NAME

ztrevc - compute some or all of the right and/or left eigenvectors of a complex upper triangular matrix T

SYNOPSIS

  SUBROUTINE ZTREVC( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, 
 *      LDVR, MM, M, WORK, RWORK, INFO)
  CHARACTER * 1 SIDE, HOWMNY
  DOUBLE COMPLEX T(LDT,*), VL(LDVL,*), VR(LDVR,*), WORK(*)
  INTEGER N, LDT, LDVL, LDVR, MM, M, INFO
  LOGICAL SELECT(*)
  DOUBLE PRECISION RWORK(*)

  SUBROUTINE ZTREVC_64( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, 
 *      LDVR, MM, M, WORK, RWORK, INFO)
  CHARACTER * 1 SIDE, HOWMNY
  DOUBLE COMPLEX T(LDT,*), VL(LDVL,*), VR(LDVR,*), WORK(*)
  INTEGER*8 N, LDT, LDVL, LDVR, MM, M, INFO
  LOGICAL*8 SELECT(*)
  DOUBLE PRECISION RWORK(*)

F95 INTERFACE

  SUBROUTINE TREVC( SIDE, HOWMNY, SELECT, [N], T, [LDT], VL, [LDVL], 
 *       VR, [LDVR], MM, M, [WORK], [RWORK], [INFO])
  CHARACTER(LEN=1) :: SIDE, HOWMNY
  COMPLEX(8), DIMENSION(:) :: WORK
  COMPLEX(8), DIMENSION(:,:) :: T, VL, VR
  INTEGER :: N, LDT, LDVL, LDVR, MM, M, INFO
  LOGICAL, DIMENSION(:) :: SELECT
  REAL(8), DIMENSION(:) :: RWORK

  SUBROUTINE TREVC_64( SIDE, HOWMNY, SELECT, [N], T, [LDT], VL, [LDVL], 
 *       VR, [LDVR], MM, M, [WORK], [RWORK], [INFO])
  CHARACTER(LEN=1) :: SIDE, HOWMNY
  COMPLEX(8), DIMENSION(:) :: WORK
  COMPLEX(8), DIMENSION(:,:) :: T, VL, VR
  INTEGER(8) :: N, LDT, LDVL, LDVR, MM, M, INFO
  LOGICAL(8), DIMENSION(:) :: SELECT
  REAL(8), DIMENSION(:) :: RWORK

C INTERFACE

#include <sunperf.h>

void ztrevc(char side, char howmny, logical *select, int n, doublecomplex *t, int ldt, doublecomplex *vl, int ldvl, doublecomplex *vr, int ldvr, int mm, int *m, int *info);

void ztrevc_64(char side, char howmny, logical *select, long n, doublecomplex *t, long ldt, doublecomplex *vl, long ldvl, doublecomplex *vr, long ldvr, long mm, long *m, long *info);

PURPOSE

ztrevc computes some or all of the 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'*T = w*y'

where y' denotes the conjugate transpose of the vector y.

If all eigenvectors are requested, 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', then Q*X and Q*Y are the matrices of right or left eigenvectors of A.

ARGUMENTS

SIDE (input)

 = 'R':  compute right eigenvectors only;

 = 'L':  compute left eigenvectors only;

 = 'B':  compute both right and left eigenvectors.

HOWMNY (input)

 = 'A':  compute all right and/or left eigenvectors;

 = 'B':  compute all right and/or left eigenvectors,
and backtransform them using the input matrices
supplied in VR and/or VL;
 = 'S':  compute selected right and/or left eigenvectors,
specified by the logical array SELECT.

SELECT (input/output)
If HOWMNY = 'S', SELECT specifies the eigenvectors to be computed. If HOWMNY = 'A' or 'B', SELECT is not referenced. To select the eigenvector corresponding to the j-th eigenvalue, SELECT(j) must be set to .TRUE..
N (input)
The order of the matrix T. N > = 0.
T (input/output)
The upper triangular matrix T. T is modified, but restored on exit.
LDT (input)
The leading dimension of the array T. LDT > = max(1,N).
VL (input/output)
On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must contain an N-by-N matrix Q (usually the unitary matrix Q of Schur vectors returned by CHSEQR). On exit, if SIDE = 'L' or 'B', VL contains: if HOWMNY = 'A', the matrix Y of left eigenvectors of T; VL is lower triangular. The i-th column VL(i) of VL is the eigenvector corresponding to T(i,i). if HOWMNY = 'B', 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 SIDE = 'R', VL is not referenced.
LDVL (input)
The leading dimension of the array VL. LDVL > = max(1,N) if SIDE = 'L' or 'B'; LDVL > = 1 otherwise.
VR (input/output)
On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must contain an N-by-N matrix Q (usually the unitary matrix Q of Schur vectors returned by CHSEQR). On exit, if SIDE = 'R' or 'B', VR contains: if HOWMNY = 'A', the matrix X of right eigenvectors of T; VR is upper triangular. The i-th column VR(i) of VR is the eigenvector corresponding to T(i,i). if HOWMNY = 'B', 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 SIDE = 'L', VR is not referenced.
LDVR (input)
The leading dimension of the array VR. LDVR > = max(1,N) if SIDE = 'R' or 'B'; LDVR > = 1 otherwise.
MM (input)
The number of columns in the arrays VL and/or VR. MM > = M.
M (output)
The number of columns in the arrays VL and/or VR actually used to store the eigenvectors. If HOWMNY = 'A' or 'B', M is set to N. Each selected eigenvector occupies one column.
WORK (workspace)
dimension(2*N)
RWORK (workspace)
dimension(N)

INFO (output)

 = 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 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|.