1*> \brief \b SORMBR
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download SORMBR + 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/sormbr.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE SORMBR( 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*       REAL               A( LDA, * ), C( LDC, * ), TAU( * ),
30*      $                   WORK( * )
31*       ..
32*
33*
34*> \par Purpose:
35*  =============
36*>
37*> \verbatim
38*>
39*> If VECT = 'Q', SORMBR overwrites the general real M-by-N matrix C
40*> with
41*>                 SIDE = 'L'     SIDE = 'R'
42*> TRANS = 'N':      Q * C          C * Q
43*> TRANS = 'T':      Q**T * C       C * Q**T
44*>
45*> If VECT = 'P', SORMBR overwrites the general real M-by-N matrix C
46*> with
47*>                 SIDE = 'L'     SIDE = 'R'
48*> TRANS = 'N':      P * C          C * P
49*> TRANS = 'T':      P**T * C       C * P**T
50*>
51*> Here Q and P**T are the orthogonal matrices determined by SGEBRD when
52*> reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and
53*> P**T are defined as products of elementary reflectors H(i) and G(i)
54*> respectively.
55*>
56*> Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
57*> order of the orthogonal matrix Q or P**T that is applied.
58*>
59*> If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
60*> if nq >= k, Q = H(1) H(2) . . . H(k);
61*> if nq < k, Q = H(1) H(2) . . . H(nq-1).
62*>
63*> If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
64*> if k < nq, P = G(1) G(2) . . . G(k);
65*> if k >= nq, P = G(1) G(2) . . . G(nq-1).
66*> \endverbatim
67*
68*  Arguments:
69*  ==========
70*
71*> \param[in] VECT
72*> \verbatim
73*>          VECT is CHARACTER*1
74*>          = 'Q': apply Q or Q**T;
75*>          = 'P': apply P or P**T.
76*> \endverbatim
77*>
78*> \param[in] SIDE
79*> \verbatim
80*>          SIDE is CHARACTER*1
81*>          = 'L': apply Q, Q**T, P or P**T from the Left;
82*>          = 'R': apply Q, Q**T, P or P**T from the Right.
83*> \endverbatim
84*>
85*> \param[in] TRANS
86*> \verbatim
87*>          TRANS is CHARACTER*1
88*>          = 'N':  No transpose, apply Q  or P;
89*>          = 'T':  Transpose, apply Q**T or P**T.
90*> \endverbatim
91*>
92*> \param[in] M
93*> \verbatim
94*>          M is INTEGER
95*>          The number of rows of the matrix C. M >= 0.
96*> \endverbatim
97*>
98*> \param[in] N
99*> \verbatim
100*>          N is INTEGER
101*>          The number of columns of the matrix C. N >= 0.
102*> \endverbatim
103*>
104*> \param[in] K
105*> \verbatim
106*>          K is INTEGER
107*>          If VECT = 'Q', the number of columns in the original
108*>          matrix reduced by SGEBRD.
109*>          If VECT = 'P', the number of rows in the original
110*>          matrix reduced by SGEBRD.
111*>          K >= 0.
112*> \endverbatim
113*>
114*> \param[in] A
115*> \verbatim
116*>          A is REAL array, dimension
117*>                                (LDA,min(nq,K)) if VECT = 'Q'
118*>                                (LDA,nq)        if VECT = 'P'
119*>          The vectors which define the elementary reflectors H(i) and
120*>          G(i), whose products determine the matrices Q and P, as
121*>          returned by SGEBRD.
122*> \endverbatim
123*>
124*> \param[in] LDA
125*> \verbatim
126*>          LDA is INTEGER
127*>          The leading dimension of the array A.
128*>          If VECT = 'Q', LDA >= max(1,nq);
129*>          if VECT = 'P', LDA >= max(1,min(nq,K)).
130*> \endverbatim
131*>
132*> \param[in] TAU
133*> \verbatim
134*>          TAU is REAL array, dimension (min(nq,K))
135*>          TAU(i) must contain the scalar factor of the elementary
136*>          reflector H(i) or G(i) which determines Q or P, as returned
137*>          by SGEBRD in the array argument TAUQ or TAUP.
