--- rpl/lapack/lapack/dggev.f 2010/12/21 13:53:26 1.7
+++ rpl/lapack/lapack/dggev.f 2011/11/21 20:42:52 1.8
@@ -1,10 +1,235 @@
+*> \brief DGGEV 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 DGGEV + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI,
+* BETA, VL, LDVL, VR, LDVR, WORK, LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER JOBVL, JOBVR
+* INTEGER INFO, LDA, LDB, LDVL, LDVR, LWORK, N
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION A( LDA, * ), ALPHAI( * ), ALPHAR( * ),
+* $ B( LDB, * ), BETA( * ), VL( LDVL, * ),
+* $ VR( LDVR, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DGGEV computes for a pair of N-by-N real nonsymmetric matrices (A,B)
+*> the generalized eigenvalues, and optionally, the left and/or right
+*> generalized eigenvectors.
+*>
+*> A generalized eigenvalue for a pair of matrices (A,B) is a scalar
+*> lambda or a ratio alpha/beta = lambda, such that A - lambda*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.
+*>
+*> The right eigenvector v(j) corresponding to the eigenvalue lambda(j)
+*> of (A,B) satisfies
+*>
+*> A * v(j) = lambda(j) * B * v(j).
+*>
+*> The left eigenvector u(j) corresponding to the eigenvalue lambda(j)
+*> of (A,B) satisfies
+*>
+*> u(j)**H * A = lambda(j) * u(j)**H * B .
+*>
+*> where u(j)**H is the conjugate-transpose of u(j).
+*>
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] JOBVL
+*> \verbatim
+*> JOBVL is CHARACTER*1
+*> = 'N': do not compute the left generalized eigenvectors;
+*> = 'V': compute the left generalized eigenvectors.
+*> \endverbatim
+*>
+*> \param[in] JOBVR
+*> \verbatim
+*> JOBVR is CHARACTER*1
+*> = 'N': do not compute the right generalized eigenvectors;
+*> = 'V': compute the right generalized eigenvectors.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrices A, B, VL, and VR. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is DOUBLE PRECISION array, dimension (LDA, N)
+*> On entry, the matrix A in the pair (A,B).
+*> On exit, A has been overwritten.
+*> \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 in the pair (A,B).
+*> On exit, B has been overwritten.
+*> \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)
+*> \endverbatim
+*>
+*> \param[out] ALPHAI
+*> \verbatim
+*> ALPHAI is DOUBLE PRECISION array, dimension (N)
+*> \endverbatim
+*>
+*> \param[out] BETA
+*> \verbatim
+*> BETA is DOUBLE PRECISION array, dimension (N)
+*> On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will
+*> be the generalized eigenvalues. 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) negative.
+*>
+*> Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(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, ALPHAR and ALPHAI 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] VL
+*> \verbatim
+*> VL is DOUBLE PRECISION array, dimension (LDVL,N)
+*> If JOBVL = 'V', the left eigenvectors u(j) are stored one
+*> after another in the columns of VL, in the same order as
+*> their eigenvalues. If the j-th eigenvalue is real, then
+*> u(j) = VL(:,j), the j-th column of VL. If the j-th and
+*> (j+1)-th eigenvalues form a complex conjugate pair, then
+*> u(j) = VL(:,j)+i*VL(:,j+1) and u(j+1) = VL(:,j)-i*VL(:,j+1).
+*> Each eigenvector is scaled so the largest component has
+*> abs(real part)+abs(imag. part)=1.
+*> Not referenced if JOBVL = 'N'.
+*> \endverbatim
+*>
+*> \param[in] LDVL
+*> \verbatim
+*> LDVL is INTEGER
+*> The leading dimension of the matrix VL. LDVL >= 1, and
+*> if JOBVL = 'V', LDVL >= N.
+*> \endverbatim
+*>
+*> \param[out] VR
+*> \verbatim
+*> VR is DOUBLE PRECISION array, dimension (LDVR,N)
+*> If JOBVR = 'V', the right eigenvectors v(j) are stored one
+*> after another in the columns of VR, in the same order as
+*> their eigenvalues. If the j-th eigenvalue is real, then
+*> v(j) = VR(:,j), the j-th column of VR. If the j-th and
+*> (j+1)-th eigenvalues form a complex conjugate pair, then
+*> v(j) = VR(:,j)+i*VR(:,j+1) and v(j+1) = VR(:,j)-i*VR(:,j+1).
+*> Each eigenvector is scaled so the largest component has
+*> abs(real part)+abs(imag. part)=1.
+*> Not referenced if JOBVR = 'N'.
+*> \endverbatim
+*>
+*> \param[in] LDVR
+*> \verbatim
+*> LDVR is INTEGER
+*> The leading dimension of the matrix VR. LDVR >= 1, and
+*> if JOBVR = 'V', LDVR >= 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(1,8*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] 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. No eigenvectors have been
+*> calculated, but ALPHAR(j), ALPHAI(j), and BETA(j)
+*> should be correct for j=INFO+1,...,N.
