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CHSEIN(l)					)					CHSEIN(l)

NAME
       CHSEIN  - use inverse iteration to find specified right and/or left eigenvectors of a com-
       plex upper Hessenberg matrix H

SYNOPSIS
       SUBROUTINE CHSEIN( SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W, VL, LDVL, VR, LDVR,  MM,  M,
			  WORK, RWORK, IFAILL, IFAILR, INFO )

	   CHARACTER	  EIGSRC, INITV, SIDE

	   INTEGER	  INFO, LDH, LDVL, LDVR, M, MM, N

	   LOGICAL	  SELECT( * )

	   INTEGER	  IFAILL( * ), IFAILR( * )

	   REAL 	  RWORK( * )

	   COMPLEX	  H( LDH, * ), VL( LDVL, * ), VR( LDVR, * ), W( * ), WORK( * )

PURPOSE
       CHSEIN  uses  inverse iteration to find specified right and/or left eigenvectors of a com-
       plex upper Hessenberg matrix H.	The right eigenvector x and the left eigenvector y of the
       matrix H corresponding to an eigenvalue w are defined by:

		    H * x = w * x,     y**h * H = w * y**h

       where y**h denotes the conjugate transpose of the vector y.

ARGUMENTS
       SIDE    (input) CHARACTER*1
	       = 'R': compute right eigenvectors only;
	       = 'L': compute left eigenvectors only;
	       = 'B': compute both right and left eigenvectors.

       EIGSRC  (input) CHARACTER*1
	       Specifies the source of eigenvalues supplied in W:
	       =  'Q':	the  eigenvalues were found using CHSEQR; thus, if H has zero subdiagonal
	       elements, and so is block-triangular, then the j-th eigenvalue can be  assumed  to
	       be  an  eigenvalue  of  the  block  containing the j-th row/column.  This property
	       allows CHSEIN to perform inverse iteration on just one diagonal block.  = 'N':  no
	       assumptions  are  made  on  the	correspondence	between  eigenvalues and diagonal
	       blocks.	In this case, CHSEIN must always  perform  inverse  iteration  using  the
	       whole matrix H.

       INITV   (input) CHARACTER*1
	       = 'N': no initial vectors are supplied;
	       = 'U': user-supplied initial vectors are stored in the arrays VL and/or VR.

       SELECT  (input) LOGICAL array, dimension (N)
	       Specifies the eigenvectors to be computed. To select the eigenvector corresponding
	       to the eigenvalue W(j), SELECT(j) must be set to .TRUE..

       N       (input) INTEGER
	       The order of the matrix H.  N >= 0.

       H       (input) COMPLEX array, dimension (LDH,N)
	       The upper Hessenberg matrix H.

       LDH     (input) INTEGER
	       The leading dimension of the array H.  LDH >= max(1,N).

       W       (input/output) COMPLEX array, dimension (N)
	       On entry, the eigenvalues of H.	On exit, the  real  parts  of  W  may  have  been
	       altered	since  close eigenvalues are perturbed slightly in searching for indepen-
	       dent eigenvectors.

       VL      (input/output) COMPLEX array, dimension (LDVL,MM)
	       On entry, if INITV = 'U' and SIDE = 'L' or 'B', VL must contain	starting  vectors
	       for  the inverse iteration for the left eigenvectors; the starting vector for each
	       eigenvector must be in the same column in which the eigenvector	will  be  stored.
	       On  exit,  if SIDE = 'L' or 'B', the left eigenvectors specified by SELECT will be
	       stored consecutively in the columns of VL, in the same order as their eigenvalues.
	       If SIDE = 'R', VL is not referenced.

       LDVL    (input) INTEGER
	       The  leading  dimension	of  the array VL.  LDVL >= max(1,N) if SIDE = 'L' or 'B';
	       LDVL >= 1 otherwise.

       VR      (input/output) COMPLEX array, dimension (LDVR,MM)
	       On entry, if INITV = 'U' and SIDE = 'R' or 'B', VR must contain	starting  vectors
	       for the inverse iteration for the right eigenvectors; the starting vector for each
	       eigenvector must be in the same column in which the eigenvector	will  be  stored.
	       On  exit, if SIDE = 'R' or 'B', the right eigenvectors specified by SELECT will be
	       stored consecutively in the columns of VR, in the same order as their eigenvalues.
	       If SIDE = 'L', VR is not referenced.

       LDVR    (input) INTEGER
	       The  leading  dimension	of  the array VR.  LDVR >= max(1,N) if SIDE = 'R' or 'B';
	       LDVR >= 1 otherwise.

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

       M       (output) INTEGER
	       The number of columns in the arrays VL and/or VR required to store  the	eigenvec-
	       tors (= the number of .TRUE. elements in SELECT).

       WORK    (workspace) COMPLEX array, dimension (N*N)

       RWORK   (workspace) REAL array, dimension (N)

       IFAILL  (output) INTEGER array, dimension (MM)
	       If SIDE = 'L' or 'B', IFAILL(i) = j > 0 if the left eigenvector in the i-th column
	       of VL (corresponding to the eigenvalue w(j)) failed to converge; IFAILL(i) = 0  if
	       the  eigenvector  converged  satisfactorily.   If SIDE = 'R', IFAILL is not refer-
	       enced.

       IFAILR  (output) INTEGER array, dimension (MM)
	       If SIDE = 'R' or 'B', IFAILR(i) = j > 0 if the right eigenvector in the i-th  col-
	       umn of VR (corresponding to the eigenvalue w(j)) failed to converge; IFAILR(i) = 0
	       if the eigenvector converged satisfactorily.  If SIDE = 'L', IFAILR is not  refer-
	       enced.

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value
	       >  0:   if INFO = i, i is the number of eigenvectors which failed to converge; see
	       IFAILL and IFAILR for further details.

FURTHER DETAILS
       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|.

LAPACK version 3.0			   15 June 2000 				CHSEIN(l)
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