LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
sormlq.f
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1 *> \brief \b SORMLQ
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 SORMLQ( 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 * REAL A( LDA, * ), C( LDC, * ), TAU( * ),
30 * $ WORK( * )
31 * ..
32 *
33 *
34 *> \par Purpose:
35 * =============
36 *>
37 *> \verbatim
38 *>
39 *> SORMLQ overwrites the general real M-by-N matrix C with
40 *>
41 *> SIDE = 'L' SIDE = 'R'
42 *> TRANS = 'N': Q * C C * Q
43 *> TRANS = 'T': Q**T * C C * Q**T
44 *>
45 *> where Q is a real orthogonal matrix defined as the product of k
46 *> elementary reflectors
47 *>
48 *> Q = H(k) . . . H(2) H(1)
49 *>
50 *> as returned by SGELQF. Q is of order M if SIDE = 'L' and of order N
51 *> if SIDE = 'R'.
52 *> \endverbatim
53 *
54 * Arguments:
55 * ==========
56 *
57 *> \param[in] SIDE
58 *> \verbatim
59 *> SIDE is CHARACTER*1
60 *> = 'L': apply Q or Q**T from the Left;
61 *> = 'R': apply Q or Q**T from the Right.
62 *> \endverbatim
63 *>
64 *> \param[in] TRANS
65 *> \verbatim
66 *> TRANS is CHARACTER*1
67 *> = 'N': No transpose, apply Q;
68 *> = 'T': Transpose, apply Q**T.
69 *> \endverbatim
70 *>
71 *> \param[in] M
72 *> \verbatim
73 *> M is INTEGER
74 *> The number of rows of the matrix C. M >= 0.
75 *> \endverbatim
76 *>
77 *> \param[in] N
78 *> \verbatim
79 *> N is INTEGER
80 *> The number of columns of the matrix C. N >= 0.
81 *> \endverbatim
82 *>
83 *> \param[in] K
84 *> \verbatim
85 *> K is INTEGER
86 *> The number of elementary reflectors whose product defines
87 *> the matrix Q.
88 *> If SIDE = 'L', M >= K >= 0;
89 *> if SIDE = 'R', N >= K >= 0.
90 *> \endverbatim
91 *>
92 *> \param[in] A
93 *> \verbatim
94 *> A is REAL array, dimension
95 *> (LDA,M) if SIDE = 'L',
96 *> (LDA,N) if SIDE = 'R'
97 *> The i-th row must contain the vector which defines the
98 *> elementary reflector H(i), for i = 1,2,...,k, as returned by
99 *> SGELQF in the first k rows of its array argument A.
100 *> \endverbatim
101 *>
102 *> \param[in] LDA
103 *> \verbatim
104 *> LDA is INTEGER
105 *> The leading dimension of the array A. LDA >= max(1,K).
106 *> \endverbatim
107 *>
108 *> \param[in] TAU
109 *> \verbatim
110 *> TAU is REAL array, dimension (K)
111 *> TAU(i) must contain the scalar factor of the elementary
112 *> reflector H(i), as returned by SGELQF.
113 *> \endverbatim
114 *>
115 *> \param[in,out] C
116 *> \verbatim
117 *> C is REAL array, dimension (LDC,N)
118 *> On entry, the M-by-N matrix C.
119 *> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
120 *> \endverbatim
121 *>
122 *> \param[in] LDC
123 *> \verbatim
124 *> LDC is INTEGER
125 *> The leading dimension of the array C. LDC >= max(1,M).
126 *> \endverbatim
127 *>
128 *> \param[out] WORK
129 *> \verbatim
130 *> WORK is REAL array, dimension (MAX(1,LWORK))
131 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
132 *> \endverbatim
133 *>
134 *> \param[in] LWORK
135 *> \verbatim
136 *> LWORK is INTEGER
137 *> The dimension of the array WORK.
138 *> If SIDE = 'L', LWORK >= max(1,N);
139 *> if SIDE = 'R', LWORK >= max(1,M).
140 *> For good performance, LWORK should generally be larger.
141 *>
142 *> If LWORK = -1, then a workspace query is assumed; the routine
143 *> only calculates the optimal size of the WORK array, returns
144 *> this value as the first entry of the WORK array, and no error
145 *> message related to LWORK is issued by XERBLA.
146 *> \endverbatim
147 *>
148 *> \param[out] INFO
149 *> \verbatim
150 *> INFO is INTEGER
151 *> = 0: successful exit
152 *> < 0: if INFO = -i, the i-th argument had an illegal value
153 *> \endverbatim
154 *
155 * Authors:
156 * ========
157 *
158 *> \author Univ. of Tennessee
159 *> \author Univ. of California Berkeley
160 *> \author Univ. of Colorado Denver
161 *> \author NAG Ltd.
162 *
163 *> \ingroup realOTHERcomputational
164 *
165 * =====================================================================
166  SUBROUTINE sormlq( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
167  $ WORK, LWORK, INFO )
168 *
169 * -- LAPACK computational routine --
170 * -- LAPACK is a software package provided by Univ. of Tennessee, --
171 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
172 *
173 * .. Scalar Arguments ..
174  CHARACTER SIDE, TRANS
175  INTEGER INFO, K, LDA, LDC, LWORK, M, N
176 * ..
177 * .. Array Arguments ..
178  REAL A( LDA, * ), C( LDC, * ), TAU( * ),
179  $ work( * )
180 * ..
181 *
182 * =====================================================================
183 *
184 * .. Parameters ..
