LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
cgemlqt.f
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1 *> \brief \b CGEMLQT
2 *
3 * Definition:
4 * ===========
5 *
6 * SUBROUTINE CGEMLQT( SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT,
7 * C, LDC, WORK, INFO )
8 *
9 * .. Scalar Arguments ..
10 * CHARACTER SIDE, TRANS
11 * INTEGER INFO, K, LDV, LDC, M, N, MB, LDT
12 * ..
13 * .. Array Arguments ..
14 * COMPLEX V( LDV, * ), C( LDC, * ), T( LDT, * ), WORK( * )
15 * ..
16 *
17 *
18 *> \par Purpose:
19 * =============
20 *>
21 *> \verbatim
22 *>
23 *> CGEMLQT overwrites the general complex M-by-N matrix C with
24 *>
25 *> SIDE = 'L' SIDE = 'R'
26 *> TRANS = 'N': Q C C Q
27 *> TRANS = 'C': Q**H C C Q**H
28 *>
29 *> where Q is a complex unitary matrix defined as the product of K
30 *> elementary reflectors:
31 *>
32 *> Q = H(1) H(2) . . . H(K) = I - V T V**H
33 *>
34 *> generated using the compact WY representation as returned by CGELQT.
35 *>
36 *> Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.
37 *> \endverbatim
38 *
39 * Arguments:
40 * ==========
41 *
42 *> \param[in] SIDE
43 *> \verbatim
44 *> SIDE is CHARACTER*1
45 *> = 'L': apply Q or Q**H from the Left;
46 *> = 'R': apply Q or Q**H from the Right.
47 *> \endverbatim
48 *>
49 *> \param[in] TRANS
50 *> \verbatim
51 *> TRANS is CHARACTER*1
52 *> = 'N': No transpose, apply Q;
53 *> = 'C': Conjugate transpose, apply Q**H.
54 *> \endverbatim
55 *>
56 *> \param[in] M
57 *> \verbatim
58 *> M is INTEGER
59 *> The number of rows of the matrix C. M >= 0.
60 *> \endverbatim
61 *>
62 *> \param[in] N
63 *> \verbatim
64 *> N is INTEGER
65 *> The number of columns of the matrix C. N >= 0.
66 *> \endverbatim
67 *>
68 *> \param[in] K
69 *> \verbatim
70 *> K is INTEGER
71 *> The number of elementary reflectors whose product defines
72 *> the matrix Q.
73 *> If SIDE = 'L', M >= K >= 0;
74 *> if SIDE = 'R', N >= K >= 0.
75 *> \endverbatim
76 *>
77 *> \param[in] MB
78 *> \verbatim
79 *> MB is INTEGER
80 *> The block size used for the storage of T. K >= MB >= 1.
81 *> This must be the same value of MB used to generate T
82 *> in CGELQT.
83 *> \endverbatim
84 *>
85 *> \param[in] V
86 *> \verbatim
87 *> V is COMPLEX array, dimension
88 *> (LDV,M) if SIDE = 'L',
89 *> (LDV,N) if SIDE = 'R'
90 *> The i-th row must contain the vector which defines the
91 *> elementary reflector H(i), for i = 1,2,...,k, as returned by
92 *> CGELQT in the first K rows of its array argument A.
93 *> \endverbatim
94 *>
95 *> \param[in] LDV
96 *> \verbatim
97 *> LDV is INTEGER
98 *> The leading dimension of the array V. LDV >= max(1,K).
99 *> \endverbatim
100 *>
101 *> \param[in] T
102 *> \verbatim
103 *> T is COMPLEX array, dimension (LDT,K)
104 *> The upper triangular factors of the block reflectors
105 *> as returned by CGELQT, stored as a MB-by-K matrix.
106 *> \endverbatim
107 *>
108 *> \param[in] LDT
109 *> \verbatim
110 *> LDT is INTEGER
111 *> The leading dimension of the array T. LDT >= MB.
112 *> \endverbatim
113 *>
114 *> \param[in,out] C
115 *> \verbatim
116 *> C is COMPLEX array, dimension (LDC,N)
117 *> On entry, the M-by-N matrix C.
118 *> On exit, C is overwritten by Q C, Q**H C, C Q**H 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 COMPLEX array. The dimension of
130 *> WORK is N*MB if SIDE = 'L', or M*MB if SIDE = 'R'.
131 *> \endverbatim
132 *>
133 *> \param[out] INFO
134 *> \verbatim
135 *> INFO is INTEGER
136 *> = 0: successful exit
137 *> < 0: if INFO = -i, the i-th argument had an illegal value
138 *> \endverbatim
139 *
140 * Authors:
141 * ========
142 *
143 *> \author Univ. of Tennessee
144 *> \author Univ. of California Berkeley
145 *> \author Univ. of Colorado Denver
146 *> \author NAG Ltd.
