1*> \brief \b DORMBR
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download DORMBR + dependencies
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11*> [TGZ]</a>
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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dormbr.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE DORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
22*                          LDC, WORK, LWORK, INFO )
23*
24*       .. Scalar Arguments ..
25*       CHARACTER          SIDE, TRANS, VECT
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*> If VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C
39*> with
40*>                 SIDE = 'L'     SIDE = 'R'
41*> TRANS = 'N':      Q * C          C * Q
42*> TRANS = 'T':      Q**T * C       C * Q**T
43*>
44*> If VECT = 'P', DORMBR overwrites the general real M-by-N matrix C
45*> with
46*>                 SIDE = 'L'     SIDE = 'R'
47*> TRANS = 'N':      P * C          C * P
48*> TRANS = 'T':      P**T * C       C * P**T
49*>
50*> Here Q and P**T are the orthogonal matrices determined by DGEBRD when
51*> reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and
52*> P**T are defined as products of elementary reflectors H(i) and G(i)
53*> respectively.
54*>
55*> Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
56*> order of the orthogonal matrix Q or P**T that is applied.
57*>
58*> If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
59*> if nq >= k, Q = H(1) H(2) . . . H(k);
60*> if nq < k, Q = H(1) H(2) . . . H(nq-1).
61*>
62*> If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
63*> if k < nq, P = G(1) G(2) . . . G(k);
64*> if k >= nq, P = G(1) G(2) . . . G(nq-1).
65*> \endverbatim
66*
67*  Arguments:
68*  ==========
69*
70*> \param[in] VECT
71*> \verbatim
72*>          VECT is CHARACTER*1
73*>          = 'Q': apply Q or Q**T;
74*>          = 'P': apply P or P**T.
75*> \endverbatim
76*>
77*> \param[in] SIDE
78*> \verbatim
79*>          SIDE is CHARACTER*1
80*>          = 'L': apply Q, Q**T, P or P**T from the Left;
81*>          = 'R': apply Q, Q**T, P or P**T from the Right.
82*> \endverbatim
83*>
84*> \param[in] TRANS
85*> \verbatim
86*>          TRANS is CHARACTER*1
87*>          = 'N':  No transpose, apply Q  or P;
88*>          = 'T':  Transpose, apply Q**T or P**T.
89*> \endverbatim
90*>
91*> \param[in] M
92*> \verbatim
93*>          M is INTEGER
94*>          The number of rows of the matrix C. M >= 0.
95*> \endverbatim
96*>
97*> \param[in] N
98*> \verbatim
99*>          N is INTEGER
100*>          The number of columns of the matrix C. N >= 0.
101*> \endverbatim
102*>
103*> \param[in] K
104*> \verbatim
105*>          K is INTEGER
106*>          If VECT = 'Q', the number of columns in the original
107*>          matrix reduced by DGEBRD.
108*>          If VECT = 'P', the number of rows in the original
109*>          matrix reduced by DGEBRD.
110*>          K >= 0.
111*> \endverbatim
112*>
113*> \param[in] A
114*> \verbatim
115*>          A is DOUBLE PRECISION array, dimension
116*>                                (LDA,min(nq,K)) if VECT = 'Q'
117*>                                (LDA,nq)        if VECT = 'P'
118*>          The vectors which define the elementary reflectors H(i) and
119*>          G(i), whose products determine the matrices Q and P, as
120*>          returned by DGEBRD.
121*> \endverbatim
122*>
123*> \param[in] LDA
124*> \verbatim
125*>          LDA is INTEGER
126*>          The leading dimension of the array A.
127*>          If VECT = 'Q', LDA >= max(1,nq);
128*>          if VECT = 'P', LDA >= max(1,min(nq,K)).
