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dlaref(3) [debian man page]

DLAREF(l)					      LAPACK auxiliary routine (version 1.5)						 DLAREF(l)

NAME

       DLAREF  -  applie one or several Householder reflectors of size 3  to one or two matrices (if column is specified) on either their  rows or
       columns

SYNOPSIS

       SUBROUTINE DLAREF( TYPE, A, LDA, WANTZ, Z, LDZ, BLOCK, IROW1, ICOL1, ISTART, ISTOP, ITMP1, ITMP2, LILOZ, LIHIZ, VECS, V2, V3, T1, T2, T3 )

	   LOGICAL	  BLOCK, WANTZ

	   CHARACTER	  TYPE

	   INTEGER	  ICOL1, IROW1, ISTART, ISTOP, ITMP1, ITMP2, LDA, LDZ, LIHIZ, LILOZ

	   DOUBLE	  PRECISION T1, T2, T3, V2, V3

	   DOUBLE	  PRECISION A( LDA, * ), VECS( * ), Z( LDZ, * )

PURPOSE

       DLAREF applies one or several Householder reflectors of size 3
	  to one or two matrices (if column is specified) on either their
	  rows or columns.

ARGUMENTS

       TYPE    (global input) CHARACTER*1
	       If 'R': Apply reflectors to the rows of the matrix (apply from left) Otherwise: Apply reflectors  to  the  columns  of  the  matrix
	       Unchanged on exit.

       A       (global input/output) DOUBLE PRECISION array, (LDA,*)
	       On entry, the matrix to receive the reflections.  The updated matrix on exit.

       LDA     (local input) INTEGER
	       On entry, the leading dimension of A.  Unchanged on exit.

       WANTZ   (global input) LOGICAL
	       If .TRUE., then apply any column reflections to Z as well.  If .FALSE., then do no additional work on Z.

       Z       (global input/output) DOUBLE PRECISION array, (LDZ,*)
	       On entry, the second matrix to receive column reflections.  This is changed only if WANTZ is set.

       LDZ     (local input) INTEGER
	       On entry, the leading dimension of Z.  Unchanged on exit.

       BLOCK   (global input) LOGICAL
	       If  .TRUE.,  then apply several reflectors at once and read their data from the VECS array.  If .FALSE., apply the single reflector
	       given by V2, V3, T1, T2, and T3.

       IROW1   (local input/output) INTEGER
	       On entry, the local row element of A.  Undefined on output.

       ICOL1   (local input/output) INTEGER
	       On entry, the local column element of A.  Undefined on output.

       ISTART  (global input) INTEGER
	       Specifies the "number" of the first reflector.  This is used as an index into VECS if BLOCK is set.  ISTART is ignored if BLOCK	is
	       .FALSE..

       ISTOP   (global input) INTEGER
	       Specifies  the  "number"  of the last reflector.  This is used as an index into VECS if BLOCK is set.  ISTOP is ignored if BLOCK is
	       .FALSE..

       ITMP1   (local input) INTEGER
	       Starting range into A.  For rows, this is the local first column.  For columns, this is the local first row.

       ITMP2   (local input) INTEGER
	       Ending range into A.  For rows, this is the local last column.  For columns, this is the local last row.

	       LILOZ LIHIZ   (local input) INTEGER These serve the same purpose as ITMP1,ITMP2 but for Z when WANTZ is set.

       VECS    (global input) DOUBLE PRECISION array of size 3*N (matrix
	       size) This holds the size 3 reflectors one after another and this is only accessed when BLOCK is .TRUE.

	       V2 V3 T1 T2 T3	   (global input/output) DOUBLE PRECISION This holds information on a single size 3 Householder reflector  and	is
	       read when BLOCK is .FALSE., and overwritten when BLOCK is .TRUE.

	       Implemented by:	G. Henry, May 1, 1997

LAPACK version 1.5						    12 May 1997 							 DLAREF(l)

Check Out this Related Man Page

DLAQP2(l)								 )								 DLAQP2(l)

NAME

       DLAQP2 - compute a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N)

SYNOPSIS

       SUBROUTINE DLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2, WORK )

	   INTEGER	  LDA, M, N, OFFSET

	   INTEGER	  JPVT( * )

	   DOUBLE	  PRECISION A( LDA, * ), TAU( * ), VN1( * ), VN2( * ), WORK( * )

PURPOSE

       DLAQP2  computes  a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N). The block A(1:OFFSET,1:N) is accordingly pivoted,
       but not factorized.

ARGUMENTS

       M       (input) INTEGER
	       The number of rows of the matrix A. M >= 0.

       N       (input) INTEGER
	       The number of columns of the matrix A. N >= 0.

       OFFSET  (input) INTEGER
	       The number of rows of the matrix A that must be pivoted but no factorized. OFFSET >= 0.

       A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
	       On entry, the M-by-N matrix A.  On exit, the upper triangle of block A(OFFSET+1:M,1:N) is the triangular factor obtained; the  ele-
	       ments in block A(OFFSET+1:M,1:N) below the diagonal, together with the array TAU, represent the orthogonal matrix Q as a product of
	       elementary reflectors. Block A(1:OFFSET,1:N) has been accordingly pivoted, but no factorized.

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

       JPVT    (input/output) INTEGER array, dimension (N)
	       On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted to the front of A*P (a leading column); if JPVT(i) = 0, the i-th col-
	       umn of A is a free column.  On exit, if JPVT(i) = k, then the i-th column of A*P was the k-th column of A.

       TAU     (output) DOUBLE PRECISION array, dimension (min(M,N))
	       The scalar factors of the elementary reflectors.

       VN1     (input/output) DOUBLE PRECISION array, dimension (N)
	       The vector with the partial column norms.

       VN2     (input/output) DOUBLE PRECISION array, dimension (N)
	       The vector with the exact column norms.

       WORK    (workspace) DOUBLE PRECISION array, dimension (N)

FURTHER DETAILS

       Based on contributions by
	 G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
	 X. Sun, Computer Science Dept., Duke University, USA

LAPACK version 3.0						   15 June 2000 							 DLAQP2(l)
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