dgehd2()

subroutine dgehd2	(	integer	n,
		integer	ilo,
		integer	ihi,
		double precision, dimension( lda, * )	a,
		integer	lda,
		double precision, dimension( * )	tau,
		double precision, dimension( * )	work,
		integer	info )

DGEHD2 reduces a general square matrix to upper Hessenberg form using an unblocked algorithm.

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Purpose:

!>
!> DGEHD2 reduces a real general matrix A to upper Hessenberg form H by
!> an orthogonal similarity transformation:  Q**T * A * Q = H .
!> 

Parameters

[in]	N	!> N is INTEGER !> The order of the matrix A. N >= 0. !>
[in]	ILO	!> ILO is INTEGER !>
[in]	IHI	!> IHI is 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. !> 1 <= ILO <= IHI <= max(1,N). !>
[in,out]	A	!> A is 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. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !>
[out]	TAU	!> TAU is DOUBLE PRECISION array, dimension (N-1) !> The scalar factors of the elementary reflectors (see Further !> Details). !>
[out]	WORK	!> WORK is DOUBLE PRECISION array, dimension (N) !>
[out]	INFO	!> INFO is INTEGER !> = 0: successful exit. !> < 0: if INFO = -i, the i-th argument had an illegal value. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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**T
!>
!>  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).
!>