SCALAPACK 2.2.2
LAPACK: Linear Algebra PACKage
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pzunmrq.f
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1 SUBROUTINE pzunmrq( SIDE, TRANS, M, N, K, A, IA, JA, DESCA, TAU,
2 $ C, IC, JC, DESCC, WORK, LWORK, INFO )
3*
4* -- ScaLAPACK routine (version 1.7) --
5* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
6* and University of California, Berkeley.
7* May 25, 2001
8*
9* .. Scalar Arguments ..
10 CHARACTER SIDE, TRANS
11 INTEGER IA, IC, INFO, JA, JC, K, LWORK, M, N
12* ..
13* .. Array Arguments ..
14 INTEGER DESCA( * ), DESCC( * )
15 COMPLEX*16 A( * ), C( * ), TAU( * ), WORK( * )
16* ..
17*
18* Purpose
19* =======
20*
21* PZUNMRQ overwrites the general complex M-by-N distributed matrix
22* sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with
23*
24* SIDE = 'L' SIDE = 'R'
25* TRANS = 'N': Q * sub( C ) sub( C ) * Q
26* TRANS = 'C': Q**H * sub( C ) sub( C ) * Q**H
27*
28* where Q is a complex unitary distributed matrix defined as the
29* product of K elementary reflectors
30*
31* Q = H(1)' H(2)' . . . H(k)'
32*
33* as returned by PZGERQF. Q is of order M if SIDE = 'L' and of order N
34* if SIDE = 'R'.
35*
36* Notes
37* =====
38*
39* Each global data object is described by an associated description
40* vector. This vector stores the information required to establish
41* the mapping between an object element and its corresponding process
42* and memory location.
43*
44* Let A be a generic term for any 2D block cyclicly distributed array.
45* Such a global array has an associated description vector DESCA.
46* In the following comments, the character _ should be read as
47* "of the global array".
48*
49* NOTATION STORED IN EXPLANATION
50* --------------- -------------- --------------------------------------
51* DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
52* DTYPE_A = 1.
53* CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
54* the BLACS process grid A is distribu-
55* ted over. The context itself is glo-
56* bal, but the handle (the integer
57* value) may vary.
58* M_A (global) DESCA( M_ ) The number of rows in the global
59* array A.
60* N_A (global) DESCA( N_ ) The number of columns in the global
61* array A.
62* MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
63* the rows of the array.
64* NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
65* the columns of the array.
66* RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
67* row of the array A is distributed.
68* CSRC_A (global) DESCA( CSRC_ ) The process column over which the
69* first column of the array A is
70* distributed.
71* LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
72* array. LLD_A >= MAX(1,LOCr(M_A)).
73*
74* Let K be the number of rows or columns of a distributed matrix,
75* and assume that its process grid has dimension p x q.
76* LOCr( K ) denotes the number of elements of K that a process
77* would receive if K were distributed over the p processes of its
78* process column.
79* Similarly, LOCc( K ) denotes the number of elements of K that a
80* process would receive if K were distributed over the q processes of
81* its process row.
82* The values of LOCr() and LOCc() may be determined via a call to the
83* ScaLAPACK tool function, NUMROC:
84* LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
85* LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
86* An upper bound for these quantities may be computed by:
87* LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
88* LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
89*
90* Arguments
91* =========
92*
93* SIDE (global input) CHARACTER
94* = 'L': apply Q or Q**H from the Left;
95* = 'R': apply Q or Q**H from the Right.
96*
97* TRANS (global input) CHARACTER
98* = 'N': No transpose, apply Q;
99* = 'C': Conjugate transpose, apply Q**H.
100*
101* M (global input) INTEGER
102* The number of rows to be operated on i.e the number of rows
103* of the distributed submatrix sub( C ). M >= 0.
104*
105* N (global input) INTEGER
106* The number of columns to be operated on i.e the number of
107* columns of the distributed submatrix sub( C ). N >= 0.
108*
109* K (global input) INTEGER
110* The number of elementary reflectors whose product defines the
111* matrix Q. If SIDE = 'L', M >= K >= 0, if SIDE = 'R',
112* N >= K >= 0.
