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