185  INTEGER NBMAX, LDT, TSIZE
186  parameter( nbmax = 64, ldt = nbmax+1,
187  $ tsize = ldt*nbmax )
188 * ..
189 * .. Local Scalars ..
190  LOGICAL LEFT, LQUERY, NOTRAN
191  CHARACTER TRANST
192  INTEGER I, I1, I2, I3, IB, IC, IINFO, IWT, JC, LDWORK,
193  $ lwkopt, mi, nb, nbmin, ni, nq, nw
194 * ..
195 * .. External Functions ..
196  LOGICAL LSAME
197  INTEGER ILAENV
198  EXTERNAL lsame, ilaenv
199 * ..
200 * .. External Subroutines ..
201  EXTERNAL slarfb, slarft, sorml2, xerbla
202 * ..
203 * .. Intrinsic Functions ..
204  INTRINSIC max, min
205 * ..
206 * .. Executable Statements ..
207 *
208 * Test the input arguments
209 *
210  info = 0
211  left = lsame( side, 'L' )
212  notran = lsame( trans, 'N' )
213  lquery = ( lwork.EQ.-1 )
214 *
215 * NQ is the order of Q and NW is the minimum dimension of WORK
216 *
217  IF( left ) THEN
218  nq = m
219  nw = max( 1, n )
220  ELSE
221  nq = n
222  nw = max( 1, m )
223  END IF
224  IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
225  info = -1
226  ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
227  info = -2
228  ELSE IF( m.LT.0 ) THEN
229  info = -3
230  ELSE IF( n.LT.0 ) THEN
231  info = -4
232  ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
233  info = -5
234  ELSE IF( lda.LT.max( 1, k ) ) THEN
235  info = -7
236  ELSE IF( ldc.LT.max( 1, m ) ) THEN
237  info = -10
238  ELSE IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
239  info = -12
240  END IF
241 *
242  IF( info.EQ.0 ) THEN
243 *
244 * Compute the workspace requirements
245 *
246  nb = min( nbmax, ilaenv( 1, 'SORMLQ', side // trans, m, n, k,
247  $ -1 ) )
248  lwkopt = nw*nb + tsize
249  work( 1 ) = lwkopt
250  END IF
251 *
252  IF( info.NE.0 ) THEN
253  CALL xerbla( 'SORMLQ', -info )
254  RETURN
255  ELSE IF( lquery ) THEN
256  RETURN
257  END IF
258 *
259 * Quick return if possible
260 *
261  IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) THEN
262  work( 1 ) = 1
263  RETURN
264  END IF
265 *
266  nbmin = 2
267  ldwork = nw
268  IF( nb.GT.1 .AND. nb.LT.k ) THEN
269  IF( lwork.LT.lwkopt ) THEN
270  nb = (lwork-tsize) / ldwork
271  nbmin = max( 2, ilaenv( 2, 'SORMLQ', side // trans, m, n, k,
272  $ -1 ) )
273  END IF
274  END IF
275 *
276  IF( nb.LT.nbmin .OR. nb.GE.k ) THEN
277 *
278 * Use unblocked code
279 *
280  CALL sorml2( side, trans, m, n, k, a, lda, tau, c, ldc, work,
281  $ iinfo )
282  ELSE
283 *
284 * Use blocked code
285 *
286  iwt = 1 + nw*nb
287  IF( ( left .AND. notran ) .OR.
288  $ ( .NOT.left .AND. .NOT.notran ) ) THEN
289  i1 = 1
290  i2 = k
291  i3 = nb
292  ELSE
293  i1 = ( ( k-1 ) / nb )*nb + 1
294  i2 = 1
295  i3 = -nb
296  END IF
297 *
298  IF( left ) THEN
299  ni = n
300  jc = 1
301  ELSE
302  mi = m
303  ic = 1
304  END IF
305 *
306  IF( notran ) THEN
307  transt = 'T'
308  ELSE
309  transt = 'N'
310  END IF
311 *
312  DO 10 i = i1, i2, i3
313  ib = min( nb, k-i+1 )
314 *
315 * Form the triangular factor of the block reflector
316 * H = H(i) H(i+1) . . . H(i+ib-1)
317 *
318  CALL slarft( 'Forward', 'Rowwise', nq-i+1, ib, a( i, i ),
319  $ lda, tau( i ), work( iwt ), ldt )
320  IF( left ) THEN
321 *
322 * H or H**T is applied to C(i:m,1:n)
323 *
324  mi = m - i + 1
325  ic = i
326  ELSE
327 *
328 * H or H**T is applied to C(1:m,i:n)
329 *
330  ni = n - i + 1
331  jc = i
332  END IF
333 *
334 * Apply H or H**T
335 *
336  CALL slarfb( side, transt, 'Forward', 'Rowwise', mi, ni, ib,
337  $ a( i, i ), lda, work( iwt ), ldt,
338  $ c( ic, jc ), ldc, work, ldwork )
339  10 CONTINUE
340  END IF
341  work( 1 ) = lwkopt
342  RETURN
343 *
344 * End of SORMLQ
345 *
346  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine slarfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
SLARFB applies a block reflector or its transpose to a general rectangular matrix.
Definition: slarfb.f:197
subroutine slarft(DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)
SLARFT forms the triangular factor T of a block reflector H = I - vtvH
Definition: slarft.f:163
subroutine sorml2(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO)
SORML2 multiplies a general matrix by the orthogonal matrix from a LQ factorization determined by sge...
Definition: sorml2.f:159
subroutine sormlq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
SORMLQ
Definition: sormlq.f:168