138*> \endverbatim
139*>
140*> \param[in,out] C
141*> \verbatim
142*>          C is REAL array, dimension (LDC,N)
143*>          On entry, the M-by-N matrix C.
144*>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q
145*>          or P*C or P**T*C or C*P or C*P**T.
146*> \endverbatim
147*>
148*> \param[in] LDC
149*> \verbatim
150*>          LDC is INTEGER
151*>          The leading dimension of the array C. LDC >= max(1,M).
152*> \endverbatim
153*>
154*> \param[out] WORK
155*> \verbatim
156*>          WORK is REAL array, dimension (MAX(1,LWORK))
157*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
158*> \endverbatim
159*>
160*> \param[in] LWORK
161*> \verbatim
162*>          LWORK is INTEGER
163*>          The dimension of the array WORK.
164*>          If SIDE = 'L', LWORK >= max(1,N);
165*>          if SIDE = 'R', LWORK >= max(1,M).
166*>          For optimum performance LWORK >= N*NB if SIDE = 'L', and
167*>          LWORK >= M*NB if SIDE = 'R', where NB is the optimal
168*>          blocksize.
169*>
170*>          If LWORK = -1, then a workspace query is assumed; the routine
171*>          only calculates the optimal size of the WORK array, returns
172*>          this value as the first entry of the WORK array, and no error
173*>          message related to LWORK is issued by XERBLA.
174*> \endverbatim
175*>
176*> \param[out] INFO
177*> \verbatim
178*>          INFO is INTEGER
179*>          = 0:  successful exit
180*>          < 0:  if INFO = -i, the i-th argument had an illegal value
181*> \endverbatim
182*
183*  Authors:
184*  ========
185*
186*> \author Univ. of Tennessee
187*> \author Univ. of California Berkeley
188*> \author Univ. of Colorado Denver
189*> \author NAG Ltd.
190*
191*> \ingroup realOTHERcomputational
192*
193*  =====================================================================
194      SUBROUTINE SORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
195     $                   LDC, WORK, LWORK, INFO )
196*
197*  -- LAPACK computational routine --
198*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
199*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
200*
201*     .. Scalar Arguments ..
202      CHARACTER          SIDE, TRANS, VECT
203      INTEGER            INFO, K, LDA, LDC, LWORK, M, N
204*     ..
205*     .. Array Arguments ..
206      REAL               A( LDA, * ), C( LDC, * ), TAU( * ),
207     $                   WORK( * )
208*     ..
209*
210*  =====================================================================
211*
212*     .. Local Scalars ..
213      LOGICAL            APPLYQ, LEFT, LQUERY, NOTRAN
214      CHARACTER          TRANST
215      INTEGER            I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW
216*     ..
217*     .. External Functions ..
218      LOGICAL            LSAME
219      INTEGER            ILAENV
220      EXTERNAL           ILAENV, LSAME
221*     ..
222*     .. External Subroutines ..
223      EXTERNAL           SORMLQ, SORMQR, XERBLA
224*     ..
225*     .. Intrinsic Functions ..
226      INTRINSIC          MAX, MIN
227*     ..
228*     .. Executable Statements ..
