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ctrevc.f(3)				      LAPACK				      ctrevc.f(3)

NAME
       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 (characterSIDE, characterHOWMNY, logical, dimension( * )SELECT, integerN,
       complex, dimension( ldt, * )T, integerLDT, complex, dimension( ldvl, * )VL, integerLDVL,
       complex, dimension( ldvr, * )VR, integerLDVR, integerMM, integerM, complex, dimension( *
       )WORK, real, dimension( * )RWORK, integerINFO)
       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:
	   November 2011

       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 218 of file ctrevc.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      ctrevc.f(3)
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