DGGBAK forms the right or left eigenvectors of a real generalized


 eigenvalue problem A*x = lambda*B*x, by backward transformation on


 the computed eigenvectors of the balanced pair of matrices output by


 DGGBAL.

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 DGGBAL.

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 DGGBAL.


          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.

LSCALE

          LSCALE is DOUBLE PRECISION array, dimension (N)


          Details of the permutations and/or scaling factors applied


          to the left side of A and B, as returned by DGGBAL.

RSCALE

          RSCALE is DOUBLE PRECISION array, dimension (N)


          Details of the permutations and/or scaling factors applied


          to the right side of A and B, as returned by DGGBAL.

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 DTGEVC.


          On exit, V is overwritten by the transformed eigenvectors.

LDV

          LDV is INTEGER


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

INFO

          INFO is INTEGER


          = 0:  successful exit.


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

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

December 2016

  See R.C. Ward, Balancing the generalized eigenvalue problem,


                 SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.