LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
dormlq.f
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1 *> \brief \b DORMLQ
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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15 *> [TXT]</a>
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 good performance, LWORK should generally be larger.
140 *>
141 *> If LWORK = -1, then a workspace query is assumed; the routine
142 *> only calculates the optimal size of the WORK array, returns
143 *> this value as the first entry of the WORK array, and no error
144 *> message related to LWORK is issued by XERBLA.
145 *> \endverbatim
146 *>
147 *> \param[out] INFO
148 *> \verbatim
149 *> INFO is INTEGER
150 *> = 0: successful exit
151 *> < 0: if INFO = -i, the i-th argument had an illegal value
152 *> \endverbatim
153 *
154 * Authors:
155 * ========
156 *
157 *> \author Univ. of Tennessee
158 *> \author Univ. of California Berkeley
159 *> \author Univ. of Colorado Denver
160 *> \author NAG Ltd.
161 *
162 *> \ingroup doubleOTHERcomputational
163 *
164 * =====================================================================
165  SUBROUTINE dormlq( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
166  $ WORK, LWORK, INFO )
167 *
168 * -- LAPACK computational routine --
169 * -- LAPACK is a software package provided by Univ. of Tennessee, --
170 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
171 *
172 * .. Scalar Arguments ..
173  CHARACTER SIDE, TRANS
174  INTEGER INFO, K, LDA, LDC, LWORK, M, N
175 * ..
176 * .. Array Arguments ..
177  DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
178 * ..
179 *
180 * =====================================================================
181 *
182 * .. Parameters ..
183  INTEGER NBMAX, LDT, TSIZE
184  parameter( nbmax = 64, ldt = nbmax+1,
185  $ tsize = ldt*nbmax )
186 * ..
187 * .. Local Scalars ..
188  LOGICAL LEFT, LQUERY, NOTRAN
189  CHARACTER TRANST
190  INTEGER I, I1, I2, I3, IB, IC, IINFO, IWT, JC, LDWORK,
191  $ lwkopt, mi, nb, nbmin, ni, nq, nw
192 * ..
193 * .. External Functions ..
194  LOGICAL LSAME
195  INTEGER ILAENV
196  EXTERNAL lsame, ilaenv
197 * ..
198 * .. External Subroutines ..
199  EXTERNAL dlarfb, dlarft, dorml2, xerbla
200 * ..
201 * .. Intrinsic Functions ..
202  INTRINSIC max, min
203 * ..
204 * .. Executable Statements ..
205 *
206 * Test the input arguments
207 *
208  info = 0
209  left = lsame( side, 'L' )
210  notran = lsame( trans, 'N' )
211  lquery = ( lwork.EQ.-1 )
212 *
213 * NQ is the order of Q and NW is the minimum dimension of WORK
214 *
215  IF( left ) THEN
216  nq = m
217  nw = max( 1, n )
218  ELSE
219  nq = n
220  nw = max( 1, m )
221  END IF
222  IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
223  info = -1
224  ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
225  info = -2
226  ELSE IF( m.LT.0 ) THEN
227  info = -3
228  ELSE IF( n.LT.0 ) THEN
229  info = -4
230  ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
231  info = -5
232  ELSE IF( lda.LT.max( 1, k ) ) THEN
233  info = -7
234  ELSE IF( ldc.LT.max( 1, m ) ) THEN
235  info = -10
236  ELSE IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
237  info = -12
238  END IF
239 *
240  IF( info.EQ.0 ) THEN
241 *
242 * Compute the workspace requirements
243 *
244  nb = min( nbmax, ilaenv( 1, 'DORMLQ', side // trans, m, n, k,
245  $ -1 ) )
246  lwkopt = nw*nb + tsize
247  work( 1 ) = lwkopt
248  END IF
249 *
250  IF( info.NE.0 ) THEN
251  CALL xerbla( 'DORMLQ', -info )
252  RETURN
253  ELSE IF( lquery ) THEN
254  RETURN
255  END IF
256 *
257 * Quick return if possible
258 *
259  IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) THEN
260  work( 1 ) = 1
261  RETURN
262  END IF
263 *
264  nbmin = 2
265  ldwork = nw
266  IF( nb.GT.1 .AND. nb.LT.k ) THEN
267  IF( lwork.LT.lwkopt ) THEN
268  nb = (lwork-tsize) / ldwork
269  nbmin = max( 2, ilaenv( 2, 'DORMLQ', side // trans, m, n, k,
270  $ -1 ) )
271  END IF
272  END IF
273 *
274  IF( nb.LT.nbmin .OR. nb.GE.k ) THEN
275 *
276 * Use unblocked code
277 *
278  CALL dorml2( side, trans, m, n, k, a, lda, tau, c, ldc, work,
279  $ iinfo )
280  ELSE
281 *
282 * Use blocked code
283 *
284  iwt = 1 + nw*nb
285  IF( ( left .AND. notran ) .OR.
286  $ ( .NOT.left .AND. .NOT.notran ) ) THEN
287  i1 = 1
288  i2 = k
289  i3 = nb
290  ELSE
291  i1 = ( ( k-1 ) / nb )*nb + 1
292  i2 = 1
293  i3 = -nb
294  END IF
295 *
296  IF( left ) THEN
297  ni = n
298  jc = 1
299  ELSE
300  mi = m
301  ic = 1
302  END IF
303 *
304  IF( notran ) THEN
305  transt = 'T'
306  ELSE
307  transt = 'N'
308  END IF
309 *
310  DO 10 i = i1, i2, i3
311  ib = min( nb, k-i+1 )
312 *
313 * Form the triangular factor of the block reflector
314 * H = H(i) H(i+1) . . . H(i+ib-1)
315 *
316  CALL dlarft( 'Forward', 'Rowwise', nq-i+1, ib, a( i, i ),
317  $ lda, tau( i ), work( iwt ), ldt )
318  IF( left ) THEN
319 *
320 * H or H**T is applied to C(i:m,1:n)
321 *
322  mi = m - i + 1
323  ic = i
324  ELSE
325 *
326 * H or H**T is applied to C(1:m,i:n)
327 *
328  ni = n - i + 1
329  jc = i
330  END IF
331 *
332 * Apply H or H**T
333 *
334  CALL dlarfb( side, transt, 'Forward', 'Rowwise', mi, ni, ib,
335  $ a( i, i ), lda, work( iwt ), ldt,
336  $ c( ic, jc ), ldc, work, ldwork )
337  10 CONTINUE
338  END IF
339  work( 1 ) = lwkopt
340  RETURN
341 *
342 * End of DORMLQ
343 *
344  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dlarft(DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)
DLARFT forms the triangular factor T of a block reflector H = I - vtvH
Definition: dlarft.f:163
subroutine dlarfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
DLARFB applies a block reflector or its transpose to a general rectangular matrix.
Definition: dlarfb.f:197
subroutine dormlq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
DORMLQ
Definition: dormlq.f:167
subroutine dorml2(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO)
DORML2 multiplies a general matrix by the orthogonal matrix from a LQ factorization determined by sge...
Definition: dorml2.f:159