cgehd2.f man page on Oracle

Man page or keyword search:  
man Server   33470 pages
apropos Keyword Search (all sections)
Output format
Oracle logo
[printable version]

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

       cgehd2.f -

       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.


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


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


		     TAU is COMPLEX array, dimension (N-1)
		     The scalar factors of the elementary reflectors (see Further


		     WORK is COMPLEX array, dimension (N)


		     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.

	   September 2012

       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**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.

       Generated automatically by Doxygen for LAPACK from the source code.

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

List of man pages available for Oracle

Copyright (c) for man pages and the logo by the respective OS vendor.

For those who want to learn more, the polarhome community provides shell access and support.

[legal] [privacy] [GNU] [policy] [cookies] [netiquette] [sponsors] [FAQ]
Polarhome, production since 1999.
Member of Polarhome portal.
Based on Fawad Halim's script.
Vote for polarhome
Free Shell Accounts :: the biggest list on the net