strevc.f(3)							      LAPACK							       strevc.f(3)

NAME

       strevc.f -

SYNOPSIS

   Functions/Subroutines
       subroutine strevc (SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, MM, M, WORK, INFO)
	   STREVC

Function/Subroutine Documentation
   subroutine strevc (characterSIDE, characterHOWMNY, logical, dimension( * )SELECT, integerN, real, dimension( ldt, * )T, integerLDT, real,
       dimension( ldvl, * )VL, integerLDVL, real, dimension( ldvr, * )VR, integerLDVR, integerMM, integerM, real, dimension( * )WORK, integerINFO)
       STREVC

       Purpose:

	    STREVC computes some or all of the right and/or left eigenvectors of
	    a real upper quasi-triangular matrix T.
	    Matrices of this type are produced by the Schur factorization of
	    a real general matrix:  A = Q*T*Q**T, as computed by SHSEQR.

	    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)*T = w*(y**T)

	    where y**T denotes the transpose of y.
	    The eigenvalues are not input to this routine, but are read directly
	    from the diagonal blocks 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 orthogonal 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 by the matrices 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.
		     If w(j) is a real eigenvalue, the corresponding real
		     eigenvector is computed if SELECT(j) is .TRUE..
		     If w(j) and w(j+1) are the real and imaginary parts of a
		     complex eigenvalue, the corresponding complex eigenvector is
		     computed if either SELECT(j) or SELECT(j+1) is .TRUE., and
		     on exit SELECT(j) is set to .TRUE. and SELECT(j+1) is set to
		     .FALSE..
		     Not referenced if HOWMNY = 'A' or 'B'.

	   N

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

	   T

		     T is REAL array, dimension (LDT,N)
		     The upper quasi-triangular matrix T in Schur canonical form.

	   LDT

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

	   VL

		     VL is REAL 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 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;
		     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.
		     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 REAL 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 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;
		     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.
		     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 real eigenvector occupies one column and each
		     selected complex eigenvector occupies two columns.

	   WORK

		     WORK is REAL array, dimension (3*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 222 of file strevc.f.

Author
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Version 3.4.1							  Sun May 26 2013						       strevc.f(3)