Unix/Linux Go Back    


CentOS 7.0 - man page for zgehd2 (centos section 3)

Linux & Unix Commands - Search Man Pages
Man Page or Keyword Search:   man
Select Man Page Set:       apropos Keyword Search (sections above)


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

NAME
       zgehd2.f -

SYNOPSIS
   Functions/Subroutines
       subroutine zgehd2 (N, ILO, IHI, A, LDA, TAU, WORK, INFO)
	   ZGEHD2 reduces a general square matrix to upper Hessenberg form using an unblocked
	   algorithm.

Function/Subroutine Documentation
   subroutine zgehd2 (integerN, integerILO, integerIHI, complex*16, dimension( lda, * )A,
       integerLDA, complex*16, dimension( * )TAU, complex*16, dimension( * )WORK, integerINFO)
       ZGEHD2 reduces a general square matrix to upper Hessenberg form using an unblocked
       algorithm.

       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:
	   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 zgehd2.f.

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

Version 3.4.2				 Tue Sep 25 2012			      zgehd2.f(3)
Unix & Linux Commands & Man Pages : ©2000 - 2018 Unix and Linux Forums


All times are GMT -4. The time now is 03:17 AM.