
NAMEzgees.f SYNOPSISFunctions/Subroutinessubroutine zgees (JOBVS, SORT, SELECT, N, A, LDA, SDIM, W, VS, LDVS, WORK, LWORK, RWORK, BWORK, INFO) Function/Subroutine Documentationsubroutine zgees (characterJOBVS, characterSORT, logical, externalSELECT, integerN, complex*16, dimension( lda, * )A, integerLDA, integerSDIM, complex*16, dimension( * )W, complex*16, dimension( ldvs, * )VS, integerLDVS, complex*16, dimension( * )WORK, integerLWORK, double precision, dimension( * )RWORK, logical, dimension( * )BWORK, integerINFO)ZGEES computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors for GE matrices Purpose:ZGEES computes for an NbyN complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z. This gives the Schur factorization A = Z*T*(Z**H). Optionally, it also orders the eigenvalues on the diagonal of the Schur form so that selected eigenvalues are at the top left. The leading columns of Z then form an orthonormal basis for the invariant subspace corresponding to the selected eigenvalues. A complex matrix is in Schur form if it is upper triangular. JOBVS
Author:
JOBVS is CHARACTER*1 = 'N': Schur vectors are not computed; = 'V': Schur vectors are computed.SORT SORT is CHARACTER*1 Specifies whether or not to order the eigenvalues on the diagonal of the Schur form. = 'N': Eigenvalues are not ordered: = 'S': Eigenvalues are ordered (see SELECT).SELECT SELECT is a LOGICAL FUNCTION of one COMPLEX*16 argument SELECT must be declared EXTERNAL in the calling subroutine. If SORT = 'S', SELECT is used to select eigenvalues to order to the top left of the Schur form. IF SORT = 'N', SELECT is not referenced. The eigenvalue W(j) is selected if SELECT(W(j)) is true.N N is INTEGER The order of the matrix A. N >= 0.A A is COMPLEX*16 array, dimension (LDA,N) On entry, the NbyN matrix A. On exit, A has been overwritten by its Schur form T.LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).SDIM SDIM is INTEGER If SORT = 'N', SDIM = 0. If SORT = 'S', SDIM = number of eigenvalues for which SELECT is true.W W is COMPLEX*16 array, dimension (N) W contains the computed eigenvalues, in the same order that they appear on the diagonal of the output Schur form T.VS VS is COMPLEX*16 array, dimension (LDVS,N) If JOBVS = 'V', VS contains the unitary matrix Z of Schur vectors. If JOBVS = 'N', VS is not referenced.LDVS LDVS is INTEGER The leading dimension of the array VS. LDVS >= 1; if JOBVS = 'V', LDVS >= N.WORK WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.LWORK LWORK is INTEGER The dimension of the array WORK. LWORK >= max(1,2*N). For good performance, LWORK must generally be larger. If LWORK = 1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.RWORK RWORK is DOUBLE PRECISION array, dimension (N)BWORK BWORK is LOGICAL array, dimension (N) Not referenced if SORT = 'N'.INFO INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value. > 0: if INFO = i, and i is <= N: the QR algorithm failed to compute all the eigenvalues; elements 1:ILO1 and i+1:N of W contain those eigenvalues which have converged; if JOBVS = 'V', VS contains the matrix which reduces A to its partially converged Schur form. = N+1: the eigenvalues could not be reordered because some eigenvalues were too close to separate (the problem is very illconditioned); = N+2: after reordering, roundoff changed values of some complex eigenvalues so that leading eigenvalues in the Schur form no longer satisfy SELECT = .TRUE.. This could also be caused by underflow due to scaling. Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Definition at line 197 of file zgees.f.
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