LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
dormlq.f
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1 *> \brief \b DORMLQ
2 *
3 * =========== DOCUMENTATION ===========
4 *
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16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE DORMLQ( 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 *> DORMLQ 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 DGELQF. 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 *> DGELQF in the first 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 DGELQF.
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 dormlq( 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  CHARACTER transt
194  INTEGER i, i1, i2, i3, ib, ic, iinfo, iws, jc, ldwork,
195  \$ lwkopt, mi, nb, nbmin, ni, nq, nw
196 * ..
197 * .. Local Arrays ..
198  DOUBLE PRECISION t( ldt, nbmax )
199 * ..
200 * .. External Functions ..
201  LOGICAL lsame
202  INTEGER ilaenv
203  EXTERNAL lsame, ilaenv
204 * ..
205 * .. External Subroutines ..
206  EXTERNAL dlarfb, dlarft, dorml2, xerbla
207 * ..
208 * .. Intrinsic Functions ..
209  INTRINSIC max, min
210 * ..
211 * .. Executable Statements ..
212 *
213 * Test the input arguments
214 *
215  info = 0
216  left = lsame( side, 'L' )
217  notran = lsame( trans, 'N' )
218  lquery = ( lwork.EQ.-1 )
219 *
220 * NQ is the order of Q and NW is the minimum dimension of WORK
221 *
222  IF( left ) THEN
223  nq = m
224  nw = n
225  ELSE
226  nq = n
227  nw = m
228  END IF
229  IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
230  info = -1
231  ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
232  info = -2
233  ELSE IF( m.LT.0 ) THEN
234  info = -3
235  ELSE IF( n.LT.0 ) THEN
236  info = -4
237  ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
238  info = -5
239  ELSE IF( lda.LT.max( 1, k ) ) THEN
240  info = -7
241  ELSE IF( ldc.LT.max( 1, m ) ) THEN
242  info = -10
243  ELSE IF( lwork.LT.max( 1, nw ) .AND. .NOT.lquery ) THEN
244  info = -12
245  END IF
246 *
247  IF( info.EQ.0 ) THEN
248 *
249 * Determine the block size. NB may be at most NBMAX, where NBMAX
250 * is used to define the local array T.
251 *
252  nb = min( nbmax, ilaenv( 1, 'DORMLQ', side // trans, m, n, k,
253  \$ -1 ) )
254  lwkopt = max( 1, nw )*nb
255  work( 1 ) = lwkopt
256  END IF
257 *
258  IF( info.NE.0 ) THEN
259  CALL xerbla( 'DORMLQ', -info )
260  return
261  ELSE IF( lquery ) THEN
262  return
263  END IF
264 *
265 * Quick return if possible
266 *
267  IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) THEN
268  work( 1 ) = 1
269  return
270  END IF
271 *
272  nbmin = 2
273  ldwork = nw
274  IF( nb.GT.1 .AND. nb.LT.k ) THEN
275  iws = nw*nb
276  IF( lwork.LT.iws ) THEN
277  nb = lwork / ldwork
278  nbmin = max( 2, ilaenv( 2, 'DORMLQ', side // trans, m, n, k,
279  \$ -1 ) )
280  END IF
281  ELSE
282  iws = nw
283  END IF
284 *
285  IF( nb.LT.nbmin .OR. nb.GE.k ) THEN
286 *
287 * Use unblocked code
288 *
289  CALL dorml2( side, trans, m, n, k, a, lda, tau, c, ldc, work,
290  \$ iinfo )
291  ELSE
292 *
293 * Use blocked code
294 *
295  IF( ( left .AND. notran ) .OR.
296  \$ ( .NOT.left .AND. .NOT.notran ) ) THEN
297  i1 = 1
298  i2 = k
299  i3 = nb
300  ELSE
301  i1 = ( ( k-1 ) / nb )*nb + 1
302  i2 = 1
303  i3 = -nb
304  END IF
305 *
306  IF( left ) THEN
307  ni = n
308  jc = 1
309  ELSE
310  mi = m
311  ic = 1
312  END IF
313 *
314  IF( notran ) THEN
315  transt = 'T'
316  ELSE
317  transt = 'N'
318  END IF
319 *
320  DO 10 i = i1, i2, i3
321  ib = min( nb, k-i+1 )
322 *
323 * Form the triangular factor of the block reflector
324 * H = H(i) H(i+1) . . . H(i+ib-1)
325 *
326  CALL dlarft( 'Forward', 'Rowwise', nq-i+1, ib, a( i, i ),
327  \$ lda, tau( i ), t, ldt )
328  IF( left ) THEN
329 *
330 * H or H**T is applied to C(i:m,1:n)
331 *
332  mi = m - i + 1
333  ic = i
334  ELSE
335 *
336 * H or H**T is applied to C(1:m,i:n)
337 *
338  ni = n - i + 1
339  jc = i
340  END IF
341 *
342 * Apply H or H**T
343 *
344  CALL dlarfb( side, transt, 'Forward', 'Rowwise', mi, ni, ib,
345  \$ a( i, i ), lda, t, ldt, c( ic, jc ), ldc, work,
346  \$ ldwork )
347  10 continue
348  END IF
349  work( 1 ) = lwkopt
350  return
351 *
352 * End of DORMLQ
353 *
354  END