test/loops/LU.java

/*
 * Written by Doug Lea with assistance from members of JCP JSR-166
 * Expert Group and released to the public domain, as explained at
 * http://creativecommons.org/publicdomain/zero/1.0/
 */

//import jsr166y.*;
import java.util.concurrent.*;

/**
 * LU matrix decomposition demo
 * Based on those in Cilk and Hood
 */
public final class LU {

    /** for time conversion */
    static final long NPS = (1000L * 1000 * 1000);

    // granularity is hard-wired as compile-time constant here
    static final int BLOCK_SIZE = 16;
    static final boolean CHECK = false; // set true to check answer

    public static void main(String[] args) throws Exception {

        final String usage = "Usage: java LU <threads> <matrix size (must be a power of two)> [runs] \n For example, try java LU 2 512";

        int procs = 0;
        int n = 2048;
        int runs = 32;
        try {
            if (args.length > 0)
                procs = Integer.parseInt(args[0]);
            if (args.length > 1)
                n = Integer.parseInt(args[1]);
            if (args.length > 2)
                runs = Integer.parseInt(args[2]);
        } catch (Exception e) {
            System.out.println(usage);
            return;
        }

        if ( ((n & (n - 1)) != 0)) {
            System.out.println(usage);
            return;
        }
        ForkJoinPool pool = (procs == 0) ? ForkJoinPool.commonPool() :
            new ForkJoinPool(procs);
        System.out.println("procs: " + pool.getParallelism() +
                           " n: " + n + " runs: " + runs);
        for (int run = 0; run < runs; ++run) {
            double[][] m = new double[n][n];
            randomInit(m, n);
            double[][] copy = null;
            if (CHECK) {
                copy = new double[n][n];
                for (int i = 0; i < n; ++i) {
                    for (int j = 0; j < n; ++j) {
                        copy[i][j] = m[i][j];
                    }
                }
            }
            Block M = new Block(m, 0, 0);
            long start = System.nanoTime();
            pool.invoke(new LowerUpper(n, M));
            long time = System.nanoTime() - start;
            double secs = ((double)time) / NPS;
            System.out.printf("Time: %7.3f ", secs);
            if ((run & 3) == 3) System.out.println();

            if (CHECK) check(m, copy, n);
        }
        System.out.println(pool.toString());
        pool.shutdown();
    }

    static void randomInit(double[][] M, int n) {
        java.util.Random rng = new java.util.Random();
        for (int i = 0; i < n; ++i)
            for (int j = 0; j < n; ++j)
                M[i][j] = rng.nextDouble();
        // for compatibility with hood demo, force larger diagonals
        for (int k = 0; k < n; ++k)
            M[k][k] *= 10.0;
    }

    static void check(double[][] LU, double[][] M, int n) {
        double maxDiff = 0.0; // track max difference
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < n; ++j) {
                double v = 0.0;
                int k;
                for (k = 0; k < i && k <= j; k++ ) v += LU[i][k] * LU[k][j];
                if (k == i && k <= j ) v += LU[k][j];
                double diff = M[i][j] - v;
                if (diff < 0) diff = -diff;
                if (diff > 0.001) {
                    System.out.println("large diff at[" + i + "," + j + "]: " + M[i][j] + " vs " + v);
                }
                if (diff > maxDiff) maxDiff = diff;
            }
        }

        System.out.println("Max difference = " + maxDiff);
    }

    // Blocks record underlying matrix, and offsets into current block
    static final class Block {
        final double[][] m;
        final int loRow;
        final int loCol;

        Block(double[][] mat, int lr, int lc) {
            m = mat; loRow = lr; loCol = lc;
        }
    }

    static final class Schur extends RecursiveAction {
        final int size;
        final Block V;
        final Block W;
        final Block M;

