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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

DORMR3(l)								 )								 DORMR3(l)

NAME

       DORMR3  - overwrite the general real m by n matrix C with  Q * C if SIDE = 'L' and TRANS = 'N', or  Q'* C if SIDE = 'L' and TRANS = 'T', or
       C * Q if SIDE = 'R' and TRANS = 'N', or	C * Q' if SIDE = 'R' and TRANS = 'T',

SYNOPSIS

       SUBROUTINE DORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, INFO )

	   CHARACTER	  SIDE, TRANS

	   INTEGER	  INFO, K, L, LDA, LDC, M, N

	   DOUBLE	  PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )

PURPOSE

       DORMR3 overwrites the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C *
       Q  if  SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T', where Q is a real orthogonal matrix defined as the product of k
       elementary reflectors

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

       as returned by DTZRZF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'.

ARGUMENTS

       SIDE    (input) CHARACTER*1
	       = 'L': apply Q or Q' from the Left
	       = 'R': apply Q or Q' from the Right

       TRANS   (input) CHARACTER*1
	       = 'N': apply Q  (No transpose)
	       = 'T': apply Q' (Transpose)

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

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

       K       (input) INTEGER
	       The number of elementary reflectors whose product defines the matrix Q.	If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0.

       L       (input) INTEGER
	       The number of columns of the matrix A containing the meaningful part of the Householder reflectors.  If SIDE = 'L', M >= L >= 0, if
	       SIDE = 'R', N >= L >= 0.

       A       (input) DOUBLE PRECISION array, dimension
	       (LDA,M)	if SIDE = 'L', (LDA,N) if SIDE = 'R' The i-th row must contain the vector which defines the elementary reflector H(i), for
	       i = 1,2,...,k, as returned by DTZRZF in the last k rows of its array argument A.  A is modified by  the	routine  but  restored	on
	       exit.

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

       TAU     (input) DOUBLE PRECISION array, dimension (K)
	       TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DTZRZF.

       C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)
	       On entry, the m-by-n matrix C.  On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.

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

       WORK    (workspace) DOUBLE PRECISION array, dimension
	       (N) if SIDE = 'L', (M) if SIDE = 'R'

       INFO    (output) INTEGER
	       = 0: successful exit
	       < 0: if INFO = -i, the i-th argument had an illegal value

FURTHER DETAILS

       Based on contributions by
	 A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

LAPACK version 3.0						   15 June 2000 							 DORMR3(l)
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