LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
sgemlq.f
Go to the documentation of this file.
1 *> \brief \b SGEMLQ
2 *
3 * Definition:
4 * ===========
5 *
6 * SUBROUTINE SGEMLQ( SIDE, TRANS, M, N, K, A, LDA, T,
7 * $ TSIZE, C, LDC, WORK, LWORK, INFO )
8 *
9 *
10 * .. Scalar Arguments ..
11 * CHARACTER SIDE, TRANS
12 * INTEGER INFO, LDA, M, N, K, LDT, TSIZE, LWORK, LDC
13 * ..
14 * .. Array Arguments ..
15 * REAL A( LDA, * ), T( * ), C(LDC, * ), WORK( * )
16 * ..
17 *
18 *> \par Purpose:
19 * =============
20 *>
21 *> \verbatim
22 *>
23 *> SGEMLQ overwrites the general real M-by-N matrix C with
24 *>
25 *> SIDE = 'L' SIDE = 'R'
26 *> TRANS = 'N': Q * C C * Q
27 *> TRANS = 'T': Q**T * C C * Q**T
28 *> where Q is a real orthogonal matrix defined as the product
29 *> of blocked elementary reflectors computed by short wide LQ
30 *> factorization (SGELQ)
31 *>
32 *> \endverbatim
33 *
34 * Arguments:
35 * ==========
36 *
37 *> \param[in] SIDE
38 *> \verbatim
39 *> SIDE is CHARACTER*1
40 *> = 'L': apply Q or Q**T from the Left;
41 *> = 'R': apply Q or Q**T from the Right.
42 *> \endverbatim
43 *>
44 *> \param[in] TRANS
45 *> \verbatim
46 *> TRANS is CHARACTER*1
47 *> = 'N': No transpose, apply Q;
48 *> = 'T': Transpose, apply Q**T.
49 *> \endverbatim
50 *>
51 *> \param[in] M
52 *> \verbatim
53 *> M is INTEGER
54 *> The number of rows of the matrix A. M >=0.
55 *> \endverbatim
56 *>
57 *> \param[in] N
58 *> \verbatim
59 *> N is INTEGER
60 *> The number of columns of the matrix C. N >= 0.
61 *> \endverbatim
62 *>
63 *> \param[in] K
64 *> \verbatim
65 *> K is INTEGER
66 *> The number of elementary reflectors whose product defines
67 *> the matrix Q.
68 *> If SIDE = 'L', M >= K >= 0;
69 *> if SIDE = 'R', N >= K >= 0.
70 *> \endverbatim
71 *>
72 *> \param[in] A
73 *> \verbatim
74 *> A is REAL array, dimension
75 *> (LDA,M) if SIDE = 'L',
76 *> (LDA,N) if SIDE = 'R'
77 *> Part of the data structure to represent Q as returned by DGELQ.
78 *> \endverbatim
79 *>
80 *> \param[in] LDA
81 *> \verbatim
82 *> LDA is INTEGER
83 *> The leading dimension of the array A. LDA >= max(1,K).
84 *> \endverbatim
85 *>
86 *> \param[in] T
87 *> \verbatim
88 *> T is REAL array, dimension (MAX(5,TSIZE)).
89 *> Part of the data structure to represent Q as returned by SGELQ.
90 *> \endverbatim
91 *>
92 *> \param[in] TSIZE
93 *> \verbatim
94 *> TSIZE is INTEGER
95 *> The dimension of the array T. TSIZE >= 5.
96 *> \endverbatim
97 *>
98 *> \param[in,out] C
99 *> \verbatim
100 *> C is REAL array, dimension (LDC,N)
101 *> On entry, the M-by-N matrix C.
102 *> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
103 *> \endverbatim
104 *>
105 *> \param[in] LDC
106 *> \verbatim
107 *> LDC is INTEGER
108 *> The leading dimension of the array C. LDC >= max(1,M).
109 *> \endverbatim
110 *>
111 *> \param[out] WORK
112 *> \verbatim
113 *> (workspace) REAL array, dimension (MAX(1,LWORK))
114 *> \endverbatim
115 *>
116 *> \param[in] LWORK
117 *> \verbatim
118 *> LWORK is INTEGER
119 *> The dimension of the array WORK.
120 *> If LWORK = -1, then a workspace query is assumed. The routine
121 *> only calculates the size of the WORK array, returns this
122 *> value as WORK(1), and no error message related to WORK
123 *> is issued by XERBLA.
124 *> \endverbatim
125 *>
126 *> \param[out] INFO
127 *> \verbatim
128 *> INFO is INTEGER
129 *> = 0: successful exit
130 *> < 0: if INFO = -i, the i-th argument had an illegal value
131 *> \endverbatim
132 *
133 * Authors:
134 * ========
135 *
136 *> \author Univ. of Tennessee
137 *> \author Univ. of California Berkeley
138 *> \author Univ. of Colorado Denver
139 *> \author NAG Ltd.
140 *
141 *> \par Further Details
142 * ====================
143 *>
144 *> \verbatim
145 *>
146 *> These details are particular for this LAPACK implementation. Users should not
147 *> take them for granted. These details may change in the future, and are not likely
148 *> true for another LAPACK implementation. These details are relevant if one wants
149 *> to try to understand the code. They are not part of the interface.
