SCALAPACK 2.2.2
LAPACK: Linear Algebra PACKage
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psormr2.f
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1 SUBROUTINE psormr2( 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 REAL A( * ), C( * ), TAU( * ), WORK( * )
16* ..
17*
18* Purpose
19* =======
20*
21* PSORMR2 overwrites the general real 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 = 'T': Q**T * sub( C ) sub( C ) * Q**T
27*
28* where Q is a real orthogonal 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 PSGERQF. 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**T from the Left;
95* = 'R': apply Q or Q**T from the Right.
96*
97* TRANS (global input) CHARACTER
98* = 'N': No transpose, apply Q;
99* = 'T': Transpose, apply Q**T.
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) REAL 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 PSGERQF 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) REAL, 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 PSGERQF.
138* TAU is tied to the distributed matrix A.
139*
140* C (local input/local output) REAL 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) REAL 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', LWORK >= MpC0 + MAX( MAX( 1, NqC0 ), NUMROC(
165* NUMROC( M+IROFFC,MB_A,0,0,NPROW ),MB_A,0,0,LCMP ) );
166* if SIDE = 'R', LWORK >= NqC0 + MAX( 1, MpC0 );
167*
168* where LCMP = LCM / NPROW with LCM = ICLM( NPROW, NPCOL ),
169*
170* IROFFC = MOD( IC-1, MB_C ), ICOFFC = MOD( JC-1, NB_C ),
171* ICROW = INDXG2P( IC, MB_C, MYROW, RSRC_C, NPROW ),
172* ICCOL = INDXG2P( JC, NB_C, MYCOL, CSRC_C, NPCOL ),
173* MpC0 = NUMROC( M+IROFFC, MB_C, MYROW, ICROW, NPROW ),
174* NqC0 = NUMROC( N+ICOFFC, NB_C, MYCOL, ICCOL, NPCOL ),
175*
176* ILCM, INDXG2P and NUMROC are ScaLAPACK tool functions;
177* MYROW, MYCOL, NPROW and NPCOL can be determined by calling
178* the subroutine BLACS_GRIDINFO.
179*
180* If LWORK = -1, then LWORK is global input and a workspace
181* query is assumed; the routine only calculates the minimum
182* and optimal size for all work arrays. Each of these
183* values is returned in the first entry of the corresponding
184* work array, and no error message is issued by PXERBLA.
185*
186*
187* INFO (local output) INTEGER
188* = 0: successful exit
189* < 0: If the i-th argument is an array and the j-entry had
190* an illegal value, then INFO = -(i*100+j), if the i-th
191* argument is a scalar and had an illegal value, then
192* INFO = -i.
193*
194* Alignment requirements
195* ======================
196*
197* The distributed submatrices A(IA:*, JA:*) and C(IC:IC+M-1,JC:JC+N-1)
198* must verify some alignment properties, namely the following
199* expressions should be true:
200*
201* If SIDE = 'L',
202* ( NB_A.EQ.MB_C .AND. ICOFFA.EQ.IROFFC )
203* If SIDE = 'R',
204* ( NB_A.EQ.NB_C .AND. ICOFFA.EQ.ICOFFC .AND. IACOL.EQ.ICCOL )
205*
206* =====================================================================
207*
208* .. Parameters ..
209 INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
210 $ lld_, mb_, m_, nb_, n_, rsrc_
211 parameter( block_cyclic_2d = 1, dlen_ = 9, dtype_ = 1,
212 $ ctxt_ = 2, m_ = 3, n_ = 4, mb_ = 5, nb_ = 6,
213 $ rsrc_ = 7, csrc_ = 8, lld_ = 9 )
214 REAL ONE
215 parameter( one = 1.0e+0 )
216* ..
217* .. Local Scalars ..
218 LOGICAL LEFT, LQUERY, NOTRAN
219 CHARACTER COLBTOP, ROWBTOP
220 INTEGER I, I1, I2, I3, IACOL, ICCOL, ICOFFA, ICOFFC,
221 $ icrow, ictxt, iroffc, lcm, lcmp, lwmin, mi,
222 $ mpc0, mycol, myrow, ni, npcol, nprow, nq, nqc0
223 REAL AII
224* ..
225* .. External Subroutines ..
226 EXTERNAL blacs_abort, blacs_gridinfo, chk1mat, pselset,
227 $ pselset2, pslarf, pb_topget, pb_topset, pxerbla
228* ..
229* .. External Functions ..
230 LOGICAL LSAME
231 INTEGER ILCM, INDXG2P, NUMROC
232 EXTERNAL ilcm, indxg2p, lsame, numroc
233* ..
234* .. Intrinsic Functions ..
235 INTRINSIC max, mod, real
236* ..
237* .. Executable Statements ..
