LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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sormrz.f
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1*> \brief \b SORMRZ
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sormrz.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sormrz.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sormrz.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE SORMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
22* WORK, LWORK, INFO )
23*
24* .. Scalar Arguments ..
25* CHARACTER SIDE, TRANS
26* INTEGER INFO, K, L, LDA, LDC, LWORK, M, N
27* ..
28* .. Array Arguments ..
29* REAL A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
30* ..
31*
32*
33*> \par Purpose:
34* =============
35*>
36*> \verbatim
37*>
38*> SORMRZ overwrites the general real M-by-N matrix C with
39*>
40*> SIDE = 'L' SIDE = 'R'
41*> TRANS = 'N': Q * C C * Q
42*> TRANS = 'T': Q**T * C C * Q**T
43*>
44*> where Q is a real orthogonal matrix defined as the product of k
45*> elementary reflectors
46*>
47*> Q = H(1) H(2) . . . H(k)
48*>
49*> as returned by STZRZF. Q is of order M if SIDE = 'L' and of order N
50*> if SIDE = 'R'.
51*> \endverbatim
52*
53* Arguments:
54* ==========
55*
56*> \param[in] SIDE
57*> \verbatim
58*> SIDE is CHARACTER*1
59*> = 'L': apply Q or Q**T from the Left;
60*> = 'R': apply Q or Q**T from the Right.
61*> \endverbatim
62*>
63*> \param[in] TRANS
64*> \verbatim
65*> TRANS is CHARACTER*1
66*> = 'N': No transpose, apply Q;
67*> = 'T': Transpose, apply Q**T.
68*> \endverbatim
69*>
70*> \param[in] M
71*> \verbatim
72*> M is INTEGER
73*> The number of rows of the matrix C. M >= 0.
74*> \endverbatim
75*>
76*> \param[in] N
77*> \verbatim
78*> N is INTEGER
79*> The number of columns of the matrix C. N >= 0.
80*> \endverbatim
81*>
82*> \param[in] K
83*> \verbatim
84*> K is INTEGER
85*> The number of elementary reflectors whose product defines
86*> the matrix Q.
87*> If SIDE = 'L', M >= K >= 0;
88*> if SIDE = 'R', N >= K >= 0.
89*> \endverbatim
90*>
91*> \param[in] L
92*> \verbatim
93*> L is INTEGER
94*> The number of columns of the matrix A containing
95*> the meaningful part of the Householder reflectors.
96*> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
97*> \endverbatim
98*>
99*> \param[in] A
100*> \verbatim
101*> A is REAL array, dimension
102*> (LDA,M) if SIDE = 'L',
103*> (LDA,N) if SIDE = 'R'
104*> The i-th row must contain the vector which defines the
105*> elementary reflector H(i), for i = 1,2,...,k, as returned by
106*> STZRZF in the last k rows of its array argument A.
107*> A is modified by the routine but restored on exit.
108*> \endverbatim
109*>
110*> \param[in] LDA
111*> \verbatim
112*> LDA is INTEGER
113*> The leading dimension of the array A. LDA >= max(1,K).
114*> \endverbatim
115*>
116*> \param[in] TAU
117*> \verbatim
118*> TAU is REAL array, dimension (K)
119*> TAU(i) must contain the scalar factor of the elementary
120*> reflector H(i), as returned by STZRZF.
121*> \endverbatim
122*>
123*> \param[in,out] C
124*> \verbatim
125*> C is REAL array, dimension (LDC,N)
126*> On entry, the M-by-N matrix C.
127*> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
128*> \endverbatim
129*>
130*> \param[in] LDC
131*> \verbatim
132*> LDC is INTEGER
133*> The leading dimension of the array C. LDC >= max(1,M).
