SCALAPACK 2.2.2
LAPACK: Linear Algebra PACKage
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psorgqr.f
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1 SUBROUTINE psorgqr( M, N, K, A, IA, JA, DESCA, TAU, WORK, LWORK,
2 $ 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 INTEGER IA, INFO, JA, K, LWORK, M, N
11* ..
12* .. Array Arguments ..
13 INTEGER DESCA( * )
14 REAL A( * ), TAU( * ), WORK( * )
15* ..
16*
17* Purpose
18* =======
19*
20* PSORGQR generates an M-by-N real distributed matrix Q denoting
21* A(IA:IA+M-1,JA:JA+N-1) with orthonormal columns, which is defined as
22* the first N columns of a product of K elementary reflectors of order
23* M
24*
25* Q = H(1) H(2) . . . H(k)
26*
27* as returned by PSGEQRF.
28*
29* Notes
30* =====
31*
32* Each global data object is described by an associated description
33* vector. This vector stores the information required to establish
34* the mapping between an object element and its corresponding process
35* and memory location.
36*
37* Let A be a generic term for any 2D block cyclicly distributed array.
38* Such a global array has an associated description vector DESCA.
39* In the following comments, the character _ should be read as
40* "of the global array".
41*
42* NOTATION STORED IN EXPLANATION
43* --------------- -------------- --------------------------------------
44* DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
45* DTYPE_A = 1.
46* CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
47* the BLACS process grid A is distribu-
48* ted over. The context itself is glo-
49* bal, but the handle (the integer
50* value) may vary.
51* M_A (global) DESCA( M_ ) The number of rows in the global
52* array A.
53* N_A (global) DESCA( N_ ) The number of columns in the global
54* array A.
55* MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
56* the rows of the array.
57* NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
58* the columns of the array.
59* RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
60* row of the array A is distributed.
61* CSRC_A (global) DESCA( CSRC_ ) The process column over which the
62* first column of the array A is
63* distributed.
64* LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
65* array. LLD_A >= MAX(1,LOCr(M_A)).
66*
67* Let K be the number of rows or columns of a distributed matrix,
68* and assume that its process grid has dimension p x q.
69* LOCr( K ) denotes the number of elements of K that a process
70* would receive if K were distributed over the p processes of its
71* process column.
72* Similarly, LOCc( K ) denotes the number of elements of K that a
73* process would receive if K were distributed over the q processes of
74* its process row.
75* The values of LOCr() and LOCc() may be determined via a call to the
76* ScaLAPACK tool function, NUMROC:
77* LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
78* LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
79* An upper bound for these quantities may be computed by:
80* LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
81* LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
82*
83* Arguments
84* =========
85*
86* M (global input) INTEGER
87* The number of rows to be operated on i.e the number of rows
88* of the distributed submatrix Q. M >= 0.
89*
90* N (global input) INTEGER
91* The number of columns to be operated on i.e the number of
92* columns of the distributed submatrix Q. M >= N >= 0.
93*
94* K (global input) INTEGER
95* The number of elementary reflectors whose product defines the
96* matrix Q. N >= K >= 0.
97*
98* A (local input/local output) REAL pointer into the
99* local memory to an array of dimension (LLD_A,LOCc(JA+N-1)).
100* On entry, the j-th column must contain the vector which
101* defines the elementary reflector H(j), JA <= j <= JA+K-1, as
102* returned by PSGEQRF in the K columns of its distributed
103* matrix argument A(IA:*,JA:JA+K-1). On exit, this array
104* contains the local pieces of the M-by-N distributed matrix Q.
105*
106* IA (global input) INTEGER
107* The row index in the global array A indicating the first
108* row of sub( A ).
109*
110* JA (global input) INTEGER
111* The column index in the global array A indicating the
112* first column of sub( A ).
113*
114* DESCA (global and local input) INTEGER array of dimension DLEN_.
115* The array descriptor for the distributed matrix A.
116*
117* TAU (local input) REAL, array, dimension LOCc(JA+K-1)
118* This array contains the scalar factors TAU(j) of the
119* elementary reflectors H(j) as returned by PSGEQRF.
120* TAU is tied to the distributed matrix A.
121*
122* WORK (local workspace/local output) REAL array,
123* dimension (LWORK)
124* On exit, WORK(1) returns the minimal and optimal LWORK.
125*
126* LWORK (local or global input) INTEGER
127* The dimension of the array WORK.
