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
|
//------------------------------------------------------------------------------
// GraphBLAS/Demo/Program/tri_demo.c: count triangles
//------------------------------------------------------------------------------
// SuiteSparse:GraphBLAS, Timothy A. Davis, (c) 2017-2020, All Rights Reserved.
// http://suitesparse.com See GraphBLAS/Doc/License.txt for license.
//------------------------------------------------------------------------------
// Read a graph from a file and count the # of triangles using two methods.
// Usage:
//
// tri_demo < infile
// tri_demo 1 < infile
// tri_demo 0 nrows ncols ntuples method
// tri_demo 1 nx ny method
//
// Where infile has one line per edge in the graph; these have the form
//
// i j x
//
// where A(i,j)=x is performed by GrB_Matrix_build, to construct the matrix.
// The default file format is 0-based, but with "tri_demo 1 < infile" the
// matrix is assumed to be 1-based.
// The dimensions of A are assumed to be the largest row and column indices,
// plus one if the matrix is 1-based. This is done in read_matrix.c.
//
// For the second usage (tri_demo 0 ...), a random symmetric matrix is created
// of size nrows-by-ncols with ntuples edges (some will be duplicates so the
// actual number of edges will be slightly less). The method is 0 for
// setElement and 1 for build. The matrix will not have any self-edges, which
// cause the tricount method to fail.
//
// The 3rd usage (tri_demo 1 ...) creates a finite-element matrix on an
// nx-by-ny grid. Method is 0 to 3; refer to wathen.c for details.
// macro used by OK(...) to free workspace if an error occurs
#define FREE_ALL \
GxB_Scalar_free (&Thunk) ; \
GrB_Matrix_free (&C) ; \
GrB_Matrix_free (&A) ; \
GrB_Matrix_free (&L) ; \
GrB_Matrix_free (&U) ;
#include "graphblas_demos.h"
int main (int argc, char **argv)
{
GrB_Matrix C = NULL, A = NULL, L = NULL, U = NULL ;
GxB_Scalar Thunk = NULL ;
GrB_Info info ;
double tic [2], r1, r2 ;
OK (GrB_init (GrB_NONBLOCKING)) ;
int nthreads ;
OK (GxB_Global_Option_get (GxB_GLOBAL_NTHREADS, &nthreads)) ;
fprintf (stderr, "tri_demo: nthreads %d\n", nthreads) ;
printf ("--------------------------------------------------------------\n");
//--------------------------------------------------------------------------
// get a symmetric matrix with no self edges
//--------------------------------------------------------------------------
// get_matrix reads in a boolean matrix. It could easily be changed to
// read in int32 matrix instead, but this would affect the other GraphBLAS
// demos. So the time to typecast A = (int32) C is added to the read
// time, not the prep time for triangle counting.
simple_tic (tic) ;
OK (get_matrix (&C, argc, argv, true, true)) ;
GrB_Index n, nedges ;
OK (GrB_Matrix_nrows (&n, C)) ;
GrB_Type ctype = GrB_INT32 ;
// A = spones (C), and typecast to int32
OK (GrB_Matrix_new (&A, ctype, n, n)) ;
OK (GrB_Matrix_apply (A, NULL, NULL, GxB_ONE_INT32, C, NULL)) ;
double t_read = simple_toc (tic) ;