        Schur(int size, Block V, Block W, Block M) {
            this.size = size; this.V = V; this.W = W; this.M = M;
        }

        void schur() { // base case
            for (int j = 0; j < BLOCK_SIZE; ++j) {
                for (int i = 0; i < BLOCK_SIZE; ++i) {
                    double s = M.m[i+M.loRow][j+M.loCol];
                    for (int k = 0; k < BLOCK_SIZE; ++k) {
                        s -= V.m[i+V.loRow][k+V.loCol] * W.m[k+W.loRow][j+W.loCol];
                    }
                    M.m[i+M.loRow][j+M.loCol] = s;
                }
            }
        }

        public void compute() {
            if (size == BLOCK_SIZE) {
                schur();
            }
            else {
                int h = size / 2;

                Block M00 = new Block(M.m, M.loRow,   M.loCol);
                Block M01 = new Block(M.m, M.loRow,   M.loCol+h);
                Block M10 = new Block(M.m, M.loRow+h, M.loCol);
                Block M11 = new Block(M.m, M.loRow+h, M.loCol+h);

                Block V00 = new Block(V.m, V.loRow,   V.loCol);
                Block V01 = new Block(V.m, V.loRow,   V.loCol+h);
                Block V10 = new Block(V.m, V.loRow+h, V.loCol);
                Block V11 = new Block(V.m, V.loRow+h, V.loCol+h);

                Block W00 = new Block(W.m, W.loRow,   W.loCol);
                Block W01 = new Block(W.m, W.loRow,   W.loCol+h);
                Block W10 = new Block(W.m, W.loRow+h, W.loCol);
                Block W11 = new Block(W.m, W.loRow+h, W.loCol+h);

                Seq2 s3 = seq(new Schur(h, V10, W01, M11),
                              new Schur(h, V11, W11, M11));
                s3.fork();
                Seq2 s2 = seq(new Schur(h, V10, W00, M10),
                              new Schur(h, V11, W10, M10));
                s2.fork();
                Seq2 s1 = seq(new Schur(h, V00, W01, M01),
                              new Schur(h, V01, W11, M01));
                s1.fork();
                new Schur(h, V00, W00, M00).compute();
                new Schur(h, V01, W10, M00).compute();
                if (s1.tryUnfork()) s1.compute(); else s1.join();
                if (s2.tryUnfork()) s2.compute(); else s2.join();
                if (s3.tryUnfork()) s3.compute(); else s3.join();
            }
        }
    }

    static final class Lower extends RecursiveAction {
        final int size;
        final Block L;
        final Block M;
        Lower(int size, Block L, Block M) {
            this.size = size; this.L = L; this.M = M;
        }

        void lower() {  // base case
            for (int i = 1; i < BLOCK_SIZE; ++i) {
                for (int k = 0; k < i; ++k) {
                    double a = L.m[i+L.loRow][k+L.loCol];
                    double[] x = M.m[k+M.loRow];
                    double[] y = M.m[i+M.loRow];
                    int n = BLOCK_SIZE;
                    for (int p = n-1; p >= 0; --p) {
                        y[p+M.loCol] -= a * x[p+M.loCol];
                    }
                }
            }
        }

        public void compute() {
            if (size == BLOCK_SIZE) {
                lower();
            }
            else {
                int h = size / 2;

                Block M00 = new Block(M.m, M.loRow,   M.loCol);
                Block M01 = new Block(M.m, M.loRow,   M.loCol+h);
                Block M10 = new Block(M.m, M.loRow+h, M.loCol);
                Block M11 = new Block(M.m, M.loRow+h, M.loCol+h);

                Block L00 = new Block(L.m, L.loRow,   L.loCol);
                Block L01 = new Block(L.m, L.loRow,   L.loCol+h);
                Block L10 = new Block(L.m, L.loRow+h, L.loCol);
                Block L11 = new Block(L.m, L.loRow+h, L.loCol+h);