113*
114* A (local input) COMPLEX*16 pointer into the local memory
115* to an array of dimension (LLD_A,LOCc(JA+M-1)) if SIDE='L',
116* and (LLD_A,LOCc(JA+N-1)) if SIDE='R', where
117* LLD_A >= MAX(1,LOCr(IA+K-1)); On entry, the i-th row must
118* contain the vector which defines the elementary reflector
119* H(i), IA <= i <= IA+K-1, as returned by PZGERQF in the
120* K rows of its distributed matrix argument A(IA:IA+K-1,JA:*).
121* A(IA:IA+K-1,JA:*) is modified by the routine but restored on
122* exit.
123*
124* IA (global input) INTEGER
125* The row index in the global array A indicating the first
126* row of sub( A ).
127*
128* JA (global input) INTEGER
129* The column index in the global array A indicating the
130* first column of sub( A ).
131*
132* DESCA (global and local input) INTEGER array of dimension DLEN_.
133* The array descriptor for the distributed matrix A.
134*
135* TAU (local input) COMPLEX*16, array, dimension LOCc(IA+K-1).
136* This array contains the scalar factors TAU(i) of the
137* elementary reflectors H(i) as returned by PZGERQF.
138* TAU is tied to the distributed matrix A.
139*
140* C (local input/local output) COMPLEX*16 pointer into the
141* local memory to an array of dimension (LLD_C,LOCc(JC+N-1)).
142* On entry, the local pieces of the distributed matrix sub(C).
143* On exit, sub( C ) is overwritten by Q*sub( C ) or Q'*sub( C )
144* or sub( C )*Q' or sub( C )*Q.
145*
146* IC (global input) INTEGER
147* The row index in the global array C indicating the first
148* row of sub( C ).
149*
150* JC (global input) INTEGER
151* The column index in the global array C indicating the
152* first column of sub( C ).
153*
154* DESCC (global and local input) INTEGER array of dimension DLEN_.
155* The array descriptor for the distributed matrix C.
156*
157* WORK (local workspace/local output) COMPLEX*16 array,
158* dimension (LWORK)
159* On exit, WORK(1) returns the minimal and optimal LWORK.
160*
161* LWORK (local or global input) INTEGER
162* The dimension of the array WORK.
163* LWORK is local input and must be at least
164* if SIDE = 'L',
165* LWORK >= MAX( (MB_A*(MB_A-1))/2, ( MpC0 + MAX( MqA0 +
166* NUMROC( NUMROC( M+IROFFC, MB_A, 0, 0, NPROW ),
167* MB_A, 0, 0, LCMP ), NqC0 ) )*MB_A ) +
168* MB_A * MB_A
169* else if SIDE = 'R',
170* LWORK >= MAX( (MB_A*(MB_A-1))/2, (MpC0 + NqC0)*MB_A ) +
171* MB_A * MB_A
172* end if
173*
174* where LCMP = LCM / NPROW with LCM = ICLM( NPROW, NPCOL ),
175*
176* IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ),
177* IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ),
178* MqA0 = NUMROC( M+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ),
179*
180* IROFFC = MOD( IC-1, MB_C ), ICOFFC = MOD( JC-1, NB_C ),
181* ICROW = INDXG2P( IC, MB_C, MYROW, RSRC_C, NPROW ),
182* ICCOL = INDXG2P( JC, NB_C, MYCOL, CSRC_C, NPCOL ),
183* MpC0 = NUMROC( M+IROFFC, MB_C, MYROW, ICROW, NPROW ),
184* NqC0 = NUMROC( N+ICOFFC, NB_C, MYCOL, ICCOL, NPCOL ),
185*
186* ILCM, INDXG2P and NUMROC are ScaLAPACK tool functions;
187* MYROW, MYCOL, NPROW and NPCOL can be determined by calling
188* the subroutine BLACS_GRIDINFO.
189*
190* If LWORK = -1, then LWORK is global input and a workspace
191* query is assumed; the routine only calculates the minimum
192* and optimal size for all work arrays. Each of these
193* values is returned in the first entry of the corresponding
194* work array, and no error message is issued by PXERBLA.
195*
196*
197* INFO (global output) INTEGER
198* = 0: successful exit
199* < 0: If the i-th argument is an array and the j-entry had
200* an illegal value, then INFO = -(i*100+j), if the i-th
201* argument is a scalar and had an illegal value, then
202* INFO = -i.
