• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

ctgevc - compute some or all of the right and/or left generalized eigenvectors of a pair of complex upper triangular matrices (A,B)

SYNOPSIS

  SUBROUTINE CTGEVC( SIDE, HOWMNY, SELECT, N, A, LDA, B, LDB, VL, 
 *      LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO)
  CHARACTER * 1 SIDE, HOWMNY
  COMPLEX A(LDA,*), B(LDB,*), VL(LDVL,*), VR(LDVR,*), WORK(*)
  INTEGER N, LDA, LDB, LDVL, LDVR, MM, M, INFO
  LOGICAL SELECT(*)
  REAL RWORK(*)

  SUBROUTINE CTGEVC_64( SIDE, HOWMNY, SELECT, N, A, LDA, B, LDB, VL, 
 *      LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO)
  CHARACTER * 1 SIDE, HOWMNY
  COMPLEX A(LDA,*), B(LDB,*), VL(LDVL,*), VR(LDVR,*), WORK(*)
  INTEGER*8 N, LDA, LDB, LDVL, LDVR, MM, M, INFO
  LOGICAL*8 SELECT(*)
  REAL RWORK(*)

F95 INTERFACE

  SUBROUTINE TGEVC( SIDE, HOWMNY, SELECT, [N], A, [LDA], B, [LDB], VL, 
 *       [LDVL], VR, [LDVR], MM, M, [WORK], [RWORK], [INFO])
  CHARACTER(LEN=1) :: SIDE, HOWMNY
  COMPLEX, DIMENSION(:) :: WORK
  COMPLEX, DIMENSION(:,:) :: A, B, VL, VR
  INTEGER :: N, LDA, LDB, LDVL, LDVR, MM, M, INFO
  LOGICAL, DIMENSION(:) :: SELECT
  REAL, DIMENSION(:) :: RWORK

  SUBROUTINE TGEVC_64( SIDE, HOWMNY, SELECT, [N], A, [LDA], B, [LDB], 
 *       VL, [LDVL], VR, [LDVR], MM, M, [WORK], [RWORK], [INFO])
  CHARACTER(LEN=1) :: SIDE, HOWMNY
  COMPLEX, DIMENSION(:) :: WORK
  COMPLEX, DIMENSION(:,:) :: A, B, VL, VR
  INTEGER(8) :: N, LDA, LDB, LDVL, LDVR, MM, M, INFO
  LOGICAL(8), DIMENSION(:) :: SELECT
  REAL, DIMENSION(:) :: RWORK

C INTERFACE

#include <sunperf.h>

void ctgevc(char side, char howmny, logical *select, int n, complex *a, int lda, complex *b, int ldb, complex *vl, int ldvl, complex *vr, int ldvr, int mm, int *m, int *info);

void ctgevc_64(char side, char howmny, logical *select, long n, complex *a, long lda, complex *b, long ldb, complex *vl, long ldvl, complex *vr, long ldvr, long mm, long *m, long *info);

PURPOSE

ctgevc computes some or all of the right and/or left generalized eigenvectors of a pair of complex upper triangular matrices (A,B).

The right generalized eigenvector x and the left generalized eigenvector y of (A,B) corresponding to a generalized eigenvalue w are defined by:

        (A - wB) * x = 0  and  y**H * (A - wB) = 0

where y**H denotes the conjugate tranpose of y.

If an eigenvalue w is determined by zero diagonal elements of both A and B, a unit vector is returned as the corresponding eigenvector.

If all eigenvectors are requested, the routine may either return the matrices X and/or Y of right or left eigenvectors of (A,B), or the products Z*X and/or Q*Y, where Z and Q are input unitary matrices. If (A,B) was obtained from the generalized Schur factorization of an original pair of matrices

   (A0,B0) = (Q*A*Z**H,Q*B*Z**H),

then Z*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)
  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 matrices A and B. N > = 0.

• A (input)
  The upper triangular matrix A.

• LDA (input)
  The leading dimension of array A. LDA > = max(1,N).

• B (input)
  The upper triangular matrix B. B must have real diagonal elements.

• LDB (input)
  The leading dimension of array B. LDB > = 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 left Schur vectors returned by CHGEQZ). On exit, if SIDE = 'L' or 'B', VL contains: if HOWMNY = 'A', the matrix Y of left eigenvectors of (A,B); if HOWMNY = 'B', the matrix Q*Y; if HOWMNY = 'S', the left eigenvectors of (A,B) 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 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 Z of right Schur vectors returned by CHGEQZ). On exit, if SIDE = 'R' or 'B', VR contains: if HOWMNY = 'A', the matrix X of right eigenvectors of (A,B); if HOWMNY = 'B', the matrix Z*X; if HOWMNY = 'S', the right eigenvectors of (A,B) 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(2*N)

• INFO (output)
  

   = 0:  successful exit.

   < 0:  if INFO  = -i, the i-th argument had an illegal value.