1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
|
SUBROUTINE PSORG2R( M, N, K, A, IA, JA, DESCA, TAU, WORK, LWORK,
$ INFO )
*
* -- ScaLAPACK routine (version 1.7) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* May 25, 2001
*
* .. Scalar Arguments ..
INTEGER IA, INFO, JA, K, LWORK, M, N
* ..
* .. Array Arguments ..
INTEGER DESCA( * )
REAL A( * ), TAU( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* PSORG2R generates an M-by-N real distributed matrix Q denoting
* A(IA:IA+M-1,JA:JA+N-1) with orthonormal columns, which is defined as
* the first N columns of a product of K elementary reflectors of order
* M
*
* Q = H(1) H(2) . . . H(k)
*
* as returned by PSGEQRF.
*
* Notes
* =====
*
* Each global data object is described by an associated description
* vector. This vector stores the information required to establish
* the mapping between an object element and its corresponding process
* and memory location.
*
* Let A be a generic term for any 2D block cyclicly distributed array.
* Such a global array has an associated description vector DESCA.
* In the following comments, the character _ should be read as
* "of the global array".
*
* NOTATION STORED IN EXPLANATION
* --------------- -------------- --------------------------------------
* DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
* DTYPE_A = 1.
* CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
* the BLACS process grid A is distribu-
* ted over. The context itself is glo-
* bal, but the handle (the integer
* value) may vary.
* M_A (global) DESCA( M_ ) The number of rows in the global
* array A.
* N_A (global) DESCA( N_ ) The number of columns in the global
* array A.
* MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
* the rows of the array.
* NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
* the columns of the array.
* RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
* row of the array A is distributed.
* CSRC_A (global) DESCA( CSRC_ ) The process column over which the
* first column of the array A is
* distributed.
* LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
* array. LLD_A >= MAX(1,LOCr(M_A)).
*
* Let K be the number of rows or columns of a distributed matrix,
* and assume that its process grid has dimension p x q.
* LOCr( K ) denotes the number of elements of K that a process
* would receive if K were distributed over the p processes of its
* process column.
* Similarly, LOCc( K ) denotes the number of elements of K that a
* process would receive if K were distributed over the q processes of
* its process row.
* The values of LOCr() and LOCc() may be determined via a call to the
* ScaLAPACK tool function, NUMROC:
* LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
* LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
* An upper bound for these quantities may be computed by:
* LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
* LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
*
* Arguments
* =========
*
* M (global input) INTEGER
* The number of rows to be operated on i.e the number of rows
* of the distributed submatrix Q. M >= 0.
*
* N (global input) INTEGER
* The number of columns to be operated on i.e the number of
* columns of the distributed submatrix Q. M >= N >= 0.
*
* K (global input) INTEGER
* The number of elementary reflectors whose product defines the
* matrix Q. N >= K >= 0.
*
* A (local input/local output) REAL pointer into the
* local memory to an array of dimension (LLD_A,LOCc(JA+N-1)).
* On entry, the j-th column must contain the vector which
* defines the elementary reflector H(j), JA <= j <= JA+K-1, as
* returned by PSGEQRF in the K columns of its array
* argument A(IA:*,JA:JA+K-1). On exit, this array contains
* the local pieces of the M-by-N distributed matrix Q.
*
* IA (global input) INTEGER
* The row index in the global array A indicating the first
* row of sub( A ).
*
* JA (global input) INTEGER
* The column index in the global array A indicating the
* first column of sub( A ).
*
* DESCA (global and local input) INTEGER array of dimension DLEN_.
* The array descriptor for the distributed matrix A.
*
* TAU (local input) REAL, array, dimension LOCc(JA+K-1).
* This array contains the scalar factors TAU(j) of the
* elementary reflectors H(j) as returned by PSGEQRF.
* TAU is tied to the distributed matrix A.
*
* WORK (local workspace/local output) REAL array,
* dimension (LWORK)
* On exit, WORK(1) returns the minimal and optimal LWORK.
*
* LWORK (local or global input) INTEGER
* The dimension of the array WORK.
* LWORK is local input and must be at least
* LWORK >= MpA0 + MAX( 1, NqA0 ), where
*
* IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ),
* IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ),
* IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ),
* MpA0 = NUMROC( M+IROFFA, MB_A, MYROW, IAROW, NPROW ),
* NqA0 = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ),
*
* INDXG2P and NUMROC are ScaLAPACK tool functions;
* MYROW, MYCOL, NPROW and NPCOL can be determined by calling
* the subroutine BLACS_GRIDINFO.
*
* If LWORK = -1, then LWORK is global input and a workspace
* query is assumed; the routine only calculates the minimum
* and optimal size for all work arrays. Each of these
* values is returned in the first entry of the corresponding
* work array, and no error message is issued by PXERBLA.