203*
204* Alignment requirements
205* ======================
206*
207* The distributed submatrices A(IA:*, JA:*) and C(IC:IC+M-1,JC:JC+N-1)
208* must verify some alignment properties, namely the following
209* expressions should be true:
210*
211* If SIDE = 'L',
212* ( NB_A.EQ.MB_C .AND. ICOFFA.EQ.IROFFC )
213* If SIDE = 'R',
214* ( NB_A.EQ.NB_C .AND. ICOFFA.EQ.ICOFFC .AND. IACOL.EQ.ICCOL )
215*
216* =====================================================================
217*
218* .. Parameters ..
219 INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
220 $ lld_, mb_, m_, nb_, n_, rsrc_
221 parameter( block_cyclic_2d = 1, dlen_ = 9, dtype_ = 1,
222 $ ctxt_ = 2, m_ = 3, n_ = 4, mb_ = 5, nb_ = 6,
223 $ rsrc_ = 7, csrc_ = 8, lld_ = 9 )
224* ..
225* .. Local Scalars ..
226 LOGICAL LEFT, LQUERY, NOTRAN, RIGHT, TRAN
227 CHARACTER COLBTOP, ROWBTOP, TRANST
228 INTEGER I, I1, I2, I3, IACOL, IB, ICCOL, ICOFFA,
229 $ icoffc, icrow, ictxt, iinfo, ipw, iroffc, lcm,
230 $ lcmp, lwmin, mi, mpc0, mqa0, mycol, myrow, ni,
231 $ npcol, nprow, nq, nqc0
232* ..
233* .. Local Arrays ..
234 INTEGER IDUM1( 4 ), IDUM2( 4 )
235* ..
236* .. External Subroutines ..
237 EXTERNAL blacs_gridinfo, chk1mat, pchk2mat, pb_topget,
238 $ pb_topset, pxerbla, pzlarfb, pzlarft,
239 $ pzunmr2
240* ..
241* .. External Functions ..
242 LOGICAL LSAME
243 INTEGER ICEIL, ILCM, INDXG2P, NUMROC
244 EXTERNAL iceil, ilcm, indxg2p, lsame, numroc
245* ..
246* .. Intrinsic Functions ..
247 INTRINSIC dble, dcmplx, ichar, max, min, mod
248* ..
249* .. Executable Statements ..
250*
251* Get grid parameters
252*
253 ictxt = desca( ctxt_ )
254 CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
255*
256* Test the input parameters
257*
258 info = 0
259 IF( nprow.EQ.-1 ) THEN
260 info = -(900+ctxt_)
261 ELSE
262 IF( lsame( side, 'L' ) ) THEN
263 left = .true.
264 right = .false.
265 ELSE
266 left = .false.
267 right = .true.
268 END IF
269 IF( lsame( trans, 'N' ) ) THEN
270 notran = .true.
271 tran = .false.
272 ELSE
273 notran = .false.
274 tran = .true.
275 END IF
276*
277* NQ is the order of Q
278*
279 IF( left ) THEN
280 nq = m
281 CALL chk1mat( k, 5, m, 3, ia, ja, desca, 9, info )
282 ELSE
283 nq = n
284 CALL chk1mat( k, 5, n, 4, ia, ja, desca, 9, info )
285 END IF
286 CALL chk1mat( m, 3, n, 4, ic, jc, descc, 14, info )
287 IF( info.EQ.0 ) THEN
288 icoffa = mod( ja-1, desca( nb_ ) )
289 iroffc = mod( ic-1, descc( mb_ ) )
