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# sorml2

```
NAME
SORML2 - 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 SORML2( 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
SORML2 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(k) . . . H(2) H(1)

as returned by SGELQF. 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,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 SGELQF in the first 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) REAL array, dimension (K)
TAU(i) must contain the scalar factor of the elemen-
tary reflector H(i), as returned by SGELQF.

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
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