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
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
|
*
*
SUBROUTINE PCGSEPCHK( IBTYPE, MS, NV, A, IA, JA, DESCA, B, IB, JB,
$ DESCB, THRESH, Q, IQ, JQ, DESCQ, C, IC, JC,
$ DESCC, W, WORK, LWORK, TSTNRM, RESULT )
*
* -- ScaLAPACK routine (version 1.7) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* April 15, 1997
*
* .. Scalar Arguments ..
INTEGER IA, IB, IBTYPE, IC, IQ, JA, JB, JC, JQ, LWORK,
$ MS, NV, RESULT
REAL THRESH, TSTNRM
* ..
* .. Array Arguments ..
*
INTEGER DESCA( * ), DESCB( * ), DESCC( * ), DESCQ( * )
REAL W( * ), WORK( * )
COMPLEX A( * ), B( * ), C( * ), Q( * )
* ..
*
*
* Purpose
* =======
*
* PCGSEPCHK checks a decomposition of the form
*
* A Q = B Q D or
* A B Q = Q D or
* B A Q = Q D
*
* where A is a symmetric matrix, B is
* symmetric positive definite, Q is orthogonal, and D is diagonal.
*
* One of the following test ratios is computed:
*
* IBTYPE = 1: TSTNRM = | A Q - B Q D | / ( |A| |Q| n ulp )
*
* IBTYPE = 2: TSTNRM = | A B Q - Q D | / ( |A| |Q| n ulp )
*
* IBTYPE = 3: TSTNRM = | B A Q - Q D | / ( |A| |Q| n ulp )
*
*
* 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
* =========
*
* MP = number of local rows in A, B and Q
* MQ = number of local columns in A
* NQ = number of local columns in B and Q
*
* IBTYPE (input) INTEGER
* The form of the symmetric generalized eigenproblem.
* = 1: A*Q = (lambda)*B*Q
* = 2: A*B*Q = (lambda)*Q
* = 3: B*A*Q = (lambda)*Q
*
* MS (global input) INTEGER
* Matrix size.
* The number of global rows in A, B, C and Q
* Also, the number of columns in A
*
* NV (global input) INTEGER
* Number of eigenvectors
* The number of global columns in C and Q.
*
* A (local input) REAL pointer to an
* array in local memory of dimension (LLD_A, LOCc(JA+N-1)).
* This array contains the local pieces of the M-by-N
* distributed test matrix A
*
* IA (global input) INTEGER
* A's global row index, which points to the beginning of the
* submatrix which is to be operated on.
*
* JA (global input) INTEGER
* A's global column index, which points to the beginning of
* the submatrix which is to be operated on.
*
* DESCA (global and local input) INTEGER array of dimension 8
* The array descriptor for the distributed matrix A.
*
* B (local input) REAL pointer to an
* array in local memory of dimension (LLD_B, LOCc(JB+N-1)).
* This array contains the local pieces of the M-by-N
* distributed test matrix B
*
* IB (global input) INTEGER
* B's global row index, which points to the beginning of the
* submatrix which is to be operated on.
*
* JB (global input) INTEGER
* B's global column index, which points to the beginning of
* the submatrix which is to be operated on.
*
* DESCB (global and local input) INTEGER array of dimension 8
* The array descriptor for the distributed matrix B.
*
* THRESH (input) REAL
* A test will count as "failed" if the "error", computed as
* described below, exceeds THRESH. Note that the error
* is scaled to be O(1), so THRESH should be a reasonably
* small multiple of 1, e.g., 10 or 100. In particular,
* it should not depend on the precision (single vs. double)
* or the size of the matrix. It must be at least zero.
*
* Q (local input) REAL array
* global dimension (MS, NV),
* local dimension (DESCA( DLEN_ ), NQ)
*
* Contains the eigenvectors as computed by PSSYEVX
*
* IQ (global input) INTEGER
* Q's global row index, which points to the beginning of the
* submatrix which is to be operated on.
*
* JQ (global input) INTEGER
* Q's global column index, which points to the beginning of
* the submatrix which is to be operated on.
*
* DESCQ (global and local input) INTEGER array of dimension 8
* The array descriptor for the distributed matrix Q.
*
* C (local workspace) REAL array,
* global dimension (MS, NV),
* local dimension (DESCA( DLEN_ ), MQ)
*
* Accumulator for computing AQ -QL
*
* IC (global input) INTEGER
* C's global row index, which points to the beginning of the
* submatrix which is to be operated on.
*
* JC (global input) INTEGER
* C's global column index, which points to the beginning of
* the submatrix which is to be operated on.
*
* DESCC (global and local input) INTEGER array of dimension 8
* The array descriptor for the distributed matrix C.
*
* W (global input) REAL array, dimension (NV)
*
* Contains the computed eigenvalues
*
* WORK (local workspace) REAL array,
* dimension (LWORK)
*
* LWORK (local input) INTEGER
* The length of the array WORK.
* LWORK >= NUMROC( NV, DESCA( NB_ ), MYCOL, 0, NPCOL )
*
* TSTNRM (global output) REAL
*
* RESULT (global output) INTEGER
* 0 if the test passes
* 1 if the test fails
*
* .. Local Scalars ..
*
INTEGER I, INFO, MYCOL, MYROW, NPCOL, NPROW, NQ
REAL ANORM, ULP
* ..
* .. Parameters ..
INTEGER BLOCK_CYCLIC_2D, DLEN_, DTYPE_, CTXT_, M_, N_,
$ MB_, NB_, RSRC_, CSRC_, LLD_
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 )
COMPLEX CONE, CNEGONE, CZERO
PARAMETER ( CONE = 1.0E+0, CNEGONE = -1.0E+0,
$ CZERO = 0.0E+0 )
* ..
