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shsein.f(3)				      LAPACK				      shsein.f(3)

NAME
       shsein.f -

SYNOPSIS
   Functions/Subroutines
       subroutine shsein (SIDE, EIGSRC, INITV, SELECT, N, H, LDH, WR, WI, VL, LDVL, VR, LDVR, MM,
	   M, WORK, IFAILL, IFAILR, INFO)
	   SHSEIN

Function/Subroutine Documentation
   subroutine shsein (characterSIDE, characterEIGSRC, characterINITV, logical, dimension( *
       )SELECT, integerN, real, dimension( ldh, * )H, integerLDH, real, dimension( * )WR, real,
       dimension( * )WI, real, dimension( ldvl, * )VL, integerLDVL, real, dimension( ldvr, * )VR,
       integerLDVR, integerMM, integerM, real, dimension( * )WORK, integer, dimension( * )IFAILL,
       integer, dimension( * )IFAILR, integerINFO)
       SHSEIN

       Purpose:

	    SHSEIN uses inverse iteration to find specified right and/or left
	    eigenvectors of a real 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 (WR,WI):
		     = 'Q': the eigenvalues were found using SHSEQR; 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 SHSEIN 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, SHSEIN 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
		     real eigenvector corresponding to a real eigenvalue WR(j),
		     SELECT(j) must be set to .TRUE.. To select the complex
		     eigenvector corresponding to a complex eigenvalue
		     (WR(j),WI(j)), with complex conjugate (WR(j+1),WI(j+1)),
		     either SELECT(j) or SELECT(j+1) or both must be set to
		     .TRUE.; then on exit SELECT(j) is .TRUE. and SELECT(j+1) is
		     .FALSE..

	   N

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

	   H

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

	   LDH

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

	   WR

		     WR is REAL array, dimension (N)

	   WI

		     WI is REAL array, dimension (N)

		     On entry, the real and imaginary parts of the eigenvalues of
		     H; a complex conjugate pair of eigenvalues must be stored in
		     consecutive elements of WR and WI.
		     On exit, WR may have been altered since close eigenvalues
		     are perturbed slightly in searching for independent
		     eigenvectors.

	   VL

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

	   WORK

		     WORK is REAL array, dimension ((N+2)*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 the i-th and (i+1)th
		     columns of VL hold a complex eigenvector, then IFAILL(i) and
		     IFAILL(i+1) are set to the same value.
		     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 the i-th and (i+1)th
		     columns of VR hold a complex eigenvector, then IFAILR(i) and
		     IFAILR(i+1) are set to the same value.
		     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 261 of file shsein.f.

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

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