229*
230*     Test the input arguments
231*
232      INFO = 0
233      APPLYQ = LSAME( VECT, 'Q' )
234      LEFT = LSAME( SIDE, 'L' )
235      NOTRAN = LSAME( TRANS, 'N' )
236      LQUERY = ( LWORK.EQ.-1 )
237*
238*     NQ is the order of Q or P and NW is the minimum dimension of WORK
239*
240      IF( LEFT ) THEN
241         NQ = M
242         NW = MAX( 1, N )
243      ELSE
244         NQ = N
245         NW = MAX( 1, M )
246      END IF
247      IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
248         INFO = -1
249      ELSE IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
250         INFO = -2
251      ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
252         INFO = -3
253      ELSE IF( M.LT.0 ) THEN
254         INFO = -4
255      ELSE IF( N.LT.0 ) THEN
256         INFO = -5
257      ELSE IF( K.LT.0 ) THEN
258         INFO = -6
259      ELSE IF( ( APPLYQ .AND. LDA.LT.MAX( 1, NQ ) ) .OR.
260     $         ( .NOT.APPLYQ .AND. LDA.LT.MAX( 1, MIN( NQ, K ) ) ) )
261     $          THEN
262         INFO = -8
263      ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
264         INFO = -11
265      ELSE IF( LWORK.LT.NW .AND. .NOT.LQUERY ) THEN
266         INFO = -13
267      END IF
268*
269      IF( INFO.EQ.0 ) THEN
270         IF( APPLYQ ) THEN
271            IF( LEFT ) THEN
272               NB = ILAENV( 1, 'SORMQR', SIDE // TRANS, M-1, N, M-1,
273     $                      -1 )
274            ELSE
275               NB = ILAENV( 1, 'SORMQR', SIDE // TRANS, M, N-1, N-1,
276     $                      -1 )
277            END IF
278         ELSE
279            IF( LEFT ) THEN
280               NB = ILAENV( 1, 'SORMLQ', SIDE // TRANS, M-1, N, M-1,
281     $                      -1 )
282            ELSE
283               NB = ILAENV( 1, 'SORMLQ', SIDE // TRANS, M, N-1, N-1,
284     $                      -1 )
285            END IF
286         END IF
287         LWKOPT = NW*NB
288         WORK( 1 ) = LWKOPT
289      END IF
290*
291      IF( INFO.NE.0 ) THEN
292         CALL XERBLA( 'SORMBR', -INFO )
293         RETURN
294      ELSE IF( LQUERY ) THEN
295         RETURN
296      END IF
297*
298*     Quick return if possible
299*
300      WORK( 1 ) = 1
301      IF( M.EQ.0 .OR. N.EQ.0 )
302     $   RETURN
303*
304      IF( APPLYQ ) THEN
305*
306*        Apply Q
307*
308         IF( NQ.GE.K ) THEN
309*
310*           Q was determined by a call to SGEBRD with nq >= k
311*
312            CALL SORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
313     $                   WORK, LWORK, IINFO )
314         ELSE IF( NQ.GT.1 ) THEN
315*
316*           Q was determined by a call to SGEBRD with nq < k
317*
318            IF( LEFT ) THEN
319               MI = M - 1
320               NI = N
321               I1 = 2
322               I2 = 1
323            ELSE
324               MI = M
325               NI = N - 1
326               I1 = 1
327               I2 = 2
328            END IF
329            CALL SORMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU,
330     $                   C( I1, I2 ), LDC, WORK, LWORK, IINFO )
331         END IF
332      ELSE
333*
334*        Apply P
335*
336         IF( NOTRAN ) THEN
337            TRANST = 'T'
338         ELSE
339            TRANST = 'N'
340         END IF
341         IF( NQ.GT.K ) THEN
342*
343*           P was determined by a call to SGEBRD with nq > k
344*
345            CALL SORMLQ( SIDE, TRANST, M, N, K, A, LDA, TAU, C, LDC,
346     $                   WORK, LWORK, IINFO )
347         ELSE IF( NQ.GT.1 ) THEN
348*
349*           P was determined by a call to SGEBRD with nq <= k
350*
351            IF( LEFT ) THEN
352               MI = M - 1
353               NI = N
354               I1 = 2
355               I2 = 1
356            ELSE
357               MI = M
358               NI = N - 1
359               I1 = 1
360               I2 = 2
361            END IF
362            CALL SORMLQ( SIDE, TRANST, MI, NI, NQ-1, A( 1, 2 ), LDA,
363     $                   TAU, C( I1, I2 ), LDC, WORK, LWORK, IINFO )
364         END IF
365      END IF
366      WORK( 1 ) = LWKOPT
367      RETURN
368*
369*     End of SORMBR
370*
371      END
372