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
|
// SuiteSparse/MATLAB_Tools/SSMULT/ssmult_template.c
// SSMULT, Copyright (c) 2007-2011, Timothy A Davis. All Rights Reserved.
// SPDX-License-Identifier: GPL-2.0+
/* ========================================================================== */
/* === ssmult_template.c ==================================================== */
/* ========================================================================== */
/* C = A*B, where A and B are sparse. The column pointers for C (the Cp array)
* have already been computed. entries are dropped. This code fragment is
* #include'd into ssmult.c four times, with all four combinations of ACOMPLEX
* (defined or not) and BCOMPLEX (defined or not).
*
* By default, C is returned with sorted column indices, and with explicit
* zero entries dropped. If C is complex with an all-zero imaginary part, then
* the imaginary part is freed and C becomes real. Thus, C is a pure MATLAB
* sparse matrix.
*
* If UNSORTED is defined (-DUNSORTED), then the nonzero pattern of C is
* returned with unsorted column indices. This is much faster than returning a
* pure MATLAB sparse matrix, but the result must eventually be sorted prior to
* returning to MATLAB.
*
* If the compiler bug discussed below does not affect you, then uncomment the
* following line, or compile with code with -DNO_GCC_BUG.
#define NO_GCC_BUG
* The gcc bug occurs when cij underflows to zero:
*
* cij = aik * bkj ;
* if (cij == 0)
* {
* drop this entry
* }
*
* If cij underflows, cij is zero but the above test is incorrectly FALSE with
* gcc -O, using gcc version 4.1.0 on an Intel Pentium. The bug does not appear
* on an AMD Opteron with the same compiler. The solution is to store cij to
* memory first, and then to read it back in and test it, which is slower.
*/
/* -------------------------------------------------------------------------- */
/* MULT: multiply (or multiply and accumulate, depending on op) */
/* -------------------------------------------------------------------------- */
/* op can be "=" or "+=" */
#ifdef ACOMPLEX
#ifdef BCOMPLEX
#define MULT(x,z,op) \
azik = (ac ? (-Az [pa]) : (Az [pa])) ; \
x op Ax [pa] * bkj - azik * bzkj ; \
z op azik * bkj + Ax [pa] * bzkj ;
#else
#define MULT(x,z,op) \
azik = (ac ? (-Az [pa]) : (Az [pa])) ; \
x op Ax [pa] * bkj ; \
z op azik * bkj ;
#endif
#else
#ifdef BCOMPLEX
#define MULT(x,z,op) \
x op Ax [pa] * bkj ; \
z op Ax [pa] * bzkj ;
#else
#define MULT(x,z,op) \
x op Ax [pa] * bkj ;
#endif
#endif
/* -------------------------------------------------------------------------- */
/* ASSIGN_BKJ: copy B(k,j) into a local scalar */
/* -------------------------------------------------------------------------- */
#ifdef BCOMPLEX
#define ASSIGN_BKJ \
bkj = Bx [pb] ; \
bzkj = (bc ? (-Bz [pb]) : (Bz [pb])) ;
#else
#define ASSIGN_BKJ \
bkj = Bx [pb] ;
#endif
/* -------------------------------------------------------------------------- */
/* DROP_CHECK: check if an entry must be dropped */
/* -------------------------------------------------------------------------- */
#if defined (ACOMPLEX) || defined (BCOMPLEX)
#define DROP_CHECK(x,z) \
if (x == 0 && z == 0) drop = 1 ; \
if (z != 0) zallzero = 0 ;
#else
#define DROP_CHECK(x,z) if (x == 0) drop = 1 ;
#endif
/* -------------------------------------------------------------------------- */
/* sparse matrix multiply template */
/* -------------------------------------------------------------------------- */
{
#ifdef ACOMPLEX
double azik ;
#endif
/* ---------------------------------------------------------------------- */
/* initialize drop tests */
/* ---------------------------------------------------------------------- */
