.TH DORMR3 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) "
.SH NAME
DORMR3 - the general real m by n matrix C with Q * C if SIDE = \(aqL\(aq and TRANS = \(aqN\(aq, or Q\(aq* C if SIDE = \(aqL\(aq and TRANS = \(aqT\(aq, or C * Q if SIDE = \(aqR\(aq and TRANS = \(aqN\(aq, or C * Q\(aq if SIDE = \(aqR\(aq and TRANS = \(aqT\(aq,
.SH SYNOPSIS
.TP 19
SUBROUTINE DORMR3(
SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
WORK, INFO )
.TP 19
.ti +4
CHARACTER
SIDE, TRANS
.TP 19
.ti +4
INTEGER
INFO, K, L, LDA, LDC, M, N
.TP 19
.ti +4
DOUBLE
PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
.SH PURPOSE
DORMR3 overwrites the general real m by n matrix C with
where Q is a real orthogonal matrix defined as the product of k
elementary reflectors
.br
Q = H(1) H(2) . . . H(k)
.br
as returned by DTZRZF. Q is of order m if SIDE = \(aqL\(aq and of order n
if SIDE = \(aqR\(aq.
.br
.SH ARGUMENTS
.TP 8
SIDE (input) CHARACTER*1
= \(aqL\(aq: apply Q or Q\(aq from the Left
.br
= \(aqR\(aq: apply Q or Q\(aq from the Right
.TP 8
TRANS (input) CHARACTER*1
.br
= \(aqN\(aq: apply Q (No transpose)
.br
= \(aqT\(aq: apply Q\(aq (Transpose)
.TP 8
M (input) INTEGER
The number of rows of the matrix C. M >= 0.
.TP 8
N (input) INTEGER
The number of columns of the matrix C. N >= 0.
.TP 8
K (input) INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = \(aqL\(aq, M >= K >= 0;
if SIDE = \(aqR\(aq, N >= K >= 0.
.TP 8
L (input) INTEGER
The number of columns of the matrix A containing
the meaningful part of the Householder reflectors.
If SIDE = \(aqL\(aq, M >= L >= 0, if SIDE = \(aqR\(aq, N >= L >= 0.
.TP 8
A (input) DOUBLE PRECISION array, dimension
(LDA,M) if SIDE = \(aqL\(aq,
(LDA,N) if SIDE = \(aqR\(aq
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.
.TP 8
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,K).
.TP 8
TAU (input) DOUBLE PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DTZRZF.
.TP 8
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\(aq*C or C*Q\(aq or C*Q.
.TP 8
LDC (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
.TP 8
WORK (workspace) DOUBLE PRECISION array, dimension
(N) if SIDE = \(aqL\(aq,
(M) if SIDE = \(aqR\(aq
.TP 8
INFO (output) INTEGER
= 0: successful exit
.br
< 0: if INFO = -i, the i-th argument had an illegal value
.SH FURTHER DETAILS
Based on contributions by
.br
A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA