-
Notifications
You must be signed in to change notification settings - Fork 3
/
Copy pathsparse_matrix_operations.f90
671 lines (523 loc) · 16.4 KB
/
sparse_matrix_operations.f90
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
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
MODULE sparse_matrix_operations
!
! Author: Jacopo Canton
! E-mail: [email protected]
! Last revision: 25/8/2013
!
USE global_variables ! MPI variables
IMPLICIT NONE
CONTAINS
!------------------------------------------------------------------------------
! subroutines for real matrices
!------------------------------------------------------------------------------
!
!
SUBROUTINE dAlinB_s (alpha, a, beta, b, c)
!
!-----------------------------------------------------------------------
! C = alpha A + beta B
!-----------------------------------------------------------------------
! linearly combine two matrices
! Matrices are stored in compressed sparse row storage.
! The three matrices need to have the same sparsity pattern
!
! Author: Jacopo Canton
! E-mail: [email protected]
! Last revision: 25/8/2013
!
! on entry:
!----------
! a, b = input real matrices in compressed sparse row format
!
! alpha,
! beta = real coefficients of the linear combination
!
!
! on return:
!-----------
! c = real matrix, containing the sum C = alpha A + beta B
!
!-----------------------------------------------------------------------
IMPLICIT NONE
! input variables
REAL(KIND=8), INTENT(IN) :: alpha, beta
REAL(KIND=8), DIMENSION(:), INTENT(IN) :: a, b
! output variables
REAL(KIND=8), DIMENSION(:) :: c
! local variables
INTEGER :: i
!$OMP PARALLEL DO
DO i = 1, SIZE(a)
c(i) = alpha*a(i) + beta*b(i)
END DO
!$OMP END PARALLEL DO
END SUBROUTINE dAlinB_s
!------------------------------------------------------------------------------
SUBROUTINE dAtimx (y, a, ja, ia, x)
!
!-----------------------------------------------------------------------
! A times a vector
!-----------------------------------------------------------------------
! multiplies a matrix by a vector using the dot product form
! Matrix A is stored in compressed sparse row storage.
!
! Author: Jacopo Canton
! E-mail: [email protected]
! Last revision: 25/8/2013
!
! on entry:
!----------
! x = real array of length equal to the column dimension of
! the A matrix.
! a, ja,
! ia = input matrix in compressed sparse row format.
!
! on return:
!-----------
! y = real array, containing the product y = A*x
!
!-----------------------------------------------------------------------
IMPLICIT NONE
! input variables
REAL(KIND=8), DIMENSION(:), INTENT(IN) :: a
INTEGER, DIMENSION(:), INTENT(IN) :: ja, ia
REAL(KIND=8), DIMENSION(:), INTENT(IN) :: x
! output variables
REAL(KIND=8), DIMENSION(:) :: y
! local variables
REAL(KIND=8) :: yi
INTEGER :: number_of_rows, i, p
number_of_rows = SIZE(ia)-1
! check dimension consistency
! A - x
IF ( SIZE(x) /= number_of_rows ) THEN
WRITE(*,*) '--> dAtimx Error: wrong A - x size'
WRITE(*,*) ' SIZE(x) = ', SIZE(x), ' SIZE(A,1) = ', number_of_rows
WRITE(*,*) ' STOP.'
CALL MPI_ABORT(MPI_COMM_WORLD, mpiErrC, mpiIerr)
END IF
! A - y
IF ( SIZE(y) /= number_of_rows ) THEN
WRITE(*,*) '--> dAtimx Error: wrong A - y size'
WRITE(*,*) ' SIZE(y) = ', SIZE(y), ' SIZE(A,1) = ', number_of_rows
WRITE(*,*) ' STOP.'
CALL MPI_ABORT(MPI_COMM_WORLD, mpiErrC, mpiIerr)
END IF
! not necessary to check x-y consistency because A has to be square
! compute y <-- A*x
!$OMP PARALLEL DO
DO i = 1, number_of_rows
! compute the inner product of row i with vector x
yi = 0d0
DO p = ia(i), ia(i+1)-1
yi = yi + a(p)*x(ja(p))
END DO
! store result in y(i)
y(i) = yi
END DO
!$OMP END PARALLEL DO
END SUBROUTINE dAtimx
!------------------------------------------------------------------------------
SUBROUTINE dAtimx_T (y, a, ja, ia, x)
!
!-----------------------------------------------------------------------
! transpose(A) times a vector
!-----------------------------------------------------------------------
! multiplies the transpose of a matrix by a vector using the dot product form
! Matrix A is stored in compressed sparse row storage.
!
! Author: Jacopo Canton
! E-mail: [email protected]
! Last revision: 25/8/2013
!
