--- rpl/lapack/lapack/zgeesx.f 2010/12/21 13:53:43 1.8
+++ rpl/lapack/lapack/zgeesx.f 2011/11/21 20:43:08 1.9
@@ -1,11 +1,248 @@
+*> \brief ZGEESX computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors for GE matrices
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZGEESX + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZGEESX( JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM, W,
+* VS, LDVS, RCONDE, RCONDV, WORK, LWORK, RWORK,
+* BWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER JOBVS, SENSE, SORT
+* INTEGER INFO, LDA, LDVS, LWORK, N, SDIM
+* DOUBLE PRECISION RCONDE, RCONDV
+* ..
+* .. Array Arguments ..
+* LOGICAL BWORK( * )
+* DOUBLE PRECISION RWORK( * )
+* COMPLEX*16 A( LDA, * ), VS( LDVS, * ), W( * ), WORK( * )
+* ..
+* .. Function Arguments ..
+* LOGICAL SELECT
+* EXTERNAL SELECT
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> 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.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] JOBVS
+*> \verbatim
+*> JOBVS is CHARACTER*1
+*> = 'N': Schur vectors are not computed;
+*> = 'V': Schur vectors are computed.
+*> \endverbatim
+*>
+*> \param[in] SORT
+*> \verbatim
+*> 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).
+*> \endverbatim
+*>
+*> \param[in] SELECT
+*> \verbatim
+*> SELECT is procedure) 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.
+*> \endverbatim
+*>
+*> \param[in] SENSE
+*> \verbatim
+*> SENSE is 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'.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is COMPLEX*16 array, dimension (LDA, N)
+*> On entry, the N-by-N matrix A.
+*> On exit, A is overwritten by its Schur form T.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] SDIM
+*> \verbatim
+*> SDIM is INTEGER
+*> If SORT = 'N', SDIM = 0.
+*> If SORT = 'S', SDIM = number of eigenvalues for which
+*> SELECT is true.
+*> \endverbatim
+*>
+*> \param[out] W
+*> \verbatim
+*> 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.
+*> \endverbatim
+*>
+*> \param[out] VS
+*> \verbatim
+*> 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.
+*> \endverbatim
+*>
+*> \param[in] LDVS
+*> \verbatim
+*> LDVS is INTEGER
+*> The leading dimension of the array VS. LDVS >= 1, and if
+*> JOBVS = 'V', LDVS >= N.
+*> \endverbatim
+*>
+*> \param[out] RCONDE
+*> \verbatim
+*> RCONDE is 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'.
+*> \endverbatim
+*>
+*> \param[out] RCONDV
+*> \verbatim
+*> RCONDV is 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'.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
+*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is 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. Note also
+*> that an error is only returned if LWORK < max(1,2*N), but if
+*> SENSE = 'E' or 'V' or 'B' this may not be large enough.
+*> For good performance, LWORK must generally be larger.
+*>
+*> If LWORK = -1, then a workspace query is assumed; the routine
+*> only calculates upper bound on the optimal size of the
+*> array WORK, returns this value as the first entry of the WORK
+*> array, and no error message related to LWORK is issued by
+*> XERBLA.
+*> \endverbatim
+*>
+*> \param[out] RWORK
+*> \verbatim
+*> RWORK is DOUBLE PRECISION array, dimension (N)
+*> \endverbatim
+*>
+*> \param[out] BWORK
+*> \verbatim
+*> BWORK is LOGICAL array, dimension (N)
+*> Not referenced if SORT = 'N'.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is 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.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup complex16GEeigen
+*
+* =====================================================================
SUBROUTINE ZGEESX( JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM, W,
$ VS, LDVS, RCONDE, RCONDV, WORK, LWORK, RWORK,
$ BWORK, INFO )
*
-* -- LAPACK driver routine (version 3.2.2) --
+* -- LAPACK driver routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* June 2010
+* November 2011
*
* .. Scalar Arguments ..
CHARACTER JOBVS, SENSE, SORT
@@ -22,133 +259,6 @@
EXTERNAL SELECT
* ..
*
-* Purpose
-* =======
-*
-* 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.
-*
-* Arguments
-* =========
-*
-* 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 (external procedure) 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 (MAX(1,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. Note also
-* that an error is only returned if LWORK < max(1,2*N), but if
-* SENSE = 'E' or 'V' or 'B' this may not be large enough.
-* For good performance, LWORK must generally be larger.
-*
-* If LWORK = -1, then a workspace query is assumed; the routine
-* only calculates upper bound on the optimal size of the
-* array WORK, returns this value as the first entry of the WORK
-* array, and no error message related to LWORK is issued by
-* XERBLA.
-*
-* 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.
-*
* =====================================================================
*
* .. Parameters ..