ztgevc.f (3) - Linux Manuals

NAME

ztgevc.f -

SYNOPSIS

Functions/Subroutines

subroutine ztgevc (SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO)
ZTGEVC

Function/Subroutine Documentation

subroutine ztgevc (characterSIDE, characterHOWMNY, logical, dimension( * )SELECT, integerN, complex*16, dimension( lds, * )S, integerLDS, complex*16, dimension( ldp, * )P, integerLDP, complex*16, dimension( ldvl, * )VL, integerLDVL, complex*16, dimension( ldvr, * )VR, integerLDVR, integerMM, integerM, complex*16, dimension( * )WORK, double precision, dimension( * )RWORK, integerINFO)

ZTGEVC

Purpose:

 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).

 

Parameters:

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.

 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 219 of file ztgevc.f.

Author

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