*
*
* INFO (local output) INTEGER
* = 0: successful exit
* < 0: If the i-th argument is an array and the j-entry had
* an illegal value, then INFO = -(i*100+j), if the i-th
* argument is a scalar and had an illegal value, then
* INFO = -i.
*
* =====================================================================
*
* .. Parameters ..
INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
$ LLD_, MB_, M_, NB_, N_, RSRC_
PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1,
$ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6,
$ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 )
REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL LQUERY
CHARACTER COLBTOP, ROWBTOP
INTEGER IACOL, IAROW, ICTXT, J, JJ, KQ, LWMIN, MPA0,
$ MYCOL, MYROW, NPCOL, NPROW, NQA0
REAL TAUJ
* ..
* .. External Subroutines ..
EXTERNAL BLACS_ABORT, BLACS_GRIDINFO, CHK1MAT, PSELSET,
$ PSLARF, PSLASET, PSSCAL, PB_TOPGET,
$ PB_TOPSET, PXERBLA
* ..
* .. External Functions ..
INTEGER INDXG2L, INDXG2P, NUMROC
EXTERNAL INDXG2L, INDXG2P, NUMROC
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN, MOD, REAL
* ..
* .. Executable Statements ..
*
* Get grid parameters
*
ICTXT = DESCA( CTXT_ )
CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
*
* Test the input parameters
*
INFO = 0
IF( NPROW.EQ.-1 ) THEN
INFO = -(700+CTXT_)
ELSE
CALL CHK1MAT( M, 1, N, 2, IA, JA, DESCA, 7, INFO )
IF( INFO.EQ.0 ) THEN
IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ),
$ NPROW )
IACOL = INDXG2P( JA, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ),
$ NPCOL )
MPA0 = NUMROC( M+MOD( IA-1, DESCA( MB_ ) ), DESCA( MB_ ),
$ MYROW, IAROW, NPROW )
NQA0 = NUMROC( N+MOD( JA-1, DESCA( NB_ ) ), DESCA( NB_ ),
$ MYCOL, IACOL, NPCOL )
LWMIN = MPA0 + MAX( 1, NQA0 )
*
WORK( 1 ) = REAL( LWMIN )
LQUERY = ( LWORK.EQ.-1 )
IF( N.GT.M ) THEN
INFO = -2
ELSE IF( K.LT.0 .OR. K.GT.N ) THEN
INFO = -3
ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
INFO = -10
END IF
END IF
END IF
IF( INFO.NE.0 ) THEN
CALL PXERBLA( ICTXT, 'PSORG2R', -INFO )
CALL BLACS_ABORT( ICTXT, 1 )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
* Quick return if possible
*
IF( N.LE.0 )
$ RETURN
*
CALL PB_TOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP )
CALL PB_TOPGET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP )
CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', 'D-ring' )
CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', ' ' )
*
* Initialise columns ja+k:ja+n-1 to columns of the unit matrix
*
CALL PSLASET( 'All', K, N-K, ZERO, ZERO, A, IA, JA+K, DESCA )
CALL PSLASET( 'All', M-K, N-K, ZERO, ONE, A, IA+K, JA+K, DESCA )
*
TAUJ = ZERO
KQ = MAX( 1, NUMROC( JA+K-1, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ),
$ NPCOL ) )
DO 10 J = JA+K-1, JA, -1
*
* Apply H(j) to A(ia+j-ja:ia+m-1,j:ja+n-1) from the left
*
IF( J.LT.JA+N-1 ) THEN
CALL PSELSET( A, IA+J-JA, J, DESCA, ONE )
CALL PSLARF( 'Left', M-J+JA, JA+N-J-1, A, IA+J-JA, J, DESCA,
$ 1, TAU, A, IA+J-JA, J+1, DESCA, WORK )
END IF
*
JJ = INDXG2L( J, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ), NPCOL )
IACOL = INDXG2P( J, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ),
$ NPCOL )
IF( MYCOL.EQ.IACOL )
$ TAUJ = TAU( MIN( JJ, KQ ) )
IF( J-JA.LT.M-1 )
$ CALL PSSCAL( M-J+JA-1, -TAUJ, A, IA+J-JA+1, J, DESCA, 1 )
CALL PSELSET( A, IA+J-JA, J, DESCA, ONE-TAUJ )
*
* Set A(ia:ia+j-ja-1,j) to zero
*
CALL PSLASET( 'All', J-JA, 1, ZERO, ZERO, A, IA, J, DESCA )
*
10 CONTINUE
*
CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP )
CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP )
*
WORK( 1 ) = REAL( LWMIN )
*
RETURN
*
* End of PSORG2R
*
END
|
