DORMR2(3) 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',

## SYNOPSIS

SUBROUTINE DORMR2(
SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO )

CHARACTER SIDE, TRANS

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

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

## PURPOSE

DORMR2 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

Q = H(1) H(2) . . . H(k)
as returned by DGERQF. 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.
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 DGERQF 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 DGERQF.
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