147 *
148 *> \ingroup doubleGEcomputational
149 *
150 * =====================================================================
151  SUBROUTINE cgemlqt( SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT,
152  $ C, LDC, WORK, INFO )
153 *
154 * -- LAPACK computational routine --
155 * -- LAPACK is a software package provided by Univ. of Tennessee, --
156 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
157 *
158 * .. Scalar Arguments ..
159  CHARACTER SIDE, TRANS
160  INTEGER INFO, K, LDV, LDC, M, N, MB, LDT
161 * ..
162 * .. Array Arguments ..
163  COMPLEX V( LDV, * ), C( LDC, * ), T( LDT, * ), WORK( * )
164 * ..
165 *
166 * =====================================================================
167 *
168 * ..
169 * .. Local Scalars ..
170  LOGICAL LEFT, RIGHT, TRAN, NOTRAN
171  INTEGER I, IB, LDWORK, KF, Q
172 * ..
173 * .. External Functions ..
174  LOGICAL LSAME
175  EXTERNAL lsame
176 * ..
177 * .. External Subroutines ..
178  EXTERNAL xerbla, clarfb
179 * ..
180 * .. Intrinsic Functions ..
181  INTRINSIC max, min
182 * ..
183 * .. Executable Statements ..
184 *
185 * .. Test the input arguments ..
186 *
187  info = 0
188  left = lsame( side, 'L' )
189  right = lsame( side, 'R' )
190  tran = lsame( trans, 'C' )
191  notran = lsame( trans, 'N' )
192 *
193  IF( left ) THEN
194  ldwork = max( 1, n )
195  q = m
196  ELSE IF ( right ) THEN
197  ldwork = max( 1, m )
198  q = n
199  END IF
200  IF( .NOT.left .AND. .NOT.right ) THEN
201  info = -1
202  ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
203  info = -2
204  ELSE IF( m.LT.0 ) THEN
205  info = -3
206  ELSE IF( n.LT.0 ) THEN
207  info = -4
208  ELSE IF( k.LT.0 .OR. k.GT.q ) THEN
209  info = -5
210  ELSE IF( mb.LT.1 .OR. (mb.GT.k .AND. k.GT.0)) THEN
211  info = -6
212  ELSE IF( ldv.LT.max( 1, k ) ) THEN
213  info = -8
214  ELSE IF( ldt.LT.mb ) THEN
215  info = -10
216  ELSE IF( ldc.LT.max( 1, m ) ) THEN
217  info = -12
218  END IF
219 *
220  IF( info.NE.0 ) THEN
221  CALL xerbla( 'CGEMLQT', -info )
222  RETURN
223  END IF
224 *
225 * .. Quick return if possible ..
226 *
227  IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) RETURN
228 *
229  IF( left .AND. notran ) THEN
230 *
231  DO i = 1, k, mb
232  ib = min( mb, k-i+1 )
233  CALL clarfb( 'L', 'C', 'F', 'R', m-i+1, n, ib,
234  $ v( i, i ), ldv, t( 1, i ), ldt,
235  $ c( i, 1 ), ldc, work, ldwork )
236  END DO
237 *
238  ELSE IF( right .AND. tran ) THEN
239 *
240  DO i = 1, k, mb
241  ib = min( mb, k-i+1 )
242  CALL clarfb( 'R', 'N', 'F', 'R', m, n-i+1, ib,
243  $ v( i, i ), ldv, t( 1, i ), ldt,
244  $ c( 1, i ), ldc, work, ldwork )
245  END DO
246 *
247  ELSE IF( left .AND. tran ) THEN
248 *
249  kf = ((k-1)/mb)*mb+1
250  DO i = kf, 1, -mb
251  ib = min( mb, k-i+1 )
252  CALL clarfb( 'L', 'N', 'F', 'R', m-i+1, n, ib,
253  $ v( i, i ), ldv, t( 1, i ), ldt,
254  $ c( i, 1 ), ldc, work, ldwork )
255  END DO
256 *
257  ELSE IF( right .AND. notran ) THEN
258 *
259  kf = ((k-1)/mb)*mb+1
260  DO i = kf, 1, -mb
261  ib = min( mb, k-i+1 )
262  CALL clarfb( 'R', 'C', 'F', 'R', m, n-i+1, ib,
263  $ v( i, i ), ldv, t( 1, i ), ldt,
264  $ c( 1, i ), ldc, work, ldwork )
265  END DO
266 *
267  END IF
268 *
269  RETURN
270 *
271 * End of CGEMLQT
272 *
273  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine clarfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
CLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix.
Definition: clarfb.f:197
subroutine cgemlqt(SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT, C, LDC, WORK, INFO)
CGEMLQT
Definition: cgemlqt.f:153