290 icoffc = mod( jc-1, descc( nb_ ) )
291 iacol = indxg2p( ja, desca( nb_ ), mycol, desca( csrc_ ),
292 $ npcol )
293 icrow = indxg2p( ic, descc( mb_ ), myrow, descc( rsrc_ ),
294 $ nprow )
295 iccol = indxg2p( jc, descc( nb_ ), mycol, descc( csrc_ ),
296 $ npcol )
297 mpc0 = numroc( m+iroffc, descc( mb_ ), myrow, icrow, nprow )
298 nqc0 = numroc( n+icoffc, descc( nb_ ), mycol, iccol, npcol )
299*
300 IF( left ) THEN
301 mqa0 = numroc( m+icoffa, desca( nb_ ), mycol, iacol,
302 $ npcol )
303 lcm = ilcm( nprow, npcol )
304 lcmp = lcm / nprow
305 lwmin = max( ( desca( mb_ ) * ( desca( mb_ ) - 1 ) )
306 $ / 2, ( mpc0 + max( mqa0 + numroc( numroc(
307 $ m+iroffc, desca( mb_ ), 0, 0, nprow ),
308 $ desca( mb_ ), 0, 0, lcmp ), nqc0 ) ) *
309 $ desca( mb_ ) ) + desca( mb_ ) * desca( mb_ )
310 ELSE
311 lwmin = max( ( desca( mb_ ) * ( desca( mb_ ) - 1 ) ) / 2,
312 $ ( mpc0 + nqc0 ) * desca( mb_ ) ) +
313 $ desca( mb_ ) * desca( mb_ )
314 END IF
315*
316 work( 1 ) = dcmplx( dble( lwmin ) )
317 lquery = ( lwork.EQ.-1 )
318 IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
319 info = -1
320 ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'C' ) ) THEN
321 info = -2
322 ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
323 info = -5
324 ELSE IF( left .AND. desca( nb_ ).NE.descc( mb_ ) ) THEN
325 info = -(900+nb_)
326 ELSE IF( left .AND. icoffa.NE.iroffc ) THEN
327 info = -12
328 ELSE IF( .NOT.left .AND. icoffa.NE.icoffc ) THEN
329 info = -13
330 ELSE IF( .NOT.left .AND. iacol.NE.iccol ) THEN
331 info = -13
332 ELSE IF( .NOT.left .AND. desca( nb_ ).NE.descc( nb_ ) ) THEN
333 info = -(1400+nb_)
334 ELSE IF( ictxt.NE.descc( ctxt_ ) ) THEN
335 info = -(1400+ctxt_)
336 ELSE IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
337 info = -16
338 END IF
339 END IF
340 IF( left ) THEN
341 idum1( 1 ) = ichar( 'L' )
342 ELSE
343 idum1( 1 ) = ichar( 'R' )
344 END IF
345 idum2( 1 ) = 1
346 IF( notran ) THEN
347 idum1( 2 ) = ichar( 'N' )
348 ELSE
349 idum1( 2 ) = ichar( 'C' )
350 END IF
351 idum2( 2 ) = 2
352 idum1( 3 ) = k
353 idum2( 3 ) = 5
354 IF( lwork.EQ.-1 ) THEN
355 idum1( 4 ) = -1
356 ELSE
357 idum1( 4 ) = 1
358 END IF
359 idum2( 4 ) = 16
360 IF( left ) THEN
361 CALL pchk2mat( k, 5, m, 3, ia, ja, desca, 9, m, 3, n, 4,
362 $ ic, jc, descc, 14, 4, idum1, idum2, info )
363 ELSE
364 CALL pchk2mat( k, 5, n, 4, ia, ja, desca, 9, m, 3, n, 4,
365 $ ic, jc, descc, 14, 4, idum1, idum2, info )
