Home Man
Search
Today's Posts
Register

Linux & Unix Commands - Search Man Pages

RedHat 9 (Linux i386) - man page for dlabrd (redhat section l)

DLABRD(l)					)					DLABRD(l)

NAME
       DLABRD  -  reduce the first NB rows and columns of a real general m by n matrix A to upper
       or lower bidiagonal form by an orthogonal transformation Q' *  A  *  P,	and  returns  the
       matrices X and Y which are needed to apply the transformation to the unreduced part of A

SYNOPSIS
       SUBROUTINE DLABRD( M, N, NB, A, LDA, D, E, TAUQ, TAUP, X, LDX, Y, LDY )

	   INTEGER	  LDA, LDX, LDY, M, N, NB

	   DOUBLE	  PRECISION  A( LDA, * ), D( * ), E( * ), TAUP( * ), TAUQ( * ), X( LDX, *
			  ), Y( LDY, * )

PURPOSE
       DLABRD reduces the first NB rows and columns of a real general m by n matrix A to upper or
       lower bidiagonal form by an orthogonal transformation Q' * A * P, and returns the matrices
       X and Y which are needed to apply the transformation to the unreduced part of A.  If m  >=
       n, A is reduced to upper bidiagonal form; if m < n, to lower bidiagonal form.

       This is an auxiliary routine called by DGEBRD

ARGUMENTS
       M       (input) INTEGER
	       The number of rows in the matrix A.

       N       (input) INTEGER
	       The number of columns in the matrix A.

       NB      (input) INTEGER
	       The number of leading rows and columns of A to be reduced.

       A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
	       On entry, the m by n general matrix to be reduced.  On exit, the first NB rows and
	       columns of the matrix are overwritten; the rest of the array is unchanged.   If	m
	       >=  n,  elements on and below the diagonal in the first NB columns, with the array
	       TAUQ, represent the orthogonal matrix Q as a product of elementary reflectors; and
	       elements  above	the diagonal in the first NB rows, with the array TAUP, represent
	       the orthogonal matrix P as a product of elementary reflectors.  If m < n, elements
	       below  the  diagonal  in  the first NB columns, with the array TAUQ, represent the
	       orthogonal matrix Q as a product of elementary reflectors,  and	elements  on  and
	       above  the  diagonal  in  the  first  NB  rows, with the array TAUP, represent the
	       orthogonal matrix P as a product of elementary reflectors.  See	Further  Details.
	       LDA     (input) INTEGER The leading dimension of the array A.  LDA >= max(1,M).

       D       (output) DOUBLE PRECISION array, dimension (NB)
	       The  diagonal  elements	of  the  first NB rows and columns of the reduced matrix.
	       D(i) = A(i,i).

       E       (output) DOUBLE PRECISION array, dimension (NB)
	       The off-diagonal elements of the first NB rows and columns of the reduced matrix.

       TAUQ    (output) DOUBLE PRECISION array dimension (NB)
	       The scalar factors of the elementary reflectors	which  represent  the  orthogonal
	       matrix Q. See Further Details.  TAUP    (output) DOUBLE PRECISION array, dimension
	       (NB) The scalar factors of the elementary reflectors which represent the  orthogo-
	       nal  matrix  P.	See  Further  Details.	 X	 (output) DOUBLE PRECISION array,
	       dimension (LDX,NB) The m-by-nb matrix X required to update the unreduced  part  of
	       A.

       LDX     (input) INTEGER
	       The leading dimension of the array X. LDX >= M.

       Y       (output) DOUBLE PRECISION array, dimension (LDY,NB)
	       The n-by-nb matrix Y required to update the unreduced part of A.

       LDY     (output) INTEGER
	       The leading dimension of the array Y. LDY >= N.

FURTHER DETAILS
       The matrices Q and P are represented as products of elementary reflectors:

	  Q = H(1) H(2) . . . H(nb)  and  P = G(1) G(2) . . . G(nb)

       Each H(i) and G(i) has the form:

	  H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'

       where tauq and taup are real scalars, and v and u are real vectors.

       If  m  >= n, v(1:i-1) = 0, v(i) = 1, and v(i:m) is stored on exit in A(i:m,i); u(1:i) = 0,
       u(i+1) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n); tauq is stored  in  TAUQ(i)  and
       taup in TAUP(i).

       If m < n, v(1:i) = 0, v(i+1) = 1, and v(i+1:m) is stored on exit in A(i+2:m,i); u(1:i-1) =
       0, u(i) = 1, and u(i:n) is stored on exit in A(i,i+1:n); tauq is  stored  in  TAUQ(i)  and
       taup in TAUP(i).

       The  elements  of  the  vectors v and u together form the m-by-nb matrix V and the nb-by-n
       matrix U' which are needed, with X and Y, to apply the  transformation  to  the	unreduced
       part of the matrix, using a block update of the form:  A := A - V*Y' - X*U'.

       The contents of A on exit are illustrated by the following examples with nb = 2:

       m = 6 and n = 5 (m > n): 	 m = 5 and n = 6 (m < n):

	 (  1	1   u1	u1  u1 )	   (  1   u1  u1  u1  u1  u1 )
	 (  v1	1   1	u2  u2 )	   (  1   1   u2  u2  u2  u2 )
	 (  v1	v2  a	a   a  )	   (  v1  1   a   a   a   a  )
	 (  v1	v2  a	a   a  )	   (  v1  v2  a   a   a   a  )
	 (  v1	v2  a	a   a  )	   (  v1  v2  a   a   a   a  )
	 (  v1	v2  a	a   a  )

       where  a  denotes an element of the original matrix which is unchanged, vi denotes an ele-
       ment of the vector defining H(i), and ui an element of the vector defining G(i).

LAPACK version 3.0			   15 June 2000 				DLABRD(l)


All times are GMT -4. The time now is 11:22 AM.

Unix & Linux Forums Content Copyrightę1993-2018. All Rights Reserved.
UNIX.COM Login
Username:
Password:  
Show Password