CXML
        	    
LAPACK version 3.0
dgebak(3)

PURPOSE
  DGEBAK - form the right or left eigenvectors of a real general matrix by
  backward transformation on the computed eigenvectors of the balanced matrix
  output by DGEBAL

SYNTAX
  SUBROUTINE DGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV, INFO )

      CHARACTER	     JOB, SIDE

      INTEGER	     IHI, ILO, INFO, LDV, M, N

      DOUBLE	     PRECISION SCALE( * ), V( LDV, * )

DESCRIPTION
  DGEBAK forms the right or left eigenvectors of a real general matrix by
  backward transformation on the computed eigenvectors of the balanced matrix
  output by DGEBAL.

ARGUMENTS
  JOB	  (input) CHARACTER*1
	  Specifies the type of backward transformation required: = 'N', do
	  nothing, return immediately; = 'P', do backward transformation for
	  permutation only; = 'S', do backward transformation for scaling
	  only; = 'B', do backward transformations for both permutation and
	  scaling.  JOB must be the same as the argument JOB supplied to
	  DGEBAL.

  SIDE	  (input) CHARACTER*1
	  = 'R':  V contains right eigenvectors;
	  = 'L':  V contains left eigenvectors.

  N	  (input) INTEGER
	  The number of rows of the matrix V.  N >= 0.

  ILO	  (input) INTEGER
	  IHI	  (input) INTEGER The integers ILO and IHI determined by
	  DGEBAL.  1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.

  SCALE	  (input) DOUBLE PRECISION array, dimension (N)
	  Details of the permutation and scaling factors, as returned by
	  DGEBAL.

  M	  (input) INTEGER
	  The number of columns of the matrix V.  M >= 0.

  V	  (input/output) DOUBLE PRECISION array, dimension (LDV,M)
	  On entry, the matrix of right or left eigenvectors to be
	  transformed, as returned by DHSEIN or DTREVC.	 On exit, V is
	  overwritten by the transformed eigenvectors.

  LDV	  (input) INTEGER
	  The leading dimension of the array V. LDV >= max(1,N).

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