LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
cgemqr.f
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1 *> \brief \b CGEMQR
2 *
3 * Definition:
4 * ===========
5 *
6 * SUBROUTINE CGEMQR( 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 A( LDA, * ), T( * ), C( LDC, * ), WORK( * )
16 * ..
17 *
18 *> \par Purpose:
19 * =============
20 *>
21 *> \verbatim
22 *>
23 *> CGEMQR 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**H * C C * Q**H
28 *>
29 *> where Q is a complex unitary matrix defined as the product
30 *> of blocked elementary reflectors computed by tall skinny
31 *> QR factorization (CGEQR)
32 *>
33 *> \endverbatim
34 *
35 * Arguments:
36 * ==========
37 *
38 *> \param[in] SIDE
39 *> \verbatim
40 *> SIDE is CHARACTER*1
41 *> = 'L': apply Q or Q**H from the Left;
42 *> = 'R': apply Q or Q**H from the Right.
43 *> \endverbatim
44 *>
45 *> \param[in] TRANS
46 *> \verbatim
47 *> TRANS is CHARACTER*1
48 *> = 'N': No transpose, apply Q;
49 *> = 'C': Conjugate transpose, apply Q**H.
50 *> \endverbatim
51 *>
52 *> \param[in] M
53 *> \verbatim
54 *> M is INTEGER
55 *> The number of rows of the matrix A. M >=0.
56 *> \endverbatim
57 *>
58 *> \param[in] N
59 *> \verbatim
60 *> N is INTEGER
61 *> The number of columns of the matrix C. N >= 0.
62 *> \endverbatim
63 *>
64 *> \param[in] K
65 *> \verbatim
66 *> K is INTEGER
67 *> The number of elementary reflectors whose product defines
68 *> the matrix Q.
69 *> If SIDE = 'L', M >= K >= 0;
70 *> if SIDE = 'R', N >= K >= 0.
71 *> \endverbatim
72 *>
73 *> \param[in] A
74 *> \verbatim
75 *> A is COMPLEX array, dimension (LDA,K)
76 *> Part of the data structure to represent Q as returned by CGEQR.
77 *> \endverbatim
78 *>
79 *> \param[in] LDA
80 *> \verbatim
81 *> LDA is INTEGER
82 *> The leading dimension of the array A.
83 *> If SIDE = 'L', LDA >= max(1,M);
84 *> if SIDE = 'R', LDA >= max(1,N).
85 *> \endverbatim
86 *>
87 *> \param[in] T
88 *> \verbatim
89 *> T is COMPLEX array, dimension (MAX(5,TSIZE)).
90 *> Part of the data structure to represent Q as returned by CGEQR.
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 COMPLEX array, dimension (LDC,N)
102 *> On entry, the M-by-N matrix C.
103 *> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H 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) COMPLEX 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 *> CLATSQR or CGEQRT
158 *>
159 *> Depending on the matrix dimensions M and N, and row and column
160 *> block sizes MB and NB returned by ILAENV, CGEQR will use either
161 *> CLATSQR (if the matrix is tall-and-skinny) or CGEQRT to compute
162 *> the QR factorization.
163 *> This version of CGEMQR will use either CLAMTSQR or CGEMQRT to
164 *> multiply matrix Q by another matrix.
165 *> Further Details in CLAMTSQR or CGEMQRT.
166 *>
167 *> \endverbatim
168 *>
169 * =====================================================================
170  SUBROUTINE cgemqr( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE,
171  $ C, LDC, WORK, LWORK, INFO )
172 *
173 * -- LAPACK computational routine --
174 * -- LAPACK is a software package provided by Univ. of Tennessee, --
175 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
176 *
177 * .. Scalar Arguments ..
178  CHARACTER SIDE, TRANS
179  INTEGER INFO, LDA, M, N, K, TSIZE, LWORK, LDC
180 * ..
181 * .. Array Arguments ..
182  COMPLEX A( LDA, * ), T( * ), C( LDC, * ), WORK( * )
183 * ..
184 *
185 * =====================================================================
186 *
187 * ..
