LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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sgemqr.f
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1*> \brief \b SGEMQR
2*
3* Definition:
4* ===========
5*
6* SUBROUTINE SGEMQR( 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* REAL A( LDA, * ), T( * ), C( LDC, * ), WORK( * )
16* ..
17*
18*> \par Purpose:
19* =============
20*>
21*> \verbatim
22*>
23*> SGEMQR 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**T * C C * Q**T
28*>
29*> where Q is a real orthogonal matrix defined as the product
30*> of blocked elementary reflectors computed by tall skinny
31*> QR factorization (SGEQR)
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**T from the Left;
42*> = 'R': apply Q or Q**T from the Right.
43*> \endverbatim
44*>
45*> \param[in] TRANS
46*> \verbatim
47*> TRANS is CHARACTER*1
48*> = 'N': No transpose, apply Q;
49*> = 'T': Transpose, apply Q**T.
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 REAL array, dimension (LDA,K)
76*> Part of the data structure to represent Q as returned by SGEQR.
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 REAL array, dimension (MAX(5,TSIZE)).
90*> Part of the data structure to represent Q as returned by SGEQR.
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 REAL array, dimension (LDC,N)
102*> On entry, the M-by-N matrix C.
103*> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T 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) REAL 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*> SLATSQR or SGEQRT
158*>
159*> Depending on the matrix dimensions M and N, and row and column
160*> block sizes MB and NB returned by ILAENV, SGEQR will use either
161*> SLATSQR (if the matrix is tall-and-skinny) or SGEQRT to compute
162*> the QR factorization.
163*> This version of SGEMQR will use either SLAMTSQR or SGEMQRT to
164*> multiply matrix Q by another matrix.
165*> Further Details in SLAMTSQR or SGEMQRT.
166*>
167*> \endverbatim
168*>
169*> \ingroup gemqr
170*>
171* =====================================================================
172 SUBROUTINE sgemqr( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE,
173 \$ C, LDC, WORK, LWORK, INFO )
174*
175* -- LAPACK computational routine --
176* -- LAPACK is a software package provided by Univ. of Tennessee, --
177* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
178*
179* .. Scalar Arguments ..
180 CHARACTER SIDE, TRANS
181 INTEGER INFO, LDA, M, N, K, TSIZE, LWORK, LDC
182* ..
183* .. Array Arguments ..
184 REAL A( LDA, * ), T( * ), C( LDC, * ), WORK( * )
185* ..
186*
187* =====================================================================
188*
189* ..
190* .. Local Scalars ..
191 LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY
192 INTEGER MB, NB, LW, NBLCKS, MN
193* ..
194* .. External Functions ..
195 LOGICAL LSAME
196 REAL SROUNDUP_LWORK
197 EXTERNAL lsame, sroundup_lwork
198* ..
199* .. External Subroutines ..
200 EXTERNAL sgemqrt, slamtsqr, xerbla
201* ..
202* .. Intrinsic Functions ..
203 INTRINSIC int, max, min, mod
204* ..
205* .. Executable Statements ..
206*
207* Test the input arguments
208*
209 lquery = lwork.EQ.-1
210 notran = lsame( trans, 'N' )
211 tran = lsame( trans, 'T' )
212 left = lsame( side, 'L' )
213 right = lsame( side, 'R' )
214*
215 mb = int( t( 2 ) )
216 nb = int( t( 3 ) )
217 IF( left ) THEN
218 lw = n * nb
219 mn = m
220 ELSE
221 lw = mb * nb
222 mn = n
223 END IF
224*
225 IF( ( mb.GT.k ) .AND. ( mn.GT.k ) ) THEN
226 IF( mod( mn - k, mb - k ).EQ.0 ) THEN
227 nblcks = ( mn - k ) / ( mb - k )
228 ELSE
229 nblcks = ( mn - k ) / ( mb - k ) + 1
230 END IF
231 ELSE
232 nblcks = 1
233 END IF
234*
235 info = 0
236 IF( .NOT.left .AND. .NOT.right ) THEN
237 info = -1
238 ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
239 info = -2
240 ELSE IF( m.LT.0 ) THEN
241 info = -3
242 ELSE IF( n.LT.0 ) THEN
243 info = -4
244 ELSE IF( k.LT.0 .OR. k.GT.mn ) THEN
245 info = -5
246 ELSE IF( lda.LT.max( 1, mn ) ) THEN
247 info = -7
248 ELSE IF( tsize.LT.5 ) THEN
249 info = -9
250 ELSE IF( ldc.LT.max( 1, m ) ) THEN
251 info = -11
252 ELSE IF( ( lwork.LT.max( 1, lw ) ) .AND. ( .NOT.lquery ) ) THEN
253 info = -13
254 END IF
255*
256 IF( info.EQ.0 ) THEN
257 work( 1 ) = sroundup_lwork(lw)
258 END IF
259*
260 IF( info.NE.0 ) THEN
261 CALL xerbla( 'SGEMQR', -info )
262 RETURN
263 ELSE IF( lquery ) THEN
264 RETURN
265 END IF
266*
267* Quick return if possible
268*
269 IF( min( m, n, k ).EQ.0 ) THEN
270 RETURN
271 END IF
272*
273 IF( ( left .AND. m.LE.k ) .OR. ( right .AND. n.LE.k )
274 \$ .OR. ( mb.LE.k ) .OR. ( mb.GE.max( m, n, k ) ) ) THEN
275 CALL sgemqrt( side, trans, m, n, k, nb, a, lda, t( 6 ),
276 \$ nb, c, ldc, work, info )
277 ELSE
278 CALL slamtsqr( side, trans, m, n, k, mb, nb, a, lda, t( 6 ),
279 \$ nb, c, ldc, work, lwork, info )
280 END IF
281*
282 work( 1 ) = sroundup_lwork(lw)
283*
284 RETURN
285*
286* End of SGEMQR
287*
288 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine sgemqr(side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
SGEMQR
Definition sgemqr.f:174
subroutine sgemqrt(side, trans, m, n, k, nb, v, ldv, t, ldt, c, ldc, work, info)
SGEMQRT
Definition sgemqrt.f:168
subroutine slamtsqr(side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)
SLAMTSQR
Definition slamtsqr.f:199