printf ("\ntotal time to read A matrix: %14.6f sec\n", t_read) ;
GrB_Matrix_free (&C) ;
OK (GxB_Scalar_new (&Thunk, GrB_INT64)) ;
// U = triu (A,1)
simple_tic (tic) ;
OK (GxB_Scalar_setElement_INT64 (Thunk, (int64_t) 1)) ;
OK (GrB_Matrix_new (&U, ctype, n, n)) ;
OK (GxB_Matrix_select (U, NULL, NULL, GxB_TRIU, A, Thunk, NULL)) ;
OK (GrB_Matrix_nvals (&nedges, U)) ;
printf ("\nn %.16g # edges %.16g\n", (double) n, (double) nedges) ;
double t_U = simple_toc (tic) ;
printf ("U=triu(A) time: %14.6f sec\n", t_U) ;
// L = tril (A,-1)
simple_tic (tic) ;
OK (GrB_Matrix_new (&L, ctype, n, n)) ;
OK (GxB_Scalar_setElement_INT64 (Thunk, (int64_t) (-1))) ;
OK (GxB_Matrix_select (L, NULL, NULL, GxB_TRIL, A, Thunk, NULL)) ;
double t_L = simple_toc (tic) ;
printf ("L=tril(A) time: %14.6f sec\n", t_L) ;
OK (GrB_Matrix_free (&A)) ;
int nthreads_max = 1 ;
#if defined ( _OPENMP )
nthreads_max = omp_get_max_threads ( ) ;
#endif
//--------------------------------------------------------------------------
// count the triangles via C<L> = L*U' (dot-produt)
//--------------------------------------------------------------------------
printf ("\n------------------------------------- dot product method:\n") ;
#define NTHREADS_MAX 2048
nthreads_max = MIN (nthreads_max, NTHREADS_MAX) ;
int64_t ntri2 [NTHREADS_MAX+1], nt = -1 ;
double t1 ;
for (int nthreads = 1 ; nthreads <= nthreads_max ; nthreads *= 2)
{
GxB_Global_Option_set (GxB_GLOBAL_NTHREADS, nthreads) ;
double t_dot [2] ;
OK (tricount (&(ntri2 [nthreads]), 5, NULL, NULL, L, U, t_dot)) ;
if (nthreads == 1)
{
printf ("# triangles %.16g\n", (double) ntri2 [nthreads]) ;
fprintf (stderr, "# triangles %.16g\n", (double) ntri2 [nthreads]) ;
nt = ntri2 [1] ;
}
if (ntri2 [nthreads] != nt)
{
printf ("error 5!\n") ;
fprintf (stderr, "error!\n") ;
exit (1) ;
}
printf ("L*U' time (dot): %14.6f sec", t_dot [0]) ;
if (nthreads == 1)
{
t1 = t_dot [0] ;
}
else
{
printf (" (nthreads: %d speedup %g)", nthreads, t1 / t_dot [0]) ;
}
printf ("\ntricount time: %14.6f sec (dot product method)\n",
t_dot [0] + t_dot [1]) ;
printf ("tri+prep time: %14.6f sec (incl time to compute L and U)\n",
t_dot [0] + t_dot [1] + t_U + t_L) ;
printf ("compute C time: %14.6f sec\n", t_dot [0]) ;
printf ("reduce (C) time: %14.6f sec\n", t_dot [1]) ;
r1 = 1e-6*nedges / (t_dot [0] + t_dot [1] + t_U + t_L) ;
r2 = 1e-6*nedges / (t_dot [0] + t_dot [1]) ;
printf ("rate %8.2f million edges/sec (incl time for U=triu(A))\n",r1);
printf ("rate %8.2f million edges/sec (just tricount itself)\n", r2);
fprintf (stderr, "GrB: C<L>=L*U' (dot) "
"rate %8.2f (w/ prep), %8.2f (tri)", r1, r2) ;
if (nthreads > 1) fprintf (stderr, " speedup: %6.2f", t1/ t_dot [0]) ;
fprintf (stderr, "\n") ;
}
if (nthreads_max > 1) fprintf (stderr, "\n") ;
//--------------------------------------------------------------------------
// method 6: C<U> = U*L' (dot)
//--------------------------------------------------------------------------
for (int nthreads = 1 ; nthreads <= nthreads_max ; nthreads *= 2)
{
GxB_Global_Option_set (GxB_GLOBAL_NTHREADS, nthreads) ;
double t_dot [2] ;
