LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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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*> On exit, if INFO = 0, WORK(1) returns the minimal LWORK.
116*> \endverbatim
117*>
118*> \param[in] LWORK
119*> \verbatim
120*> LWORK is INTEGER
121*> The dimension of the array WORK. LWORK >= 1.
122*> If LWORK = -1, then a workspace query is assumed. The routine
123*> only calculates the size of the WORK array, returns this
124*> value as WORK(1), and no error message related to WORK
125*> is issued by XERBLA.
126*> \endverbatim
127*>
128*> \param[out] INFO
129*> \verbatim
130*> INFO is INTEGER
131*> = 0: successful exit
132*> < 0: if INFO = -i, the i-th argument had an illegal value
133*> \endverbatim
134*
135* Authors:
136* ========
137*
138*> \author Univ. of Tennessee
139*> \author Univ. of California Berkeley
140*> \author Univ. of Colorado Denver
141*> \author NAG Ltd.
142*
143*> \par Further Details
144* ====================
145*>
146*> \verbatim
147*>
148*> These details are particular for this LAPACK implementation. Users should not
149*> take them for granted. These details may change in the future, and are not likely
150*> true for another LAPACK implementation. These details are relevant if one wants
151*> to try to understand the code. They are not part of the interface.
152*>
153*> In this version,
154*>
155*> T(2): row block size (MB)
156*> T(3): column block size (NB)
157*> T(6:TSIZE): data structure needed for Q, computed by
158*> CLATSQR or CGEQRT
159*>
160*> Depending on the matrix dimensions M and N, and row and column
161*> block sizes MB and NB returned by ILAENV, CGEQR will use either
162*> CLATSQR (if the matrix is tall-and-skinny) or CGEQRT to compute
163*> the QR factorization.
164*> This version of CGEMQR will use either CLAMTSQR or CGEMQRT to
165*> multiply matrix Q by another matrix.
166*> Further Details in CLAMTSQR or CGEMQRT.
167*>
168*> \endverbatim
169*>
170*> \ingroup gemqr
171*>
172* =====================================================================
173 SUBROUTINE cgemqr( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE,
174 $ C, LDC, WORK, LWORK, INFO )
175*
176* -- LAPACK computational routine --
177* -- LAPACK is a software package provided by Univ. of Tennessee, --
178* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
179*
180* .. Scalar Arguments ..
181 CHARACTER SIDE, TRANS
182 INTEGER INFO, LDA, M, N, K, TSIZE, LWORK, LDC
183* ..
184* .. Array Arguments ..
185 COMPLEX A( LDA, * ), T( * ), C( LDC, * ), WORK( * )
186* ..
187*
188* =====================================================================
189*
190* ..
191* .. Local Scalars ..
192 LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY
193 INTEGER MB, NB, LW, NBLCKS, MN, MINMNK, LWMIN
194* ..
195* .. External Functions ..
196 LOGICAL LSAME
197 REAL SROUNDUP_LWORK
198 EXTERNAL lsame, sroundup_lwork
199* ..
200* .. External Subroutines ..
201 EXTERNAL cgemqrt, clamtsqr, xerbla
202* ..
203* .. Intrinsic Functions ..
204 INTRINSIC int, max, min, mod
205* ..
206* .. Executable Statements ..
207*
208* Test the input arguments
209*
210 lquery = ( lwork.EQ.-1 )
211 notran = lsame( trans, 'N' )
212 tran = lsame( trans, 'C' )
213 left = lsame( side, 'L' )
214 right = lsame( side, 'R' )
215*
216 mb = int( t( 2 ) )
217 nb = int( t( 3 ) )
218 IF( left ) THEN
219 lw = n * nb
220 mn = m
221 ELSE
222 lw = mb * nb
223 mn = n
224 END IF
225*
226 minmnk = min( m, n, k )
227 IF( minmnk.EQ.0 ) THEN
228 lwmin = 1
229 ELSE
230 lwmin = max( 1, lw )
231 END IF
232*
233 IF( ( mb.GT.k ) .AND. ( mn.GT.k ) ) THEN
234 IF( mod( mn - k, mb - k ).EQ.0 ) THEN
235 nblcks = ( mn - k ) / ( mb - k )
236 ELSE
237 nblcks = ( mn - k ) / ( mb - k ) + 1
238 END IF
239 ELSE
240 nblcks = 1
241 END IF
242*
243 info = 0
244 IF( .NOT.left .AND. .NOT.right ) THEN
245 info = -1
246 ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
247 info = -2
248 ELSE IF( m.LT.0 ) THEN
249 info = -3
250 ELSE IF( n.LT.0 ) THEN
251 info = -4
252 ELSE IF( k.LT.0 .OR. k.GT.mn ) THEN
253 info = -5
254 ELSE IF( lda.LT.max( 1, mn ) ) THEN
255 info = -7
256 ELSE IF( tsize.LT.5 ) THEN
257 info = -9
258 ELSE IF( ldc.LT.max( 1, m ) ) THEN
259 info = -11
260 ELSE IF( ( lwork.LT.max( 1, lw ) ) .AND. ( .NOT.lquery ) ) THEN
261 info = -13
262 END IF
263*
264 IF( info.EQ.0 ) THEN
265 work( 1 ) = sroundup_lwork( lwmin )
266 END IF
267*
268 IF( info.NE.0 ) THEN
269 CALL xerbla( 'CGEMQR', -info )
270 RETURN
271 ELSE IF( lquery ) THEN
272 RETURN
273 END IF
274*
275* Quick return if possible
276*
277 IF( minmnk.EQ.0 ) THEN
278 RETURN
279 END IF
280*
281 IF( ( left .AND. m.LE.k ) .OR. ( right .AND. n.LE.k )
282 $ .OR. ( mb.LE.k ) .OR. ( mb.GE.max( m, n, k ) ) ) THEN
283 CALL cgemqrt( side, trans, m, n, k, nb, a, lda, t( 6 ),
284 $ nb, c, ldc, work, info )
285 ELSE
286 CALL clamtsqr( side, trans, m, n, k, mb, nb, a, lda, t( 6 ),
287 $ nb, c, ldc, work, lwork, info )
288 END IF
289*
290 work( 1 ) = sroundup_lwork( lwmin )
291*
292 RETURN
293*
294* End of CGEMQR
295*
296 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine cgemqr(side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
CGEMQR
Definition cgemqr.f:175
subroutine cgemqrt(side, trans, m, n, k, nb, v, ldv, t, ldt, c, ldc, work, info)
CGEMQRT
Definition cgemqrt.f:166
subroutine clamtsqr(side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)
CLAMTSQR
Definition clamtsqr.f:201