--- rpl/lapack/lapack/dgees.f 2010/12/21 13:53:25 1.7
+++ rpl/lapack/lapack/dgees.f 2011/11/21 20:42:50 1.8
@@ -1,10 +1,225 @@
+*> \brief DGEES 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 DGEES + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DGEES( JOBVS, SORT, SELECT, N, A, LDA, SDIM, WR, WI,
+* VS, LDVS, WORK, LWORK, BWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER JOBVS, SORT
+* INTEGER INFO, LDA, LDVS, LWORK, N, SDIM
+* ..
+* .. Array Arguments ..
+* LOGICAL BWORK( * )
+* DOUBLE PRECISION A( LDA, * ), VS( LDVS, * ), WI( * ), WORK( * ),
+* $ WR( * )
+* ..
+* .. Function Arguments ..
+* LOGICAL SELECT
+* EXTERNAL SELECT
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DGEES computes for an N-by-N real nonsymmetric matrix A, the
+*> eigenvalues, the real Schur form T, and, optionally, the matrix of
+*> Schur vectors Z. This gives the Schur factorization A = Z*T*(Z**T).
+*>
+*> Optionally, it also orders the eigenvalues on the diagonal of the
+*> real 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 matrix is in real Schur form if it is upper quasi-triangular with
+*> 1-by-1 and 2-by-2 blocks. 2-by-2 blocks will be standardized in the
+*> form
+*> [ a b ]
+*> [ c a ]
+*>
+*> where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc).
+*> \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 two DOUBLE PRECISION arguments
+*> SELECT must be declared EXTERNAL in the calling subroutine.
+*> If SORT = 'S', SELECT is used to select eigenvalues to sort
+*> to the top left of the Schur form.
+*> If SORT = 'N', SELECT is not referenced.
+*> An eigenvalue WR(j)+sqrt(-1)*WI(j) is selected if
+*> SELECT(WR(j),WI(j)) is true; i.e., if either one of a complex
+*> conjugate pair of eigenvalues is selected, then both complex
+*> eigenvalues are selected.
+*> Note that a selected complex eigenvalue may no longer
+*> satisfy SELECT(WR(j),WI(j)) = .TRUE. after ordering, since
+*> ordering may change the value of complex eigenvalues
+*> (especially if the eigenvalue is ill-conditioned); in this
+*> case INFO is set to N+2 (see INFO below).
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is DOUBLE PRECISION array, dimension (LDA,N)
+*> On entry, the N-by-N matrix A.
+*> On exit, A has been overwritten by its real 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 (after sorting)
+*> for which SELECT is true. (Complex conjugate
+*> pairs for which SELECT is true for either
+*> eigenvalue count as 2.)
+*> \endverbatim
+*>
+*> \param[out] WR
+*> \verbatim
+*> WR is DOUBLE PRECISION array, dimension (N)
+*> \endverbatim
+*>
+*> \param[out] WI
+*> \verbatim
+*> WI is DOUBLE PRECISION array, dimension (N)
+*> WR and WI contain the real and imaginary parts,
+*> respectively, of the computed eigenvalues in the same order
+*> that they appear on the diagonal of the output Schur form T.
+*> Complex conjugate pairs of eigenvalues will appear
+*> consecutively with the eigenvalue having the positive
+*> imaginary part first.
+*> \endverbatim
+*>
+*> \param[out] VS
+*> \verbatim
+*> VS is DOUBLE PRECISION array, dimension (LDVS,N)
+*> If JOBVS = 'V', VS contains the orthogonal 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; if
+*> JOBVS = 'V', LDVS >= N.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
+*> On exit, if INFO = 0, WORK(1) contains the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER
+*> The dimension of the array WORK. LWORK >= max(1,3*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.
+*> \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 WR and WI
+*> 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 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 doubleGEeigen
+*
+* =====================================================================
SUBROUTINE DGEES( JOBVS, SORT, SELECT, N, A, LDA, SDIM, WR, WI,
$ VS, LDVS, WORK, LWORK, BWORK, INFO )
*
-* -- LAPACK driver routine (version 3.2) --
+* -- 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..--
-* November 2006
+* November 2011
*
* .. Scalar Arguments ..
CHARACTER JOBVS, SORT
@@ -20,121 +235,6 @@
EXTERNAL SELECT
* ..
*
-* Purpose
-* =======
-*
-* DGEES computes for an N-by-N real nonsymmetric matrix A, the
-* eigenvalues, the real Schur form T, and, optionally, the matrix of
-* Schur vectors Z. This gives the Schur factorization A = Z*T*(Z**T).
-*
-* Optionally, it also orders the eigenvalues on the diagonal of the
-* real 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 matrix is in real Schur form if it is upper quasi-triangular with
-* 1-by-1 and 2-by-2 blocks. 2-by-2 blocks will be standardized in the
-* form
-* [ a b ]
-* [ c a ]
-*
-* where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc).
-*
-* 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 two DOUBLE PRECISION arguments
-* SELECT must be declared EXTERNAL in the calling subroutine.
-* If SORT = 'S', SELECT is used to select eigenvalues to sort
-* to the top left of the Schur form.
-* If SORT = 'N', SELECT is not referenced.
-* An eigenvalue WR(j)+sqrt(-1)*WI(j) is selected if
-* SELECT(WR(j),WI(j)) is true; i.e., if either one of a complex
-* conjugate pair of eigenvalues is selected, then both complex
-* eigenvalues are selected.
-* Note that a selected complex eigenvalue may no longer
-* satisfy SELECT(WR(j),WI(j)) = .TRUE. after ordering, since
-* ordering may change the value of complex eigenvalues
-* (especially if the eigenvalue is ill-conditioned); in this
-* case INFO is set to N+2 (see INFO below).
-*
-* N (input) INTEGER
-* The order of the matrix A. N >= 0.
-*
-* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
-* On entry, the N-by-N matrix A.
-* On exit, A has been overwritten by its real 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 (after sorting)
-* for which SELECT is true. (Complex conjugate
-* pairs for which SELECT is true for either
-* eigenvalue count as 2.)
-*
-* WR (output) DOUBLE PRECISION array, dimension (N)
-* WI (output) DOUBLE PRECISION array, dimension (N)
-* WR and WI contain the real and imaginary parts,
-* respectively, of the computed eigenvalues in the same order
-* that they appear on the diagonal of the output Schur form T.
-* Complex conjugate pairs of eigenvalues will appear
-* consecutively with the eigenvalue having the positive
-* imaginary part first.
-*
-* VS (output) DOUBLE PRECISION array, dimension (LDVS,N)
-* If JOBVS = 'V', VS contains the orthogonal matrix Z of Schur
-* vectors.
-* If JOBVS = 'N', VS is not referenced.
-*
-* LDVS (input) INTEGER
-* The leading dimension of the array VS. LDVS >= 1; if
-* JOBVS = 'V', LDVS >= N.
-*
-* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
-* On exit, if INFO = 0, WORK(1) contains the optimal LWORK.
-*
-* LWORK (input) INTEGER
-* The dimension of the array WORK. LWORK >= max(1,3*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.
-*
-* 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 WR and WI
-* 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 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 ..