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GNU/Linux |
CentOS 4.8 |
i386 |
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zgeesx(l) |
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ZGEESX - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z
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SUBROUTINE ZGEESX( |
JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM, W, VS, LDVS, RCONDE, RCONDV, WORK, LWORK, RWORK, BWORK, INFO ) | ||
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CHARACTER |
JOBVS, SENSE, SORT | ||
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INTEGER |
INFO, LDA, LDVS, LWORK, N, SDIM | ||
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DOUBLE |
PRECISION RCONDE, RCONDV | ||
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LOGICAL |
BWORK( * ) | ||
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DOUBLE |
PRECISION RWORK( * ) | ||
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COMPLEX*16 |
A( LDA, * ), VS( LDVS, * ), W( * ), WORK( * ) | ||
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LOGICAL |
SELECT | ||
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EXTERNAL |
SELECT |
ZGEESX computes for an N-by-N 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; computes a reciprocal condition number for the average of the selected eigenvalues (RCONDE); and computes a reciprocal condition number for the right invariant subspace corresponding to the selected eigenvalues (RCONDV). The leading columns of Z form an orthonormal basis for this invariant subspace.
For further explanation of the reciprocal condition numbers RCONDE and RCONDV, see Section 4.10 of the LAPACK Users’ Guide (where these quantities are called s and sep respectively).
A complex matrix is in Schur form if it is upper triangular.
JOBVS (input) CHARACTER*1
= ’N’: Schur
vectors are not computed;
= ’V’: Schur vectors are computed.
SORT (input) 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 (input) 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. An eigenvalue W(j) is selected if SELECT(W(j)) is true.
SENSE (input) CHARACTER*1
Determines which reciprocal
condition numbers are computed. = ’N’: None are
computed;
= ’E’: Computed for average of selected
eigenvalues only;
= ’V’: Computed for selected right invariant
subspace only;
= ’B’: Computed for both. If SENSE =
’E’, ’V’ or ’B’, SORT
must equal ’S’.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA, N)
On entry, the N-by-N matrix A. On exit, A is overwritten by its Schur form T.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
SDIM (output) INTEGER
If SORT = ’N’, SDIM = 0. If SORT = ’S’, SDIM = number of eigenvalues for which SELECT is true.
W (output) 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 (output) 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 (input) INTEGER
The leading dimension of the array VS. LDVS >= 1, and if JOBVS = ’V’, LDVS >= N.
RCONDE (output) DOUBLE PRECISION
If SENSE = ’E’ or ’B’, RCONDE contains the reciprocal condition number for the average of the selected eigenvalues. Not referenced if SENSE = ’N’ or ’V’.
RCONDV (output) DOUBLE PRECISION
If SENSE = ’V’ or ’B’, RCONDV contains the reciprocal condition number for the selected right invariant subspace. Not referenced if SENSE = ’N’ or ’E’.
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,2*N). Also, if SENSE = ’E’ or ’V’ or ’B’, LWORK >= 2*SDIM*(N-SDIM), where SDIM is the number of selected eigenvalues computed by this routine. Note that 2*SDIM*(N-SDIM) <= N*N/2. For good performance, LWORK must generally be larger.
RWORK (workspace) DOUBLE
PRECISION array, dimension (N)
BWORK (workspace) LOGICAL array, dimension (N)
Not referenced if SORT = ’N’.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal
value.
> 0: if INFO = i, and i is
<= N: the QR algorithm failed to compute all the
eigenvalues; elements 1:ILO-1 and i+1:N of W contain those
eigenvalues which have converged; if JOBVS =
’V’, VS contains the transformation 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
ill-conditioned); = 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.
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zgeesx(l) | |