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