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NAME DGEBAK - form the right or left eigenvectors of a real gen- eral matrix by backward transformation on the computed eigenvectors of the balanced matrix output by DGEBAL SYNOPSIS 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, * ) PURPOSE DGEBAK forms the right or left eigenvectors of a real gen- eral 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. 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. 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 eigen- vectors. 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.