[BACK]Return to dggev.f CVS log [TXT] [DIR] Up to [local] / rpl / lapack / lapack

Diff for /rpl/lapack/lapack/dggev.f between versions 1.7 and 1.8

version 1.7, 2010/12/21 13:53:26 version 1.8, 2011/11/21 20:42:52
Line 1 Line 1
   *> \brief <b> DGGEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices</b>
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DGGEV + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dggev.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dggev.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dggev.f"> 
   *> [TXT]</a>
   *> \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,        SUBROUTINE DGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI,
      $                  BETA, VL, LDVL, VR, LDVR, WORK, LWORK, INFO )       $                  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,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     November 2006  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          JOBVL, JOBVR        CHARACTER          JOBVL, JOBVR
Line 16 Line 241
      $                   VR( LDVR, * ), WORK( * )       $                   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 ..  *     .. Parameters ..
Removed from v.1.7  
changed lines
  Added in v.1.8

CVSweb interface <joel.bertrand@systella.fr>