drop = 0 ; /* true if any entry in C is zero */
zallzero = 1 ; /* true if Cz is all zero */
/* ---------------------------------------------------------------------- */
/* quick check if A is diagonal, or a permutation matrix */
/* ---------------------------------------------------------------------- */
if (Anrow == Ancol && Ap [Ancol] == Ancol)
{
/* A is square, with n == nnz (A); check the pattern */
A_is_permutation = 1 ;
A_is_diagonal = 1 ;
for (j = 0 ; j < Ancol ; j++)
{
if (Ap [j] != j)
{
/* A has a column with no entries, or more than 1 entry */
A_is_permutation = 0 ;
A_is_diagonal = 0 ;
break ;
}
}
mark-- ; /* Flag [0..n-1] != mark is now true */
for (j = 0 ; j < Ancol && (A_is_permutation || A_is_diagonal) ; j++)
{
/* A has one entry in each column, so j == Ap [j] */
i = Ai [j] ;
if (i != j)
{
/* A is not diagonal, but might still be a permutation */
A_is_diagonal = 0 ;
}
if (Flag [i] == mark)
{
/* row i appears twice; A is neither permutation nor diagonal */
A_is_permutation = 0 ;
A_is_diagonal = 0 ;
}
/* mark row i, so we know if we see it again */
Flag [i] = mark ;
}
}
else
{
/* A is not square, or nnz (A) is not equal to n */
A_is_permutation = 0 ;
A_is_diagonal = 0 ;
}
/* ---------------------------------------------------------------------- */
/* allocate workspace */
/* ---------------------------------------------------------------------- */
#ifndef UNSORTED
W = NULL ;
if (!A_is_diagonal)
{
#if defined (ACOMPLEX) || defined (BCOMPLEX)
W = mxMalloc (Anrow * 2 * sizeof (double)) ;
Wz = W + Anrow ;
#else
W = mxMalloc (Anrow * sizeof (double)) ;
#endif
}
#endif
/* ---------------------------------------------------------------------- */
/* compute C one column at a time */
/* ---------------------------------------------------------------------- */
if (A_is_diagonal)
{
/* ------------------------------------------------------------------ */
/* C = A*B where A is diagonal */
/* ------------------------------------------------------------------ */
pb = 0 ;
for (j = 0 ; j < Bncol ; j++)
{
pcstart = pb ;
pbend = Bp [j+1] ; /* column B is in Bi,Bx,Bz [pb ... pbend+1] */
for ( ; pb < pbend ; pb++)
{
k = Bi [pb] ; /* nonzero entry B(k,j) */
ASSIGN_BKJ ;
Ci [pb] = k ;
pa = k ;
MULT (Cx [pb], Cz [pb], =) ; /* C(k,j) = A(k,k)*B(k,j) */
#ifdef NO_GCC_BUG
DROP_CHECK (Cx [pb], Cz [pb]) ; /* check if C(k,j) == 0 */
#endif
}
#ifndef NO_GCC_BUG
for (pc = pcstart ; pc < pbend ; pc++)
{
DROP_CHECK (Cx [pc], Cz [pc]) ; /* check if C(k,j) == 0 */
}
#endif
}
}
else
{
/* ------------------------------------------------------------------ */
/* C = A*B, general case, or A permutation */
/* ------------------------------------------------------------------ */
pb = 0 ;
cnz = 0 ;
for (j = 0 ; j < Bncol ; j++)
{
/* -------------------------------------------------------------- */
/* compute jth column of C: C(:,j) = A * B(:,j) */
/* -------------------------------------------------------------- */
pbend = Bp [j+1] ; /* column B is in Bi,Bx,Bz [pb ... pbend+1] */
pcstart = cnz ; /* start of column j in C */
blen = pbend - pb ; /* number of entries in B */
needs_sorting = 0 ; /* true if column j needs sorting */
if (blen == 0)
{
/* ---------------------------------------------------------- */
/* nothing to do, B(:,j) and C(:,j) are empty */
/* ---------------------------------------------------------- */
continue ;
}
else if (blen == 1)
{
/* ---------------------------------------------------------- */
/* B(:,j) contains only one nonzero */
/* ---------------------------------------------------------- */
/* since there is only one entry in B, just scale column A(:,k):
* C(:,j) = A(:,k) * B(k,j)