* .. External Functions ..
INTEGER NUMROC
REAL PCLANGE, SLAMCH
EXTERNAL NUMROC, PCLANGE, SLAMCH
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, CHK1MAT, PCGEMM, PCSSCAL,
$ PXERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
* This is just to keep ftnchek happy
IF( BLOCK_CYCLIC_2D*CSRC_*CTXT_*DLEN_*DTYPE_*LLD_*MB_*M_*NB_*N_*
$ RSRC_.LT.0 )RETURN
*
RESULT = 0
*
CALL BLACS_GRIDINFO( DESCA( CTXT_ ), NPROW, NPCOL, MYROW, MYCOL )
*
INFO = 0
CALL CHK1MAT( MS, 1, MS, 2, IA, JA, DESCA, 7, INFO )
CALL CHK1MAT( MS, 1, MS, 2, IB, JB, DESCB, 11, INFO )
CALL CHK1MAT( MS, 1, NV, 2, IQ, JQ, DESCQ, 16, INFO )
CALL CHK1MAT( MS, 1, NV, 2, IB, JB, DESCB, 20, INFO )
*
IF( INFO.EQ.0 ) THEN
*
NQ = NUMROC( NV, DESCA( NB_ ), MYCOL, 0, NPCOL )
*
IF( IQ.NE.1 ) THEN
INFO = -14
ELSE IF( JQ.NE.1 ) THEN
INFO = -15
ELSE IF( IA.NE.1 ) THEN
INFO = -5
ELSE IF( JA.NE.1 ) THEN
INFO = -6
ELSE IF( IB.NE.1 ) THEN
INFO = -9
ELSE IF( JB.NE.1 ) THEN
INFO = -10
ELSE IF( LWORK.LT.NQ ) THEN
INFO = -23
END IF
END IF
*
IF( INFO.NE.0 ) THEN
CALL PXERBLA( DESCA( CTXT_ ), 'PCGSEPCHK', -INFO )
RETURN
END IF
*
RESULT = 0
ULP = SLAMCH( 'Epsilon' )
*
* Compute product of Max-norms of A and Q.
*
ANORM = PCLANGE( 'M', MS, MS, A, IA, JA, DESCA, WORK )*
$ PCLANGE( 'M', MS, NV, Q, IQ, JQ, DESCQ, WORK )
IF( ANORM.EQ.ZERO )
$ ANORM = ONE
*
IF( IBTYPE.EQ.1 ) THEN
*
* Norm of AQ - BQD
*
* C = AQ
*
CALL PCGEMM( 'N', 'N', MS, NV, MS, CONE, A, IA, JA, DESCA, Q,
$ IQ, JQ, DESCQ, CZERO, C, IC, JC, DESCC )
*
* Q = QD
*
DO 10 I = 1, NV
CALL PCSSCAL( MS, W( I ), Q, IQ, JQ+I-1, DESCQ, 1 )
10 CONTINUE
*
* C = C - BQ (i.e. AQ-BQD)
*
CALL PCGEMM( 'N', 'N', MS, NV, MS, CONE, B, IB, JB, DESCB, Q,
$ IQ, JQ, DESCQ, CNEGONE, C, IC, JC, DESCC )
*
TSTNRM = ( PCLANGE( 'M', MS, NV, C, IC, JC, DESCC, WORK ) /
$ ANORM ) / ( MAX( MS, 1 )*ULP )
*
*
ELSE IF( IBTYPE.EQ.2 ) THEN
*
* Norm of ABQ - QD
*
*
* C = BQ
*
CALL PCGEMM( 'N', 'N', MS, NV, MS, CONE, B, IB, JB, DESCB, Q,
$ IQ, JQ, DESCQ, CZERO, C, IC, JC, DESCC )
*
* Q = QD
*
DO 20 I = 1, NV
CALL PCSSCAL( MS, W( I ), Q, IQ, JQ+I-1, DESCQ, 1 )
20 CONTINUE
*
* Q = AC - Q
*
CALL PCGEMM( 'N', 'N', MS, NV, MS, CONE, A, IA, JA, DESCA, C,
$ IC, JC, DESCC, CNEGONE, Q, IQ, JQ, DESCQ )
*
TSTNRM = ( PCLANGE( 'M', MS, NV, Q, IQ, JQ, DESCQ, WORK ) /
$ ANORM ) / ( MAX( MS, 1 )*ULP )
*
ELSE IF( IBTYPE.EQ.3 ) THEN
*
* Norm of BAQ - QD
*
*
* C = AQ
*
CALL PCGEMM( 'N', 'N', MS, NV, MS, CONE, A, IA, JA, DESCA, Q,
$ IQ, JQ, DESCQ, CZERO, C, IC, JC, DESCC )
*
* Q = QD
*
DO 30 I = 1, NV
CALL PCSSCAL( MS, W( I ), Q, IQ, JQ+I-1, DESCQ, 1 )
30 CONTINUE
*
* Q = BC - Q
*
CALL PCGEMM( 'N', 'N', MS, NV, MS, CONE, B, IB, JB, DESCB, C,
$ IC, JC, DESCC, CNEGONE, Q, IQ, JQ, DESCQ )
*
TSTNRM = ( PCLANGE( 'M', MS, NV, Q, IQ, JQ, DESCQ, WORK ) /
$ ANORM ) / ( MAX( MS, 1 )*ULP )
*
END IF
*
IF( TSTNRM.GT.THRESH .OR. ( TSTNRM-TSTNRM.NE.0.0E0 ) ) THEN
RESULT = 1
END IF
RETURN
*
* End of PCGSEPCHK
*
END
|