129*> \endverbatim
130*>
131*> \param[in] TAU
132*> \verbatim
133*>          TAU is DOUBLE PRECISION array, dimension (min(nq,K))
134*>          TAU(i) must contain the scalar factor of the elementary
135*>          reflector H(i) or G(i) which determines Q or P, as returned
136*>          by DGEBRD in the array argument TAUQ or TAUP.
137*> \endverbatim
138*>
139*> \param[in,out] C
140*> \verbatim
141*>          C is DOUBLE PRECISION array, dimension (LDC,N)
142*>          On entry, the M-by-N matrix C.
143*>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q
144*>          or P*C or P**T*C or C*P or C*P**T.
145*> \endverbatim
146*>
147*> \param[in] LDC
148*> \verbatim
149*>          LDC is INTEGER
150*>          The leading dimension of the array C. LDC >= max(1,M).
151*> \endverbatim
152*>
153*> \param[out] WORK
154*> \verbatim
155*>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
156*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
157*> \endverbatim
158*>
159*> \param[in] LWORK
160*> \verbatim
161*>          LWORK is INTEGER
162*>          The dimension of the array WORK.
163*>          If SIDE = 'L', LWORK >= max(1,N);
164*>          if SIDE = 'R', LWORK >= max(1,M).
165*>          For optimum performance LWORK >= N*NB if SIDE = 'L', and
166*>          LWORK >= M*NB if SIDE = 'R', where NB is the optimal
167*>          blocksize.
168*>
169*>          If LWORK = -1, then a workspace query is assumed; the routine
170*>          only calculates the optimal size of the WORK array, returns
171*>          this value as the first entry of the WORK array, and no error
172*>          message related to LWORK is issued by XERBLA.
173*> \endverbatim
174*>
175*> \param[out] INFO
176*> \verbatim
177*>          INFO is INTEGER
178*>          = 0:  successful exit
179*>          < 0:  if INFO = -i, the i-th argument had an illegal value
180*> \endverbatim
181*
182*  Authors:
183*  ========
184*
185*> \author Univ. of Tennessee
186*> \author Univ. of California Berkeley
187*> \author Univ. of Colorado Denver
188*> \author NAG Ltd.
189*
190*> \date November 2011
191*
192*> \ingroup doubleOTHERcomputational
193*
194*  =====================================================================
195      SUBROUTINE DORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
196     $                   LDC, WORK, LWORK, INFO )
197*
198*  -- LAPACK computational routine (version 3.4.0) --
199*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
200*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
201*     November 2011
202*
203*     .. Scalar Arguments ..
204      CHARACTER          SIDE, TRANS, VECT
205      INTEGER            INFO, K, LDA, LDC, LWORK, M, N
206*     ..
207*     .. Array Arguments ..
208      DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
209*     ..
210*
211*  =====================================================================
212*
213*     .. Local Scalars ..
214      LOGICAL            APPLYQ, LEFT, LQUERY, NOTRAN
215      CHARACTER          TRANST
216      INTEGER            I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW
217*     ..
218*     .. External Functions ..
219      LOGICAL            LSAME
220      INTEGER            ILAENV
221      EXTERNAL           LSAME, ILAENV
222*     ..
223*     .. External Subroutines ..
224      EXTERNAL           DORMLQ, DORMQR, XERBLA
225*     ..
226*     .. Intrinsic Functions ..
227      INTRINSIC          MAX, MIN
228*     ..
229*     .. Executable Statements ..
