1*> \brief \b DORMQL
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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15*> [TXT]</a>
16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE DORMQL( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
22*                          WORK, LWORK, INFO )
23*
24*       .. Scalar Arguments ..
25*       CHARACTER          SIDE, TRANS
26*       INTEGER            INFO, K, LDA, LDC, LWORK, 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*> DORMQL overwrites the general real M-by-N matrix C with
39*>
40*>                 SIDE = 'L'     SIDE = 'R'
41*> TRANS = 'N':      Q * C          C * Q
42*> TRANS = 'T':      Q**T * C       C * Q**T
43*>
44*> where Q is a real orthogonal matrix defined as the product of k
45*> elementary reflectors
46*>
47*>       Q = H(k) . . . H(2) H(1)
48*>
49*> as returned by DGEQLF. Q is of order M if SIDE = 'L' and of order N
50*> if SIDE = 'R'.
51*> \endverbatim
52*
53*  Arguments:
54*  ==========
55*
56*> \param[in] SIDE
57*> \verbatim
58*>          SIDE is CHARACTER*1
59*>          = 'L': apply Q or Q**T from the Left;
60*>          = 'R': apply Q or Q**T from the Right.
61*> \endverbatim
62*>
63*> \param[in] TRANS
64*> \verbatim
65*>          TRANS is CHARACTER*1
66*>          = 'N':  No transpose, apply Q;
67*>          = 'T':  Transpose, apply Q**T.
68*> \endverbatim
69*>
70*> \param[in] M
71*> \verbatim
72*>          M is INTEGER
73*>          The number of rows of the matrix C. M >= 0.
74*> \endverbatim
75*>
76*> \param[in] N
77*> \verbatim
78*>          N is INTEGER
79*>          The number of columns of the matrix C. N >= 0.
80*> \endverbatim
81*>
82*> \param[in] K
83*> \verbatim
84*>          K is INTEGER
85*>          The number of elementary reflectors whose product defines
86*>          the matrix Q.
87*>          If SIDE = 'L', M >= K >= 0;
88*>          if SIDE = 'R', N >= K >= 0.
89*> \endverbatim
90*>
91*> \param[in] A
92*> \verbatim
93*>          A is DOUBLE PRECISION array, dimension (LDA,K)
94*>          The i-th column must contain the vector which defines the
95*>          elementary reflector H(i), for i = 1,2,...,k, as returned by
96*>          DGEQLF in the last k columns of its array argument A.
97*> \endverbatim
98*>
99*> \param[in] LDA
100*> \verbatim
101*>          LDA is INTEGER
102*>          The leading dimension of the array A.
103*>          If SIDE = 'L', LDA >= max(1,M);
104*>          if SIDE = 'R', LDA >= max(1,N).
105*> \endverbatim
106*>
107*> \param[in] TAU
108*> \verbatim
109*>          TAU is DOUBLE PRECISION array, dimension (K)
110*>          TAU(i) must contain the scalar factor of the elementary
111*>          reflector H(i), as returned by DGEQLF.
112*> \endverbatim
113*>
114*> \param[in,out] C
115*> \verbatim
116*>          C is DOUBLE PRECISION array, dimension (LDC,N)
117*>          On entry, the M-by-N matrix C.
118*>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
119*> \endverbatim
120*>
121*> \param[in] LDC
122*> \verbatim
123*>          LDC is INTEGER
124*>          The leading dimension of the array C. LDC >= max(1,M).
125*> \endverbatim
126*>
127*> \param[out] WORK
128*> \verbatim
129*>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
130*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
131*> \endverbatim
132*>
133*> \param[in] LWORK
134*> \verbatim
135*>          LWORK is INTEGER
136*>          The dimension of the array WORK.
137*>          If SIDE = 'L', LWORK >= max(1,N);
138*>          if SIDE = 'R', LWORK >= max(1,M).
139*>          For good performance, LWORK should generally be larger.
140*>
141*>          If LWORK = -1, then a workspace query is assumed; the routine
142*>          only calculates the optimal size of the WORK array, returns
143*>          this value as the first entry of the WORK array, and no error
144*>          message related to LWORK is issued by XERBLA.
145*> \endverbatim
146*>
147*> \param[out] INFO
148*> \verbatim
149*>          INFO is INTEGER
150*>          = 0:  successful exit
151*>          < 0:  if INFO = -i, the i-th argument had an illegal value
152*> \endverbatim
153*
154*  Authors:
155*  ========
156*
157*> \author Univ. of Tennessee
158*> \author Univ. of California Berkeley
159*> \author Univ. of Colorado Denver
160*> \author NAG Ltd.
161*
162*> \date December 2016
163*
164*> \ingroup doubleOTHERcomputational
165*
166*  =====================================================================
167      SUBROUTINE DORMQL( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
168     $                   WORK, LWORK, INFO )
169*
170*  -- LAPACK computational routine (version 3.7.0) --
171*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
172*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
173*     December 2016
174*
175*     .. Scalar Arguments ..
176      CHARACTER          SIDE, TRANS
177      INTEGER            INFO, K, LDA, LDC, LWORK, M, N
178*     ..
179*     .. Array Arguments ..
180      DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
181*     ..
