--- rpl/lapack/lapack/zgges.f 2010/12/21 13:53:44 1.7
+++ rpl/lapack/lapack/zgges.f 2011/11/21 20:43:10 1.8
@@ -1,11 +1,279 @@
+*> \brief ZGGES 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 ZGGES + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZGGES( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, LDB,
+* SDIM, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK,
+* LWORK, RWORK, BWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER JOBVSL, JOBVSR, SORT
+* INTEGER INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N, SDIM
+* ..
+* .. Array Arguments ..
+* LOGICAL BWORK( * )
+* DOUBLE PRECISION RWORK( * )
+* COMPLEX*16 A( LDA, * ), ALPHA( * ), B( LDB, * ),
+* $ BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, * ),
+* $ WORK( * )
+* ..
+* .. Function Arguments ..
+* LOGICAL SELCTG
+* EXTERNAL SELCTG
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZGGES computes for a pair of N-by-N complex nonsymmetric matrices
+*> (A,B), the generalized eigenvalues, the generalized complex Schur
+*> form (S, T), and optionally left and/or right Schur vectors (VSL
+*> and VSR). This gives the generalized Schur factorization
+*>
+*> (A,B) = ( (VSL)*S*(VSR)**H, (VSL)*T*(VSR)**H )
+*>
+*> where (VSR)**H is the conjugate-transpose of VSR.
+*>
+*> Optionally, it also orders the eigenvalues so that a selected cluster
+*> of eigenvalues appears in the leading diagonal blocks of the upper
+*> triangular matrix S and the upper triangular matrix T. The leading
+*> columns of VSL and VSR then form an unitary basis for the
+*> corresponding left and right eigenspaces (deflating subspaces).
+*>
+*> (If only the generalized eigenvalues are needed, use the driver
+*> ZGGEV instead, which is faster.)
+*>
+*> A generalized eigenvalue for a pair of matrices (A,B) is a scalar w
+*> or a ratio alpha/beta = w, such that A - w*B is singular. It is
+*> usually represented as the pair (alpha,beta), as there is a
+*> reasonable interpretation for beta=0, and even for both being zero.
+*>
+*> A pair of matrices (S,T) is in generalized complex Schur form if S
+*> and T are upper triangular and, in addition, the diagonal elements
+*> of T are non-negative real numbers.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] JOBVSL
+*> \verbatim
+*> JOBVSL is CHARACTER*1
+*> = 'N': do not compute the left Schur vectors;
+*> = 'V': compute the left Schur vectors.
+*> \endverbatim
+*>
+*> \param[in] JOBVSR
+*> \verbatim
+*> JOBVSR is CHARACTER*1
+*> = 'N': do not compute the right Schur vectors;
+*> = 'V': compute the right Schur vectors.
+*> \endverbatim
+*>
+*> \param[in] SORT
+*> \verbatim
+*> SORT is CHARACTER*1
+*> Specifies whether or not to order the eigenvalues on the
+*> diagonal of the generalized Schur form.
+*> = 'N': Eigenvalues are not ordered;
+*> = 'S': Eigenvalues are ordered (see SELCTG).
+*> \endverbatim
+*>
+*> \param[in] SELCTG
+*> \verbatim
+*> SELCTG is procedure) LOGICAL FUNCTION of two COMPLEX*16 arguments
+*> SELCTG must be declared EXTERNAL in the calling subroutine.
+*> If SORT = 'N', SELCTG is not referenced.
+*> If SORT = 'S', SELCTG is used to select eigenvalues to sort
+*> to the top left of the Schur form.
+*> An eigenvalue ALPHA(j)/BETA(j) is selected if
+*> SELCTG(ALPHA(j),BETA(j)) is true.
+*>
+*> Note that a selected complex eigenvalue may no longer satisfy
+*> SELCTG(ALPHA(j),BETA(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 matrices A, B, VSL, and VSR. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is COMPLEX*16 array, dimension (LDA, N)
+*> On entry, the first of the pair of matrices.
+*> On exit, A has been overwritten by its generalized Schur
+*> form S.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*> B is COMPLEX*16 array, dimension (LDB, N)
+*> On entry, the second of the pair of matrices.
+*> On exit, B has been overwritten by its generalized Schur
+*> form T.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> The leading dimension of B. LDB >= 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 SELCTG is true.
