CGEHD2 man page on Oracle

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cgehd2.f(3)			    LAPACK			   cgehd2.f(3)

NAME
       cgehd2.f -

SYNOPSIS
   Functions/Subroutines
       subroutine cgehd2 (N, ILO, IHI, A, LDA, TAU, WORK, INFO)
	   CGEHD2 reduces a general square matrix to upper Hessenberg form
	   using an unblocked algorithm.

Function/Subroutine Documentation
   subroutine cgehd2 (integerN, integerILO, integerIHI, complex, dimension(
       lda, * )A, integerLDA, complex, dimension( * )TAU, complex, dimension(
       * )WORK, integerINFO)
       CGEHD2 reduces a general square matrix to upper Hessenberg form using
       an unblocked algorithm.

       Purpose:

	    CGEHD2 reduces a complex general matrix A to upper Hessenberg form H
	    by a unitary similarity transformation:  Q**H * 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 CGEBAL; otherwise they should be
		     set to 1 and N respectively. See Further Details.
		     1 <= ILO <= IHI <= max(1,N).

	   A

		     A is COMPLEX 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 unitary 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 COMPLEX array, dimension (N-1)
		     The scalar factors of the elementary reflectors (see Further
		     Details).

	   WORK

		     WORK is COMPLEX 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**H

	     where tau is a complex scalar, and v is a complex 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 cgehd2.f.

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

Version 3.4.2			Tue Sep 25 2012			   cgehd2.f(3)
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