NAME

SYNOPSIS

  SUBROUTINE STREVC( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, 
 *      LDVR, MM, M, WORK, INFO)
  CHARACTER * 1 SIDE, HOWMNY
  INTEGER N, LDT, LDVL, LDVR, MM, M, INFO
  LOGICAL SELECT(*)
  REAL T(LDT,*), VL(LDVL,*), VR(LDVR,*), WORK(*)
 
  SUBROUTINE STREVC_64( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, 
 *      LDVR, MM, M, WORK, INFO)
  CHARACTER * 1 SIDE, HOWMNY
  INTEGER*8 N, LDT, LDVL, LDVR, MM, M, INFO
  LOGICAL*8 SELECT(*)
  REAL T(LDT,*), VL(LDVL,*), VR(LDVR,*), WORK(*)
 

F95 INTERFACE

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

C INTERFACE

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

void strevc_64(char side, char howmny, logical *select, long n, float *t, long ldt, float *vl, long ldvl, float *vr, long ldvr, long mm, long *m, long *info);

PURPOSE

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 orthogonal

matrix. If T was obtained from the real-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.

T must be in Schur canonical form (as returned by SHSEQR), that is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block has its diagonal elements equal and its off-diagonal elements of opposite sign. 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/output)

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 a 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.; then on exit SELECT(j) is .TRUE. and SELECT(j+1) is .FALSE..

* N (input)

The order of the matrix T. N >= 0.

* T (input/output)

The upper quasi-triangular matrix T in Schur canonical form.

* 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 orthogonal matrix Q of Schur vectors returned by SHSEQR). On exit, if SIDE = 'L' or 'B', VL contains: if HOWMNY = 'A', the matrix Y of left eigenvectors of T; VL has the same quasi-lower triangular form as T'. If T(i,i) is a real eigenvalue, then the i-th column VL(i) of VL is its corresponding eigenvector. If T(i:i+1,i:i+1) is a 2-by-2 block whose eigenvalues are complex-conjugate eigenvalues of T, then VL(i)+sqrt(-1)*VL(i+1) is the complex eigenvector corresponding to the eigenvalue with positive real part. 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. 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. 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 orthogonal matrix Q of Schur vectors returned by SHSEQR). On exit, if SIDE = 'R' or 'B', VR contains: if HOWMNY = 'A', the matrix X of right eigenvectors of T; VR has the same quasi-upper triangular form as T. If T(i,i) is a real eigenvalue, then the i-th column VR(i) of VR is its corresponding eigenvector. If T(i:i+1,i:i+1) is a 2-by-2 block whose eigenvalues are complex-conjugate eigenvalues of T, then VR(i)+sqrt(-1)*VR(i+1) is the complex eigenvector corresponding to the eigenvalue with positive real part. 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. 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. 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 real eigenvector occupies one column and each selected complex eigenvector occupies two columns.

* WORK (workspace)

dimension(3*N)

* INFO (output)