:), b(:, :), beta(:), &
c(:, :), d(:, :), e(:, :), vsl(:, :), vsr(:, :), work(:)
Complex (Kind=dp) :: wdum(1)
Real (Kind=dp), Allocatable :: rwork(:)
Integer, Allocatable :: irank(:)
Logical, Allocatable :: bwork(:)
Character (1) :: clabs(1), rlabs(1)
! .. Intrinsic Procedures ..
Intrinsic :: abs, all, cmplx, epsilon, max, nint, real
! .. Executable Statements ..
Write (nout, *) 'ZGGES3 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
Call zgges3('Vectors (left)', 'Vectors (right)', 'No sort', selctg, n, &
a, lda, b, ldb, sdim, alpha, beta, vsl, ldvsl, vsr, ldvsr, wdum, &
lwork, rwork, bwork, info)
! Make sure that there is enough workspace for block size nb.
lwork = max((nb+1)*n, nint(real(wdum(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)
! 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)
! 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)
! Find the generalized Schur form
Call zgges3('Vectors (left)', 'Vectors (right)', 'No sort', selctg, n, &
a, lda, b, ldb, sdim, alpha, beta, vsl, ldvsl, vsr, ldvsr, work, &
lwork, rwork, bwork, info)
If (info>0) Then
Write (nout, 100) 'Failure in ZGGES3. INFO =', info
Else
! 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)
norme = zlange('O', lde, n, e, lde, rwork)
If (normd>epsilon(1.0E0_dp)**0.75_dp .Or. norme>epsilon(1.0E0_dp)** &
0.75_dp) Then
Write (nout, *) 'Norm of A-(Q*S*Z^H) or norm of B-(Q*T*Z^H) &
&is much greater than 0.'
Write (nout, *) 'Schur factorization has failed.'
Else
! Print generalized eigenvalues
Write (nout, *) 'Generalized Eigenvalues'
If (all(abs(beta(1:n))>epsilon(1.0E0_dp))) Then
alpha(1:n) = alpha(1:n)/beta(1:n)
! Reorder eigenvalues by descending absolute value
rwork(1:n) = abs(alpha(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)
ifail = 0
Call nagf_file_print_matrix_complex_gen('Gen', ' ', 1, n, alpha, &
1, 'Eigenvalues:', ifail)
Write (nout, *)
Flush (nout)
Else
Do i = 1, n
If (beta(i)/=0.0_dp) Then
Write (nout, 110) i, alpha(i)/beta(i)
Else
Write (nout, 120) i
End If
End Do
End If
End If
End If
100 Format (1X, A, I4)
110 Format (1X, I2, 1X, '(', 1P, E11.4, ',', E11.4, ')')
120 Format (1X, I4, 'Eigenvalue is infinite')
End Program