+*> > N: =N+1: other than QZ iteration failed in DHGEQZ.
+*> =N+2: error return from DTGEVC.
+*> \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 DGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI,
$ BETA, VL, LDVL, VR, LDVR, 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 JOBVL, JOBVR
@@ -16,128 +241,6 @@
$ VR( LDVR, * ), WORK( * )
* ..
*
-* Purpose
-* =======
-*
-* DGGEV computes for a pair of N-by-N real nonsymmetric matrices (A,B)
-* the generalized eigenvalues, and optionally, the left and/or right
-* generalized eigenvectors.
-*
-* A generalized eigenvalue for a pair of matrices (A,B) is a scalar
-* lambda or a ratio alpha/beta = lambda, such that A - lambda*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.
-*
-* The right eigenvector v(j) corresponding to the eigenvalue lambda(j)
-* of (A,B) satisfies
-*
-* A * v(j) = lambda(j) * B * v(j).
-*
-* The left eigenvector u(j) corresponding to the eigenvalue lambda(j)
-* of (A,B) satisfies
-*
-* u(j)**H * A = lambda(j) * u(j)**H * B .
-*
-* where u(j)**H is the conjugate-transpose of u(j).
-*
-*
-* Arguments
-* =========
-*
-* JOBVL (input) CHARACTER*1
-* = 'N': do not compute the left generalized eigenvectors;
-* = 'V': compute the left generalized eigenvectors.
-*
-* JOBVR (input) CHARACTER*1
-* = 'N': do not compute the right generalized eigenvectors;
-* = 'V': compute the right generalized eigenvectors.
-*
-* N (input) INTEGER
-* The order of the matrices A, B, VL, and VR. N >= 0.
-*
-* A (input/output) DOUBLE PRECISION array, dimension (LDA, N)
-* On entry, the matrix A in the pair (A,B).
-* On exit, A has been overwritten.
-*
-* 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 in the pair (A,B).
-* On exit, B has been overwritten.
-*
-* LDB (input) INTEGER
-* The leading dimension of B. LDB >= max(1,N).
-*
-* ALPHAR (output) DOUBLE PRECISION array, dimension (N)
-* ALPHAI (output) DOUBLE PRECISION array, dimension (N)
-* BETA (output) DOUBLE PRECISION array, dimension (N)
-* On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will
-* be the generalized eigenvalues. 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) negative.
-*
-* Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(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, ALPHAR and ALPHAI will be always less
-* than and usually comparable with norm(A) in magnitude, and
-* BETA always less than and usually comparable with norm(B).
-*
-* VL (output) DOUBLE PRECISION array, dimension (LDVL,N)
-* If JOBVL = 'V', the left eigenvectors u(j) are stored one
-* after another in the columns of VL, in the same order as
-* their eigenvalues. If the j-th eigenvalue is real, then
-* u(j) = VL(:,j), the j-th column of VL. If the j-th and
-* (j+1)-th eigenvalues form a complex conjugate pair, then
-* u(j) = VL(:,j)+i*VL(:,j+1) and u(j+1) = VL(:,j)-i*VL(:,j+1).
-* Each eigenvector is scaled so the largest component has
-* abs(real part)+abs(imag. part)=1.
-* Not referenced if JOBVL = 'N'.
-*
-* LDVL (input) INTEGER
-* The leading dimension of the matrix VL. LDVL >= 1, and
-* if JOBVL = 'V', LDVL >= N.
-*
-* VR (output) DOUBLE PRECISION array, dimension (LDVR,N)
-* If JOBVR = 'V', the right eigenvectors v(j) are stored one
-* after another in the columns of VR, in the same order as
-* their eigenvalues. If the j-th eigenvalue is real, then
-* v(j) = VR(:,j), the j-th column of VR. If the j-th and
-* (j+1)-th eigenvalues form a complex conjugate pair, then
-* v(j) = VR(:,j)+i*VR(:,j+1) and v(j+1) = VR(:,j)-i*VR(:,j+1).
-* Each eigenvector is scaled so the largest component has
-* abs(real part)+abs(imag. part)=1.
-* Not referenced if JOBVR = 'N'.
-*
-* LDVR (input) INTEGER
-* The leading dimension of the matrix VR. LDVR >= 1, and
-* if JOBVR = 'V', LDVR >= 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(1,8*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.
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value.
-* = 1,...,N:
-* The QZ iteration failed. No eigenvectors have been
-* calculated, but ALPHAR(j), ALPHAI(j), and BETA(j)
-* should be correct for j=INFO+1,...,N.
-* > N: =N+1: other than QZ iteration failed in DHGEQZ.
-* =N+2: error return from DTGEVC.
-*
* =====================================================================
*
* .. Parameters ..