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

DHSEIN(l)					)					DHSEIN(l)

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

SYNOPSIS
       SUBROUTINE DHSEIN( 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( * )

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

PURPOSE
       DHSEIN 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 DHSEQR; 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  DHSEIN 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,  DHSEIN  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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (N)
	       WI      (input) DOUBLE PRECISION array, dimension (N) On entry, the real and imag-
	       inary  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 eigen-
	       vectors.

       VL      (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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 				DHSEIN(l)


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