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DGEBAK(l)) DGEBAK(l)NAMEDGEBAK - form the right or left eigenvectors of a real general matrix by backward trans- formation on the computed eigenvectors of the balanced matrix output by DGEBALSYNOPSISSUBROUTINE 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, * )PURPOSEDGEBAK forms the right or left eigenvectors of a real general matrix by backward transfor- mation on the computed eigenvectors of the balanced matrix output by DGEBAL.ARGUMENTSJOB (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 =, the i-th argument had an illegal value.-iLAPACK version 3.015 June 2000 DGEBAK(l)

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