188 * .. Local Scalars ..
189  LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY
190  INTEGER MB, NB, LW, NBLCKS, MN
191 * ..
192 * .. External Functions ..
193  LOGICAL LSAME
194  EXTERNAL lsame
195 * ..
196 * .. External Subroutines ..
197  EXTERNAL cgemqrt, clamtsqr, xerbla
198 * ..
199 * .. Intrinsic Functions ..
200  INTRINSIC int, max, min, mod
201 * ..
202 * .. Executable Statements ..
203 *
204 * Test the input arguments
205 *
206  lquery = lwork.EQ.-1
207  notran = lsame( trans, 'N' )
208  tran = lsame( trans, 'C' )
209  left = lsame( side, 'L' )
210  right = lsame( side, 'R' )
211 *
212  mb = int( t( 2 ) )
213  nb = int( t( 3 ) )
214  IF( left ) THEN
215  lw = n * nb
216  mn = m
217  ELSE
218  lw = mb * nb
219  mn = n
220  END IF
221 *
222  IF( ( mb.GT.k ) .AND. ( mn.GT.k ) ) THEN
223  IF( mod( mn - k, mb - k ).EQ.0 ) THEN
224  nblcks = ( mn - k ) / ( mb - k )
225  ELSE
226  nblcks = ( mn - k ) / ( mb - k ) + 1
227  END IF
228  ELSE
229  nblcks = 1
230  END IF
231 *
232  info = 0
233  IF( .NOT.left .AND. .NOT.right ) THEN
234  info = -1
235  ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
236  info = -2
237  ELSE IF( m.LT.0 ) THEN
238  info = -3
239  ELSE IF( n.LT.0 ) THEN
240  info = -4
241  ELSE IF( k.LT.0 .OR. k.GT.mn ) THEN
242  info = -5
243  ELSE IF( lda.LT.max( 1, mn ) ) THEN
244  info = -7
245  ELSE IF( tsize.LT.5 ) THEN
246  info = -9
247  ELSE IF( ldc.LT.max( 1, m ) ) THEN
248  info = -11
249  ELSE IF( ( lwork.LT.max( 1, lw ) ) .AND. ( .NOT.lquery ) ) THEN
250  info = -13
251  END IF
252 *
253  IF( info.EQ.0 ) THEN
254  work( 1 ) = lw
255  END IF
256 *
257  IF( info.NE.0 ) THEN
258  CALL xerbla( 'CGEMQR', -info )
259  RETURN
260  ELSE IF( lquery ) THEN
261  RETURN
262  END IF
263 *
264 * Quick return if possible
265 *
266  IF( min( m, n, k ).EQ.0 ) THEN
267  RETURN
268  END IF
269 *
270  IF( ( left .AND. m.LE.k ) .OR. ( right .AND. n.LE.k )
271  $ .OR. ( mb.LE.k ) .OR. ( mb.GE.max( m, n, k ) ) ) THEN
272  CALL cgemqrt( side, trans, m, n, k, nb, a, lda, t( 6 ),
273  $ nb, c, ldc, work, info )
274  ELSE
275  CALL clamtsqr( side, trans, m, n, k, mb, nb, a, lda, t( 6 ),
276  $ nb, c, ldc, work, lwork, info )
277  END IF
278 *
279  work( 1 ) = lw
280 *
281  RETURN
282 *
283 * End of CGEMQR
284 *
285  END
subroutine cgemqr(SIDE, TRANS, M, N, K, A, LDA, T, TSIZE, C, LDC, WORK, LWORK, INFO)
CGEMQR
Definition: cgemqr.f:172
subroutine clamtsqr(SIDE, TRANS, M, N, K, MB, NB, A, LDA, T, LDT, C, LDC, WORK, LWORK, INFO)
CLAMTSQR
Definition: clamtsqr.f:198
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine cgemqrt(SIDE, TRANS, M, N, K, NB, V, LDV, T, LDT, C, LDC, WORK, INFO)
CGEMQRT
Definition: cgemqrt.f:168