366 END IF
367 END IF
368*
369 IF( info.NE.0 ) THEN
370 CALL pxerbla( ictxt, 'PZUNMRQ', -info )
371 RETURN
372 ELSE IF( lquery ) THEN
373 RETURN
374 END IF
375*
376* Quick return if possible
377*
378 IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 )
379 $ RETURN
380*
381 CALL pb_topget( ictxt, 'Broadcast', 'Rowwise', rowbtop )
382 CALL pb_topget( ictxt, 'Broadcast', 'Columnwise', colbtop )
383*
384 IF( ( left .AND. .NOT.notran ) .OR.
385 $ ( .NOT.left .AND. notran ) ) THEN
386 i1 = min( iceil( ia, desca( mb_ ) ) * desca( mb_ ), ia+k-1 )
387 $ + 1
388 i2 = ia + k - 1
389 i3 = desca( mb_ )
390 ELSE
391 i1 = max( ( (ia+k-2) / desca( mb_ ) ) * desca( mb_ ) + 1, ia )
392 i2 = min( iceil( ia, desca( mb_ ) ) * desca( mb_ ), ia+k-1 )
393 $ + 1
394 i3 = -desca( mb_ )
395 END IF
396*
397 IF( left ) THEN
398 ni = n
399 ELSE
400 mi = m
401 CALL pb_topset( ictxt, 'Broadcast', 'Rowwise', ' ' )
402 IF( notran ) THEN
403 CALL pb_topset( ictxt, 'Broadcast', 'Columnwise', 'I-ring' )
404 ELSE
405 CALL pb_topset( ictxt, 'Broadcast', 'Columnwise', 'D-ring' )
406 END IF
407 END IF
408*
409 IF( notran ) THEN
410 transt = 'C'
411 ELSE
412 transt = 'N'
413 END IF
414*
415 IF( ( left .AND. .NOT.notran ) .OR.
416 $ ( .NOT.left .AND. notran ) ) THEN
417 ib = i1 - ia
418 IF( left ) THEN
419 mi = m - k + ib
420 ELSE
421 ni = n - k + ib
422 END IF
423 CALL pzunmr2( side, trans, mi, ni, ib, a, ia, ja, desca, tau,
424 $ c, ic, jc, descc, work, lwork, iinfo )
425 END IF
426*
427 ipw = desca( mb_ )*desca( mb_ ) + 1
428 DO 10 i = i1, i2, i3
429 ib = min( desca( mb_ ), k-i+ia )
430*
431* Form the triangular factor of the block reflector
432* H = H(i+ib-1) . . . H(i+1) H(i)
433*
434 CALL pzlarft( 'Backward', 'Rowwise', nq-k+i+ib-ia, ib,
435 $ a, i, ja, desca, tau, work, work( ipw ) )
436 IF( left ) THEN
437*
438* H or H' is applied to C(ic:ic+m-k+i+ib-ia-1,jc:jc+n-1)
439*
440 mi = m - k + i + ib - ia
441 ELSE
442*
443* H or H' is applied to C(ic:ic+m-1,jc:jc+n-k+i+ib-ia-1)
444*
445 ni = n - k + i + ib - ia
446 END IF
447*
448* Apply H or H'
449*
450 CALL pzlarfb( side, transt, 'Backward', 'Rowwise', mi, ni,
451 $ ib, a, i, ja, desca, work, c, ic, jc, descc,
452 $ work( ipw ) )
453 10 CONTINUE
454*
455 IF( ( right .AND. tran ) .OR.
456 $ ( left .AND. notran ) ) THEN
457 ib = i2 - ia
458 IF( left ) THEN
459 mi = m - k + ib
460 ELSE
461 ni = n - k + ib
462 END IF
463 CALL pzunmr2( side, trans, mi, ni, ib, a, ia, ja, desca, tau,
464 $ c, ic, jc, descc, work, lwork, iinfo )
465 END IF
466*
467 CALL pb_topset( ictxt, 'Broadcast', 'Rowwise', rowbtop )
468 CALL pb_topset( ictxt, 'Broadcast', 'Columnwise', colbtop )
469*
470 work( 1 ) = dcmplx( dble( lwmin ) )
471*
472 RETURN
473*
474* End of PZUNMRQ
475*
476 END
subroutine chk1mat(ma, mapos0, na, napos0, ia, ja, desca, descapos0, info)
Definition chk1mat.f:3
#define max(A, B)
Definition pcgemr.c:180
#define min(A, B)
Definition pcgemr.c:181
subroutine pchk2mat(ma, mapos0, na, napos0, ia, ja, desca, descapos0, mb, mbpos0, nb, nbpos0, ib, jb, descb, descbpos0, nextra, ex, expos, info)
Definition pchkxmat.f:175
subroutine pxerbla(ictxt, srname, info)
Definition pxerbla.f:2
subroutine pzlarfb(side, trans, direct, storev, m, n, k, v, iv, jv, descv, t, c, ic, jc, descc, work)
Definition pzlarfb.f:3
subroutine pzlarft(direct, storev, n, k, v, iv, jv, descv, tau, t, work)
Definition pzlarft.f:3
subroutine pzunmr2(side, trans, m, n, k, a, ia, ja, desca, tau, c, ic, jc, descc, work, lwork, info)
Definition pzunmr2.f:3
subroutine pzunmrq(side, trans, m, n, k, a, ia, ja, desca, tau, c, ic, jc, descc, work, lwork, info)
Definition pzunmrq.f:3