LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
sgemlqt.f
Go to the documentation of this file.
1 * Definition:
2 * ===========
3 *
4 * SUBROUTINE SGEMLQT( SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT,
5 * C, LDC, WORK, INFO )
6 *
7 * .. Scalar Arguments ..
8 * CHARACTER SIDE, TRANS
9 * INTEGER INFO, K, LDV, LDC, M, N, MB, LDT
10 * ..
11 * .. Array Arguments ..
12 * REAL V( LDV, * ), C( LDC, * ), T( LDT, * ), WORK( * )
13 * ..
14 *
15 *
16 *> \par Purpose:
17 * =============
18 *>
19 *> \verbatim
20 *>
21 *> DGEMLQT overwrites the general real M-by-N matrix C with
22 *>
23 *> SIDE = 'L' SIDE = 'R'
24 *> TRANS = 'N': Q C C Q
25 *> TRANS = 'T': Q**T C C Q**T
26 *>
27 *> where Q is a real orthogonal matrix defined as the product of K
28 *> elementary reflectors:
29 *>
30 *> Q = H(1) H(2) . . . H(K) = I - V T V**T
31 *>
32 *> generated using the compact WY representation as returned by DGELQT.
33 *>
34 *> Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.
35 *> \endverbatim
36 *
37 * Arguments:
38 * ==========
39 *
40 *> \param[in] SIDE
41 *> \verbatim
42 *> SIDE is CHARACTER*1
43 *> = 'L': apply Q or Q**T from the Left;
44 *> = 'R': apply Q or Q**T from the Right.
45 *> \endverbatim
46 *>
47 *> \param[in] TRANS
48 *> \verbatim
49 *> TRANS is CHARACTER*1
50 *> = 'N': No transpose, apply Q;
51 *> = 'C': Transpose, apply Q**T.
52 *> \endverbatim
53 *>
54 *> \param[in] M
55 *> \verbatim
56 *> M is INTEGER
57 *> The number of rows of the matrix C. M >= 0.
58 *> \endverbatim
59 *>
60 *> \param[in] N
61 *> \verbatim
62 *> N is INTEGER
63 *> The number of columns of the matrix C. N >= 0.
64 *> \endverbatim
65 *>
66 *> \param[in] K
67 *> \verbatim
68 *> K is INTEGER
69 *> The number of elementary reflectors whose product defines
70 *> the matrix Q.
71 *> If SIDE = 'L', M >= K >= 0;
72 *> if SIDE = 'R', N >= K >= 0.
73 *> \endverbatim
74 *>
75 *> \param[in] MB
76 *> \verbatim
77 *> MB is INTEGER
78 *> The block size used for the storage of T. K >= MB >= 1.
79 *> This must be the same value of MB used to generate T
80 *> in DGELQT.
81 *> \endverbatim
82 *>
83 *> \param[in] V
84 *> \verbatim
85 *> V is REAL array, dimension
86 *> (LDV,M) if SIDE = 'L',
87 *> (LDV,N) if SIDE = 'R'
88 *> The i-th row must contain the vector which defines the
89 *> elementary reflector H(i), for i = 1,2,...,k, as returned by
90 *> DGELQT in the first K rows of its array argument A.
91 *> \endverbatim
92 *>
93 *> \param[in] LDV
94 *> \verbatim
95 *> LDV is INTEGER
96 *> The leading dimension of the array V. LDV >= max(1,K).
97 *> \endverbatim
98 *>
99 *> \param[in] T
100 *> \verbatim
101 *> T is REAL array, dimension (LDT,K)
102 *> The upper triangular factors of the block reflectors
103 *> as returned by DGELQT, stored as a MB-by-K matrix.
104 *> \endverbatim
105 *>
106 *> \param[in] LDT
107 *> \verbatim
108 *> LDT is INTEGER
109 *> The leading dimension of the array T. LDT >= MB.
110 *> \endverbatim
111 *>
112 *> \param[in,out] C
113 *> \verbatim
114 *> C is REAL array, dimension (LDC,N)
115 *> On entry, the M-by-N matrix C.
116 *> On exit, C is overwritten by Q C, Q**T C, C Q**T or C Q.
117 *> \endverbatim
118 *>
119 *> \param[in] LDC
120 *> \verbatim
121 *> LDC is INTEGER
122 *> The leading dimension of the array C. LDC >= max(1,M).
123 *> \endverbatim
124 *>
125 *> \param[out] WORK
126 *> \verbatim
127 *> WORK is REAL array. The dimension of
128 *> WORK is N*MB if SIDE = 'L', or M*MB if SIDE = 'R'.
129 *> \endverbatim
130 *>
131 *> \param[out] INFO
132 *> \verbatim
133 *> INFO is INTEGER
134 *> = 0: successful exit
135 *> < 0: if INFO = -i, the i-th argument had an illegal value
136 *> \endverbatim
137 *
138 * Authors:
139 * ========
140 *
141 *> \author Univ. of Tennessee
142 *> \author Univ. of California Berkeley
143 *> \author Univ. of Colorado Denver
144 *> \author NAG Ltd.
