NAME

SYNOPSIS

  SUBROUTINE DTGEVC( SIDE, HOWMNY, SELECT, N, A, LDA, B, LDB, VL, 
 *      LDVL, VR, LDVR, MM, M, WORK, INFO)
  CHARACTER * 1 SIDE, HOWMNY
  INTEGER N, LDA, LDB, LDVL, LDVR, MM, M, INFO
  LOGICAL SELECT(*)
  DOUBLE PRECISION A(LDA,*), B(LDB,*), VL(LDVL,*), VR(LDVR,*), WORK(*)
 
  SUBROUTINE DTGEVC_64( SIDE, HOWMNY, SELECT, N, A, LDA, B, LDB, VL, 
 *      LDVL, VR, LDVR, MM, M, WORK, INFO)
  CHARACTER * 1 SIDE, HOWMNY
  INTEGER*8 N, LDA, LDB, LDVL, LDVR, MM, M, INFO
  LOGICAL*8 SELECT(*)
  DOUBLE PRECISION A(LDA,*), B(LDB,*), VL(LDVL,*), VR(LDVR,*), WORK(*)
 

F95 INTERFACE

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

C INTERFACE

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

void dtgevc_64(char side, char howmny, logical *select, long n, double *a, long lda, double *b, long ldb, double *vl, long ldvl, double *vr, long ldvr, long mm, long *m, long *info);

PURPOSE

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 orthogonal matrices. If (A,B) was obtained from the generalized real-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.

A must be block upper triangular, with 1-by-1 and 2-by-2 diagonal blocks. Corresponding to each 2-by-2 diagonal block is a complex conjugate pair of eigenvalues and eigenvectors; only one

eigenvector of the pair is computed, namely the one corresponding to the eigenvalue with positive imaginary part.

ARGUMENTS

* SIDE (input)

* HOWMNY (input)

* SELECT (input)

If HOWMNY='S', SELECT specifies the eigenvectors to be computed. If HOWMNY='A' or 'B', SELECT is not referenced. To select the real eigenvector corresponding to the real eigenvalue w(j), SELECT(j) must be set to .TRUE. To select the complex eigenvector corresponding to a complex conjugate pair w(j) and w(j+1), either SELECT(j) or SELECT(j+1) must be set to .TRUE..

* N (input)

The order of the matrices A and B. N >= 0.

* A (input)

The upper quasi-triangular matrix A.

* LDA (input)

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

* B (input)

The upper triangular matrix B. If A has a 2-by-2 diagonal block, then the corresponding 2-by-2 block of B must be diagonal with positive 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 orthogonal matrix Q of left Schur vectors returned by SHGEQZ). 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.

A complex eigenvector corresponding to a complex eigenvalue is stored in two consecutive columns, the first holding the real part, and the second the imaginary part.

* 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 orthogonal matrix Z of right Schur vectors returned by SHGEQZ). 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.

A complex eigenvector corresponding to a complex eigenvalue is stored in two consecutive columns, the first holding the real part and the second the imaginary part.

* 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 real eigenvector occupies one column and each selected complex eigenvector occupies two columns.

* WORK (workspace)

dimension(6*N)

* INFO (output)