1*> \brief \b SORML2 multiplies a general matrix by the orthogonal matrix from a LQ factorization determined by sgelqf (unblocked algorithm).
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
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14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sorml2.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE SORML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
22*                          WORK, INFO )
23*
24*       .. Scalar Arguments ..
25*       CHARACTER          SIDE, TRANS
26*       INTEGER            INFO, K, LDA, LDC, M, N
27*       ..
28*       .. Array Arguments ..
29*       REAL               A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
30*       ..
31*
32*
33*> \par Purpose:
34*  =============
35*>
36*> \verbatim
37*>
38*> SORML2 overwrites the general real m by n matrix C with
39*>
40*>       Q * C  if SIDE = 'L' and TRANS = 'N', or
41*>
42*>       Q**T* C  if SIDE = 'L' and TRANS = 'T', or
43*>
44*>       C * Q  if SIDE = 'R' and TRANS = 'N', or
45*>
46*>       C * Q**T if SIDE = 'R' and TRANS = 'T',
47*>
48*> where Q is a real orthogonal matrix defined as the product of k
49*> elementary reflectors
50*>
51*>       Q = H(k) . . . H(2) H(1)
52*>
53*> as returned by SGELQF. Q is of order m if SIDE = 'L' and of order n
54*> if SIDE = 'R'.
55*> \endverbatim
56*
57*  Arguments:
58*  ==========
59*
60*> \param[in] SIDE
61*> \verbatim
62*>          SIDE is CHARACTER*1
63*>          = 'L': apply Q or Q**T from the Left
64*>          = 'R': apply Q or Q**T from the Right
65*> \endverbatim
66*>
67*> \param[in] TRANS
68*> \verbatim
69*>          TRANS is CHARACTER*1
70*>          = 'N': apply Q  (No transpose)
71*>          = 'T': apply Q**T (Transpose)
72*> \endverbatim
73*>
74*> \param[in] M
75*> \verbatim
76*>          M is INTEGER
77*>          The number of rows of the matrix C. M >= 0.
78*> \endverbatim
79*>
80*> \param[in] N
81*> \verbatim
82*>          N is INTEGER
83*>          The number of columns of the matrix C. N >= 0.
84*> \endverbatim
85*>
86*> \param[in] K
87*> \verbatim
88*>          K is INTEGER
89*>          The number of elementary reflectors whose product defines
90*>          the matrix Q.
91*>          If SIDE = 'L', M >= K >= 0;
92*>          if SIDE = 'R', N >= K >= 0.
93*> \endverbatim
94*>
95*> \param[in] A
96*> \verbatim
97*>          A is REAL array, dimension
98*>                               (LDA,M) if SIDE = 'L',
99*>                               (LDA,N) if SIDE = 'R'
100*>          The i-th row must contain the vector which defines the
101*>          elementary reflector H(i), for i = 1,2,...,k, as returned by
102*>          SGELQF in the first k rows of its array argument A.
103*>          A is modified by the routine but restored on exit.
104*> \endverbatim
105*>
106*> \param[in] LDA
107*> \verbatim
108*>          LDA is INTEGER
109*>          The leading dimension of the array A. LDA >= max(1,K).
110*> \endverbatim
111*>
112*> \param[in] TAU
113*> \verbatim
114*>          TAU is REAL array, dimension (K)
115*>          TAU(i) must contain the scalar factor of the elementary
116*>          reflector H(i), as returned by SGELQF.
117*> \endverbatim
118*>
119*> \param[in,out] C
120*> \verbatim
121*>          C is REAL array, dimension (LDC,N)
122*>          On entry, the m by n matrix C.
123*>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
124*> \endverbatim
125*>
126*> \param[in] LDC
127*> \verbatim
128*>          LDC is INTEGER
129*>          The leading dimension of the array C. LDC >= max(1,M).