145 *
146 *> \date November 2017
147 *
148 *> \ingroup doubleGEcomputational
149 *
150 * =====================================================================
151  SUBROUTINE sgemlqt( SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT,
152  $ C, LDC, WORK, INFO )
153 *
154 * -- LAPACK computational routine (version 3.8.0) --
155 * -- LAPACK is a software package provided by Univ. of Tennessee, --
156 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
157 * November 2017
158 *
159 * .. Scalar Arguments ..
160  CHARACTER SIDE, TRANS
161  INTEGER INFO, K, LDV, LDC, M, N, MB, LDT
162 * ..
163 * .. Array Arguments ..
164  REAL V( ldv, * ), C( ldc, * ), T( ldt, * ), WORK( * )
165 * ..
166 *
167 * =====================================================================
168 *
169 * ..
170 * .. Local Scalars ..
171  LOGICAL LEFT, RIGHT, TRAN, NOTRAN
172  INTEGER I, IB, LDWORK, KF
173 * ..
174 * .. External Functions ..
175  LOGICAL LSAME
176  EXTERNAL lsame
177 * ..
178 * .. External Subroutines ..
179  EXTERNAL xerbla, slarfb
180 * ..
181 * .. Intrinsic Functions ..
182  INTRINSIC max, min
183 * ..
184 * .. Executable Statements ..
185 *
186 * .. Test the input arguments ..
187 *
188  info = 0
189  left = lsame( side, 'L' )
190  right = lsame( side, 'R' )
191  tran = lsame( trans, 'T' )
192  notran = lsame( trans, 'N' )
193 *
194  IF( left ) THEN
195  ldwork = max( 1, n )
196  ELSE IF ( right ) THEN
197  ldwork = max( 1, m )
198  END IF
199  IF( .NOT.left .AND. .NOT.right ) THEN
200  info = -1
201  ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
202  info = -2
203  ELSE IF( m.LT.0 ) THEN
204  info = -3
205  ELSE IF( n.LT.0 ) THEN
206  info = -4
207  ELSE IF( k.LT.0) THEN
208  info = -5
209  ELSE IF( mb.LT.1 .OR. (mb.GT.k .AND. k.GT.0)) THEN
210  info = -6
211  ELSE IF( ldv.LT.max( 1, k ) ) THEN
212  info = -8
213  ELSE IF( ldt.LT.mb ) THEN
214  info = -10
215  ELSE IF( ldc.LT.max( 1, m ) ) THEN
216  info = -12
217  END IF
218 *
219  IF( info.NE.0 ) THEN
220  CALL xerbla( 'SGEMLQT', -info )
221  RETURN
222  END IF
223 *
224 * .. Quick return if possible ..
225 *
226  IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) RETURN
227 *
228  IF( left .AND. notran ) THEN
229 *
230  DO i = 1, k, mb
231  ib = min( mb, k-i+1 )
232  CALL slarfb( 'L', 'T', 'F', 'R', m-i+1, n, ib,
233  $ v( i, i ), ldv, t( 1, i ), ldt,
234  $ c( i, 1 ), ldc, work, ldwork )
235  END DO
236 *
237  ELSE IF( right .AND. tran ) THEN
238 *
239  DO i = 1, k, mb
240  ib = min( mb, k-i+1 )
241  CALL slarfb( 'R', 'N', 'F', 'R', m, n-i+1, ib,
242  $ v( i, i ), ldv, t( 1, i ), ldt,
243  $ c( 1, i ), ldc, work, ldwork )
244  END DO
245 *
246  ELSE IF( left .AND. tran ) THEN
247 *
248  kf = ((k-1)/mb)*mb+1
249  DO i = kf, 1, -mb
250  ib = min( mb, k-i+1 )
251  CALL slarfb( 'L', 'N', 'F', 'R', m-i+1, n, ib,
252  $ v( i, i ), ldv, t( 1, i ), ldt,
253  $ c( i, 1 ), ldc, work, ldwork )
254  END DO
255 *
256  ELSE IF( right .AND. notran ) THEN
257 *
258  kf = ((k-1)/mb)*mb+1
259  DO i = kf, 1, -mb
260  ib = min( mb, k-i+1 )
261  CALL slarfb( 'R', 'T', 'F', 'R', m, n-i+1, ib,
262  $ v( i, i ), ldv, t( 1, i ), ldt,
263  $ c( 1, i ), ldc, work, ldwork )
264  END DO
265 *
266  END IF
267 *
268  RETURN
269 *
270 * End of SGEMLQT
271 *
272  END
subroutine sgemlqt(SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT, C, LDC, WORK, INFO)
Definition: sgemlqt.f:153
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 xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62