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NAME CTREVC - compute all or some right and/or left eigenvectors of a complex upper triangular matrix T SYNOPSIS SUBROUTINE CTREVC( JOB, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO ) CHARACTER HOWMNY, JOB INTEGER INFO, LDT, LDVL, LDVR, M, MM, N LOGICAL SELECT( * ) REAL RWORK( * ) COMPLEX T( LDT, * ), VL( LDVL, * ), VR( LDVR, * ), WORK( * ) PURPOSE CTREVC computes all or some right and/or left eigenvectors of a complex upper triangular matrix T. The right eigenvector x and the left eigenvector y of T corresponding to an eigenvalue w are defined by: T*x = w*x, y**H*T = w*y**H. The routine may either return the matrices X and/or Y of right or left eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an input unitary matrix. If T was obtained from the Schur factorization of an original matrix A = Q*T*Q**H, then Q*X and/or Q*Y are the matrices of right or left eigenvectors of A. ARGUMENTS JOB (input) CHARACTER*1 = 'R': compute right eigenvectors only; = 'L': compute left eigenvectors only; = 'B': compute both right and left eigenvectors. HOWMNY (input) CHARACTER*1 = 'A': compute all right and/or left eigenvectors; = 'O': compute all right and/or left eigenvectors, multiplied on the left by an input (generally uni- tary) matrix; = 'S': compute some right and/or left eigenvectors, specified by the logical array SELECT. SELECT (input) LOGICAL array, dimension (N) If HOWMNY = 'S', SELECT specifies the eigenvectors to be computed. To select the eigenvector corresponding to the j-th eigenvalue, SELECT(j) must be set to .TRUE.. If HOWMNY = 'A' or 'O', SELECT is not referenced. N (input) INTEGER The order of the matrix T. N >= 0. T (input/output) COMPLEX array, dimension (LDT,N) The upper triangular matrix T. T is modified, but restored on exit. LDT (input) INTEGER The leading dimension of the array T. LDT >= max(1,N). VL (input/output) COMPLEX array, dimension (LDVL,MM) On entry, if JOB = 'L' or 'B' and HOWMNY = 'O', VL must contain an N-by-N matrix Q (usually the unitary matrix Q of Schur vectors returned by CHSEQR). On exit, if JOB = 'L' or 'B', VL contains: if HOWMNY = 'A', the matrix Y of left eigenvectors of T; if HOWMNY = 'O', the matrix Q*Y; if HOWMNY = 'S', the left eigenvectors of T specified by SELECT, stored consecutively in the columns of VL, in the same order as their eigenvalues. If JOB = 'R', VL is not referenced. LDVL (input) INTEGER The leading dimension of the array VL. LDVL >= max(1,N). VR (input/output) COMPLEX array, dimension (LDVR,MM) On entry, if JOB = 'R' or 'B' and HOWMNY = 'O', VR must contain an N-by-N matrix Q (usually the unitary matrix Q of Schur vectors returned by CHSEQR). On exit, if JOB = 'R' or 'B', VR contains: if HOWMNY = 'A', the matrix X of right eigenvectors of T; if HOWMNY = 'O', the matrix Q*X; if HOWMNY = 'S', the right eigenvectors of T specified by SELECT, stored consecutively in the columns of VR, in the same order as their eigenvalues. If JOB = 'L', VR is not referenced. LDVR (input) INTEGER The leading dimension of the array VR. LDVR >= max(1,N). MM (input) INTEGER The number of columns in the arrays VL and/or VR. MM >= M. M (output) INTEGER The number of columns in the arrays VL and/or VR required to store the eigenvectors. If HOWMNY = 'A' or 'O', M is set to N. WORK (workspace) COMPLEX array, dimension (2*N) RWORK (workspace) REAL array, dimension (N) INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value FURTHER DETAILS The algorithm used in this program is basically backward (forward) substitution, with scaling to make the code robust against possible overflow. Each eigenvector is normalized so that the element of larg- est magnitude has magnitude 1; here the magnitude of a com- plex number (x,y) is taken to be |x| + |y|.