ZTGEVC(l)		LAPACK routine (version	1.1)		    ZTGEVC(l)

NAME
  ZTGEVC - compute selected left and/or	right generalized eigenvectors of a
  pair of complex upper	triangular matrices (A,B)

SYNOPSIS

  SUBROUTINE ZTGEVC( JOB, SIDE,	SELECT,	N, A, LDA, B, LDB, VL, LDVL, VR,
		     LDVR, MM, M, WORK,	RWORK, INFO )

      CHARACTER	     JOB, SIDE

      INTEGER	     INFO, LDA,	LDB, LDVL, LDVR, M, MM,	N

      LOGICAL	     SELECT( * )

      DOUBLE	     PRECISION RWORK( N, * )

      COMPLEX*16     A(	LDA, * ), B( LDB, * ), VL( LDVL, * ), VR( LDVR,	* ),
		     WORK( N, *	)

PURPOSE
  ZTGEVC computes selected left	and/or right generalized eigenvectors of a
  pair of complex upper	triangular matrices (A,B).  The	j-th generalized left
  and right eigenvectors are  y	 and  x, resp.,	such that:
	  H
	 y  (A - wB) = 0       (A - wB)x = 0

								      H	Note:
  the left eigenvector is sometimes defined as the row vector  y
	but ZTGEVC computes the	column vector y.

ARGUMENTS

  JOB	  (input) CHARACTER*1
	  = 'A': compute All (left/right/left+right) generalized eigenvectors
	  of (A,B); = 'S': compute Selected (left/right/left+right) general-
	  ized eigenvectors of (A,B) --	see the	description of the argument
	  SELECT; = 'B'	or 'T':	compute	all (left/right/left+right) general-
	  ized eigenvectors of (A,B), and Back Transform them using the	ini-
	  tial contents	of VL/VR -- see	the descriptions of the	arguments VL
	  and VR.

  SIDE	  (input) CHARACTER*1
	  Specifies for	which side eigenvectors	are to be computed:
	  = 'R': compute right eigenvectors only;
	  = 'L': compute left eigenvectors only;
	  = 'B': compute both right and	left eigenvectors.

  SELECT  (input) LOGICAL array, dimension (N)
	  If JOB='S', then SELECT specifies the	(generalized) eigenvectors to
	  be computed.	To get the eigenvector corresponding to	the j-th
	  eigenvalue, set SELECT(j) to and all eigenvectors are	selected.

  N	  (input) INTEGER
	  The order of the matrices A and B.  N	>= 0.

  A	  (input) COMPLEX*16 array, dimension (LDA,N)
	  One of the pair of matrices whose generalized	eigenvectors are to
	  be computed.	It must	be upper triangular.

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

  B	  (input) COMPLEX*16 array, dimension (LDB,N)
	  The other of the pair	of matrices whose generalized eigenvectors
	  are to be computed.  It must be upper	triangular with	real diagonal
	  elements.

  LDB	  (input) INTEGER
	  The leading dimension	of array B.  LDB >= max(1, N).

  VL	  (input/output) COMPLEX*16 array, dimension (LDVL,MM)
	  The left eigenvectors	(column	vectors	-- see the note	in "Pur-
	  pose".) If JOB='A', then all left eigenvectors of (A,B) will be
	  computed and stored in VL.  If JOB='S', then only the	eigenvectors
	  selected by SELECT will be computed; the first selected eigenvector
	  will go in column 1, the second in column 2, etc.  If	JOB='B'	or
	  'T', then all	left eigenvectors of (A,B) will	be computed and	mul-
	  tiplied (on the left)	by the matrix found in VL on entry to ZTGEVC.
	  Usually, this	will be	the Q matrix computed by ZGGHRD	and ZHGEQZ,
	  so that on exit, VL will contain the left eigenvectors of the	ori-
	  ginal	matrix pair.  In any case, each	eigenvector will be scaled so
	  the largest component	of each	vector has abs(real part) + abs(imag.
	  part)=1, *unless*  A and B both have a zero in the diagonal entry
	  corresponding	to the eigenvector, in which case the eigenvector
	  will be zero.	 If SIDE = 'R',	VL is not referenced.

  LDVL	  (input) INTEGER
	  The leading dimension	of array VL.  LDVL >= 1; if SIDE = 'B' or
	  'L', LDVL >= N.

  VR	  (input/output) COMPLEX*16 array, dimension (LDVR,MM)
	  The right eigenvectors.  If JOB='A', then all	right eigenvectors of
	  (A,B)	will be	computed and stored in VR.  If JOB='S',	then only the
	  eigenvectors selected	by SELECT will be computed; the	first
	  selected eigenvector will go in column 1, the	second in column 2,
	  etc.	If JOB='B' or 'T', then	all right eigenvectors of (A,B)	will
	  be computed and multiplied (on the left) by the matrix found in VR
	  on entry to ZTGEVC.  Usually,	this will be the Z matrix computed by
	  ZGGHRD and ZHGEQZ, so	that on	exit, VR will contain the right
	  eigenvectors of the original matrix pair.  In	any case, each eigen-
	  vector will be scaled	so the largest component of each vector	has
	  abs(real part) + abs(imag. part)=1, *unless*	A and B	both have a
	  zero in the diagonal entry corresponding to the eigenvector, in
	  which	case the eigenvector will be zero.  If SIDE = 'L', VR is not
	  referenced.

  LDVR	  (input) INTEGER
	  The leading dimension	of array VR.  LDVR >= 1; if SIDE = 'B' or
	  'R', LDVR >= N.

  MM	  (input) INTEGER
	  The number of	columns	in VL and/or VR.  If JOB='A', 'B', or 'T',
	  then MM >= N.	 If JOB='S', then MM must be at	least the number of
	  .TRUE.  values in SELECT(1:N).

  M	  (output) INTEGER
	  The number of	columns	in VL and/or VR	actually used to store the
	  eigenvectors.

  WORK	  (workspace) COMPLEX*16 array,	dimension ( 2, N )

  RWORK	  (workspace) DOUBLE PRECISION array, dimension	( 2, N )

  INFO	  (output) INTEGER
	  = 0:	successful exit.
	  < 0:	if INFO	= -i, the i-th argument	had an illegal value.