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
|
SUBROUTINE PZQRT13( SCALE, M, N, A, IA, JA, DESCA, NORMA, ISEED,
$ WORK )
*
* -- ScaLAPACK routine (version 1.7) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* May 1, 1997
*
* .. Scalar Arguments ..
INTEGER IA, ISEED, JA, M, N, SCALE
DOUBLE PRECISION NORMA
* ..
* .. Array Arguments ..
INTEGER DESCA( * )
DOUBLE PRECISION WORK( * )
COMPLEX*16 A( * )
* ..
*
* Purpose
* =======
*
* PZQRT13 generates a full-rank matrix that may be scaled to have
* large or small norm.
*
* 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
* =========
*
* SCALE (global input) INTEGER
* SCALE = 1: normally scaled matrix
* SCALE = 2: matrix scaled up
* SCALE = 3: matrix scaled down
*
* M (global input) INTEGER
* The number of rows to be operated on, i.e. the number of rows
* of the distributed submatrix sub( A ). M >= 0.
*
* N (global input) INTEGER
* The number of columns to be operated on, i.e. the number of
* columns of the distributed submatrix sub( A ). N >= 0.
*
* A (local output) COMPLEX*16 pointer into the local memory
* to an array of dimension (LLD_A,LOCc(JA+N-1)). This array
* contains the local pieces of the distributed matrix sub( A ).
*
* 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.
*
* NORMA (global output) DOUBLE PRECISION
* The one-norm of A.
*
* ISEED (global input/global output) INTEGER
* Seed for random number generator.
*
* WORK (local workspace) DOUBLE PRECISION array, dimension (LWORK)
* LWORK >= Nq0, where
*
* ICOFFA = MOD( JA-1, NB_A ),
* IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ), and
* Nq0 = 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.
*
* =====================================================================
*
* .. 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 )
DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D0 )
* ..
* .. Local Scalars ..
INTEGER I, IACOL, IAROW, ICOFFA, ICTXT, IIA, INFO,
$ IROFFA, J, JJA, MP, MYCOL, MYROW, NPCOL,
$ NPROW, NQ
DOUBLE PRECISION ASUM, BIGNUM, SMLNUM
COMPLEX*16 AJJ
* ..
* .. External Functions ..
INTEGER NUMROC
DOUBLE PRECISION PDLAMCH, PZLANGE
EXTERNAL NUMROC, PDLAMCH, PDLANGE
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, INFOG2L, PDLABAD,
$ PDZASUM, PZLASCL, PZMATGEN,
$ PZELGET, PZELSET
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, DCMPLX, MOD, SIGN
* ..
* .. Executable Statements ..
*
ICTXT = DESCA( CTXT_ )
CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
*
IF( M.LE.0 .OR. N.LE.0 )
$ RETURN
*
* generate the matrix
*
IROFFA = MOD( IA-1, DESCA( MB_ ) )
ICOFFA = MOD( JA-1, DESCA( NB_ ) )
CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA,
$ JJA, IAROW, IACOL )
MP = NUMROC( M+IROFFA, DESCA( MB_ ), MYROW, IAROW, NPROW )
NQ = NUMROC( N+ICOFFA, DESCA( NB_ ), MYCOL, IACOL, NPCOL )
IF( MYROW.EQ.IAROW )
$ MP = MP - IROFFA
IF( MYCOL.EQ.IACOL )
$ NQ = NQ - ICOFFA
*
CALL PZMATGEN( ICTXT, 'N', 'N', DESCA( M_ ), DESCA( N_ ),
$ DESCA( MB_ ), DESCA( NB_ ), A, DESCA( LLD_ ),
$ DESCA( RSRC_ ), DESCA( CSRC_ ), ISEED, IIA-1, MP,
$ JJA-1, NQ, MYROW, MYCOL, NPROW, NPCOL )
*
DO 10 J = JA, JA+N-1
I = IA + J - JA
IF( I.LE.IA+M-1 ) THEN
CALL PDZASUM( M, ASUM, A, IA, J, DESCA, 1 )
CALL PZELGET( 'Column', ' ', AJJ, A, I, J, DESCA )
AJJ = AJJ + DCMPLX( SIGN( ASUM, DBLE( AJJ ) ) )
CALL PZELSET( A, I, J, DESCA, AJJ )
END IF
10 CONTINUE
*
* scaled versions
*
IF( SCALE.NE.1 ) THEN
*
NORMA = PZLANGE( 'M', M, N, A, IA, JA, DESCA, WORK )
SMLNUM = PDLAMCH( ICTXT, 'Safe minimum' )
BIGNUM = ONE / SMLNUM
CALL PDLABAD( ICTXT, SMLNUM, BIGNUM )
SMLNUM = SMLNUM / PDLAMCH( ICTXT, 'Epsilon' )
BIGNUM = ONE / SMLNUM
*
IF( SCALE.EQ.2 ) THEN
*
* matrix scaled up
*
CALL PZLASCL( 'General', NORMA, BIGNUM, M, N, A, IA,
$ JA, DESCA, INFO )
*
ELSE IF( SCALE.EQ.3 ) THEN
*
* matrix scaled down
*
CALL PZLASCL( 'General', NORMA, SMLNUM, M, N, A, IA,
$ JA, DESCA, INFO )
*
END IF
*
END IF
*
NORMA = PZLANGE( 'One-norm', M, N, A, IA, JA, DESCA, WORK )
*
RETURN
*
* End of PZQRT13
*
END
|