                Seq3 s1 =
                    seq(new Lower(h, L00, M00),
                        new Schur(h, L10, M00, M10),
                        new Lower(h, L11, M10));
                Seq3 s2 =
                    seq(new Lower(h, L00, M01),
                        new Schur(h, L10, M01, M11),
                        new Lower(h, L11, M11));
                s2.fork();
                s1.compute();
                if (s2.tryUnfork()) s2.compute(); else s2.join();
            }
        }
    }

    static final class Upper extends RecursiveAction {
        final int size;
        final Block U;
        final Block M;
        Upper(int size, Block U, Block M) {
            this.size = size; this.U = U; this.M = M;
        }

        void upper() { // base case
            for (int i = 0; i < BLOCK_SIZE; ++i) {
                for (int k = 0; k < BLOCK_SIZE; ++k) {
                    double a = M.m[i+M.loRow][k+M.loCol] / U.m[k+U.loRow][k+U.loCol];
                    M.m[i+M.loRow][k+M.loCol] = a;
                    double[] x = U.m[k+U.loRow];
                    double[] y = M.m[i+M.loRow];
                    int n = BLOCK_SIZE - k - 1;
                    for (int p = n - 1; p >= 0; --p) {
                        y[p+k+1+M.loCol] -= a * x[p+k+1+U.loCol];
                    }
                }
            }
        }

        public void compute() {
            if (size == BLOCK_SIZE) {
                upper();
            }
            else {
                int h = size / 2;

                Block M00 = new Block(M.m, M.loRow,   M.loCol);
                Block M01 = new Block(M.m, M.loRow,   M.loCol+h);
                Block M10 = new Block(M.m, M.loRow+h, M.loCol);
                Block M11 = new Block(M.m, M.loRow+h, M.loCol+h);

                Block U00 = new Block(U.m, U.loRow,   U.loCol);
                Block U01 = new Block(U.m, U.loRow,   U.loCol+h);
                Block U10 = new Block(U.m, U.loRow+h, U.loCol);
                Block U11 = new Block(U.m, U.loRow+h, U.loCol+h);

                Seq3 s1 =
                    seq(new Upper(h, U00, M00),
                        new Schur(h, M00, U01, M01),
                        new Upper(h, U11, M01));
                Seq3 s2 =
                    seq(new Upper(h, U00, M10),
                        new Schur(h, M10, U01, M11),
                        new Upper(h, U11, M11));
                s2.fork();
                s1.compute();
                if (s2.tryUnfork()) s2.compute(); else s2.join();
            }
        }
    }

    static final class LowerUpper extends RecursiveAction {
        final int size;
        final Block M;
        LowerUpper(int size, Block M) {
            this.size = size; this.M = M;
        }

        void lu() {  // base case
            for (int k = 0; k < BLOCK_SIZE; ++k) {
                for (int i = k+1; i < BLOCK_SIZE; ++i) {
                    double b = M.m[k+M.loRow][k+M.loCol];
                    double a = M.m[i+M.loRow][k+M.loCol] / b;
                    M.m[i+M.loRow][k+M.loCol] = a;
                    double[] x = M.m[k+M.loRow];
                    double[] y = M.m[i+M.loRow];
                    int n = BLOCK_SIZE-k-1;
                    for (int p = n-1; p >= 0; --p) {
                        y[k+1+p+M.loCol] -= a * x[k+1+p+M.loCol];
                    }
                }
            }
        }

        public void compute() {
            if (size == BLOCK_SIZE) {
                lu();
            }
            else {
                int h = size / 2;
                Block M00 = new Block(M.m, M.loRow,   M.loCol);
                Block M01 = new Block(M.m, M.loRow,   M.loCol+h);
                Block M10 = new Block(M.m, M.loRow+h, M.loCol);
                Block M11 = new Block(M.m, M.loRow+h, M.loCol+h);

                new LowerUpper(h, M00).compute();
                Lower sl = new Lower(h, M00, M01);
                Upper su = new Upper(h, M00, M10);
                su.fork();
                sl.compute();
                if (su.tryUnfork()) su.compute(); else su.join();
                new Schur(h, M10, M01, M11).compute();
                new LowerUpper(h, M11).compute();
            }
        }
    }

    static Seq2 seq(RecursiveAction task1,
                               RecursiveAction task2) {
        return new Seq2(task1, task2);
    }