182*
183*  =====================================================================
184*
185*     .. Parameters ..
186      INTEGER            NBMAX, LDT, TSIZE
187      PARAMETER          ( NBMAX = 64, LDT = NBMAX+1,
188     $                     TSIZE = LDT*NBMAX )
189*     ..
190*     .. Local Scalars ..
191      LOGICAL            LEFT, LQUERY, NOTRAN
192      INTEGER            I, I1, I2, I3, IB, IINFO, IWT, LDWORK, LWKOPT,
193     $                   MI, NB, NBMIN, NI, NQ, NW
194*     ..
195*     .. External Functions ..
196      LOGICAL            LSAME
197      INTEGER            ILAENV
198      EXTERNAL           LSAME, ILAENV
199*     ..
200*     .. External Subroutines ..
201      EXTERNAL           DLARFB, DLARFT, DORM2L, XERBLA
202*     ..
203*     .. Intrinsic Functions ..
204      INTRINSIC          MAX, MIN
205*     ..
206*     .. Executable Statements ..
207*
208*     Test the input arguments
209*
210      INFO = 0
211      LEFT = LSAME( SIDE, 'L' )
212      NOTRAN = LSAME( TRANS, 'N' )
213      LQUERY = ( LWORK.EQ.-1 )
214*
215*     NQ is the order of Q and NW is the minimum dimension of WORK
216*
217      IF( LEFT ) THEN
218         NQ = M
219         NW = MAX( 1, N )
220      ELSE
221         NQ = N
222         NW = MAX( 1, M )
223      END IF
224      IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
225         INFO = -1
226      ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
227         INFO = -2
228      ELSE IF( M.LT.0 ) THEN
229         INFO = -3
230      ELSE IF( N.LT.0 ) THEN
231         INFO = -4
232      ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
233         INFO = -5
234      ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN
235         INFO = -7
236      ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
237         INFO = -10
238      ELSE IF( LWORK.LT.NW .AND. .NOT.LQUERY ) THEN
239         INFO = -12
240      END IF
241*
242      IF( INFO.EQ.0 ) THEN
243*
244*        Compute the workspace requirements
245*
246         IF( M.EQ.0 .OR. N.EQ.0 ) THEN
247            LWKOPT = 1
248         ELSE
249            NB = MIN( NBMAX, ILAENV( 1, 'DORMQL', SIDE // TRANS, M, N,
250     $                               K, -1 ) )
251            LWKOPT = NW*NB + TSIZE
252         END IF
253         WORK( 1 ) = LWKOPT
254      END IF
255*
256      IF( INFO.NE.0 ) THEN
257         CALL XERBLA( 'DORMQL', -INFO )
258         RETURN
259      ELSE IF( LQUERY ) THEN
260         RETURN
261      END IF
262*
263*     Quick return if possible
264*
265      IF( M.EQ.0 .OR. N.EQ.0 ) THEN
266         RETURN
267      END IF
268*
269      NBMIN = 2
270      LDWORK = NW
271      IF( NB.GT.1 .AND. NB.LT.K ) THEN
272         IF( LWORK.LT.NW*NB+TSIZE ) THEN
273            NB = (LWORK-TSIZE) / LDWORK
274            NBMIN = MAX( 2, ILAENV( 2, 'DORMQL', SIDE // TRANS, M, N, K,
275     $              -1 ) )
276         END IF
277      END IF
278*
279      IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
280*
281*        Use unblocked code
282*
283         CALL DORM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK,
284     $                IINFO )
285      ELSE
286*
287*        Use blocked code
288*
289         IWT = 1 + NW*NB
290         IF( ( LEFT .AND. NOTRAN ) .OR.
291     $       ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) THEN
292            I1 = 1
293            I2 = K
294            I3 = NB
295         ELSE
296            I1 = ( ( K-1 ) / NB )*NB + 1
297            I2 = 1
298            I3 = -NB
299         END IF
300*
301         IF( LEFT ) THEN
302            NI = N
303         ELSE
304            MI = M
305         END IF
306*
307         DO 10 I = I1, I2, I3
308            IB = MIN( NB, K-I+1 )
309*
310*           Form the triangular factor of the block reflector
311*           H = H(i+ib-1) . . . H(i+1) H(i)
312*
313            CALL DLARFT( 'Backward', 'Columnwise', NQ-K+I+IB-1, IB,
314     $                   A( 1, I ), LDA, TAU( I ), WORK( IWT ), LDT )
315            IF( LEFT ) THEN
316*
317*              H or H**T is applied to C(1:m-k+i+ib-1,1:n)
318*
319               MI = M - K + I + IB - 1
320            ELSE
321*
322*              H or H**T is applied to C(1:m,1:n-k+i+ib-1)
323*
324               NI = N - K + I + IB - 1
325            END IF
326*
327*           Apply H or H**T
328*
329            CALL DLARFB( SIDE, TRANS, 'Backward', 'Columnwise', MI, NI,
330     $                   IB, A( 1, I ), LDA, WORK( IWT ), LDT, C, LDC,
331     $                   WORK, LDWORK )
332   10    CONTINUE
333      END IF
334      WORK( 1 ) = LWKOPT
335      RETURN
336*
337*     End of DORMQL
338*
339      END
340