+*> \endverbatim
+*>
+*> \param[out] ALPHA
+*> \verbatim
+*> ALPHA is COMPLEX*16 array, dimension (N)
+*> \endverbatim
+*>
+*> \param[out] BETA
+*> \verbatim
+*> BETA is COMPLEX*16 array, dimension (N)
+*> On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the
+*> generalized eigenvalues. ALPHA(j), j=1,...,N and BETA(j),
+*> j=1,...,N are the diagonals of the complex Schur form (A,B)
+*> output by ZGGES. The BETA(j) will be non-negative real.
+*>
+*> Note: the quotients ALPHA(j)/BETA(j) may easily over- or
+*> underflow, and BETA(j) may even be zero. Thus, the user
+*> should avoid naively computing the ratio alpha/beta.
+*> However, ALPHA will be always less than and usually
+*> comparable with norm(A) in magnitude, and BETA always less
+*> than and usually comparable with norm(B).
+*> \endverbatim
+*>
+*> \param[out] VSL
+*> \verbatim
+*> VSL is COMPLEX*16 array, dimension (LDVSL,N)
+*> If JOBVSL = 'V', VSL will contain the left Schur vectors.
+*> Not referenced if JOBVSL = 'N'.
+*> \endverbatim
+*>
+*> \param[in] LDVSL
+*> \verbatim
+*> LDVSL is INTEGER
+*> The leading dimension of the matrix VSL. LDVSL >= 1, and
+*> if JOBVSL = 'V', LDVSL >= N.
+*> \endverbatim
+*>
+*> \param[out] VSR
+*> \verbatim
+*> VSR is COMPLEX*16 array, dimension (LDVSR,N)
+*> If JOBVSR = 'V', VSR will contain the right Schur vectors.
+*> Not referenced if JOBVSR = 'N'.
+*> \endverbatim
+*>
+*> \param[in] LDVSR
+*> \verbatim
+*> LDVSR is INTEGER
+*> The leading dimension of the matrix VSR. LDVSR >= 1, and
+*> if JOBVSR = 'V', LDVSR >= N.
+*> \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).
+*> 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] RWORK
+*> \verbatim
+*> RWORK is DOUBLE PRECISION array, dimension (8*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.
+*> =1,...,N:
+*> The QZ iteration failed. (A,B) are not in Schur
+*> form, but ALPHA(j) and BETA(j) should be correct for
+*> j=INFO+1,...,N.
+*> > N: =N+1: other than QZ iteration failed in ZHGEQZ
+*> =N+2: after reordering, roundoff changed values of
+*> some complex eigenvalues so that leading
+*> eigenvalues in the Generalized Schur form no
+*> longer satisfy SELCTG=.TRUE. This could also
+*> be caused due to scaling.
+*> =N+3: reordering falied in ZTGSEN.
+*> \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 ZGGES( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, LDB,
$ SDIM, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK,
$ LWORK, RWORK, 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 JOBVSL, JOBVSR, SORT
@@ -23,153 +291,6 @@
EXTERNAL SELCTG
* ..
*
-* Purpose
-* =======
-*
-* ZGGES computes for a pair of N-by-N complex nonsymmetric matrices
-* (A,B), the generalized eigenvalues, the generalized complex Schur
-* form (S, T), and optionally left and/or right Schur vectors (VSL
-* and VSR). This gives the generalized Schur factorization
-*
-* (A,B) = ( (VSL)*S*(VSR)**H, (VSL)*T*(VSR)**H )
-*
-* where (VSR)**H is the conjugate-transpose of VSR.
-*
-* Optionally, it also orders the eigenvalues so that a selected cluster
-* of eigenvalues appears in the leading diagonal blocks of the upper
-* triangular matrix S and the upper triangular matrix T. The leading
-* columns of VSL and VSR then form an unitary basis for the
-* corresponding left and right eigenspaces (deflating subspaces).
-*
-* (If only the generalized eigenvalues are needed, use the driver
-* ZGGEV instead, which is faster.)
-*
-* A generalized eigenvalue for a pair of matrices (A,B) is a scalar w
-* or a ratio alpha/beta = w, such that A - w*B is singular. It is
-* usually represented as the pair (alpha,beta), as there is a
-* reasonable interpretation for beta=0, and even for both being zero.
-*
-* A pair of matrices (S,T) is in generalized complex Schur form if S
-* and T are upper triangular and, in addition, the diagonal elements
-* of T are non-negative real numbers.
