--- rpl/lapack/lapack/dgegs.f 2010/12/21 13:53:25 1.7
+++ rpl/lapack/lapack/dgegs.f 2011/11/21 20:42:50 1.8
@@ -1,11 +1,236 @@
+*> \brief DGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DGEGS + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DGEGS( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHAR,
+* ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR, WORK,
+* LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER JOBVSL, JOBVSR
+* INTEGER INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION A( LDA, * ), ALPHAI( * ), ALPHAR( * ),
+* $ B( LDB, * ), BETA( * ), VSL( LDVSL, * ),
+* $ VSR( LDVSR, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> This routine is deprecated and has been replaced by routine DGGES.
+*>
+*> DGEGS computes the eigenvalues, real Schur form, and, optionally,
+*> left and or/right Schur vectors of a real matrix pair (A,B).
+*> Given two square matrices A and B, the generalized real Schur
+*> factorization has the form
+*>
+*> A = Q*S*Z**T, B = Q*T*Z**T
+*>
+*> where Q and Z are orthogonal matrices, T is upper triangular, and S
+*> is an upper quasi-triangular matrix with 1-by-1 and 2-by-2 diagonal
+*> blocks, the 2-by-2 blocks corresponding to complex conjugate pairs
+*> of eigenvalues of (A,B). The columns of Q are the left Schur vectors
+*> and the columns of Z are the right Schur vectors.
+*>
+*> If only the eigenvalues of (A,B) are needed, the driver routine
+*> DGEGV should be used instead. See DGEGV for a description of the
+*> eigenvalues of the generalized nonsymmetric eigenvalue problem
+*> (GNEP).
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] JOBVSL
+*> \verbatim
+*> JOBVSL is CHARACTER*1
+*> = 'N': do not compute the left Schur vectors;
+*> = 'V': compute the left Schur vectors (returned in VSL).
+*> \endverbatim
+*>
+*> \param[in] JOBVSR
+*> \verbatim
+*> JOBVSR is CHARACTER*1
+*> = 'N': do not compute the right Schur vectors;
+*> = 'V': compute the right Schur vectors (returned in VSR).
+*> \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 DOUBLE PRECISION array, dimension (LDA, N)
+*> On entry, the matrix A.
+*> On exit, the upper quasi-triangular matrix S from the
+*> generalized real Schur factorization.
+*> \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 DOUBLE PRECISION array, dimension (LDB, N)
+*> On entry, the matrix B.
+*> On exit, the upper triangular matrix T from the generalized
+*> real Schur factorization.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> The leading dimension of B. LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] ALPHAR
+*> \verbatim
+*> ALPHAR is DOUBLE PRECISION array, dimension (N)
+*> The real parts of each scalar alpha defining an eigenvalue
+*> of GNEP.
+*> \endverbatim
+*>
+*> \param[out] ALPHAI
+*> \verbatim
+*> ALPHAI is DOUBLE PRECISION array, dimension (N)
+*> The imaginary parts of each scalar alpha defining an
+*> eigenvalue of GNEP. If ALPHAI(j) is zero, then the j-th
+*> eigenvalue is real; if positive, then the j-th and (j+1)-st
+*> eigenvalues are a complex conjugate pair, with
+*> ALPHAI(j+1) = -ALPHAI(j).
+*> \endverbatim
+*>
+*> \param[out] BETA
+*> \verbatim
+*> BETA is DOUBLE PRECISION array, dimension (N)
+*> The scalars beta that define the eigenvalues of GNEP.
+*> Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and
+*> beta = BETA(j) represent the j-th eigenvalue of the matrix
+*> pair (A,B), in one of the forms lambda = alpha/beta or
+*> mu = beta/alpha. Since either lambda or mu may overflow,
+*> they should not, in general, be computed.
+*> \endverbatim
+*>
+*> \param[out] VSL
+*> \verbatim
+*> VSL is DOUBLE PRECISION array, dimension (LDVSL,N)
+*> If JOBVSL = 'V', the matrix of left Schur vectors Q.
+*> 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 DOUBLE PRECISION array, dimension (LDVSR,N)
+*> If JOBVSR = 'V', the matrix of right Schur vectors Z.
+*> 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 DOUBLE PRECISION 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(1,4*N).
+*> For good performance, LWORK must generally be larger.
+*> To compute the optimal value of LWORK, call ILAENV to get
+*> blocksizes (for DGEQRF, DORMQR, and DORGQR.) Then compute:
+*> NB -- MAX of the blocksizes for DGEQRF, DORMQR, and DORGQR
+*> The optimal LWORK is 2*N + N*(NB+1).
+*>
+*> 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] 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 ALPHAR(j), ALPHAI(j), and BETA(j) should
+*> be correct for j=INFO+1,...,N.