150 *>
151 *> In this version,
152 *>
153 *> T(2): row block size (MB)
154 *> T(3): column block size (NB)
155 *> T(6:TSIZE): data structure needed for Q, computed by
156 *> SLASWLQ or SGELQT
157 *>
158 *> Depending on the matrix dimensions M and N, and row and column
159 *> block sizes MB and NB returned by ILAENV, SGELQ will use either
160 *> SLASWLQ (if the matrix is wide-and-short) or SGELQT to compute
161 *> the LQ factorization.
162 *> This version of SGEMLQ will use either SLAMSWLQ or SGEMLQT to
163 *> multiply matrix Q by another matrix.
164 *> Further Details in SLAMSWLQ or SGEMLQT.
165 *> \endverbatim
166 *>
167 * =====================================================================
168  SUBROUTINE sgemlq( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE,
169  $ C, LDC, WORK, LWORK, INFO )
170 *
171 * -- LAPACK computational routine --
172 * -- LAPACK is a software package provided by Univ. of Tennessee, --
173 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
174 *
175 * .. Scalar Arguments ..
176  CHARACTER SIDE, TRANS
177  INTEGER INFO, LDA, M, N, K, TSIZE, LWORK, LDC
178 * ..
179 * .. Array Arguments ..
180  REAL A( LDA, * ), T( * ), C( LDC, * ), WORK( * )
181 * ..
182 *
183 * =====================================================================
184 *
185 * ..
186 * .. Local Scalars ..
187  LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY
188  INTEGER MB, NB, LW, NBLCKS, MN
189 * ..
190 * .. External Functions ..
191  LOGICAL LSAME
192  EXTERNAL lsame
193 * ..
194 * .. External Subroutines ..
195  EXTERNAL slamswlq, sgemlqt, xerbla
196 * ..
197 * .. Intrinsic Functions ..
198  INTRINSIC int, max, min, mod
199 * ..
200 * .. Executable Statements ..
201 *
202 * Test the input arguments
203 *
204  lquery = lwork.EQ.-1
205  notran = lsame( trans, 'N' )
206  tran = lsame( trans, 'T' )
207  left = lsame( side, 'L' )
208  right = lsame( side, 'R' )
209 *
210  mb = int( t( 2 ) )
211  nb = int( t( 3 ) )
212  IF( left ) THEN
213  lw = n * mb
214  mn = m
215  ELSE
216  lw = m * mb
217  mn = n
218  END IF
219 *
220  IF( ( nb.GT.k ) .AND. ( mn.GT.k ) ) THEN
221  IF( mod( mn - k, nb - k ) .EQ. 0 ) THEN
222  nblcks = ( mn - k ) / ( nb - k )
223  ELSE
224  nblcks = ( mn - k ) / ( nb - k ) + 1
225  END IF
226  ELSE
227  nblcks = 1
228  END IF
229 *
230  info = 0
231  IF( .NOT.left .AND. .NOT.right ) THEN
232  info = -1
233  ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
234  info = -2
235  ELSE IF( m.LT.0 ) THEN
236  info = -3
237  ELSE IF( n.LT.0 ) THEN
238  info = -4
239  ELSE IF( k.LT.0 .OR. k.GT.mn ) THEN
240  info = -5
241  ELSE IF( lda.LT.max( 1, k ) ) THEN
242  info = -7
243  ELSE IF( tsize.LT.5 ) THEN
244  info = -9
245  ELSE IF( ldc.LT.max( 1, m ) ) THEN
246  info = -11
247  ELSE IF( ( lwork.LT.max( 1, lw ) ) .AND. ( .NOT.lquery ) ) THEN
248  info = -13
249  END IF
250 *
251  IF( info.EQ.0 ) THEN
252  work( 1 ) = real( lw )
253  END IF
254 *
255  IF( info.NE.0 ) THEN
256  CALL xerbla( 'SGEMLQ', -info )
257  RETURN
258  ELSE IF( lquery ) THEN
259  RETURN
260  END IF
261 *
262 * Quick return if possible
263 *
264  IF( min( m, n, k ).EQ.0 ) THEN
265  RETURN
266  END IF
267 *
268  IF( ( left .AND. m.LE.k ) .OR. ( right .AND. n.LE.k )
269  $ .OR. ( nb.LE.k ) .OR. ( nb.GE.max( m, n, k ) ) ) THEN
270  CALL sgemlqt( side, trans, m, n, k, mb, a, lda,
271  $ t( 6 ), mb, c, ldc, work, info )
272  ELSE
273  CALL slamswlq( side, trans, m, n, k, mb, nb, a, lda, t( 6 ),
274  $ mb, c, ldc, work, lwork, info )
275  END IF
276 *
277  work( 1 ) = real( lw )
278 *
279  RETURN
280 *
281 * End of SGEMLQ
282 *
283  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine sgemlqt(SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT, C, LDC, WORK, INFO)
SGEMLQT
Definition: sgemlqt.f:153
subroutine sgemlq(SIDE, TRANS, M, N, K, A, LDA, T, TSIZE, C, LDC, WORK, LWORK, INFO)
SGEMLQ
Definition: sgemlq.f:170
subroutine slamswlq(SIDE, TRANS, M, N, K, MB, NB, A, LDA, T, LDT, C, LDC, WORK, LWORK, INFO)
SLAMSWLQ
Definition: slamswlq.f:195