SCALAPACK 2.2.2
LAPACK: Linear Algebra PACKage
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◆ pzunml2()

subroutine pzunml2 ( character  side,
character  trans,
integer  m,
integer  n,
integer  k,
complex*16, dimension( * )  a,
integer  ia,
integer  ja,
integer, dimension( * )  desca,
complex*16, dimension( * )  tau,
complex*16, dimension( * )  c,
integer  ic,
integer  jc,
integer, dimension( * )  descc,
complex*16, dimension( * )  work,
integer  lwork,
integer  info 
)

Definition at line 1 of file pzunml2.f.

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* PZUNML2 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(k)' . . . H(2)' H(1)'
32*
33* as returned by PZGELQF. 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 PZGELQF 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 PZGELQF.
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', 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 COMPLEX*16 ONE
215 parameter( one = ( 1.0d+0, 0.0d+0 ) )
216* ..
217* .. Local Scalars ..
218 LOGICAL LEFT, LQUERY, NOTRAN
219 CHARACTER COLBTOP, ROWBTOP
220 INTEGER I, I1, I2, I3, IACOL, ICC, ICCOL, ICOFFA,
221 $ ICOFFC, ICROW, ICTXT, IROFFC, JCC, LCM, LCMP,
222 $ LWMIN, MI, MPC0, MYCOL, MYROW, NI, NPCOL,
223 $ NPROW, NQ, NQC0
224 COMPLEX*16 AII
225* ..
226* .. External Subroutines ..
227 EXTERNAL blacs_abort, blacs_gridinfo, chk1mat,
228 $ pb_topget, pb_topset, pxerbla, pzelset,
229 $ pzelset2, pzlacgv, pzlarf, pzlarfc
230* ..
231* .. External Functions ..
232 LOGICAL LSAME
233 INTEGER ILCM, INDXG2P, NUMROC
234 EXTERNAL ilcm, indxg2p, lsame, numroc
235* ..
236* .. Intrinsic Functions ..
237 INTRINSIC dble, dcmplx, max, mod
238* ..
239* .. Executable Statements ..
240*
241* Get grid parameters
242*
243 ictxt = desca( ctxt_ )
244 CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
245*
246* Test the input parameters
247*
248 info = 0
249 IF( nprow.EQ.-1 ) THEN
250 info = -(900+ctxt_)
251 ELSE
252 left = lsame( side, 'L' )
253 notran = lsame( trans, 'N' )
254*
255* NQ is the order of Q
256*
257 IF( left ) THEN
258 nq = m
259 CALL chk1mat( k, 5, m, 3, ia, ja, desca, 9, info )
260 ELSE
261 nq = n
262 CALL chk1mat( k, 5, n, 4, ia, ja, desca, 9, info )
263 END IF
264 CALL chk1mat( m, 3, n, 4, ic, jc, descc, 14, info )
265 IF( info.EQ.0 ) THEN
266 icoffa = mod( ja-1, desca( nb_ ) )
267 iroffc = mod( ic-1, descc( mb_ ) )
268 icoffc = mod( jc-1, descc( nb_ ) )
269 iacol = indxg2p( ja, desca( nb_ ), mycol, desca( csrc_ ),
270 $ npcol )
271 icrow = indxg2p( ic, descc( mb_ ), myrow, descc( rsrc_ ),
272 $ nprow )
273 iccol = indxg2p( jc, descc( nb_ ), mycol, descc( csrc_ ),
274 $ npcol )
275 mpc0 = numroc( m+iroffc, descc( mb_ ), myrow, icrow, nprow )
276 nqc0 = numroc( n+icoffc, descc( nb_ ), mycol, iccol, npcol )
277*
278 IF( left ) THEN
279 lcm = ilcm( nprow, npcol )
280 lcmp = lcm / nprow
281 lwmin = mpc0 + max( max( 1, nqc0 ), numroc( numroc(
282 $ m+iroffc, desca( mb_ ), 0, 0, nprow ),
283 $ desca( mb_ ), 0, 0, lcmp ) )
284 ELSE
285 nqc0 = numroc( n+icoffc, descc( nb_ ), mycol, iccol,
286 $ npcol )
287 mpc0 = numroc( m+iroffc, descc( mb_ ), myrow, icrow,
288 $ nprow )
289 lwmin = nqc0 + max( 1, mpc0 )
290 END IF
291*
292 work( 1 ) = dcmplx( dble( lwmin ) )
293 lquery = ( lwork.EQ.-1 )
294 IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
295 info = -1
296 ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'C' ) ) THEN
297 info = -2
298 ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
299 info = -5
300 ELSE IF( left .AND. desca( nb_ ).NE.descc( mb_ ) ) THEN
