ctrevc.f man page

ctrevc.f —

Synopsis

Functions/Subroutines

subroutine ctrevc (SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO)
CTREVC

Function/Subroutine Documentation

subroutine ctrevc (character SIDE, character HOWMNY, logical, dimension( * ) SELECT, integer N, complex, dimension( ldt, * ) T, integer LDT, complex, dimension( ldvl, * ) VL, integer LDVL, complex, dimension( ldvr, * ) VR, integer LDVR, integer MM, integer M, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer INFO)

CTREVC  

Purpose:

 CTREVC computes some or all of the right and/or left eigenvectors of
 a complex upper triangular matrix T.
 Matrices of this type are produced by the Schur factorization of
 a complex general matrix:  A = Q*T*Q**H, as computed by CHSEQR.

 The right eigenvector x and the left eigenvector y of T corresponding
 to an eigenvalue w are defined by:

              T*x = w*x,     (y**H)*T = w*(y**H)

 where y**H denotes the conjugate transpose of the vector y.
 The eigenvalues are not input to this routine, but are read directly
 from the diagonal of T.

 This routine returns the matrices X and/or Y of right and left
 eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an
 input matrix.  If Q is the unitary factor that reduces a matrix A to
 Schur form T, then Q*X and Q*Y are the matrices of right and left
 eigenvectors of A.
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 using the matrices supplied in
                  VR and/or VL;
          = 'S':  compute selected right and/or left eigenvectors,
                  as indicated 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 matrix T. N >= 0.

T

          T is COMPLEX array, dimension (LDT,N)
          The upper triangular matrix T.  T is modified, but restored
          on exit.

LDT

          LDT is INTEGER
          The leading dimension of the array T. LDT >= max(1,N).

VL

          VL is COMPLEX 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
          Schur vectors returned by CHSEQR).
          On exit, if SIDE = 'L' or 'B', VL contains:
          if HOWMNY = 'A', the matrix Y of left eigenvectors of T;
          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.
          Not referenced if SIDE = 'R'.

LDVL

          LDVL is INTEGER
          The leading dimension of the array VL.  LDVL >= 1, and if
          SIDE = 'L' or 'B', LDVL >= N.

VR

          VR is COMPLEX 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 Q of
          Schur vectors returned by CHSEQR).
          On exit, if SIDE = 'R' or 'B', VR contains:
          if HOWMNY = 'A', the matrix X of right eigenvectors of T;
          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.
          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 array, dimension (2*N)

RWORK

          RWORK is REAL array, dimension (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:

December 2016

Further Details:

  The algorithm used in this program is basically backward (forward)
  substitution, with scaling to make the the code robust against
  possible overflow.

  Each eigenvector is normalized so that the element of largest
  magnitude has magnitude 1; here the magnitude of a complex number
  (x,y) is taken to be |x| + |y|.

Definition at line 220 of file ctrevc.f.

Author

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Referenced By

The man page ctrevc(3) is an alias of ctrevc.f(3).

Sat Jun 24 2017 Version 3.7.1 LAPACK