-*
-* Arguments
-* =========
-*
-* JOBVSL (input) CHARACTER*1
-* = 'N': do not compute the left Schur vectors;
-* = 'V': compute the left Schur vectors.
-*
-* JOBVSR (input) CHARACTER*1
-* = 'N': do not compute the right Schur vectors;
-* = 'V': compute the right Schur vectors.
-*
-* SORT (input) CHARACTER*1
-* Specifies whether or not to order the eigenvalues on the
-* diagonal of the generalized Schur form.
-* = 'N': Eigenvalues are not ordered;
-* = 'S': Eigenvalues are ordered (see SELCTG).
-*
-* SELCTG (external procedure) LOGICAL FUNCTION of two COMPLEX*16 arguments
-* SELCTG must be declared EXTERNAL in the calling subroutine.
-* If SORT = 'N', SELCTG is not referenced.
-* If SORT = 'S', SELCTG is used to select eigenvalues to sort
-* to the top left of the Schur form.
-* An eigenvalue ALPHA(j)/BETA(j) is selected if
-* SELCTG(ALPHA(j),BETA(j)) is true.
-*
-* Note that a selected complex eigenvalue may no longer satisfy
-* SELCTG(ALPHA(j),BETA(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 matrices A, B, VSL, and VSR. N >= 0.
-*
-* A (input/output) COMPLEX*16 array, dimension (LDA, N)
-* On entry, the first of the pair of matrices.
-* On exit, A has been overwritten by its generalized Schur
-* form S.
-*
-* LDA (input) INTEGER
-* The leading dimension of A. LDA >= max(1,N).
-*
-* B (input/output) COMPLEX*16 array, dimension (LDB, N)
-* On entry, the second of the pair of matrices.
-* On exit, B has been overwritten by its generalized Schur
-* form T.
-*
-* LDB (input) INTEGER
-* The leading dimension of B. LDB >= max(1,N).
-*
-* SDIM (output) INTEGER
-* If SORT = 'N', SDIM = 0.
-* If SORT = 'S', SDIM = number of eigenvalues (after sorting)
-* for which SELCTG is true.
-*
-* ALPHA (output) COMPLEX*16 array, dimension (N)
-* BETA (output) COMPLEX*16 array, dimension (N)
-* On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the
-* generalized eigenvalues. ALPHA(j), j=1,...,N and BETA(j),
-* j=1,...,N are the diagonals of the complex Schur form (A,B)
-* output by ZGGES. The BETA(j) will be non-negative real.
-*
-* Note: the quotients ALPHA(j)/BETA(j) may easily over- or
-* underflow, and BETA(j) may even be zero. Thus, the user
-* should avoid naively computing the ratio alpha/beta.
-* However, ALPHA will be always less than and usually
-* comparable with norm(A) in magnitude, and BETA always less
-* than and usually comparable with norm(B).
-*
-* VSL (output) COMPLEX*16 array, dimension (LDVSL,N)
-* If JOBVSL = 'V', VSL will contain the left Schur vectors.
-* Not referenced if JOBVSL = 'N'.
-*
-* LDVSL (input) INTEGER
-* The leading dimension of the matrix VSL. LDVSL >= 1, and
-* if JOBVSL = 'V', LDVSL >= N.
-*
-* VSR (output) COMPLEX*16 array, dimension (LDVSR,N)
-* If JOBVSR = 'V', VSR will contain the right Schur vectors.
-* Not referenced if JOBVSR = 'N'.
-*
-* LDVSR (input) INTEGER
-* The leading dimension of the matrix VSR. LDVSR >= 1, and
-* if JOBVSR = 'V', LDVSR >= N.
-*
-* 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).
-* 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 (workspace) DOUBLE PRECISION array, dimension (8*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.
-* =1,...,N:
-* The QZ iteration failed. (A,B) are not in Schur
-* form, but ALPHA(j) and BETA(j) should be correct for
-* j=INFO+1,...,N.
-* > N: =N+1: other than QZ iteration failed in ZHGEQZ
-* =N+2: after reordering, roundoff changed values of
-* some complex eigenvalues so that leading
-* eigenvalues in the Generalized Schur form no
-* longer satisfy SELCTG=.TRUE. This could also
-* be caused due to scaling.
-* =N+3: reordering falied in ZTGSEN.
-*
* =====================================================================
*
* .. Parameters ..