128* LWORK is local input and must be at least
129* LWORK >= NB_A * ( NqA0 + MpA0 + NB_A ), where
130*
131* IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ),
132* IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ),
133* IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ),
134* MpA0 = NUMROC( M+IROFFA, MB_A, MYROW, IAROW, NPROW ),
135* NqA0 = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ),
136*
137* INDXG2P and NUMROC are ScaLAPACK tool functions;
138* MYROW, MYCOL, NPROW and NPCOL can be determined by calling
139* the subroutine BLACS_GRIDINFO.
140*
141* If LWORK = -1, then LWORK is global input and a workspace
142* query is assumed; the routine only calculates the minimum
143* and optimal size for all work arrays. Each of these
144* values is returned in the first entry of the corresponding
145* work array, and no error message is issued by PXERBLA.
146*
147*
148* INFO (global output) INTEGER
149* = 0: successful exit
150* < 0: If the i-th argument is an array and the j-entry had
151* an illegal value, then INFO = -(i*100+j), if the i-th
152* argument is a scalar and had an illegal value, then
153* INFO = -i.
154*
155* =====================================================================
156*
157* .. Parameters ..
158 INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
159 $ lld_, mb_, m_, nb_, n_, rsrc_
160 parameter( block_cyclic_2d = 1, dlen_ = 9, dtype_ = 1,
161 $ ctxt_ = 2, m_ = 3, n_ = 4, mb_ = 5, nb_ = 6,
162 $ rsrc_ = 7, csrc_ = 8, lld_ = 9 )
163 REAL ZERO
164 parameter( zero = 0.0e+0 )
165* ..
166* .. Local Scalars ..
167 LOGICAL LQUERY
168 CHARACTER COLBTOP, ROWBTOP
169 INTEGER I, IACOL, IAROW, ICTXT, IINFO, IPW, J, JB, JL,
170 $ jn, lwmin, mpa0, mycol, myrow, npcol, nprow,
171 $ nqa0
172* ..
173* .. Local Arrays ..
174 INTEGER IDUM1( 2 ), IDUM2( 2 )
175* ..
176* .. External Subroutines ..
177 EXTERNAL blacs_gridinfo, chk1mat, pchk1mat, pslarfb,
178 $ pslarft, pslaset, psorg2r, pb_topget,
179 $ pb_topset, pxerbla
180* ..
181* .. External Functions ..
182 INTEGER ICEIL, INDXG2P, NUMROC
183 EXTERNAL iceil, indxg2p, numroc
184* ..
185* .. Intrinsic Functions ..
186 INTRINSIC max, min, mod, real
187* ..
188* .. Executable Statements ..
189*
190* Get grid parameters
191*
192 ictxt = desca( ctxt_ )
193 CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
194*
195* Test the input parameters
196*
197 info = 0
198 IF( nprow.EQ.-1 ) THEN
199 info = -(700+ctxt_)
200 ELSE
201 CALL chk1mat( m, 1, n, 2, ia, ja, desca, 7, info )
202 IF( info.EQ.0 ) THEN
203 iarow = indxg2p( ia, desca( mb_ ), myrow, desca( rsrc_ ),
204 $ nprow )
205 iacol = indxg2p( ja, desca( nb_ ), mycol, desca( csrc_ ),
206 $ npcol )
207 mpa0 = numroc( m+mod( ia-1, desca( mb_ ) ), desca( mb_ ),
208 $ myrow, iarow, nprow )
209 nqa0 = numroc( n+mod( ja-1, desca( nb_ ) ), desca( nb_ ),
210 $ mycol, iacol, npcol )
211 lwmin = desca( nb_ ) * ( mpa0 + nqa0 + desca( nb_ ) )
212*
213 work( 1 ) = real( lwmin )
214 lquery = ( lwork.EQ.-1 )
215 IF( n.GT.m ) THEN
216 info = -2
217 ELSE IF( k.LT.0 .OR. k.GT.n ) THEN
218 info = -3
219 ELSE IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
220 info = -10
221 END IF
222 END IF
223 idum1( 1 ) = k
224 idum2( 1 ) = 3
225 IF( lwork.EQ.-1 ) THEN
226 idum1( 2 ) = -1
227 ELSE
228 idum1( 2 ) = 1
229 END IF
230 idum2( 2 ) = 10
231 CALL pchk1mat( m, 1, n, 2, ia, ja, desca, 7, 2, idum1, idum2,
232 $ info )
233 END IF
234*
235 IF( info.NE.0 ) THEN
236 CALL pxerbla( ictxt, 'PSORGQR', -info )
237 RETURN
238 ELSE IF( lquery ) THEN
239 RETURN
240 END IF
241*
242* Quick return if possible
243*
244 IF( n.LE.0 )
245 $ RETURN
246*
247 ipw = desca( nb_ )*desca( nb_ ) + 1
248 jn = min( iceil( ja, desca( nb_ ) ) * desca( nb_ ), ja+k-1 )
249 jl = max( ( (ja+k-2) / desca( nb_ ) ) * desca( nb_ ) + 1, ja )
250 CALL pb_topget( ictxt, 'Broadcast', 'Rowwise', rowbtop )
251 CALL pb_topget( ictxt, 'Broadcast', 'Columnwise', colbtop )
252 CALL pb_topset( ictxt, 'Broadcast', 'Rowwise', 'D-ring' )
253 CALL pb_topset( ictxt, 'Broadcast', 'Columnwise', ' ' )
254*
255 CALL pslaset( 'All', jl-ja, ja+n-jl, zero, zero, a, ia, jl,
256 $ desca )
257*
258* Use unblocked code for the last or only block.
