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dgehrd.f(3)				      LAPACK				      dgehrd.f(3)

       dgehrd.f -

       subroutine dgehrd (N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO)

Function/Subroutine Documentation
   subroutine dgehrd (integerN, integerILO, integerIHI, double precision, dimension( lda, * )A,
       integerLDA, double precision, dimension( * )TAU, double precision, dimension( * )WORK,
       integerLWORK, integerINFO)


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


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


		     ILO is INTEGER


		     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 <= N, if N > 0; ILO=1 and IHI=0, if N=0.


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


		     TAU is DOUBLE PRECISION array, dimension (N-1)
		     The scalar factors of the elementary reflectors (see Further
		     Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to


		     WORK is DOUBLE PRECISION array, dimension (LWORK)
		     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.


		     The length of the array WORK.  LWORK >= max(1,N).
		     For optimum performance LWORK >= N*NB, where NB is the
		     optimal blocksize.

		     If LWORK = -1, then a workspace query is assumed; the routine
		     only calculates the optimal size of the WORK array, returns
		     this value as the first entry of the WORK array, and no error
		     message related to LWORK is issued by XERBLA.


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

	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

	   November 2011

       Further Details:

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

		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).

	     This file is a slight modification of LAPACK-3.0's DGEHRD
	     subroutine incorporating improvements proposed by Quintana-Orti and
	     Van de Geijn (2006). (See DLAHR2.)

       Definition at line 169 of file dgehrd.f.

       Generated automatically by Doxygen for LAPACK from the source code.

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