    static final class Seq2 extends RecursiveAction {
        final RecursiveAction fst;
        final RecursiveAction snd;
        public Seq2(RecursiveAction task1, RecursiveAction task2) {
            fst = task1;
            snd = task2;
        }
        public void compute() {
            fst.invoke();
            snd.invoke();
        }
    }

    static Seq3 seq(RecursiveAction task1,
                    RecursiveAction task2,
                    RecursiveAction task3) {
        return new Seq3(task1, task2, task3);
    }

    static final class Seq3 extends RecursiveAction {
        final RecursiveAction fst;
        final RecursiveAction snd;
        final RecursiveAction thr;
        public Seq3(RecursiveAction task1,
                    RecursiveAction task2,
                    RecursiveAction task3) {
            fst = task1;
            snd = task2;
            thr = task3;
        }
        public void compute() {
            fst.invoke();
            snd.invoke();
            thr.invoke();
        }
    }
}
Revision:	1.9
Committed:	Sat Sep 12 18:59:08 2015 UTC (8 years, 7 months ago) by dl
Branch:	MAIN
CVS Tags:	HEAD
Changes since 1.8:	+4 -3 lines
Log Message:	Use commonPool
#	Content
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	//import jsr166y.*;
8	import java.util.concurrent.*;
9
10	/**
11	* LU matrix decomposition demo
12	* Based on those in Cilk and Hood
13	*/
14	public final class LU {
15
16	/** for time conversion */
17	static final long NPS = (1000L * 1000 * 1000);
18
19	// granularity is hard-wired as compile-time constant here
20	static final int BLOCK_SIZE = 16;
21	static final boolean CHECK = false; // set true to check answer
22
23	public static void main(String[] args) throws Exception {
24
25	final String usage = "Usage: java LU <threads> <matrix size (must be a power of two)> [runs] \n For example, try java LU 2 512";
26
27	int procs = 0;
28	int n = 2048;
29	int runs = 32;
30	try {
31	if (args.length > 0)
32	procs = Integer.parseInt(args[0]);
33	if (args.length > 1)
34	n = Integer.parseInt(args[1]);
35	if (args.length > 2)
36	runs = Integer.parseInt(args[2]);
37	} catch (Exception e) {
38	System.out.println(usage);
39	return;
40	}
41
42	if ( ((n & (n - 1)) != 0)) {
43	System.out.println(usage);
44	return;
45	}
46	ForkJoinPool pool = (procs == 0) ? ForkJoinPool.commonPool() :
47	new ForkJoinPool(procs);
48	System.out.println("procs: " + pool.getParallelism() +
49	" n: " + n + " runs: " + runs);
50	for (int run = 0; run < runs; ++run) {
51	double[][] m = new double[n][n];
52	randomInit(m, n);
53	double[][] copy = null;
54	if (CHECK) {
55	copy = new double[n][n];
56	for (int i = 0; i < n; ++i) {
57	for (int j = 0; j < n; ++j) {
58	copy[i][j] = m[i][j];
59	}
60	}
61	}
62	Block M = new Block(m, 0, 0);
63	long start = System.nanoTime();
64	pool.invoke(new LowerUpper(n, M));
65	long time = System.nanoTime() - start;
66	double secs = ((double)time) / NPS;
67	System.out.printf("Time: %7.3f ", secs);
68	if ((run & 3) == 3) System.out.println();
69
