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
|
SUBROUTINE PDGETF2( M, N, A, IA, JA, DESCA, IPIV, INFO )
*
* -- 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, INFO, JA, M, N
* ..
* .. Array Arguments ..
INTEGER DESCA( * ), IPIV( * )
DOUBLE PRECISION A( * )
* ..
*
* Purpose
* =======
*
* PDGETF2 computes an LU factorization of a general M-by-N
* distributed matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) using
* partial pivoting with row interchanges.
*
* The factorization has the form sub( A ) = P * L * U, where P is a
* permutation matrix, L is lower triangular with unit diagonal
* elements (lower trapezoidal if m > n), and U is upper triangular
* (upper trapezoidal if m < n).
*
* This is the right-looking Parallel Level 2 BLAS version of the
* algorithm.
*
* 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
*
* This routine requires N <= NB_A-MOD(JA-1, NB_A) and square block
* decomposition ( MB_A = 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 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 ).
* NB_A-MOD(JA-1, NB_A) >= N >= 0.
*
* A (local input/local output) DOUBLE PRECISION pointer into the
* local memory to an array of dimension (LLD_A, LOCc(JA+N-1)).
* On entry, this array contains the local pieces of the M-by-N
* distributed matrix sub( A ). On exit, this array contains
* the local pieces of the factors L and U from the factoriza-
* tion sub( A ) = P*L*U; the unit diagonal elements of L are
* not stored.
*
* 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.
*
* IPIV (local output) INTEGER array, dimension ( LOCr(M_A)+MB_A )
* This array contains the pivoting information.
* IPIV(i) -> The global row local row i was swapped with.
* This array is tied to the distributed matrix A.
*
* 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.
* > 0: If INFO = K, U(IA+K-1,JA+K-1) is exactly zero.
* The factorization has been completed, but the factor U
* is exactly singular, and division by zero will occur if
* it is used to solve a system of equations.
*
* =====================================================================
*
* .. 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, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
CHARACTER ROWBTOP
INTEGER I, IACOL, IAROW, ICOFF, ICTXT, IIA, IROFF, J,
$ JJA, MN, MYCOL, MYROW, NPCOL, NPROW
DOUBLE PRECISION GMAX
* ..
* .. External Subroutines ..
EXTERNAL BLACS_ABORT, BLACS_GRIDINFO, CHK1MAT, IGEBR2D,
$ IGEBS2D, INFOG2L, PDAMAX, PDGER,
$ PDSCAL, PDSWAP, PB_TOPGET, PXERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MIN, MOD
* ..
* .. 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 = -(600+CTXT_)
ELSE
CALL CHK1MAT( M, 1, N, 2, IA, JA, DESCA, 6, INFO )
IF( INFO.EQ.0 ) THEN
IROFF = MOD( IA-1, DESCA( MB_ ) )
ICOFF = MOD( JA-1, DESCA( NB_ ) )
IF( N+ICOFF.GT.DESCA( NB_ ) ) THEN
INFO = -2
ELSE IF( IROFF.NE.0 ) THEN
INFO = -4
ELSE IF( ICOFF.NE.0 ) THEN
INFO = -5
ELSE IF( DESCA( MB_ ).NE.DESCA( NB_ ) ) THEN
INFO = -(600+NB_)
END IF
END IF
END IF
*
IF( INFO.NE.0 ) THEN
CALL PXERBLA( ICTXT, 'PDGETF2', -INFO )
CALL BLACS_ABORT( ICTXT, 1 )
RETURN
END IF
*
* Quick return if possible
*
IF( M.EQ.0 .OR. N.EQ.0 )
$ RETURN
*
MN = MIN( M, N )
CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA, JJA,
$ IAROW, IACOL )
CALL PB_TOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP )
*
IF( MYCOL.EQ.IACOL ) THEN
DO 10 J = JA, JA+MN-1
I = IA + J - JA
*
* Find pivot and test for singularity.
*
CALL PDAMAX( M-J+JA, GMAX, IPIV( IIA+J-JA ), A, I, J,
$ DESCA, 1 )
IF( GMAX.NE.ZERO ) THEN
*
* Apply the row interchanges to columns JA:JA+N-1
*
CALL PDSWAP( N, A, I, JA, DESCA, DESCA( M_ ), A,
$ IPIV( IIA+J-JA ), JA, DESCA, DESCA( M_ ) )
*
* Compute elements I+1:IA+M-1 of J-th column.
*
IF( J-JA+1.LT.M )
$ CALL PDSCAL( M-J+JA-1, ONE / GMAX, A, I+1, J,
$ DESCA, 1 )
ELSE IF( INFO.EQ.0 ) THEN
INFO = J - JA + 1
END IF
*
* Update trailing submatrix
*
IF( J-JA+1.LT.MN ) THEN
CALL PDGER( M-J+JA-1, N-J+JA-1, -ONE, A, I+1, J, DESCA,
$ 1, A, I, J+1, DESCA, DESCA( M_ ), A, I+1,
$ J+1, DESCA )
END IF
10 CONTINUE
*
CALL IGEBS2D( ICTXT, 'Rowwise', ROWBTOP, MN, 1, IPIV( IIA ),
$ MN )
*
ELSE
*
CALL IGEBR2D( ICTXT, 'Rowwise', ROWBTOP, MN, 1, IPIV( IIA ),
$ MN, MYROW, IACOL )
*
END IF
*
RETURN
*
* End of PDGETF2
*
END
|