! on entry:
!----------
! x = real array of length equal to the column dimension of
! the A matrix.
! a, ja,
! ia = input matrix in compressed sparse row format.
!
! on return:
!-----------
! y = real array, containing the product y = A'*x
!
!-----------------------------------------------------------------------
IMPLICIT NONE
! input variables
REAL(KIND=8), DIMENSION(:), INTENT(IN) :: a
INTEGER, DIMENSION(:), INTENT(IN) :: ja, ia
REAL(KIND=8), DIMENSION(:), INTENT(IN) :: x
! output variables
REAL(KIND=8), DIMENSION(:) :: y
! local variables
INTEGER :: number_of_rows, i, p
number_of_rows = SIZE(ia)-1
! check dimension consistency
! A - x
IF ( SIZE(x) /= number_of_rows ) THEN
WRITE(*,*) '--> dAtimx_T Error: wrong A - x size'
WRITE(*,*) ' SIZE(x) = ', SIZE(x), ' SIZE(A,1) = ', number_of_rows
WRITE(*,*) ' STOP.'
CALL MPI_ABORT(MPI_COMM_WORLD, mpiErrC, mpiIerr)
END IF
! A - y
IF ( SIZE(y) /= number_of_rows ) THEN
WRITE(*,*) '--> dAtimx_T Error: wrong A - y size'
WRITE(*,*) ' SIZE(y) = ', SIZE(y), ' SIZE(A,1) = ', number_of_rows
WRITE(*,*) ' STOP.'
CALL MPI_ABORT(MPI_COMM_WORLD, mpiErrC, mpiIerr)
END IF
! not necessary to check x-y consistency because A has to be square
! compute y <-- A'*x
y = 0
! $OMP PARALLEL DO & ! not working yet with big matrices,
! $OMP PRIVATE(p) & ! don't know why
! $OMP REDUCTION (+: y)
DO i = 1, number_of_rows
! compute the inner product of row i with vector x
DO p = ia(i), ia(i+1)-1
y(ja(p)) = y(ja(p)) + a(p)*x(i)
END DO
END DO
! $OMP END PARALLEL DO
END SUBROUTINE dAtimx_T
!------------------------------------------------------------------------------
SUBROUTINE dEssM (a, ja, ia, n, b, jb, ib, i_mumpsb)
!
!-----------------------------------------------------------------------
! Extract square sub-Matrix nxn
!-----------------------------------------------------------------------
! Extract a square submatrix B from matrix A
! Matrix A and B are stored in compressed sparse row storage.
!
! Author: Jacopo Canton
! E-mail: [email protected]
! Last revision: 25/8/2013
!
! on entry:
!----------
! a, ja,
! ia = input matrix in compressed sparse row format.
!
! on return:
!-----------
! b, jb,
! ib = output matrix in compressed sparse row format.
!
!-----------------------------------------------------------------------
IMPLICIT NONE
! input variables
REAL(KIND=8), DIMENSION(:), INTENT(IN) :: a
INTEGER, DIMENSION(:), INTENT(IN) :: ja, ia
INTEGER, INTENT(IN) :: n
! output variables
REAL(KIND=8), DIMENSION(:), POINTER :: b
INTEGER, DIMENSION(:), POINTER :: jb, ib
INTEGER, DIMENSION(:), POINTER, OPTIONAL :: i_mumpsb
! local variables
INTEGER :: number_of_rows, i, p, c
number_of_rows = SIZE(ia)-1
! check dimension consistency
!
IF ( n > number_of_rows ) THEN
WRITE(*,*) '--> dEssM Error: n > rows(A)'
WRITE(*,*) ' n = ', n, ' SIZE(A,1) = ', number_of_rows
WRITE(*,*) ' STOP.'
CALL MPI_ABORT(MPI_COMM_WORLD, mpiErrC, mpiIerr)
END IF
! count elements
!
c = 0
DO i = 1, n
DO p = ia(i), ia(i+1) - 1
IF ( ja(p) <= n ) THEN
c = c + 1
ENDIF
ENDDO
ENDDO
ALLOCATE( ib(n+1) )
ALLOCATE( jb(c), b(c) )
! fill matrix
!
c = 0
DO i = 1, n
ib(i) = c + 1
DO p = ia(i), ia(i+1) - 1
IF ( ja(p) <= n ) THEN
c = c + 1
jb(c) = ja(p)
b(c) = a(p)
ENDIF
ENDDO
ENDDO
ib(n+1) = c + 1
IF (PRESENT(i_mumpsb)) THEN
ALLOCATE( i_mumpsb(SIZE(jb)) )
DO i = 1, SIZE(ib) - 1
DO p = ib(i), ib(i+1) - 1
i_mumpsb(p) = i
ENDDO
END DO
ENDIF
END SUBROUTINE dEssM
!
