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RedHat 9 (Linux i386) - man page for dgehd2 (redhat section l)

DGEHD2(l)					)					DGEHD2(l)

NAME
       DGEHD2  - reduce a real general matrix A to upper Hessenberg form H by an orthogonal simi-
       larity transformation

SYNOPSIS
       SUBROUTINE DGEHD2( N, ILO, IHI, A, LDA, TAU, WORK, INFO )

	   INTEGER	  IHI, ILO, INFO, LDA, N

	   DOUBLE	  PRECISION A( LDA, * ), TAU( * ), WORK( * )

PURPOSE
       DGEHD2 reduces a real general matrix A to upper Hessenberg form H by an	orthogonal  simi-
       larity transformation: Q' * A * Q = H .

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

       ILO     (input) INTEGER
	       IHI	(input)  INTEGER It is assumed that A is already upper triangular in rows
	       and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally set by a  previous  call
	       to  DGEBAL;  otherwise  they  should  be  set to 1 and N respectively. See Further
	       Details.

       A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
	       On entry, the n by n general matrix to be reduced.  On exit,  the  upper  triangle
	       and the first subdiagonal of A are overwritten with the upper Hessenberg matrix H,
	       and the elements below the first subdiagonal, with the array  TAU,  represent  the
	       orthogonal  matrix  Q  as a product of elementary reflectors. See Further Details.
	       LDA     (input) INTEGER The leading dimension of the array A.  LDA >= max(1,N).

       TAU     (output) DOUBLE PRECISION array, dimension (N-1)
	       The scalar factors of the elementary reflectors (see Further Details).

       WORK    (workspace) DOUBLE PRECISION array, dimension (N)

       INFO    (output) INTEGER
	       = 0:  successful exit.
	       < 0:  if INFO = -i, the i-th argument had an illegal value.

FURTHER DETAILS
       The matrix Q is represented as a product of (ihi-ilo) elementary reflectors

	  Q = H(ilo) H(ilo+1) . . . H(ihi-1).

       Each H(i) has the form

	  H(i) = I - tau * v * v'

       where tau is a real scalar, and v is a real vector with
       v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on exit	in  A(i+2:ihi,i),
       and tau in TAU(i).

       The  contents of A are illustrated by the following example, with n = 7, ilo = 2 and ihi =
       6:

       on entry,			on exit,

       ( a   a	 a   a	 a   a	 a )	(  a   a   h   h   h   h   a ) (     a	 a    a    a	a
       a  )	(	a   h	h   h	h   a ) (     a   a   a   a   a   a )	 (	h   h	h
       h   h   h ) (	 a   a	 a   a	 a   a )    (	   v2  h   h   h   h   h )  (	   a	a
       a    a	 a    a  )     (       v2  v3  h   h   h   h ) (     a	 a   a	 a   a	 a )	(
       v2  v3  v4  h   h   h ) (			 a )	(			   a )

       where a denotes an element of the original matrix A, h denotes a modified element  of  the
       upper Hessenberg matrix H, and vi denotes an element of the vector defining H(i).

LAPACK version 3.0			   15 June 2000 				DGEHD2(l)


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