debian man page for zgehd2

zgehd2.f(3)							      LAPACK							       zgehd2.f(3)

NAME
       zgehd2.f -

SYNOPSIS
   Functions/Subroutines
       subroutine zgehd2 (N, ILO, IHI, A, LDA, TAU, WORK, INFO)
	   ZGEHD2

Function/Subroutine Documentation
   subroutine zgehd2 (integerN, integerILO, integerIHI, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, complex*16,
       dimension( * )WORK, integerINFO)
       ZGEHD2

       Purpose:

	    ZGEHD2 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 ZGEBAL; otherwise they should be
		     set to 1 and N respectively. See Further Details.
		     1 <= ILO <= IHI <= max(1,N).

	   A

		     A is COMPLEX*16 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*16 array, dimension (N-1)
		     The scalar factors of the elementary reflectors (see Further
		     Details).

	   WORK

		     WORK is COMPLEX*16 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:
	   November 2011

       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 zgehd2.f.

Author
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Version 3.4.1							  Sun May 26 2013						       zgehd2.f(3)