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dormql.f
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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
9 *> Download DORMQL + 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/dormql.f">
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 optimum performance LWORK >= N*NB if SIDE = 'L', and
140 *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal
141 *> blocksize.
142 *>
143 *> If LWORK = -1, then a workspace query is assumed; the routine
144 *> only calculates the optimal size of the WORK array, returns
145 *> this value as the first entry of the WORK array, and no error
146 *> message related to LWORK is issued by XERBLA.
147 *> \endverbatim
148 *>
149 *> \param[out] INFO
150 *> \verbatim
151 *> INFO is INTEGER
152 *> = 0: successful exit
153 *> < 0: if INFO = -i, the i-th argument had an illegal value
154 *> \endverbatim
155 *
156 * Authors:
157 * ========
158 *
159 *> \author Univ. of Tennessee
160 *> \author Univ. of California Berkeley
161 *> \author Univ. of Colorado Denver
162 *> \author NAG Ltd.
163 *
164 *> \date November 2011
165 *
166 *> \ingroup doubleOTHERcomputational
167 *
168 * =====================================================================
169  SUBROUTINE dormql( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
170  $ work, lwork, info )
171 *
172 * -- LAPACK computational routine (version 3.4.0) --
173 * -- LAPACK is a software package provided by Univ. of Tennessee, --
174 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
175 * November 2011
176 *
177 * .. Scalar Arguments ..
178  CHARACTER side, trans
179  INTEGER info, k, lda, ldc, lwork, m, n
180 * ..
181 * .. Array Arguments ..
182  DOUBLE PRECISION a( lda, * ), c( ldc, * ), tau( * ), work( * )
183 * ..
184 *
185 * =====================================================================
186 *
187 * .. Parameters ..
188  INTEGER nbmax, ldt
189  parameter( nbmax = 64, ldt = nbmax+1 )
190 * ..
191 * .. Local Scalars ..
192  LOGICAL left, lquery, notran
193  INTEGER i, i1, i2, i3, ib, iinfo, iws, ldwork, lwkopt,
194  $ mi, nb, nbmin, ni, nq, nw
195 * ..
196 * .. Local Arrays ..
197  DOUBLE PRECISION t( ldt, nbmax )
198 * ..
199 * .. External Functions ..
200  LOGICAL lsame
201  INTEGER ilaenv
202  EXTERNAL lsame, ilaenv
203 * ..
204 * .. External Subroutines ..
205  EXTERNAL dlarfb, dlarft, dorm2l, xerbla
206 * ..
207 * .. Intrinsic Functions ..
208  INTRINSIC max, min
209 * ..
210 * .. Executable Statements ..
211 *
212 * Test the input arguments
213 *
214  info = 0
215  left = lsame( side, 'L' )
216  notran = lsame( trans, 'N' )
217  lquery = ( lwork.EQ.-1 )
218 *
219 * NQ is the order of Q and NW is the minimum dimension of WORK
220 *
221  IF( left ) THEN
222  nq = m
223  nw = max( 1, n )
224  ELSE
225  nq = n
226  nw = max( 1, m )
227  END IF
228  IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
229  info = -1
230  ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
231  info = -2
232  ELSE IF( m.LT.0 ) THEN
233  info = -3
234  ELSE IF( n.LT.0 ) THEN
235  info = -4
236  ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
237  info = -5
238  ELSE IF( lda.LT.max( 1, nq ) ) THEN
239  info = -7
240  ELSE IF( ldc.LT.max( 1, m ) ) THEN
241  info = -10
242  END IF
243 *
244  IF( info.EQ.0 ) THEN
245  IF( m.EQ.0 .OR. n.EQ.0 ) THEN
246  lwkopt = 1
247  ELSE
248 *
249 * Determine the block size. NB may be at most NBMAX, where
250 * NBMAX is used to define the local array T.
251 *
252  nb = min( nbmax, ilaenv( 1, 'DORMQL', side // trans, m, n,
253  $ k, -1 ) )
254  lwkopt = nw*nb
255  END IF
256  work( 1 ) = lwkopt
257 *
258  IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
259  info = -12
260  END IF
261  END IF
262 *
263  IF( info.NE.0 ) THEN
264  CALL xerbla( 'DORMQL', -info )
265  return
266  ELSE IF( lquery ) THEN
267  return
268  END IF
269 *
270 * Quick return if possible
271 *
272  IF( m.EQ.0 .OR. n.EQ.0 ) THEN
273  return
274  END IF
275 *
276  nbmin = 2
277  ldwork = nw
278  IF( nb.GT.1 .AND. nb.LT.k ) THEN
279  iws = nw*nb
280  IF( lwork.LT.iws ) THEN
281  nb = lwork / ldwork
282  nbmin = max( 2, ilaenv( 2, 'DORMQL', side // trans, m, n, k,
283  $ -1 ) )
284  END IF
285  ELSE
286  iws = nw
287  END IF
288 *
289  IF( nb.LT.nbmin .OR. nb.GE.k ) THEN
290 *
291 * Use unblocked code
292 *
293  CALL dorm2l( side, trans, m, n, k, a, lda, tau, c, ldc, work,
294  $ iinfo )
295  ELSE
296 *
297 * Use blocked code
298 *
299  IF( ( left .AND. notran ) .OR.
300  $ ( .NOT.left .AND. .NOT.notran ) ) THEN
301  i1 = 1
302  i2 = k
303  i3 = nb
304  ELSE
305  i1 = ( ( k-1 ) / nb )*nb + 1
306  i2 = 1
307  i3 = -nb
308  END IF
309 *
310  IF( left ) THEN
311  ni = n
312  ELSE
313  mi = m
314  END IF
315 *
316  DO 10 i = i1, i2, i3
317  ib = min( nb, k-i+1 )
318 *
319 * Form the triangular factor of the block reflector
320 * H = H(i+ib-1) . . . H(i+1) H(i)
321 *
322  CALL dlarft( 'Backward', 'Columnwise', nq-k+i+ib-1, ib,
323  $ a( 1, i ), lda, tau( i ), t, ldt )
324  IF( left ) THEN
325 *
326 * H or H**T is applied to C(1:m-k+i+ib-1,1:n)
327 *
328  mi = m - k + i + ib - 1
329  ELSE
330 *
331 * H or H**T is applied to C(1:m,1:n-k+i+ib-1)
332 *
333  ni = n - k + i + ib - 1
334  END IF
335 *
336 * Apply H or H**T
337 *
338  CALL dlarfb( side, trans, 'Backward', 'Columnwise', mi, ni,
339  $ ib, a( 1, i ), lda, t, ldt, c, ldc, work,
340  $ ldwork )
341  10 continue
342  END IF
343  work( 1 ) = lwkopt
344  return
345 *
346 * End of DORMQL
347 *
348  END