301 info = -(900+nb_)
302 ELSE IF( left .AND. icoffa.NE.iroffc ) THEN
303 info = -12
304 ELSE IF( .NOT.left .AND. icoffa.NE.icoffc ) THEN
305 info = -13
306 ELSE IF( .NOT.left .AND. iacol.NE.iccol ) THEN
307 info = -13
308 ELSE IF( .NOT.left .AND. desca( nb_ ).NE.descc( nb_ ) ) THEN
309 info = -(1400+nb_)
310 ELSE IF( ictxt.NE.descc( ctxt_ ) ) THEN
311 info = -(1400+ctxt_)
312 ELSE IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
313 info = -16
314 END IF
315 END IF
316 END IF
317*
318 IF( info.NE.0 ) THEN
319 CALL pxerbla( ictxt, 'PZUNML2', -info )
320 CALL blacs_abort( ictxt, 1 )
321 RETURN
322 ELSE IF( lquery ) THEN
323 RETURN
324 END IF
325*
326* Quick return if possible
327*
328 IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 )
329 $ RETURN
330*
331 CALL pb_topget( ictxt, 'Broadcast', 'Rowwise', rowbtop )
332 CALL pb_topget( ictxt, 'Broadcast', 'Columnwise', colbtop )
333*
334 IF( ( left .AND. notran .OR. .NOT.left .AND. .NOT.notran ) ) THEN
335 i1 = ia
336 i2 = ia + k - 1
337 i3 = 1
338 ELSE
339 i1 = ia + k -1
340 i2 = ia
341 i3 = -1
342 END IF
343*
344 IF( left ) THEN
345 ni = n
346 jcc = jc
347 ELSE
348 mi = m
349 icc = ic
350 CALL pb_topset( ictxt, 'Broadcast', 'Rowwise', ' ' )
351 IF( notran ) THEN
352 CALL pb_topset( ictxt, 'Broadcast', 'Columnwise', 'D-ring' )
353 ELSE
354 CALL pb_topset( ictxt, 'Broadcast', 'Columnwise', 'I-ring' )
355 END IF
356 END IF
357*
358 DO 10 i = i1, i2, i3
359 IF( left ) THEN
360*
361* H(i) or H(i)' is applied to C(i:ic+m-1,jc:jc+n-1)
362*
363 mi = m - i + ia
364 icc = ic + i - ia
365 ELSE
366*
367* H(i) or H(i)' is applied to C(ic:ic+m-1,jc+i-ia:jc+n-1)
368*
369 ni = n - i + ia
370 jcc = jc + i - ia
371 END IF
372*
373* Apply H(i) or H(i)'
374*
375 IF( i-ia+1.LT.nq )
376 $ CALL pzlacgv( nq-i+ia-1, a, i, ja+i-ia+1, desca,
377 $ desca( m_ ) )
378 CALL pzelset2( aii, a, i, ja+i-ia, desca, one )
379 IF( notran ) THEN
380 CALL pzlarfc( side, mi, ni, a, i, ja+i-ia, desca,
381 $ desca( m_ ), tau, c, icc, jcc, descc, work )
382 ELSE
383 CALL pzlarf( side, mi, ni, a, i, ja+i-ia, desca,
384 $ desca( m_ ), tau, c, icc, jcc, descc, work )
385 END IF
386 CALL pzelset( a, i, ja+i-ia, desca, aii )
387 IF( i-ia+1.LT.nq )
388 $ CALL pzlacgv( nq-i+ia-1, a, i, ja+i-ia+1, desca,
389 $ desca( m_ ) )
390*
391 10 CONTINUE
392*
393 CALL pb_topget( ictxt, 'Broadcast', 'Rowwise', rowbtop )
394 CALL pb_topget( ictxt, 'Broadcast', 'Columnwise', colbtop )
395*
396 work( 1 ) = dcmplx( dble( lwmin ) )
397*
398 RETURN
399*
400* End of PZUNML2
401*
chk1mat
subroutine chk1mat(ma, mapos0, na, napos0, ia, ja, desca, descapos0, info)
Definition chk1mat.f:3
ilcm
integer function ilcm(m, n)
Definition ilcm.f:2
indxg2p
integer function indxg2p(indxglob, nb, iproc, isrcproc, nprocs)
Definition indxg2p.f:2
numroc
integer function numroc(n, nb, iproc, isrcproc, nprocs)
Definition numroc.f:2
max
#define max(A, B)
Definition pcgemr.c:180
pxerbla
subroutine pxerbla(ictxt, srname, info)
Definition pxerbla.f:2
pzelset2
subroutine pzelset2(alpha, a, ia, ja, desca, beta)
Definition pzelset2.f:2
pzelset
subroutine pzelset(a, ia, ja, desca, alpha)
Definition pzelset.f:2
pzlacgv
subroutine pzlacgv(n, x, ix, jx, descx, incx)
Definition pzlacgv.f:2
pzlarf
subroutine pzlarf(side, m, n, v, iv, jv, descv, incv, tau, c, ic, jc, descc, work)
Definition pzlarf.f:3
pzlarfc
subroutine pzlarfc(side, m, n, v, iv, jv, descv, incv, tau, c, ic, jc, descc, work)
Definition pzlarfc.f:3
lsame
logical function lsame(ca, cb)
Definition tools.f:1724
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