134*> \endverbatim
135*>
136*> \param[out] WORK
137*> \verbatim
138*> WORK is REAL array, dimension (MAX(1,LWORK))
139*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
140*> \endverbatim
141*>
142*> \param[in] LWORK
143*> \verbatim
144*> LWORK is INTEGER
145*> The dimension of the array WORK.
146*> If SIDE = 'L', LWORK >= max(1,N);
147*> if SIDE = 'R', LWORK >= max(1,M).
148*> For good performance, LWORK should generally be larger.
149*>
150*> If LWORK = -1, then a workspace query is assumed; the routine
151*> only calculates the optimal size of the WORK array, returns
152*> this value as the first entry of the WORK array, and no error
153*> message related to LWORK is issued by XERBLA.
154*> \endverbatim
155*>
156*> \param[out] INFO
157*> \verbatim
158*> INFO is INTEGER
159*> = 0: successful exit
160*> < 0: if INFO = -i, the i-th argument had an illegal value
161*> \endverbatim
162*
163* Authors:
164* ========
165*
166*> \author Univ. of Tennessee
167*> \author Univ. of California Berkeley
168*> \author Univ. of Colorado Denver
169*> \author NAG Ltd.
170*
171*> \ingroup realOTHERcomputational
172*
173*> \par Contributors:
174* ==================
175*>
176*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
177*
178*> \par Further Details:
179* =====================
180*>
181*> \verbatim
182*> \endverbatim
183*>
184* =====================================================================
185 SUBROUTINE sormrz( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
186 \$ WORK, LWORK, INFO )
187*
188* -- LAPACK computational routine --
189* -- LAPACK is a software package provided by Univ. of Tennessee, --
190* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
191*
192* .. Scalar Arguments ..
193 CHARACTER SIDE, TRANS
194 INTEGER INFO, K, L, LDA, LDC, LWORK, M, N
195* ..
196* .. Array Arguments ..
197 REAL A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
198* ..
199*
200* =====================================================================
201*
202* .. Parameters ..
203 INTEGER NBMAX, LDT, TSIZE
204 parameter( nbmax = 64, ldt = nbmax+1,
205 \$ tsize = ldt*nbmax )
206* ..
207* .. Local Scalars ..
208 LOGICAL LEFT, LQUERY, NOTRAN
209 CHARACTER TRANST
210 INTEGER I, I1, I2, I3, IB, IC, IINFO, IWT, JA, JC,
211 \$ ldwork, lwkopt, mi, nb, nbmin, ni, nq, nw
212* ..
213* .. External Functions ..
214 LOGICAL LSAME
215 INTEGER ILAENV
216 EXTERNAL lsame, ilaenv
217* ..
218* .. External Subroutines ..
219 EXTERNAL slarzb, slarzt, sormr3, xerbla
220* ..
221* .. Intrinsic Functions ..
222 INTRINSIC max, min
223* ..
224* .. Executable Statements ..
225*
226* Test the input arguments
227*
228 info = 0
229 left = lsame( side, 'L' )
230 notran = lsame( trans, 'N' )
231 lquery = ( lwork.EQ.-1 )
232*
233* NQ is the order of Q and NW is the minimum dimension of WORK
234*
235 IF( left ) THEN
236 nq = m
237 nw = max( 1, n )
238 ELSE
239 nq = n
240 nw = max( 1, m )