238*
239* Get grid parameters
240*
241 ictxt = desca( ctxt_ )
242 CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
243*
244* Test the input parameters
245*
246 info = 0
247 IF( nprow.EQ.-1 ) THEN
248 info = -(900+ctxt_)
249 ELSE
250 left = lsame( side, 'L' )
251 notran = lsame( trans, 'N' )
252*
253* NQ is the order of Q
254*
255 IF( left ) THEN
256 nq = m
257 CALL chk1mat( k, 5, m, 3, ia, ja, desca, 9, info )
258 ELSE
259 nq = n
260 CALL chk1mat( k, 5, n, 4, ia, ja, desca, 9, info )
261 END IF
262 CALL chk1mat( m, 3, n, 4, ic, jc, descc, 14, info )
263 IF( info.EQ.0 ) THEN
264 icoffa = mod( ja-1, desca( nb_ ) )
265 iroffc = mod( ic-1, descc( mb_ ) )
266 icoffc = mod( jc-1, descc( nb_ ) )
267 iacol = indxg2p( ja, desca( nb_ ), mycol, desca( csrc_ ),
268 $ npcol )
269 icrow = indxg2p( ic, descc( mb_ ), myrow, descc( rsrc_ ),
270 $ nprow )
271 iccol = indxg2p( jc, descc( nb_ ), mycol, descc( csrc_ ),
272 $ npcol )
273 mpc0 = numroc( m+iroffc, descc( mb_ ), myrow, icrow, nprow )
274 nqc0 = numroc( n+icoffc, descc( nb_ ), mycol, iccol, npcol )
275*
276 IF( left ) THEN
277 lcm = ilcm( nprow, npcol )
278 lcmp = lcm / nprow
279 lwmin = mpc0 + max( max( 1, nqc0 ), numroc( numroc(
280 $ m+iroffc, desca( mb_ ), 0, 0, nprow ),
281 $ desca( mb_ ), 0, 0, lcmp ) )
282 ELSE
283 lwmin = nqc0 + max( 1, mpc0 )
284 END IF
285*
286 work( 1 ) = real( lwmin )
287 lquery = ( lwork.EQ.-1 )
288 IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
289 info = -1
290 ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
291 info = -2
292 ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
293 info = -5
294 ELSE IF( left .AND. desca( nb_ ).NE.descc( mb_ ) ) THEN
295 info = -(900+nb_)
296 ELSE IF( left .AND. icoffa.NE.iroffc ) THEN
297 info = -12
298 ELSE IF( .NOT.left .AND. icoffa.NE.icoffc ) THEN
299 info = -13
300 ELSE IF( .NOT.left .AND. iacol.NE.iccol ) THEN
301 info = -13
302 ELSE IF( .NOT.left .AND. desca( nb_ ).NE.descc( nb_ ) ) THEN
303 info = -(1400+nb_)
304 ELSE IF( ictxt.NE.descc( ctxt_ ) ) THEN
305 info = -(1400+ctxt_)
306 ELSE IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
307 info = -16
308 END IF
309 END IF
310 END IF
311*
312 IF( info.NE.0 ) THEN
313 CALL pxerbla( ictxt, 'PSORMR2', -info )
314 CALL blacs_abort( ictxt, 1 )
315 RETURN
316 ELSE IF( lquery ) THEN
317 RETURN
318 END IF
319*
320* Quick return if possible
321*
322 IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 )
323 $ RETURN
324*
325 CALL pb_topget( ictxt, 'Broadcast', 'Rowwise', rowbtop )
326 CALL pb_topget( ictxt, 'Broadcast', 'Columnwise', colbtop )
327*
328 IF( ( left .AND. .NOT.notran .OR. .NOT.left .AND. notran ) ) THEN
329 i1 = ia
330 i2 = ia + k - 1
331 i3 = 1
332 ELSE
333 i1 = ia + k - 1
334 i2 = ia
335 i3 = -1
336 END IF
337*
338 IF( left ) THEN
339 ni = n
340 ELSE
341 mi = m
342 CALL pb_topset( ictxt, 'Broadcast', 'Rowwise', ' ' )
343 IF( notran ) THEN
344 CALL pb_topset( ictxt, 'Broadcast', 'Columnwise', 'I-ring' )
345 ELSE
346 CALL pb_topset( ictxt, 'Broadcast', 'Columnwise', 'D-ring' )
347 END IF
348 END IF
349*
350 DO 10 i = i1, i2, i3
351 IF( left ) THEN
352*
353* H(i) or H(i)' is applied to C(ic:ic+m-k+i-ia,jc:jc+n-1)
354*
355 mi = m - k + i - ia + 1
356 ELSE
357*
358* H(i) or H(i)' is applied to C(ic:ic+m-1,jc:jc+n-k+i-ia+1)
359*
360 ni = n - k + i - ia + 1
361 END IF
362*
363* Apply H(i) or H(i)'
364*
365 CALL pselset2( aii, a, i, ja+nq-k+i-ia, desca, one )
366 CALL pslarf( side, mi, ni, a, i, ja, desca, desca( m_ ),
367 $ tau, c, ic, jc, descc, work )
368 CALL pselset( a, i, ja+nq-k+i-ia, desca, aii )
369*
370 10 CONTINUE
371*
372 CALL pb_topset( ictxt, 'Broadcast', 'Rowwise', rowbtop )
373 CALL pb_topset( ictxt, 'Broadcast', 'Columnwise', colbtop )
374*
375 work( 1 ) = real( lwmin )
376*
377 RETURN
378*
379* End of PSORMR2
380*
381 END
subroutine chk1mat(ma, mapos0, na, napos0, ia, ja, desca, descapos0, info)
Definition chk1mat.f:3
#define max(A, B)
Definition pcgemr.c:180
subroutine pselset2(alpha, a, ia, ja, desca, beta)
Definition pselset2.f:2
subroutine pselset(a, ia, ja, desca, alpha)
Definition pselset.f:2
subroutine pslarf(side, m, n, v, iv, jv, descv, incv, tau, c, ic, jc, descc, work)
Definition pslarf.f:3
subroutine psormr2(side, trans, m, n, k, a, ia, ja, desca, tau, c, ic, jc, descc, work, lwork, info)
Definition psormr2.f:3
subroutine pxerbla(ictxt, srname, info)
Definition pxerbla.f:2