!
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
! subroutines for complex matrices
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
!
!
SUBROUTINE zAlinB_s (alpha, a, beta, b, c)
!
!-----------------------------------------------------------------------
! C = alpha A + beta B
!-----------------------------------------------------------------------
! linearly combine two matrices
! Matrices are stored in compressed sparse row storage.
! The three matrices need to have the same sparsity pattern
!
! Author: Jacopo Canton
! E-mail: [email protected]
! Last revision: 25/8/2013
!
! on entry:
!----------
! a, b = input complex matrices in compressed sparse row format
!
! alpha,
! beta = complex coefficients of the linear combination
!
!
! on return:
!-----------
! c = complex matrix, containing the sum C = alpha A + beta B
!
!-----------------------------------------------------------------------
IMPLICIT NONE
! input variables
COMPLEX(KIND=8), INTENT(IN) :: alpha, beta
COMPLEX(KIND=8), DIMENSION(:), INTENT(IN) :: a, b
! output variables
COMPLEX(KIND=8), DIMENSION(:) :: c
! local variables
INTEGER :: i
!$OMP PARALLEL DO
DO i = 1, SIZE(a)
c(i) = alpha*a(i) + beta*b(i)
END DO
!$OMP END PARALLEL DO
END SUBROUTINE zAlinB_s
!------------------------------------------------------------------------------
SUBROUTINE zAtimx (y, a, ja, ia, x)
!
!-----------------------------------------------------------------------
! A times a vector
!-----------------------------------------------------------------------
! multiplies a matrix by a vector using the dot product form
! Matrix A is stored in compressed sparse row storage.
!
! Author: Jacopo Canton
! E-mail: [email protected]
! Last revision: 22/3/2013
!
! on entry:
!----------
! x = complex array of length equal to the column dimension of
! the A matrix.
! a, ja,
! ia = input matrix in compressed sparse row format.
!
! on return:
!-----------
! y = complex array, containing the product y = A*x
!
!-----------------------------------------------------------------------
IMPLICIT NONE
! input variables
COMPLEX(KIND=8), DIMENSION(:), INTENT(IN) :: a
INTEGER, DIMENSION(:), INTENT(IN) :: ja, ia
COMPLEX(KIND=8), DIMENSION(:), INTENT(IN) :: x
! output variables
COMPLEX(KIND=8), DIMENSION(:) :: y
! local variables
COMPLEX(KIND=8) :: yi
INTEGER :: number_of_rows, i, p
number_of_rows = SIZE(ia)-1
! check dimension consistency
! A - x
IF ( SIZE(x) /= number_of_rows ) THEN
WRITE(*,*) '--> zAtimx Error: wrong A - x size'
WRITE(*,*) ' SIZE(x) = ', SIZE(x), ' SIZE(A,1) = ', number_of_rows
WRITE(*,*) ' STOP.'
CALL MPI_ABORT(MPI_COMM_WORLD, mpiErrC, mpiIerr)
END IF
! A - y
IF ( SIZE(y) /= number_of_rows ) THEN
WRITE(*,*) '--> zAtimx Error: wrong A - y size'
WRITE(*,*) ' SIZE(y) = ', SIZE(y), ' SIZE(A,1) = ', number_of_rows
WRITE(*,*) ' STOP.'
CALL MPI_ABORT(MPI_COMM_WORLD, mpiErrC, mpiIerr)
END IF
! not necessary to check x-y consistency because A has to be square
! compute y <-- A*x
!$OMP PARALLEL DO
DO i = 1, number_of_rows
! compute the inner product of row i with vector x
yi = CMPLX(0d0, 0d0, KIND=8)
DO p = ia(i), ia(i+1)-1
yi = yi + a(p)*x(ja(p))
END DO
! store result in y(i)
y(i) = yi
END DO
!$OMP END PARALLEL DO
END SUBROUTINE zAtimx
!------------------------------------------------------------------------------
SUBROUTINE zAtimx_T (y, a, ja, ia, x)
!
!-----------------------------------------------------------------------
! transpose(A) times a vector
!-----------------------------------------------------------------------
! multiplies the transpose of a matrix by a vector using the dot product form
! Matrix A is stored in compressed sparse row storage.
!
! Author: Jacopo Canton
! E-mail: [email protected]
! Last revision: 22/3/2013
!
! on entry:
!----------
! x = complex array of length equal to the column dimension of
! the A matrix.
! a, ja,
! ia = input matrix in compressed sparse row format.
!
! on return:
!-----------
! y = complex array, containing the product y = A'*x
!
