1*> \brief \b DORMRQ
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 DORMRQ( 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*> DORMRQ 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(1) H(2) . . . H(k)
48*>
49*> as returned by DGERQF. 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
94*>                               (LDA,M) if SIDE = 'L',
95*>                               (LDA,N) if SIDE = 'R'
96*>          The i-th row must contain the vector which defines the
97*>          elementary reflector H(i), for i = 1,2,...,k, as returned by
98*>          DGERQF in the last k rows of its array argument A.
99*> \endverbatim
100*>
101*> \param[in] LDA
102*> \verbatim
103*>          LDA is INTEGER
104*>          The leading dimension of the array A. LDA >= max(1,K).
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 DGERQF.
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*> \ingroup doubleOTHERcomputational
163*
164*  =====================================================================
165      SUBROUTINE DORMRQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
166     $                   WORK, LWORK, INFO )
167*
168*  -- LAPACK computational routine --
169*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
170*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
171*
172*     .. Scalar Arguments ..
173      CHARACTER          SIDE, TRANS
174      INTEGER            INFO, K, LDA, LDC, LWORK, M, N
175*     ..
176*     .. Array Arguments ..
177      DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
178*     ..
179*
180*  =====================================================================
181*
182*     .. Parameters ..
183      INTEGER            NBMAX, LDT, TSIZE
184      PARAMETER          ( NBMAX = 64, LDT = NBMAX+1,
185     $                     TSIZE = LDT*NBMAX )
186*     ..
187*     .. Local Scalars ..
188      LOGICAL            LEFT, LQUERY, NOTRAN
189      CHARACTER          TRANST
190      INTEGER            I, I1, I2, I3, IB, IINFO, IWT, LDWORK, LWKOPT,
191     $                   MI, NB, NBMIN, NI, NQ, NW
192*     ..
193*     .. External Functions ..
194      LOGICAL            LSAME
195      INTEGER            ILAENV
196      EXTERNAL           LSAME, ILAENV
197*     ..
198*     .. External Subroutines ..
199      EXTERNAL           DLARFB, DLARFT, DORMR2, XERBLA
200*     ..
201*     .. Intrinsic Functions ..
202      INTRINSIC          MAX, MIN
203*     ..
204*     .. Executable Statements ..
205*
206*     Test the input arguments
207*
208      INFO = 0
209      LEFT = LSAME( SIDE, 'L' )
210      NOTRAN = LSAME( TRANS, 'N' )
211      LQUERY = ( LWORK.EQ.-1 )
212*
213*     NQ is the order of Q and NW is the minimum dimension of WORK
214*
215      IF( LEFT ) THEN
216         NQ = M
217         NW = MAX( 1, N )
218      ELSE
219         NQ = N
220         NW = MAX( 1, M )
221      END IF
222      IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
223         INFO = -1
224      ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
225         INFO = -2
226      ELSE IF( M.LT.0 ) THEN
227         INFO = -3
228      ELSE IF( N.LT.0 ) THEN
229         INFO = -4
230      ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
231         INFO = -5
232      ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
233         INFO = -7
234      ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
235         INFO = -10
236      ELSE IF( LWORK.LT.NW .AND. .NOT.LQUERY ) THEN
237         INFO = -12
238      END IF
239*
240      IF( INFO.EQ.0 ) THEN
241*
242*        Compute the workspace requirements
243*
244         IF( M.EQ.0 .OR. N.EQ.0 ) THEN
245            LWKOPT = 1
246         ELSE
247            NB = MIN( NBMAX, ILAENV( 1, 'DORMRQ', SIDE // TRANS, M, N,
248     $                               K, -1 ) )
249            LWKOPT = NW*NB + TSIZE
250         END IF
251         WORK( 1 ) = LWKOPT
252      END IF
253*
254      IF( INFO.NE.0 ) THEN
255         CALL XERBLA( 'DORMRQ', -INFO )
256         RETURN
257      ELSE IF( LQUERY ) THEN
258         RETURN
259      END IF
260*
261*     Quick return if possible
262*
263      IF( M.EQ.0 .OR. N.EQ.0 ) THEN
264         RETURN
265      END IF
266*
267      NBMIN = 2
268      LDWORK = NW
269      IF( NB.GT.1 .AND. NB.LT.K ) THEN
270         IF( LWORK.LT.LWKOPT ) THEN
271            NB = (LWORK-TSIZE) / LDWORK
272            NBMIN = MAX( 2, ILAENV( 2, 'DORMRQ', SIDE // TRANS, M, N, K,
273     $              -1 ) )
274         END IF
275      END IF
276*
277      IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
278*
279*        Use unblocked code
280*
281         CALL DORMR2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK,
282     $                IINFO )
283      ELSE
284*
285*        Use blocked code
286*
287         IWT = 1 + NW*NB
288         IF( ( LEFT .AND. .NOT.NOTRAN ) .OR.
289     $       ( .NOT.LEFT .AND. NOTRAN ) ) THEN
290            I1 = 1
291            I2 = K
292            I3 = NB
293         ELSE
294            I1 = ( ( K-1 ) / NB )*NB + 1
295            I2 = 1
296            I3 = -NB
297         END IF
298*
299         IF( LEFT ) THEN
300            NI = N
301         ELSE
302            MI = M
303         END IF
304*
305         IF( NOTRAN ) THEN
306            TRANST = 'T'
307         ELSE
308            TRANST = 'N'
309         END IF
310*
311         DO 10 I = I1, I2, I3
312            IB = MIN( NB, K-I+1 )
313*
314*           Form the triangular factor of the block reflector
315*           H = H(i+ib-1) . . . H(i+1) H(i)
316*
317            CALL DLARFT( 'Backward', 'Rowwise', NQ-K+I+IB-1, IB,
318     $                   A( I, 1 ), LDA, TAU( I ), WORK( IWT ), LDT )
319            IF( LEFT ) THEN
320*
321*              H or H**T is applied to C(1:m-k+i+ib-1,1:n)
322*
323               MI = M - K + I + IB - 1
324            ELSE
325*
326*              H or H**T is applied to C(1:m,1:n-k+i+ib-1)
327*
328               NI = N - K + I + IB - 1
329            END IF
330*
331*           Apply H or H**T
332*
333            CALL DLARFB( SIDE, TRANST, 'Backward', 'Rowwise', MI, NI,
334     $                   IB, A( I, 1 ), LDA, WORK( IWT ), LDT, C, LDC,
335     $                   WORK, LDWORK )
336   10    CONTINUE
337      END IF
338      WORK( 1 ) = LWKOPT
339      RETURN
340*
341*     End of DORMRQ
342*
343      END
344