70	if (CHECK) check(m, copy, n);
71	}
72	System.out.println(pool.toString());
73	pool.shutdown();
74	}
75
76	static void randomInit(double[][] M, int n) {
77	java.util.Random rng = new java.util.Random();
78	for (int i = 0; i < n; ++i)
79	for (int j = 0; j < n; ++j)
80	M[i][j] = rng.nextDouble();
81	// for compatibility with hood demo, force larger diagonals
82	for (int k = 0; k < n; ++k)
83	M[k][k] *= 10.0;
84	}
85
86	static void check(double[][] LU, double[][] M, int n) {
87	double maxDiff = 0.0; // track max difference
88	for (int i = 0; i < n; ++i) {
89	for (int j = 0; j < n; ++j) {
90	double v = 0.0;
91	int k;
92	for (k = 0; k < i && k <= j; k++ ) v += LU[i][k] * LU[k][j];
93	if (k == i && k <= j ) v += LU[k][j];
94	double diff = M[i][j] - v;
95	if (diff < 0) diff = -diff;
96	if (diff > 0.001) {
97	System.out.println("large diff at[" + i + "," + j + "]: " + M[i][j] + " vs " + v);
98	}
99	if (diff > maxDiff) maxDiff = diff;
100	}
101	}
102
103	System.out.println("Max difference = " + maxDiff);
104	}
105
106	// Blocks record underlying matrix, and offsets into current block
107	static final class Block {
108	final double[][] m;
109	final int loRow;
110	final int loCol;
111
112	Block(double[][] mat, int lr, int lc) {
113	m = mat; loRow = lr; loCol = lc;
114	}
115	}
116
117	static final class Schur extends RecursiveAction {
118	final int size;
119	final Block V;
120	final Block W;
121	final Block M;
122
123	Schur(int size, Block V, Block W, Block M) {
124	this.size = size; this.V = V; this.W = W; this.M = M;
125	}
126
127	void schur() { // base case
128	for (int j = 0; j < BLOCK_SIZE; ++j) {
129	for (int i = 0; i < BLOCK_SIZE; ++i) {
130	double s = M.m[i+M.loRow][j+M.loCol];
131	for (int k = 0; k < BLOCK_SIZE; ++k) {
132	s -= V.m[i+V.loRow][k+V.loCol] * W.m[k+W.loRow][j+W.loCol];
133	}
134	M.m[i+M.loRow][j+M.loCol] = s;
135	}
136	}
137	}
138
139	public void compute() {
140	if (size == BLOCK_SIZE) {
141	schur();
142	}
143	else {
144	int h = size / 2;
145
146	Block M00 = new Block(M.m, M.loRow, M.loCol);
147	Block M01 = new Block(M.m, M.loRow, M.loCol+h);
148	Block M10 = new Block(M.m, M.loRow+h, M.loCol);
149	Block M11 = new Block(M.m, M.loRow+h, M.loCol+h);
150
151	Block V00 = new Block(V.m, V.loRow, V.loCol);
152	Block V01 = new Block(V.m, V.loRow, V.loCol+h);
153	Block V10 = new Block(V.m, V.loRow+h, V.loCol);
154	Block V11 = new Block(V.m, V.loRow+h, V.loCol+h);
155
156	Block W00 = new Block(W.m, W.loRow, W.loCol);
157	Block W01 = new Block(W.m, W.loRow, W.loCol+h);
158	Block W10 = new Block(W.m, W.loRow+h, W.loCol);
159	Block W11 = new Block(W.m, W.loRow+h, W.loCol+h);
160
161	Seq2 s3 = seq(new Schur(h, V10, W01, M11),
162	new Schur(h, V11, W11, M11));
163	s3.fork();
164	Seq2 s2 = seq(new Schur(h, V10, W00, M10),
165	new Schur(h, V11, W10, M10));
166	s2.fork();
167	Seq2 s1 = seq(new Schur(h, V00, W01, M01),
168	new Schur(h, V01, W11, M01));
169	s1.fork();
170	new Schur(h, V00, W00, M00).compute();
171	new Schur(h, V01, W10, M00).compute();
172	if (s1.tryUnfork()) s1.compute(); else s1.join();
