1 |
/* |
2 |
* Written by Doug Lea with assistance from members of JCP JSR-166 |
3 |
* Expert Group and released to the public domain, as explained at |
4 |
* http://creativecommons.org/publicdomain/zero/1.0/ |
5 |
*/ |
6 |
|
7 |
// Jacobi iteration on a mesh. Based loosely on a Filaments demo |
8 |
|
9 |
import java.util.concurrent.*; |
10 |
|
11 |
public class CCJacobi { |
12 |
|
13 |
// static final int DEFAULT_GRANULARITY = 4096; |
14 |
static final int DEFAULT_GRANULARITY = 256; |
15 |
|
16 |
/** |
17 |
* The maximum number of matrix cells |
18 |
* at which to stop recursing down and instead directly update. |
19 |
*/ |
20 |
static final double EPSILON = 0.0001; // convergence criterion |
21 |
|
22 |
public static void main(String[] args) throws Exception { |
23 |
int n = 2048; |
24 |
int steps = 1000; |
25 |
int granularity = DEFAULT_GRANULARITY; |
26 |
|
27 |
try { |
28 |
if (args.length > 0) |
29 |
n = Integer.parseInt(args[0]); |
30 |
if (args.length > 1) |
31 |
steps = Integer.parseInt(args[1]); |
32 |
if (args.length > 2) |
33 |
granularity = Integer.parseInt(args[2]); |
34 |
} |
35 |
|
36 |
catch (Exception e) { |
37 |
System.out.println("Usage: java FJJacobi <matrix size> <max steps> [<leafcells>]"); |
38 |
return; |
39 |
} |
40 |
|
41 |
ForkJoinPool fjp = new ForkJoinPool(); |
42 |
|
43 |
// allocate enough space for edges |
44 |
int dim = n+2; |
45 |
int ncells = dim * dim; |
46 |
double[][] a = new double[dim][dim]; |
47 |
double[][] b = new double[dim][dim]; |
48 |
// Initialize interiors to small value |
49 |
double smallVal = EPSILON; // 1.0/dim; |
50 |
for (int i = 1; i < dim-1; ++i) { |
51 |
for (int j = 1; j < dim-1; ++j) |
52 |
a[i][j] = smallVal; |
53 |
} |
54 |
// Fill all edges with 1's. |
55 |
for (int k = 0; k < dim; ++k) { |
56 |
a[k][0] = 1.0; |
57 |
a[k][n+1] = 1.0; |
58 |
a[0][k] = 1.0; |
59 |
a[n+1][k] = 1.0; |
60 |
b[k][0] = 1.0; |
61 |
b[k][n+1] = 1.0; |
62 |
b[0][k] = 1.0; |
63 |
b[n+1][k] = 1.0; |
64 |
} |
65 |
int nreps = 10; |
66 |
for (int rep = 0; rep < nreps; ++rep) { |
67 |
Driver driver = new Driver(a, b, 1, n, 1, n, steps, granularity); |
68 |
|
69 |
long startTime = System.currentTimeMillis(); |
70 |
fjp.invoke(driver); |
71 |
|
72 |
long time = System.currentTimeMillis() - startTime; |
73 |
double secs = ((double)time) / 1000.0; |
74 |
|
75 |
System.out.println("Compute Time: " + secs); |
76 |
System.out.println(fjp); |
77 |
} |
78 |
} |
79 |
|
80 |
|
81 |
abstract static class MatrixTree extends CountedCompleter<Void> { |
82 |
// maximum difference between old and new values |
83 |
double maxDiff; |
84 |
MatrixTree(CountedCompleter<?> p, int c) { super(p, c); } |
85 |
} |
86 |
|
87 |
|
88 |
static final class LeafNode extends MatrixTree { |
89 |
final double[][] A; // matrix to get old values from |
90 |
final double[][] B; // matrix to put new values into |
91 |
|
92 |
// indices of current submatrix |
93 |
final int loRow; final int hiRow; |
94 |
final int loCol; final int hiCol; |
95 |
|
96 |
int steps = 0; // track even/odd steps |
97 |
|
98 |
LeafNode(CountedCompleter<?> p, |
99 |
double[][] A, double[][] B, |
100 |
int loRow, int hiRow, |
101 |
int loCol, int hiCol) { |
102 |
super(p, 0); |
103 |
this.A = A; this.B = B; |
104 |
this.loRow = loRow; this.hiRow = hiRow; |
105 |
this.loCol = loCol; this.hiCol = hiCol; |
106 |
} |
107 |
|
108 |
public final void compute() { |
109 |
boolean AtoB = (steps++ & 1) == 0; |
110 |
double[][] a = AtoB ? A : B; |
111 |
double[][] b = AtoB ? B : A; |
112 |
|
113 |
double md = 0.0; // local for computing max diff |
114 |
|
115 |
for (int i = loRow; i <= hiRow; ++i) { |
116 |
for (int j = loCol; j <= hiCol; ++j) { |
117 |
double v = 0.25 * (a[i-1][j] + a[i][j-1] + |
118 |
a[i+1][j] + a[i][j+1]); |
119 |
b[i][j] = v; |
120 |
|
121 |
double diff = v - a[i][j]; |
122 |