241 END IF
242 IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
243 info = -1
244 ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
245 info = -2
246 ELSE IF( m.LT.0 ) THEN
247 info = -3
248 ELSE IF( n.LT.0 ) THEN
249 info = -4
250 ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
251 info = -5
252 ELSE IF( l.LT.0 .OR. ( left .AND. ( l.GT.m ) ) .OR.
253 \$ ( .NOT.left .AND. ( l.GT.n ) ) ) THEN
254 info = -6
255 ELSE IF( lda.LT.max( 1, k ) ) THEN
256 info = -8
257 ELSE IF( ldc.LT.max( 1, m ) ) THEN
258 info = -11
259 ELSE IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
260 info = -13
261 END IF
262*
263 IF( info.EQ.0 ) THEN
264*
265* Compute the workspace requirements
266*
267 IF( m.EQ.0 .OR. n.EQ.0 ) THEN
268 lwkopt = 1
269 ELSE
270 nb = min( nbmax, ilaenv( 1, 'SORMRQ', side // trans, m, n,
271 \$ k, -1 ) )
272 lwkopt = nw*nb + tsize
273 END IF
274 work( 1 ) = lwkopt
275 END IF
276*
277 IF( info.NE.0 ) THEN
278 CALL xerbla( 'SORMRZ', -info )
279 RETURN
280 ELSE IF( lquery ) THEN
281 RETURN
282 END IF
283*
284* Quick return if possible
285*
286 IF( m.EQ.0 .OR. n.EQ.0 ) THEN
287 RETURN
288 END IF
289*
290 nbmin = 2
291 ldwork = nw
292 IF( nb.GT.1 .AND. nb.LT.k ) THEN
293 IF( lwork.LT.lwkopt ) THEN
294 nb = (lwork-tsize) / ldwork
295 nbmin = max( 2, ilaenv( 2, 'SORMRQ', side // trans, m, n, k,
296 \$ -1 ) )
297 END IF
298 END IF
299*
300 IF( nb.LT.nbmin .OR. nb.GE.k ) THEN
301*
302* Use unblocked code
303*
304 CALL sormr3( side, trans, m, n, k, l, a, lda, tau, c, ldc,
305 \$ work, iinfo )
306 ELSE
307*
308* Use blocked code
309*
310 iwt = 1 + nw*nb
311 IF( ( left .AND. .NOT.notran ) .OR.
312 \$ ( .NOT.left .AND. notran ) ) THEN
313 i1 = 1
314 i2 = k
315 i3 = nb
316 ELSE
317 i1 = ( ( k-1 ) / nb )*nb + 1
318 i2 = 1
319 i3 = -nb
320 END IF
321*
322 IF( left ) THEN
323 ni = n
324 jc = 1
325 ja = m - l + 1
326 ELSE
327 mi = m
328 ic = 1
329 ja = n - l + 1
330 END IF
331*
332 IF( notran ) THEN
333 transt = 'T'
334 ELSE
335 transt = 'N'
336 END IF
337*
338 DO 10 i = i1, i2, i3
339 ib = min( nb, k-i+1 )
340*
341* Form the triangular factor of the block reflector
342* H = H(i+ib-1) . . . H(i+1) H(i)
343*
344 CALL slarzt( 'Backward', 'Rowwise', l, ib, a( i, ja ), lda,
345 \$ tau( i ), work( iwt ), ldt )
346*
347 IF( left ) THEN
348*
349* H or H**T is applied to C(i:m,1:n)
350*
351 mi = m - i + 1
352 ic = i
353 ELSE
354*
355* H or H**T is applied to C(1:m,i:n)
356*
357 ni = n - i + 1
358 jc = i
359 END IF
360*
361* Apply H or H**T
362*
363 CALL slarzb( side, transt, 'Backward', 'Rowwise', mi, ni,
364 \$ ib, l, a( i, ja ), lda, work( iwt ), ldt,
365 \$ c( ic, jc ), ldc, work, ldwork )
366 10 CONTINUE
367*
368 END IF
369*
370 work( 1 ) = lwkopt
371*
372 RETURN
373*
374* End of SORMRZ
375*
376 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine slarzb(SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
SLARZB applies a block reflector or its transpose to a general matrix.
Definition: slarzb.f:183
subroutine sormrz(SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
SORMRZ
Definition: sormrz.f:187
subroutine sormr3(SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, INFO)
SORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stz...
Definition: sormr3.f:178
subroutine slarzt(DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)
SLARZT forms the triangular factor T of a block reflector H = I - vtvH.
Definition: slarzt.f:185