!-----------------------------------------------------------------------
IMPLICIT NONE
! input variables
COMPLEX(KIND=8), DIMENSION(:), INTENT(IN) :: a
INTEGER, DIMENSION(:), INTENT(IN) :: ja, ia
COMPLEX(KIND=8), DIMENSION(:), INTENT(IN) :: x
! output variables
COMPLEX(KIND=8), DIMENSION(:) :: y
! local variables
INTEGER :: number_of_rows, i, p
number_of_rows = SIZE(ia)-1
! check dimension consistency
! A - x
IF ( SIZE(x) /= number_of_rows ) THEN
WRITE(*,*) '--> zAtimx_T Error: wrong A - x size'
WRITE(*,*) ' SIZE(x) = ', SIZE(x), ' SIZE(A,1) = ', number_of_rows
WRITE(*,*) ' STOP.'
CALL MPI_ABORT(MPI_COMM_WORLD, mpiErrC, mpiIerr)
END IF
! A - y
IF ( SIZE(y) /= number_of_rows ) THEN
WRITE(*,*) '--> zAtimx_T Error: wrong A - y size'
WRITE(*,*) ' SIZE(y) = ', SIZE(y), ' SIZE(A,1) = ', number_of_rows
WRITE(*,*) ' STOP.'
CALL MPI_ABORT(MPI_COMM_WORLD, mpiErrC, mpiIerr)
END IF
! not necessary to check x-y consistency because A has to be square
! compute y <-- A'*x
y = CMPLX(0d0, 0d0, KIND=8)
! $OMP PARALLEL DO & ! not working yet with big matrices,
! $OMP PRIVATE(p) & ! don't know why
! $OMP REDUCTION (+: y)
DO i = 1, number_of_rows
! compute the inner product of row i with vector x
DO p = ia(i), ia(i+1)-1
y(ja(p)) = y(ja(p)) + a(p)*x(i)
END DO
END DO
! $OMP END PARALLEL DO
END SUBROUTINE zAtimx_T
!------------------------------------------------------------------------------
SUBROUTINE zEssM (a, ja, ia, n, b, jb, ib, i_mumpsb)
!
!-----------------------------------------------------------------------
! Extract square sub-Matrix nxn
!-----------------------------------------------------------------------
! Extract a square submatrix B from matrix A
! Matrix A and B are stored in compressed sparse row storage.
!
! Author: Jacopo Canton
! E-mail: [email protected]
! Last revision: 16/03/2014
!
! on entry:
!----------
! a, ja,
! ia = input matrix in compressed sparse row format.
!
! on return:
!-----------
! b, jb,
! ib = output matrix in compressed sparse row format.
!
!-----------------------------------------------------------------------
IMPLICIT NONE
! input variables
COMPLEX(KIND=8), DIMENSION(:), INTENT(IN) :: a
INTEGER, DIMENSION(:), INTENT(IN) :: ja, ia
INTEGER, INTENT(IN) :: n
! output variables
COMPLEX(KIND=8), DIMENSION(:), POINTER :: b
INTEGER, DIMENSION(:), POINTER :: jb, ib
INTEGER, DIMENSION(:), POINTER, OPTIONAL :: i_mumpsb
! local variables
INTEGER :: number_of_rows, i, p, c
number_of_rows = SIZE(ia)-1
! check dimension consistency
!
IF ( n > number_of_rows ) THEN
WRITE(*,*) '--> zEssM Error: n > rows(A)'
WRITE(*,*) ' n = ', n, ' SIZE(A,1) = ', number_of_rows
WRITE(*,*) ' STOP.'
CALL MPI_ABORT(MPI_COMM_WORLD, mpiErrC, mpiIerr)
END IF
! count elements
!
c = 0
DO i = 1, n
DO p = ia(i), ia(i+1) - 1
IF ( ja(p) <= n ) THEN
c = c + 1
ENDIF
ENDDO
ENDDO
ALLOCATE( ib(n+1) )
ALLOCATE( jb(c), b(c) )
! fill matrix
!
c = 0
DO i = 1, n
ib(i) = c + 1
DO p = ia(i), ia(i+1) - 1
IF ( ja(p) <= n ) THEN
c = c + 1
jb(c) = ja(p)
b(c) = a(p)
ENDIF
ENDDO
ENDDO
ib(n+1) = c + 1
IF (PRESENT(i_mumpsb)) THEN
ALLOCATE( i_mumpsb(SIZE(jb)) )
DO i = 1, SIZE(ib) - 1
DO p = ib(i), ib(i+1) - 1
i_mumpsb(p) = i
ENDDO
END DO
ENDIF
END SUBROUTINE zEssM
!
!
!==============================================================================
END MODULE sparse_matrix_operations