ctrevc (l)  Linux Man Pages
ctrevc: computes some or all of the right and/or left eigenvectors of a complex upper triangular matrix T
NAME
CTREVC  computes some or all of the right and/or left eigenvectors of a complex upper triangular matrix TSYNOPSIS
 SUBROUTINE CTREVC(
 SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO )
 CHARACTER HOWMNY, SIDE
 INTEGER INFO, LDT, LDVL, LDVR, M, MM, N
 LOGICAL SELECT( * )
 REAL RWORK( * )
 COMPLEX T( LDT, * ), VL( LDVL, * ), VR( LDVR, * ), WORK( * )
PURPOSE
CTREVC computes some or all of the right and/or left eigenvectors of a complex upper triangular matrix T. Matrices of this type are produced by the Schur factorization of a complex general matrix: A = Q*T*Q**H, as computed by CHSEQR.The right eigenvector x and the left eigenvector y of T corresponding to an eigenvalue w are defined by:
where y**H denotes the conjugate transpose of the vector y. The eigenvalues are not input to this routine, but are read directly from the diagonal of T.
This routine returns the matrices X and/or Y of right and left eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an input matrix. If Q is the unitary factor that reduces a matrix A to Schur form T, then Q*X and Q*Y are the matrices of right and left eigenvectors of A.
ARGUMENTS
 SIDE (input) CHARACTER*1

= aqRaq: compute right eigenvectors only;
= aqLaq: compute left eigenvectors only;
= aqBaq: compute both right and left eigenvectors.  HOWMNY (input) CHARACTER*1

= aqAaq: compute all right and/or left eigenvectors;
= aqBaq: compute all right and/or left eigenvectors, backtransformed using the matrices supplied in VR and/or VL; = aqSaq: compute selected right and/or left eigenvectors, as indicated by the logical array SELECT.  SELECT (input) LOGICAL array, dimension (N)
 If HOWMNY = aqSaq, SELECT specifies the eigenvectors to be computed. The eigenvector corresponding to the jth eigenvalue is computed if SELECT(j) = .TRUE.. Not referenced if HOWMNY = aqAaq or aqBaq.
 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 SIDE = aqLaq or aqBaq and HOWMNY = aqBaq, VL must contain an NbyN matrix Q (usually the unitary matrix Q of Schur vectors returned by CHSEQR). On exit, if SIDE = aqLaq or aqBaq, VL contains: if HOWMNY = aqAaq, the matrix Y of left eigenvectors of T; if HOWMNY = aqBaq, the matrix Q*Y; if HOWMNY = aqSaq, the left eigenvectors of T specified by SELECT, stored consecutively in the columns of VL, in the same order as their eigenvalues. Not referenced if SIDE = aqRaq.
 LDVL (input) INTEGER
 The leading dimension of the array VL. LDVL >= 1, and if SIDE = aqLaq or aqBaq, LDVL >= N.
 VR (input/output) COMPLEX array, dimension (LDVR,MM)
 On entry, if SIDE = aqRaq or aqBaq and HOWMNY = aqBaq, VR must contain an NbyN matrix Q (usually the unitary matrix Q of Schur vectors returned by CHSEQR). On exit, if SIDE = aqRaq or aqBaq, VR contains: if HOWMNY = aqAaq, the matrix X of right eigenvectors of T; if HOWMNY = aqBaq, the matrix Q*X; if HOWMNY = aqSaq, the right eigenvectors of T specified by SELECT, stored consecutively in the columns of VR, in the same order as their eigenvalues. Not referenced if SIDE = aqLaq.
 LDVR (input) INTEGER
 The leading dimension of the array VR. LDVR >= 1, and if SIDE = aqRaq or aqBaq; LDVR >= 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 actually used to store the eigenvectors. If HOWMNY = aqAaq or aqBaq, M is set to N. Each selected eigenvector occupies one column.
 WORK (workspace) COMPLEX array, dimension (2*N)
 RWORK (workspace) REAL array, dimension (N)
 INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
FURTHER DETAILS
The algorithm used in this program is basically backward (forward) substitution, with scaling to make the the code robust against possible overflow.Each eigenvector is normalized so that the element of largest magnitude has magnitude 1; here the magnitude of a complex number (x,y) is taken to be x + y.