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.

JOB

          JOB is 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

          SIDE is CHARACTER*1


          = 'R':  V contains right eigenvectors;


          = 'L':  V contains left eigenvectors.

N

          N is INTEGER


          The number of rows of the matrix V.  N >= 0.

ILO

          ILO is INTEGER

IHI

          IHI is 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

          SCALE is DOUBLE PRECISION array, dimension (N)


          Details of the permutation and scaling factors, as returned


          by DGEBAL.

M

          M is INTEGER


          The number of columns of the matrix V.  M >= 0.

V

          V is 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

          LDV is INTEGER


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

INFO

          INFO is INTEGER


          = 0:  successful exit


          < 0:  if INFO = -i, the i-th argument had an illegal value.

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