LAPACK  3.10.0 LAPACK: Linear Algebra PACKage
dormbr.f
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1 *> \brief \b DORMBR
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
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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 *> \ingroup doubleOTHERcomputational
191 *
192 * =====================================================================
193  SUBROUTINE dormbr( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
194  \$ LDC, WORK, LWORK, INFO )
195 *
196 * -- LAPACK computational routine --
197 * -- LAPACK is a software package provided by Univ. of Tennessee, --
198 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
199 *
200 * .. Scalar Arguments ..
201  CHARACTER SIDE, TRANS, VECT
202  INTEGER INFO, K, LDA, LDC, LWORK, M, N
203 * ..
204 * .. Array Arguments ..
205  DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
206 * ..
207 *
208 * =====================================================================
209 *
210 * .. Local Scalars ..
211  LOGICAL APPLYQ, LEFT, LQUERY, NOTRAN
212  CHARACTER TRANST
213  INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW
214 * ..
215 * .. External Functions ..
216  LOGICAL LSAME
217  INTEGER ILAENV
218  EXTERNAL lsame, ilaenv
219 * ..
220 * .. External Subroutines ..
221  EXTERNAL dormlq, dormqr, xerbla
222 * ..
223 * .. Intrinsic Functions ..
224  INTRINSIC max, min
225 * ..
226 * .. Executable Statements ..
227 *
228 * Test the input arguments
229 *
230  info = 0
231  applyq = lsame( vect, 'Q' )
232  left = lsame( side, 'L' )
233  notran = lsame( trans, 'N' )
234  lquery = ( lwork.EQ.-1 )
235 *
236 * NQ is the order of Q or P and NW is the minimum dimension of WORK
237 *
238  IF( left ) THEN
239  nq = m
240  nw = max( 1, n )
241  ELSE
242  nq = n
243  nw = max( 1, m )
244  END IF
245  IF( .NOT.applyq .AND. .NOT.lsame( vect, 'P' ) ) THEN
246  info = -1
247  ELSE IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
248  info = -2
249  ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
250  info = -3
251  ELSE IF( m.LT.0 ) THEN
252  info = -4
253  ELSE IF( n.LT.0 ) THEN
254  info = -5
255  ELSE IF( k.LT.0 ) THEN
256  info = -6
257  ELSE IF( ( applyq .AND. lda.LT.max( 1, nq ) ) .OR.
258  \$ ( .NOT.applyq .AND. lda.LT.max( 1, min( nq, k ) ) ) )
259  \$ THEN
260  info = -8
261  ELSE IF( ldc.LT.max( 1, m ) ) THEN
262  info = -11
263  ELSE IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
264  info = -13
265  END IF
266 *
267  IF( info.EQ.0 ) THEN
268  IF( applyq ) THEN
269  IF( left ) THEN
270  nb = ilaenv( 1, 'DORMQR', side // trans, m-1, n, m-1,
271  \$ -1 )
272  ELSE
273  nb = ilaenv( 1, 'DORMQR', side // trans, m, n-1, n-1,
274  \$ -1 )
275  END IF
276  ELSE
277  IF( left ) THEN
278  nb = ilaenv( 1, 'DORMLQ', side // trans, m-1, n, m-1,
279  \$ -1 )
280  ELSE
281  nb = ilaenv( 1, 'DORMLQ', side // trans, m, n-1, n-1,
282  \$ -1 )
283  END IF
284  END IF
285  lwkopt = nw*nb
286  work( 1 ) = lwkopt
287  END IF
288 *
289  IF( info.NE.0 ) THEN
290  CALL xerbla( 'DORMBR', -info )
291  RETURN
292  ELSE IF( lquery ) THEN
293  RETURN
294  END IF
295 *
296 * Quick return if possible
297 *
298  work( 1 ) = 1
299  IF( m.EQ.0 .OR. n.EQ.0 )
300  \$ RETURN
301 *
302  IF( applyq ) THEN
303 *
304 * Apply Q
305 *
306  IF( nq.GE.k ) THEN
307 *
308 * Q was determined by a call to DGEBRD with nq >= k
309 *
310  CALL dormqr( side, trans, m, n, k, a, lda, tau, c, ldc,
311  \$ work, lwork, iinfo )
312  ELSE IF( nq.GT.1 ) THEN
313 *
314 * Q was determined by a call to DGEBRD with nq < k
315 *
316  IF( left ) THEN
317  mi = m - 1
318  ni = n
319  i1 = 2
320  i2 = 1
321  ELSE
322  mi = m
323  ni = n - 1
324  i1 = 1
325  i2 = 2
326  END IF
327  CALL dormqr( side, trans, mi, ni, nq-1, a( 2, 1 ), lda, tau,
328  \$ c( i1, i2 ), ldc, work, lwork, iinfo )
329  END IF
330  ELSE
331 *
332 * Apply P
333 *
334  IF( notran ) THEN
335  transt = 'T'
336  ELSE
337  transt = 'N'
338  END IF
339  IF( nq.GT.k ) THEN
340 *
341 * P was determined by a call to DGEBRD with nq > k
342 *
343  CALL dormlq( side, transt, m, n, k, a, lda, tau, c, ldc,
344  \$ work, lwork, iinfo )
345  ELSE IF( nq.GT.1 ) THEN
346 *
347 * P was determined by a call to DGEBRD with nq <= k
348 *
349  IF( left ) THEN
350  mi = m - 1
351  ni = n
352  i1 = 2
353  i2 = 1
354  ELSE
355  mi = m
356  ni = n - 1
357  i1 = 1
358  i2 = 2
359  END IF
360  CALL dormlq( side, transt, mi, ni, nq-1, a( 1, 2 ), lda,
361  \$ tau, c( i1, i2 ), ldc, work, lwork, iinfo )
362  END IF
363  END IF
364  work( 1 ) = lwkopt
365  RETURN
366 *
367 * End of DORMBR
368 *
369  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dormqr(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
DORMQR
Definition: dormqr.f:167
subroutine dormlq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
DORMLQ
Definition: dormlq.f:167
subroutine dormbr(VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
DORMBR
Definition: dormbr.f:195