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RedHat 9 (Linux i386) - man page for shsein (redhat section l)

SHSEIN(l)					)					SHSEIN(l)

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

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

	   CHARACTER	  EIGSRC, INITV, SIDE

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

	   LOGICAL	  SELECT( * )

	   INTEGER	  IFAILL( * ), IFAILR( * )

	   REAL 	  H( LDH, * ), VL( LDVL, * ), VR( LDVR, * ), WI( * ), WORK( * ), WR( * )

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.

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 (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   (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/output) LOGICAL array, dimension (N)
	       Specifies  the  eigenvectors to be computed. To select the real eigenvector corre-
	       sponding 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

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

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

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

       WR      (input/output) REAL array, dimension (N)
	       WI	(input)  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      (input/output) 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 con-
	       secutive columns, the first holding the real part and  the  second  the	imaginary
	       part.  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) 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 con-
	       secutive columns, the first holding the real part and  the  second  the	imaginary
	       part.  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; each selected real eigenvector occupies one column and each selected complex
	       eigenvector occupies two columns.

       WORK    (workspace) REAL array, dimension ((N+2)*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 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  (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 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    (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 				SHSEIN(l)


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