OK (tricount (&(ntri2 [nthreads]), 6, NULL, NULL, L, U, t_dot)) ;
// printf ("# triangles %.16g\n", (double) ntri2 [nthreads]) ;
// fprintf (stderr, "# triangles %.16g\n", (double) ntri2 [nthreads]) ;
if (ntri2 [nthreads] != nt)
{
printf ("error 6!\n") ;
fprintf (stderr, "error!\n") ;
exit (1) ;
}
printf ("L*U' time (dot): %14.6f sec", t_dot [0]) ;
if (nthreads == 1)
{
t1 = t_dot [0] ;
}
else
{
printf (" (nthreads: %d speedup %g)", nthreads, t1 / t_dot [0]) ;
}
printf ("\ntricount time: %14.6f sec (dot product method)\n",
t_dot [0] + t_dot [1]) ;
printf ("tri+prep time: %14.6f sec (incl time to compute L and U)\n",
t_dot [0] + t_dot [1] + t_U + t_L) ;
printf ("compute C time: %14.6f sec\n", t_dot [0]) ;
printf ("reduce (C) time: %14.6f sec\n", t_dot [1]) ;
r1 = 1e-6*nedges / (t_dot [0] + t_dot [1] + t_U + t_L) ;
r2 = 1e-6*nedges / (t_dot [0] + t_dot [1]) ;
printf ("rate %8.2f million edges/sec (incl time for U=triu(A))\n",r1);
printf ("rate %8.2f million edges/sec (just tricount itself)\n", r2);
fprintf (stderr, "GrB: C<U>=U*L' (dot) "
"rate %8.2f (w/ prep), %8.2f (tri)", r1, r2) ;
if (nthreads > 1) fprintf (stderr, " speedup: %6.2f", t1/ t_dot [0]) ;
fprintf (stderr, "\n") ;
}
if (nthreads_max > 1) fprintf (stderr, "\n") ;
//--------------------------------------------------------------------------
// count the triangles via C<L> = L*L (saxpy)
//--------------------------------------------------------------------------
printf ("\n----------------------------------- saxpy method:\n") ;
int64_t ntri1 [NTHREADS_MAX+1] ;
for (int nthreads = 1 ; nthreads <= nthreads_max ; nthreads *= 2)
{
GxB_Global_Option_set (GxB_GLOBAL_NTHREADS, nthreads) ;
double t_mark [2] = { 0, 0 } ;
OK (tricount (&ntri1 [nthreads], 3, NULL, NULL, L, NULL, t_mark)) ;
printf ("triangles, method 3: %0.16g\n", (double) ntri1 [nthreads]) ;
if (ntri1 [nthreads] != nt)
{
printf ("error 3!\n") ;
fprintf (stderr, "error!\n") ;
exit (1) ;
}
printf ("C<L>=L*L time (saxpy): %14.6f sec", t_mark [0]) ;
if (nthreads == 1)
{
t1 = t_mark [0] ;
}
else
{
printf (" (nthreads: %d speedup %g)", nthreads, t1 / t_mark [0]) ;
}
printf ("\ntricount time: %14.6f sec (saxpy method)\n",
t_mark [0] + t_mark [1]) ;
printf ("tri+prep time: %14.6f sec (incl time to compute L)\n",
t_mark [0] + t_mark [1] + t_L) ;
printf ("compute C time: %14.6f sec\n", t_mark [0]) ;
printf ("reduce (C) time: %14.6f sec\n", t_mark [1]) ;
r1 = 1e-6*((double)nedges) / (t_mark [0] + t_mark [1] + t_L) ;
r2 = 1e-6*((double)nedges) / (t_mark [0] + t_mark [1]) ;
printf ("rate %8.2f million edges/sec (incl time for L=tril(A))\n",r1);
printf ("rate %8.2f million edges/sec (just tricount itself)\n", r2);
fprintf (stderr, "GrB: C<L>=L*L (saxpy) "
"rate %8.2f (w/ prep), %8.2f (tri)", r1, r2) ;
if (nthreads > 1) fprintf (stderr, " speedup: %6.2f", t1/ t_mark [0]) ;
fprintf (stderr, "\n") ;
}
//--------------------------------------------------------------------------
// free workspace
//--------------------------------------------------------------------------
FREE_ALL ;
GrB_finalize ( ) ;
printf ("\n") ;
fprintf (stderr, "\n") ;
}
|
