NAME

SORM2R - 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 SORM2R(
SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO )

CHARACTER SIDE, TRANS

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

REAL A( LDA, ∗ ), C( LDC, ∗ ), TAU( ∗ ), WORK( ∗ )

PURPOSE

SORM2R 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 SGEQRF. 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) REAL array, dimension (LDA,K)
The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGEQRF in the first k columns 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. If SIDE = ’L’, LDA >= max(1,M); if SIDE = ’R’, LDA >= max(1,N).

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

C       (input/output) REAL 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) REAL 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

  —  LAPACK version 2.0  —  08 October 1994