if (diff < 0) diff = -diff; |
123 |
if (diff > md) md = diff; |
124 |
} |
125 |
} |
126 |
|
127 |
maxDiff = md; |
128 |
tryComplete(); |
129 |
} |
130 |
} |
131 |
|
132 |
static final class FourNode extends MatrixTree { |
133 |
MatrixTree q1; |
134 |
MatrixTree q2; |
135 |
MatrixTree q3; |
136 |
MatrixTree q4; |
137 |
FourNode(CountedCompleter<?> p) { |
138 |
super(p, 3); |
139 |
} |
140 |
|
141 |
public void onCompletion(CountedCompleter<?> caller) { |
142 |
double md = q1.maxDiff, m; |
143 |
if ((m = q2.maxDiff) > md) |
144 |
md = m; |
145 |
if ((m = q3.maxDiff) > md) |
146 |
md = m; |
147 |
if ((m = q4.maxDiff) > md) |
148 |
md = m; |
149 |
maxDiff = md; |
150 |
setPendingCount(3); |
151 |
} |
152 |
|
153 |
public final void compute() { |
154 |
q4.fork(); |
155 |
q3.fork(); |
156 |
q2.fork(); |
157 |
q1.compute(); |
158 |
} |
159 |
} |
160 |
|
161 |
|
162 |
static final class TwoNode extends MatrixTree { |
163 |
MatrixTree q1; |
164 |
MatrixTree q2; |
165 |
|
166 |
TwoNode(CountedCompleter<?> p) { |
167 |
super(p, 1); |
168 |
} |
169 |
|
170 |
public void onCompletion(CountedCompleter<?> caller) { |
171 |
double md = q1.maxDiff, m; |
172 |
if ((m = q2.maxDiff) > md) |
173 |
md = m; |
174 |
maxDiff = md; |
175 |
setPendingCount(1); |
176 |
} |
177 |
|
178 |
public final void compute() { |
179 |
q2.fork(); |
180 |
q1.compute(); |
181 |
} |
182 |
|
183 |
} |
184 |
|
185 |
static final class Driver extends RecursiveAction { |
186 |
MatrixTree mat; |
187 |
double[][] A; double[][] B; |
188 |
int firstRow; int lastRow; |
189 |
int firstCol; int lastCol; |
190 |
final int steps; |
191 |
final int leafs; |
192 |
int nleaf; |
193 |
|
194 |
Driver(double[][] A, double[][] B, |
195 |
int firstRow, int lastRow, |
196 |
int firstCol, int lastCol, |
197 |
int steps, int leafs) { |
198 |
this.A = A; |
199 |
this.B = B; |
200 |
this.firstRow = firstRow; |
201 |
this.firstCol = firstCol; |
202 |
this.lastRow = lastRow; |
203 |
this.lastCol = lastCol; |
204 |
this.steps = steps; |
205 |
this.leafs = leafs; |
206 |
mat = build(null, A, B, firstRow, lastRow, firstCol, lastCol, leafs); |
207 |
System.out.println("Using " + nleaf + " segments"); |
208 |
|
209 |
} |
210 |
|
211 |
MatrixTree build(MatrixTree p, |
212 |
double[][] a, double[][] b, |
213 |
int lr, int hr, int lc, int hc, int leafs) { |
214 |
int rows = (hr - lr + 1); |
215 |
int cols = (hc - lc + 1); |
216 |
|
217 |
int mr = (lr + hr) >>> 1; // midpoints |
218 |
int mc = (lc + hc) >>> 1; |
219 |
|
220 |
int hrows = (mr - lr + 1); |
221 |
int hcols = (mc - lc + 1); |
222 |
|
223 |
if (rows * cols <= leafs) { |
224 |
++nleaf; |
225 |
return new LeafNode(p, a, b, lr, hr, lc, hc); |
226 |
} |
227 |
else if (hrows * hcols >= leafs) { |
228 |
FourNode q = new FourNode(p); |
229 |
q.q1 = build(q, a, b, lr, mr, lc, mc, leafs); |
230 |
q.q2 = build(q, a, b, lr, mr, mc+1, hc, leafs); |
231 |
q.q3 = build(q, a, b, mr+1, hr, lc, mc, leafs); |
232 |
q.q4 = build(q, a, b, mr+1, hr, mc+1, hc, leafs); |
233 |
return q; |
234 |
} |
235 |
else if (cols >= rows) { |
236 |
TwoNode q = new TwoNode(p); |
237 |
q.q1 = build(q, a, b, lr, hr, lc, mc, leafs); |
238 |
q.q2 = build(q, a, b, lr, hr, mc+1, hc, leafs); |
239 |
return q; |
240 |
} |
241 |
else { |
242 |
TwoNode q = new TwoNode(p); |
243 |
q.q1 = build(q, a, b, lr, mr, lc, hc, leafs); |
244 |
q.q2 = build(q, a, b, mr+1, hr, lc, hc, leafs); |
245 |
return q; |
246 |
} |
247 |
} |
248 |
|
249 |
static void doCompute(MatrixTree m, int s) { |
250 |
for (int i = 0; i < s; ++i) { |
251 |
m.setPendingCount(3); |
252 |
m.invoke(); |
253 |
m.reinitialize(); |
254 |
} |
255 |
} |
256 |
|
257 |
public void compute() { |
258 |
doCompute(mat, steps); |
259 |
double md = mat.maxDiff; |
260 |
System.out.println("max diff after " + steps + " steps = " + md); |
261 |
} |
262 |
} |
263 |
|
264 |
|
265 |
} |