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dgehd2.f(3)				      LAPACK				      dgehd2.f(3)

NAME
       dgehd2.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dgehd2 (N, ILO, IHI, A, LDA, TAU, WORK, INFO)
	   DGEHD2 reduces a general square matrix to upper Hessenberg form using an unblocked
	   algorithm.

Function/Subroutine Documentation
   subroutine dgehd2 (integerN, integerILO, integerIHI, double precision, dimension( lda, * )A,
       integerLDA, double precision, dimension( * )TAU, double precision, dimension( * )WORK,
       integerINFO)
       DGEHD2 reduces a general square matrix to upper Hessenberg form using an unblocked
       algorithm.

       Purpose:

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

       Parameters:
	   N

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

	   ILO

		     ILO is INTEGER

	   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).

	   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.

	   LDA

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

	   TAU

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

	   WORK

		     WORK is DOUBLE PRECISION array, dimension (N)

	   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.

       Date:
	   September 2012

       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).

       Definition at line 150 of file dgehd2.f.

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

Version 3.4.2				 Tue Sep 25 2012			      dgehd2.f(3)
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