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CentOS 7.0 - man page for chsein (centos section 3)

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chsein.f(3)				      LAPACK				      chsein.f(3)

NAME
       chsein.f -

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

Function/Subroutine Documentation
   subroutine chsein (characterSIDE, characterEIGSRC, characterINITV, logical, dimension( *
       )SELECT, integerN, complex, dimension( ldh, * )H, integerLDH, complex, dimension( * )W,
       complex, dimension( ldvl, * )VL, integerLDVL, complex, dimension( ldvr, * )VR,
       integerLDVR, integerMM, integerM, complex, dimension( * )WORK, real, dimension( * )RWORK,
       integer, dimension( * )IFAILL, integer, dimension( * )IFAILR, integerINFO)
       CHSEIN

       Purpose:

	    CHSEIN uses inverse iteration to find specified right and/or left
	    eigenvectors of a complex 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.

       Parameters:
	   SIDE

		     SIDE is CHARACTER*1
		     = 'R': compute right eigenvectors only;
		     = 'L': compute left eigenvectors only;
		     = 'B': compute both right and left eigenvectors.

	   EIGSRC

		     EIGSRC is 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

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

	   SELECT

		     SELECT is 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

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

	   H

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

	   LDH

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

	   W

		     W is 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
		     independent eigenvectors.

	   VL

		     VL is 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

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

	   VR

		     VR is 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

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

	   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 required to
		     store the eigenvectors (= the number of .TRUE. elements in
		     SELECT).

	   WORK

		     WORK is COMPLEX array, dimension (N*N)

	   RWORK

		     RWORK is REAL array, dimension (N)

	   IFAILL

		     IFAILL is 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 referenced.

	   IFAILR

		     IFAILR is INTEGER array, dimension (MM)
		     If SIDE = 'R' or 'B', IFAILR(i) = j > 0 if the right
		     eigenvector in the i-th column 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 referenced.

	   INFO

		     INFO is 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.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       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|.

       Definition at line 243 of file chsein.f.

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

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