CLAHRD man page on Oracle

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

clahrd.f(3)			    LAPACK			   clahrd.f(3)

NAME
       clahrd.f -

SYNOPSIS
   Functions/Subroutines
       subroutine clahrd (N, K, NB, A, LDA, TAU, T, LDT, Y, LDY)
	   CLAHRD reduces the first nb columns of a general rectangular matrix
	   A so that elements below the k-th subdiagonal are zero, and returns
	   auxiliary matrices which are needed to apply the transformation to
	   the unreduced part of A.

Function/Subroutine Documentation
   subroutine clahrd (integerN, integerK, integerNB, complex, dimension( lda,
       * )A, integerLDA, complex, dimension( nb )TAU, complex, dimension( ldt,
       nb )T, integerLDT, complex, dimension( ldy, nb )Y, integerLDY)
       CLAHRD reduces the first nb columns of a general rectangular matrix A
       so that elements below the k-th subdiagonal are zero, and returns
       auxiliary matrices which are needed to apply the transformation to the
       unreduced part of A.

       Purpose:

	    CLAHRD reduces the first NB columns of a complex general n-by-(n-k+1)
	    matrix A so that elements below the k-th subdiagonal are zero. The
	    reduction is performed by a unitary similarity transformation
	    Q**H * A * Q. The routine returns the matrices V and T which determine
	    Q as a block reflector I - V*T*V**H, and also the matrix Y = A * V * T.

	    This is an OBSOLETE auxiliary routine.
	    This routine will be 'deprecated' in a  future release.
	    Please use the new routine CLAHR2 instead.

       Parameters:
	   N

		     N is INTEGER
		     The order of the matrix A.

	   K

		     K is INTEGER
		     The offset for the reduction. Elements below the k-th
		     subdiagonal in the first NB columns are reduced to zero.

	   NB

		     NB is INTEGER
		     The number of columns to be reduced.

	   A

		     A is COMPLEX array, dimension (LDA,N-K+1)
		     On entry, the n-by-(n-k+1) general matrix A.
		     On exit, the elements on and above the k-th subdiagonal in
		     the first NB columns are overwritten with the corresponding
		     elements of the reduced matrix; the elements below the k-th
		     subdiagonal, with the array TAU, represent the matrix Q as a
		     product of elementary reflectors. The other columns of A are
		     unchanged. See Further Details.

	   LDA

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

	   TAU

		     TAU is COMPLEX array, dimension (NB)
		     The scalar factors of the elementary reflectors. See Further
		     Details.

	   T

		     T is COMPLEX array, dimension (LDT,NB)
		     The upper triangular matrix T.

	   LDT

		     LDT is INTEGER
		     The leading dimension of the array T.  LDT >= NB.

	   Y

		     Y is COMPLEX array, dimension (LDY,NB)
		     The n-by-nb matrix Y.

	   LDY

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

       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 nb elementary reflectors

		Q = H(1) H(2) . . . H(nb).

	     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+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in
	     A(i+k+1:n,i), and tau in TAU(i).

	     The elements of the vectors v together form the (n-k+1)-by-nb matrix
	     V which is needed, with T and Y, to apply the transformation to the
	     unreduced part of the matrix, using an update of the form:
	     A := (I - V*T*V**H) * (A - Y*V**H).

	     The contents of A on exit are illustrated by the following example
	     with n = 7, k = 3 and nb = 2:

		( a   h	  a   a	  a )
		( a   h	  a   a	  a )
		( a   h	  a   a	  a )
		( h   h	  a   a	  a )
		( v1  h	  a   a	  a )
		( v1  v2  a   a	  a )
		( v1  v2  a   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 170 of file clahrd.f.

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

Version 3.4.2			Tue Sep 25 2012			   clahrd.f(3)
[top]

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]
Tweet
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