230*
231*     Test the input arguments
232*
233      INFO = 0
234      APPLYQ = LSAME( VECT, 'Q' )
235      LEFT = LSAME( SIDE, 'L' )
236      NOTRAN = LSAME( TRANS, 'N' )
237      LQUERY = ( LWORK.EQ.-1 )
238*
239*     NQ is the order of Q or P and NW is the minimum dimension of WORK
240*
241      IF( LEFT ) THEN
242         NQ = M
243         NW = N
244      ELSE
245         NQ = N
246         NW = M
247      END IF
248      IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
249         INFO = -1
250      ELSE IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
251         INFO = -2
252      ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
253         INFO = -3
254      ELSE IF( M.LT.0 ) THEN
255         INFO = -4
256      ELSE IF( N.LT.0 ) THEN
257         INFO = -5
258      ELSE IF( K.LT.0 ) THEN
259         INFO = -6
260      ELSE IF( ( APPLYQ .AND. LDA.LT.MAX( 1, NQ ) ) .OR.
261     $         ( .NOT.APPLYQ .AND. LDA.LT.MAX( 1, MIN( NQ, K ) ) ) )
262     $          THEN
263         INFO = -8
264      ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
265         INFO = -11
266      ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
267         INFO = -13
268      END IF
269*
270      IF( INFO.EQ.0 ) THEN
271         IF( APPLYQ ) THEN
272            IF( LEFT ) THEN
273               NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M-1, N, M-1,
274     $              -1 )
275            ELSE
276               NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M, N-1, N-1,
277     $              -1 )
278            END IF
279         ELSE
280            IF( LEFT ) THEN
281               NB = ILAENV( 1, 'DORMLQ', SIDE // TRANS, M-1, N, M-1,
282     $              -1 )
283            ELSE
284               NB = ILAENV( 1, 'DORMLQ', SIDE // TRANS, M, N-1, N-1,
285     $              -1 )
286            END IF
287         END IF
288         LWKOPT = MAX( 1, NW )*NB
289         WORK( 1 ) = LWKOPT
290      END IF
291*
292      IF( INFO.NE.0 ) THEN
293         CALL XERBLA( 'DORMBR', -INFO )
294         RETURN
295      ELSE IF( LQUERY ) THEN
296         RETURN
297      END IF
298*
299*     Quick return if possible
300*
301      WORK( 1 ) = 1
302      IF( M.EQ.0 .OR. N.EQ.0 )
303     $   RETURN
304*
305      IF( APPLYQ ) THEN
306*
307*        Apply Q
308*
309         IF( NQ.GE.K ) THEN
310*
311*           Q was determined by a call to DGEBRD with nq >= k
312*
313            CALL DORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
314     $                   WORK, LWORK, IINFO )
315         ELSE IF( NQ.GT.1 ) THEN
316*
317*           Q was determined by a call to DGEBRD with nq < k
318*
319            IF( LEFT ) THEN
320               MI = M - 1
321               NI = N
322               I1 = 2
323               I2 = 1
324            ELSE
325               MI = M
326               NI = N - 1
327               I1 = 1
328               I2 = 2
329            END IF
330            CALL DORMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU,
331     $                   C( I1, I2 ), LDC, WORK, LWORK, IINFO )
332         END IF
333      ELSE
334*
335*        Apply P
336*
337         IF( NOTRAN ) THEN
338            TRANST = 'T'
339         ELSE
340            TRANST = 'N'
341         END IF
342         IF( NQ.GT.K ) THEN
343*
344*           P was determined by a call to DGEBRD with nq > k
345*
346            CALL DORMLQ( SIDE, TRANST, M, N, K, A, LDA, TAU, C, LDC,
347     $                   WORK, LWORK, IINFO )
348         ELSE IF( NQ.GT.1 ) THEN
349*
350*           P was determined by a call to DGEBRD with nq <= k
351*
352            IF( LEFT ) THEN
353               MI = M - 1
354               NI = N
355               I1 = 2
356               I2 = 1
357            ELSE
358               MI = M
359               NI = N - 1
360               I1 = 1
361               I2 = 2
362            END IF
363            CALL DORMLQ( SIDE, TRANST, MI, NI, NQ-1, A( 1, 2 ), LDA,
364     $                   TAU, C( I1, I2 ), LDC, WORK, LWORK, IINFO )
365         END IF
366      END IF
367      WORK( 1 ) = LWKOPT
368      RETURN
369*
370*     End of DORMBR
371*
372      END
373c $Id$
374