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NAME SGEBAK - 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 SGEBAL SYNOPSIS SUBROUTINE SGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV, INFO ) CHARACTER JOB, SIDE INTEGER IHI, ILO, INFO, LDV, M, N REAL V( LDV, * ), SCALE( * ) PURPOSE SGEBAK 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 SGEBAL. 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 SGEBAL. 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 SGEBAL. SCALE (input) REAL array, dimension (N) Details of the permutation and scaling factors, as returned by SGEBAL. M (input) INTEGER The number of columns of the matrix V. V (input/output) REAL array, dimension (LDV,M) On entry, the matrix of right or left eigenvectors to be transformed, as returned by SHSEIN or STREVC. 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.