1*> \brief \b DORML2 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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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorml2.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE DORML2( 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*       DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
30*       ..
31*
32*
33*> \par Purpose:
34*  =============
35*>
36*> \verbatim
37*>
38*> DORML2 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 DGELQF. 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 DOUBLE PRECISION 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*>          DGELQF 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 DOUBLE PRECISION array, dimension (K)
115*>          TAU(i) must contain the scalar factor of the elementary
116*>          reflector H(i), as returned by DGELQF.
117*> \endverbatim
118*>
119*> \param[in,out] C
120*> \verbatim
121*>          C is DOUBLE PRECISION 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 DOUBLE PRECISION 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*> \ingroup doubleOTHERcomputational
155*
156*  =====================================================================
157      SUBROUTINE DORML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
158     $                   WORK, INFO )
159*
160*  -- LAPACK computational routine --
161*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
162*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
163*
164*     .. Scalar Arguments ..
165      CHARACTER          SIDE, TRANS
166      INTEGER            INFO, K, LDA, LDC, M, N
167*     ..
168*     .. Array Arguments ..
169      DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
170*     ..
171*
172*  =====================================================================
173*
174*     .. Parameters ..
175      DOUBLE PRECISION   ONE
176      PARAMETER          ( ONE = 1.0D+0 )
177*     ..
178*     .. Local Scalars ..
179      LOGICAL            LEFT, NOTRAN
180      INTEGER            I, I1, I2, I3, IC, JC, MI, NI, NQ
181      DOUBLE PRECISION   AII
182*     ..
183*     .. External Functions ..
184      LOGICAL            LSAME
185      EXTERNAL           LSAME
186*     ..
187*     .. External Subroutines ..
188      EXTERNAL           DLARF, XERBLA
189*     ..
190*     .. Intrinsic Functions ..
191      INTRINSIC          MAX
192*     ..
193*     .. Executable Statements ..
194*
195*     Test the input arguments
196*
197      INFO = 0
198      LEFT = LSAME( SIDE, 'L' )
199      NOTRAN = LSAME( TRANS, 'N' )
200*
201*     NQ is the order of Q
202*
203      IF( LEFT ) THEN
204         NQ = M
205      ELSE
206         NQ = N
207      END IF
208      IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
209         INFO = -1
210      ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
211         INFO = -2
212      ELSE IF( M.LT.0 ) THEN
213         INFO = -3
214      ELSE IF( N.LT.0 ) THEN
215         INFO = -4
216      ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
217         INFO = -5
218      ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
219         INFO = -7
220      ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
221         INFO = -10
222      END IF
223      IF( INFO.NE.0 ) THEN
224         CALL XERBLA( 'DORML2', -INFO )
225         RETURN
226      END IF
227*
228*     Quick return if possible
229*
230      IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 )
231     $   RETURN
232*
233      IF( ( LEFT .AND. NOTRAN ) .OR. ( .NOT.LEFT .AND. .NOT.NOTRAN ) )
234     $     THEN
235         I1 = 1
236         I2 = K
237         I3 = 1
238      ELSE
239         I1 = K
240         I2 = 1
241         I3 = -1
242      END IF
243*
244      IF( LEFT ) THEN
245         NI = N
246         JC = 1
247      ELSE
248         MI = M
249         IC = 1
250      END IF
251*
252      DO 10 I = I1, I2, I3
253         IF( LEFT ) THEN
254*
255*           H(i) is applied to C(i:m,1:n)
256*
257            MI = M - I + 1
258            IC = I
259         ELSE
260*
261*           H(i) is applied to C(1:m,i:n)
262*
263            NI = N - I + 1
264            JC = I
265         END IF
266*
267*        Apply H(i)
268*
269         AII = A( I, I )
270         A( I, I ) = ONE
271         CALL DLARF( SIDE, MI, NI, A( I, I ), LDA, TAU( I ),
272     $               C( IC, JC ), LDC, WORK )
273         A( I, I ) = AII
274   10 CONTINUE
275      RETURN
276*
277*     End of DORML2
278*
279      END
280