259*
260 CALL psorg2r( m-jl+ja, ja+n-jl, ja+k-jl, a, ia+jl-ja, jl, desca,
261 $ tau, work, lwork, iinfo )
262*
263* Is there at least one block of columns to loop over ?
264*
265 IF( jl.GT.jn+1 ) THEN
266*
267* Use blocked code
268*
269 DO 10 j = jl-desca( nb_ ), jn+1, -desca( nb_ )
270 jb = min( desca( nb_ ), ja+n-j )
271 i = ia + j - ja
272*
273 IF( j+jb.LE.ja+n-1 ) THEN
274*
275* Form the triangular factor of the block reflector
276* H = H(j) H(j+1) . . . H(j+jb-1)
277*
278 CALL pslarft( 'Forward', 'Columnwise', m-i+ia, jb, a, i,
279 $ j, desca, tau, work, work( ipw ) )
280*
281* Apply H to A(i:ia+m-1,j+jb:ja+n-1) from the left
282*
283 CALL pslarfb( 'Left', 'No transpose', 'Forward',
284 $ 'Columnwise', m-i+ia, n-j-jb+ja, jb, a, i,
285 $ j, desca, work, a, i, j+jb, desca,
286 $ work( ipw ) )
287 END IF
288*
289* Apply H to rows i:ia+m-1 of current block
290*
291 CALL psorg2r( m-i+ia, jb, jb, a, i, j, desca, tau, work,
292 $ lwork, iinfo )
293*
294* Set rows ia:i-1 of current block to zero
295*
296 CALL pslaset( 'All', i-ia, jb, zero, zero, a, ia, j, desca )
297*
298 10 CONTINUE
299*
300 END IF
301*
302* Handle first block separately
303*
304 IF( jl.GT.ja ) THEN
305*
306 jb = jn - ja + 1
307*
308* Form the triangular factor of the block reflector
309* H = H(j) H(j+1) . . . H(j+jb-1)
310*
311 CALL pslarft( 'Forward', 'Columnwise', m, jb, a, ia, ja, desca,
312 $ tau, work, work( ipw ) )
313*
314* Apply H to A(ia:ia+m-1,ja+jb:ja+n-1) from the left
315*
316 CALL pslarfb( 'Left', 'No transpose', 'Forward', 'Columnwise',
317 $ m, n-jb, jb, a, ia, ja, desca, work, a, ia,
318 $ ja+jb, desca, work( ipw ) )
319*
320* Apply H to rows ia:ia+m-1 of current block
321*
322 CALL psorg2r( m, jb, jb, a, ia, ja, desca, tau, work, lwork,
323 $ iinfo )
324*
325 END IF
326*
327 CALL pb_topset( ictxt, 'Broadcast', 'Rowwise', rowbtop )
328 CALL pb_topset( ictxt, 'Broadcast', 'Columnwise', colbtop )
329*
330 work( 1 ) = real( lwmin )
331*
332 RETURN
333*
334* End of PSORGQR
335*
336 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 pchk1mat(ma, mapos0, na, napos0, ia, ja, desca, descapos0, nextra, ex, expos, info)
Definition pchkxmat.f:3
subroutine pslaset(uplo, m, n, alpha, beta, a, ia, ja, desca)
Definition psblastst.f:6863
subroutine pslarfb(side, trans, direct, storev, m, n, k, v, iv, jv, descv, t, c, ic, jc, descc, work)
Definition pslarfb.f:3
subroutine pslarft(direct, storev, n, k, v, iv, jv, descv, tau, t, work)
Definition pslarft.f:3
subroutine psorg2r(m, n, k, a, ia, ja, desca, tau, work, lwork, info)
Definition psorg2r.f:3
subroutine psorgqr(m, n, k, a, ia, ja, desca, tau, work, lwork, info)
Definition psorgqr.f:3
subroutine pxerbla(ictxt, srname, info)
Definition pxerbla.f:2