+*> > N: errors that usually indicate LAPACK problems:
+*> =N+1: error return from DGGBAL
+*> =N+2: error return from DGEQRF
+*> =N+3: error return from DORMQR
+*> =N+4: error return from DORGQR
+*> =N+5: error return from DGGHRD
+*> =N+6: error return from DHGEQZ (other than failed
+*> iteration)
+*> =N+7: error return from DGGBAK (computing VSL)
+*> =N+8: error return from DGGBAK (computing VSR)
+*> =N+9: error return from DLASCL (various places)
+*> \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 DGEGS( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHAR,
$ ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR, WORK,
$ LWORK, 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
@@ -17,129 +242,6 @@
$ VSR( LDVSR, * ), WORK( * )
* ..
*
-* Purpose
-* =======
-*
-* This routine is deprecated and has been replaced by routine DGGES.
-*
-* DGEGS computes the eigenvalues, real Schur form, and, optionally,
-* left and or/right Schur vectors of a real matrix pair (A,B).
-* Given two square matrices A and B, the generalized real Schur
-* factorization has the form
-*
-* A = Q*S*Z**T, B = Q*T*Z**T
-*
-* where Q and Z are orthogonal matrices, T is upper triangular, and S
-* is an upper quasi-triangular matrix with 1-by-1 and 2-by-2 diagonal
-* blocks, the 2-by-2 blocks corresponding to complex conjugate pairs
-* of eigenvalues of (A,B). The columns of Q are the left Schur vectors
-* and the columns of Z are the right Schur vectors.
-*
-* If only the eigenvalues of (A,B) are needed, the driver routine
-* DGEGV should be used instead. See DGEGV for a description of the
-* eigenvalues of the generalized nonsymmetric eigenvalue problem
-* (GNEP).
-*
-* Arguments
-* =========
-*
-* JOBVSL (input) CHARACTER*1
-* = 'N': do not compute the left Schur vectors;
-* = 'V': compute the left Schur vectors (returned in VSL).
-*
-* JOBVSR (input) CHARACTER*1
-* = 'N': do not compute the right Schur vectors;
-* = 'V': compute the right Schur vectors (returned in VSR).
-*
-* N (input) INTEGER
-* The order of the matrices A, B, VSL, and VSR. N >= 0.
-*
-* A (input/output) DOUBLE PRECISION array, dimension (LDA, N)
-* On entry, the matrix A.
-* On exit, the upper quasi-triangular matrix S from the
-* generalized real Schur factorization.
-*
-* LDA (input) INTEGER
-* The leading dimension of A. LDA >= max(1,N).
-*
-* B (input/output) DOUBLE PRECISION array, dimension (LDB, N)
-* On entry, the matrix B.
-* On exit, the upper triangular matrix T from the generalized
-* real Schur factorization.
-*
-* LDB (input) INTEGER
-* The leading dimension of B. LDB >= max(1,N).
-*
-* ALPHAR (output) DOUBLE PRECISION array, dimension (N)
-* The real parts of each scalar alpha defining an eigenvalue
-* of GNEP.
-*
-* ALPHAI (output) DOUBLE PRECISION array, dimension (N)
-* The imaginary parts of each scalar alpha defining an
-* eigenvalue of GNEP. If ALPHAI(j) is zero, then the j-th
-* eigenvalue is real; if positive, then the j-th and (j+1)-st
-* eigenvalues are a complex conjugate pair, with
-* ALPHAI(j+1) = -ALPHAI(j).
-*
-* BETA (output) DOUBLE PRECISION array, dimension (N)
-* The scalars beta that define the eigenvalues of GNEP.
-* Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and
-* beta = BETA(j) represent the j-th eigenvalue of the matrix
-* pair (A,B), in one of the forms lambda = alpha/beta or
-* mu = beta/alpha. Since either lambda or mu may overflow,
-* they should not, in general, be computed.
-*
-* VSL (output) DOUBLE PRECISION array, dimension (LDVSL,N)
-* If JOBVSL = 'V', the matrix of left Schur vectors Q.
-* 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) DOUBLE PRECISION array, dimension (LDVSR,N)
-* If JOBVSR = 'V', the matrix of right Schur vectors Z.
-* 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) DOUBLE PRECISION 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(1,4*N).
-* For good performance, LWORK must generally be larger.
-* To compute the optimal value of LWORK, call ILAENV to get
-* blocksizes (for DGEQRF, DORMQR, and DORGQR.) Then compute:
-* NB -- MAX of the blocksizes for DGEQRF, DORMQR, and DORGQR
-* The optimal LWORK is 2*N + N*(NB+1).
-*
-* 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.
-*
-* 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 ALPHAR(j), ALPHAI(j), and BETA(j) should
-* be correct for j=INFO+1,...,N.
-* > N: errors that usually indicate LAPACK problems:
-* =N+1: error return from DGGBAL
-* =N+2: error return from DGEQRF
-* =N+3: error return from DORMQR
-* =N+4: error return from DORGQR
-* =N+5: error return from DGGHRD
-* =N+6: error return from DHGEQZ (other than failed
-* iteration)
-* =N+7: error return from DGGBAK (computing VSL)
-* =N+8: error return from DGGBAK (computing VSR)
-* =N+9: error return from DLASCL (various places)
-*
* =====================================================================
*
* .. Parameters ..