* C is sorted only if A is sorted on input */
k = Bi [pb] ; /* nonzero entry B(k,j) */
ASSIGN_BKJ ;
paend = Ap [k+1] ;
for (pa = Ap [k] ; pa < paend ; pa++, cnz++)
{
Ci [cnz] = Ai [pa] ; /* nonzero entry A(i,k) */
MULT (Cx [cnz], Cz [cnz], =) ; /* C(i,j) = A(i,k)*B(k,j) */
#ifdef NO_GCC_BUG
DROP_CHECK (Cx [cnz], Cz [cnz]) ; /* check C(i,j) == 0 */
#endif
}
pb++ ;
#ifndef NO_GCC_BUG
for (pc = pcstart ; pc < cnz ; pc++)
{
DROP_CHECK (Cx [pc], Cz [pc]) ; /* check if C(i,j) == 0 */
}
#endif
}
else
{
/* ---------------------------------------------------------- */
/* B(:,j) has two or more entries */
/* ---------------------------------------------------------- */
if (A_is_permutation)
{
/* ------------------------------------------------------ */
/* A is a permutation matrix */
/* ------------------------------------------------------ */
needs_sorting = 1 ;
for ( ; pb < pbend ; pb++)
{
k = Bi [pb] ; /* nonzero entry B(k,j) */
ASSIGN_BKJ ;
i = Ai [k] ; /* nonzero entry A(i,k) */
Ci [pb] = i ;
pa = k ;
/* C(i,j) = A(i,k)*B(k,j) */
#ifndef UNSORTED
MULT (W [i], Wz [i], =) ;
#else
MULT (Cx [pb], Cz [pb], =) ;
#endif
}
cnz = pbend ;
}
else
{
/* ------------------------------------------------------ */
/* general case */
/* ------------------------------------------------------ */
/* first entry in jth column of B is simpler */
/* C(:,j) = A (:,k) * B (k,j) */
k = Bi [pb] ; /* nonzero entry B(k,j) */
ASSIGN_BKJ ;
paend = Ap [k+1] ;
for (pa = Ap [k] ; pa < paend ; pa++)
{
i = Ai [pa] ; /* nonzero entry A(i,k) */
Flag [i] = cnz ;
Ci [cnz] = i ; /* new entry C(i,j) */
/* C(i,j) = A(i,k)*B(k,j) */
#ifndef UNSORTED
MULT (W [i], Wz [i], =) ;
#else
MULT (Cx [cnz], Cz [cnz], =) ;
#endif
cnz++ ;
}
pb++ ;
for ( ; pb < pbend ; pb++)
{
k = Bi [pb] ; /* nonzero entry B(k,j) */
ASSIGN_BKJ ;
/* C(:,j) += A (:,k) * B (k,j) */
paend = Ap [k+1] ;
for (pa = Ap [k] ; pa < paend ; pa++)
{
i = Ai [pa] ; /* nonzero entry A(i,k) */
pc = Flag [i] ;
if (pc < pcstart)
{
pc = cnz++ ;
Flag [i] = pc ;
Ci [pc] = i ; /* new entry C(i,j) */
/* C(i,j) = A(i,k)*B(k,j) */
#ifndef UNSORTED
MULT (W [i], Wz [i], =) ;
needs_sorting = 1 ;
#else
MULT (Cx [pc], Cz [pc], =) ;
#endif
}
else
{
/* C(i,j) += A(i,k)*B(k,j) */
#ifndef UNSORTED
MULT (W [i], Wz [i], +=) ;
#else
MULT (Cx [pc], Cz [pc], +=) ;
#endif
}
}
}
}
/* ---------------------------------------------------------- */
/* sort the pattern of C(:,j) and gather the values of C(:,j) */
/* ---------------------------------------------------------- */
#ifndef UNSORTED
/* Sort the row indices in C(:,j). Use Cx as Int workspace.
* This assumes sizeof (Int) < sizeof (double). If blen <= 1,
* or if subsequent entries in B(:,j) appended entries onto C,
* there is no need to sort C(:,j), assuming A is sorted. */
if (needs_sorting)
{
ssmergesort (Ci + pcstart, (Int *) (Cx + pcstart),
cnz - pcstart) ;
}
for (pc = pcstart ; pc < cnz ; pc++)
{
#if defined (ACOMPLEX) || defined (BCOMPLEX)
i = Ci [pc] ;
cij = W [i] ; /* get C(i,j) from W */
czij = Wz [i] ;
Cx [pc] = cij ; /* copy C(i,j) into C */
Cz [pc] = czij ;
#else
cij = W [Ci [pc]] ; /* get C(i,j) from W */
Cx [pc] = cij ; /* copy C(i,j) into C */
#endif
DROP_CHECK (cij, czij) ; /* check if C(i,j) == 0 */
}
#else
/* no need to sort, but we do need to check for drop */
for (pc = pcstart ; pc < cnz ; pc++)
{
DROP_CHECK (Cx [pc], Cz [pc]) ; /* check if C(i,j) == 0 */
}
#endif
}
}
}
/* ---------------------------------------------------------------------- */
/* free workspace */
/* ---------------------------------------------------------------------- */
#ifndef UNSORTED
mxFree (W) ;
#endif
}
#undef ACOMPLEX
#undef BCOMPLEX
#undef MULT
#undef ASSIGN_BKJ
#undef DROP_CHECK
|
