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DGEGV(l)			       )			      DGEGV(l)

NAME
       DGEGV - routine is deprecated and has been replaced by routine DGGEV

SYNOPSIS
       SUBROUTINE DGEGV( JOBVL,	 JOBVR,	 N,  A,	 LDA,  B, LDB, ALPHAR, ALPHAI,
			 BETA, VL, LDVL, VR, LDVR, WORK, LWORK, INFO )

	   CHARACTER	 JOBVL, JOBVR

	   INTEGER	 INFO, LDA, LDB, LDVL, LDVR, LWORK, N

	   DOUBLE	 PRECISION A( LDA, * ), ALPHAI( * ), ALPHAR( *	),  B(
			 LDB,  *  ),  BETA( * ), VL( LDVL, * ), VR( LDVR, * ),
			 WORK( * )

PURPOSE
       This routine is deprecated and has  been	 replaced  by  routine	DGGEV.
       DGEGV computes for a pair of n-by-n real nonsymmetric matrices A and B,
       the generalized eigenvalues (alphar +/- alphai*i,  beta),  and  option‐
       ally, the left and/or right generalized eigenvectors (VL and VR).

       A  generalized  eigenvalue  for	a  pair	 of matrices (A,B) is, roughly
       speaking, 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  good beginning reference is the book, "Matrix Computations",
       by G. Golub & C. van Loan (Johns Hopkins U. Press)

       A right generalized eigenvector corresponding to a  generalized	eigen‐
       value   w  for a pair of matrices (A,B) is a vector  r  such that  (A -
       w B) r = 0 .  A left generalized eigenvector is a vector	 l  such  that
       l**H * (A - w B) = 0, where l**H is the
       conjugate-transpose of l.

       Note: this routine performs "full balancing" on A and B -- see "Further
       Details", below.

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 first of the pair of matrices  whose  generalized
	       eigenvalues and (optionally) generalized eigenvectors are to be
	       computed.  On exit, the	contents  will	have  been  destroyed.
	       (For  a	description of the contents of A on exit, see "Further
	       Details", below.)

       LDA     (input) INTEGER
	       The leading dimension of A.  LDA >= max(1,N).

       B       (input/output) DOUBLE PRECISION array, dimension (LDB, N)
	       On entry, the second of the pair of matrices whose  generalized
	       eigenvalues and (optionally) generalized eigenvectors are to be
	       computed.  On exit, the	contents  will	have  been  destroyed.
	       (For  a	description of the contents of B on exit, see "Further
	       Details", below.)

       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  gen‐
	       eralized	 eigenvalues.  If ALPHAI(j) is zero, then the j-th ei‐
	       genvalue is real; if positive, then the j-th and	 (j+1)-st  ei‐
	       genvalues  are a complex conjugate pair, with ALPHAI(j+1) nega‐
	       tive.

	       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 generalized eigenvectors.  (See "Pur‐
	       pose", above.)  Real eigenvectors take one column, complex take
	       two columns, the first for the real part and the second for the
	       imaginary part.	Complex eigenvectors correspond to  an	eigen‐
	       value  with  positive imaginary part.  Each eigenvector will be
	       scaled so the largest component	will  have  abs(real  part)  +
	       abs(imag.  part)	 =  1,	*except*  that	for  eigenvalues  with
	       alpha=beta=0, a zero vector will be returned as the correspond‐
	       ing eigenvector.	 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 generalized eigenvectors.  (See "Pur‐
	       pose", above.)  Real eigenvectors take one column, complex take
	       two columns, the first for the real part and the second for the
	       imaginary  part.	  Complex eigenvectors correspond to an eigen‐
	       value with positive imaginary part.  Each eigenvector  will  be
	       scaled  so  the	largest	 component  will have abs(real part) +
	       abs(imag.  part)	 =  1,	*except*  that	for  eigenvalues  with
	       alpha=beta=0, a zero vector will be returned as the correspond‐
	       ing eigenvector.	 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 (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.   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 + MAX( 6*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.  No eigenvectors have been
	       calculated, 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 DTGEVC
	       =N+8: error return from DGGBAK (computing VL)
	       =N+9: error return from DGGBAK (computing VR)
	       =N+10: error return from DLASCL (various calls)

FURTHER DETAILS
       Balancing
       ---------

       This  driver calls DGGBAL to both permute and scale rows and columns of
       A and B.	 The permutations PL and PR are chosen	so  that  PL*A*PR  and
       PL*B*R  will  be	 upper	triangular  except  for	 the  diagonal	blocks
       A(i:j,i:j) and B(i:j,i:j), with i and j as close together as  possible.
       The  diagonal  scaling  matrices	 DL and DR are chosen so that the pair
       DL*PL*A*PR*DR, DL*PL*B*PR*DR have elements close to one (except for the
       elements that start out zero.)

       After  the  eigenvalues	and eigenvectors of the balanced matrices have
       been computed, DGGBAK transforms the eigenvectors  back	to  what  they
       would have been (in perfect arithmetic) if they had not been balanced.

       Contents of A and B on Exit
       -------- -- - --- - -- ----

       If  any	eigenvectors  are  computed  (either JOBVL='V' or JOBVR='V' or
       both), then on exit the arrays A and B  will  contain  the  real	 Schur
       form[*]	of the "balanced" versions of A and B.	If no eigenvectors are
       computed, then only the diagonal blocks will be correct.

       [*] See DHGEQZ, DGEGS, or read the book "Matrix Computations",
	   by Golub & van Loan, pub. by Johns Hopkins U. Press.

LAPACK version 3.0		 15 June 2000			      DGEGV(l)
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