130*> \endverbatim
131*>
132*> \param[out] WORK
133*> \verbatim
134*>          WORK is REAL array, dimension
135*>                                   (N) if SIDE = 'L',
136*>                                   (M) if SIDE = 'R'
137*> \endverbatim
138*>
139*> \param[out] INFO
140*> \verbatim
141*>          INFO is INTEGER
142*>          = 0: successful exit
143*>          < 0: if INFO = -i, the i-th argument had an illegal value
144*> \endverbatim
145*
146*  Authors:
147*  ========
148*
149*> \author Univ. of Tennessee
150*> \author Univ. of California Berkeley
151*> \author Univ. of Colorado Denver
152*> \author NAG Ltd.
153*
154*> \date September 2012
155*
156*> \ingroup realOTHERcomputational
157*
158*  =====================================================================
159      SUBROUTINE SORML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
160     $                   WORK, INFO )
161*
162*  -- LAPACK computational routine (version 3.4.2) --
163*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
164*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
165*     September 2012
166*
167*     .. Scalar Arguments ..
168      CHARACTER          SIDE, TRANS
169      INTEGER            INFO, K, LDA, LDC, M, N
170*     ..
171*     .. Array Arguments ..
172      REAL               A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
173*     ..
174*
175*  =====================================================================
176*
177*     .. Parameters ..
178      REAL               ONE
179      PARAMETER          ( ONE = 1.0E+0 )
180*     ..
181*     .. Local Scalars ..
182      LOGICAL            LEFT, NOTRAN
183      INTEGER            I, I1, I2, I3, IC, JC, MI, NI, NQ
184      REAL               AII
185*     ..
186*     .. External Functions ..
187      LOGICAL            LSAME
188      EXTERNAL           LSAME
189*     ..
190*     .. External Subroutines ..
191      EXTERNAL           SLARF, XERBLA
192*     ..
193*     .. Intrinsic Functions ..
194      INTRINSIC          MAX
195*     ..
196*     .. Executable Statements ..
197*
198*     Test the input arguments
199*
200      INFO = 0
201      LEFT = LSAME( SIDE, 'L' )
202      NOTRAN = LSAME( TRANS, 'N' )
203*
204*     NQ is the order of Q
205*
206      IF( LEFT ) THEN
207         NQ = M
208      ELSE
209         NQ = N
210      END IF
211      IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
212         INFO = -1
213      ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
214         INFO = -2
215      ELSE IF( M.LT.0 ) THEN
216         INFO = -3
217      ELSE IF( N.LT.0 ) THEN
218         INFO = -4
219      ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
220         INFO = -5
221      ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
222         INFO = -7
223      ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
224         INFO = -10
225      END IF
226      IF( INFO.NE.0 ) THEN
227         CALL XERBLA( 'SORML2', -INFO )
228         RETURN
229      END IF
230*
231*     Quick return if possible
232*
233      IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 )
234     $   RETURN
235*
236      IF( ( LEFT .AND. NOTRAN ) .OR. ( .NOT.LEFT .AND. .NOT.NOTRAN ) )
237     $     THEN
238         I1 = 1
239         I2 = K
240         I3 = 1
241      ELSE
242         I1 = K
243         I2 = 1
244         I3 = -1
245      END IF
246*
247      IF( LEFT ) THEN
248         NI = N
249         JC = 1
250      ELSE
251         MI = M
252         IC = 1
253      END IF
254*
255      DO 10 I = I1, I2, I3
256         IF( LEFT ) THEN
257*
258*           H(i) is applied to C(i:m,1:n)
259*
260            MI = M - I + 1
261            IC = I
262         ELSE
263*
264*           H(i) is applied to C(1:m,i:n)
265*
266            NI = N - I + 1
267            JC = I
268         END IF
269*
270*        Apply H(i)
271*
272         AII = A( I, I )
273         A( I, I ) = ONE
274         CALL SLARF( SIDE, MI, NI, A( I, I ), LDA, TAU( I ),
275     $               C( IC, JC ), LDC, WORK )
276         A( I, I ) = AII
277   10 CONTINUE
278      RETURN
279*
280*     End of SORML2
281*
282      END
283