ZTGEVC computes some or all of the right and/or left eigenvectors of


 a pair of complex matrices (S,P), where S and P are upper triangular.


 Matrix pairs of this type are produced by the generalized Schur


 factorization of a complex matrix pair (A,B):


 


    A = Q*S*Z**H,  B = Q*P*Z**H


 


 as computed by ZGGHRD + ZHGEQZ.


 


 The right eigenvector x and the left eigenvector y of (S,P)


 corresponding to an eigenvalue w are defined by:


 


    S*x = w*P*x,  (y**H)*S = w*(y**H)*P,


 


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


 The eigenvalues are not input to this routine, but are computed


 directly from the diagonal elements of S and P.


 


 This routine returns the matrices X and/or Y of right and left


 eigenvectors of (S,P), or the products Z*X and/or Q*Y,


 where Z and Q are input matrices.


 If Q and Z are the unitary factors from the generalized Schur


 factorization of a matrix pair (A,B), then Z*X and Q*Y


 are the matrices of right and left eigenvectors of (A,B).

SIDE

          SIDE is CHARACTER*1


          = 'R': compute right eigenvectors only;


          = 'L': compute left eigenvectors only;


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

HOWMNY

          HOWMNY is CHARACTER*1


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


          = 'B': compute all right and/or left eigenvectors,


                 backtransformed by the matrices in VR and/or VL;


          = 'S': compute selected right and/or left eigenvectors,


                 specified by the logical array SELECT.

SELECT

          SELECT is LOGICAL array, dimension (N)


          If HOWMNY='S', SELECT specifies the eigenvectors to be


          computed.  The eigenvector corresponding to the j-th


          eigenvalue is computed if SELECT(j) = .TRUE..


          Not referenced if HOWMNY = 'A' or 'B'.

N

          N is INTEGER


          The order of the matrices S and P.  N >= 0.

S

          S is COMPLEX*16 array, dimension (LDS,N)


          The upper triangular matrix S from a generalized Schur


          factorization, as computed by ZHGEQZ.

LDS

          LDS is INTEGER


          The leading dimension of array S.  LDS >= max(1,N).

P

          P is COMPLEX*16 array, dimension (LDP,N)


          The upper triangular matrix P from a generalized Schur


          factorization, as computed by ZHGEQZ.  P must have real


          diagonal elements.

LDP

          LDP is INTEGER


          The leading dimension of array P.  LDP >= max(1,N).

VL

          VL is COMPLEX*16 array, dimension (LDVL,MM)


          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 ZHGEQZ).


          On exit, if SIDE = 'L' or 'B', VL contains:


          if HOWMNY = 'A', the matrix Y of left eigenvectors of (S,P);


          if HOWMNY = 'B', the matrix Q*Y;


          if HOWMNY = 'S', the left eigenvectors of (S,P) specified by


                      SELECT, stored consecutively in the columns of


                      VL, in the same order as their eigenvalues.


          Not referenced if SIDE = 'R'.

LDVL

          LDVL is INTEGER


          The leading dimension of array VL.  LDVL >= 1, and if


          SIDE = 'L' or 'l' or 'B' or 'b', LDVL >= N.

VR

          VR is COMPLEX*16 array, dimension (LDVR,MM)


          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 ZHGEQZ).


          On exit, if SIDE = 'R' or 'B', VR contains:


          if HOWMNY = 'A', the matrix X of right eigenvectors of (S,P);


          if HOWMNY = 'B', the matrix Z*X;


          if HOWMNY = 'S', the right eigenvectors of (S,P) specified by


                      SELECT, stored consecutively in the columns of


                      VR, in the same order as their eigenvalues.


          Not referenced if SIDE = 'L'.

LDVR

          LDVR is INTEGER


          The leading dimension of the array VR.  LDVR >= 1, and if


          SIDE = 'R' or 'B', LDVR >= N.

MM

          MM is INTEGER


          The number of columns in the arrays VL and/or VR. MM >= M.

M

          M is INTEGER


          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

          WORK is COMPLEX*16 array, dimension (2*N)

RWORK

          RWORK is DOUBLE PRECISION array, dimension (2*N)

INFO

          INFO is INTEGER


          = 0:  successful exit.


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

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

November 2011