173	if (s2.tryUnfork()) s2.compute(); else s2.join();
174	if (s3.tryUnfork()) s3.compute(); else s3.join();
175	}
176	}
177	}
178
179	static final class Lower extends RecursiveAction {
180	final int size;
181	final Block L;
182	final Block M;
183	Lower(int size, Block L, Block M) {
184	this.size = size; this.L = L; this.M = M;
185	}
186
187	void lower() { // base case
188	for (int i = 1; i < BLOCK_SIZE; ++i) {
189	for (int k = 0; k < i; ++k) {
190	double a = L.m[i+L.loRow][k+L.loCol];
191	double[] x = M.m[k+M.loRow];
192	double[] y = M.m[i+M.loRow];
193	int n = BLOCK_SIZE;
194	for (int p = n-1; p >= 0; --p) {
195	y[p+M.loCol] -= a * x[p+M.loCol];
196	}
197	}
198	}
199	}
200
201	public void compute() {
202	if (size == BLOCK_SIZE) {
203	lower();
204	}
205	else {
206	int h = size / 2;
207
208	Block M00 = new Block(M.m, M.loRow, M.loCol);
209	Block M01 = new Block(M.m, M.loRow, M.loCol+h);
210	Block M10 = new Block(M.m, M.loRow+h, M.loCol);
211	Block M11 = new Block(M.m, M.loRow+h, M.loCol+h);
212
213	Block L00 = new Block(L.m, L.loRow, L.loCol);
214	Block L01 = new Block(L.m, L.loRow, L.loCol+h);
215	Block L10 = new Block(L.m, L.loRow+h, L.loCol);
216	Block L11 = new Block(L.m, L.loRow+h, L.loCol+h);
217
218	Seq3 s1 =
219	seq(new Lower(h, L00, M00),
220	new Schur(h, L10, M00, M10),
221	new Lower(h, L11, M10));
222	Seq3 s2 =
223	seq(new Lower(h, L00, M01),
224	new Schur(h, L10, M01, M11),
225	new Lower(h, L11, M11));
226	s2.fork();
227	s1.compute();
228	if (s2.tryUnfork()) s2.compute(); else s2.join();
229	}
230	}
231	}
232
233	static final class Upper extends RecursiveAction {
234	final int size;
235	final Block U;
236	final Block M;
237	Upper(int size, Block U, Block M) {
238	this.size = size; this.U = U; this.M = M;
239	}
240
241	void upper() { // base case
242	for (int i = 0; i < BLOCK_SIZE; ++i) {
243	for (int k = 0; k < BLOCK_SIZE; ++k) {
244	double a = M.m[i+M.loRow][k+M.loCol] / U.m[k+U.loRow][k+U.loCol];
245	M.m[i+M.loRow][k+M.loCol] = a;
246	double[] x = U.m[k+U.loRow];
247	double[] y = M.m[i+M.loRow];
248	int n = BLOCK_SIZE - k - 1;
249	for (int p = n - 1; p >= 0; --p) {
250	y[p+k+1+M.loCol] -= a * x[p+k+1+U.loCol];
251	}
252	}
253	}
254	}
255
256	public void compute() {
257	if (size == BLOCK_SIZE) {
258	upper();
259	}
260	else {
261	int h = size / 2;
262
263	Block M00 = new Block(M.m, M.loRow, M.loCol);
264	Block M01 = new Block(M.m, M.loRow, M.loCol+h);
265	Block M10 = new Block(M.m, M.loRow+h, M.loCol);
266	Block M11 = new Block(M.m, M.loRow+h, M.loCol+h);
267
268	Block U00 = new Block(U.m, U.loRow, U.loCol);
269	Block U01 = new Block(U.m, U.loRow, U.loCol+h);
270	Block U10 = new Block(U.m, U.loRow+h, U.loCol);
271	Block U11 = new Block(U.m, U.loRow+h, U.loCol+h);
272
273	Seq3 s1 =
274	seq(new Upper(h, U00, M00),
275	new Schur(h, M00, U01, M01),
276	new Upper(h, U11, M01));
277	Seq3 s2 =
278	seq(new Upper(h, U00, M10),
279	new Schur(h, M10, U01, M11),
280	new Upper(h, U11, M11));
281	s2.fork();
282	s1.compute();
283	if (s2.tryUnfork()) s2.compute(); else s2.join();
284	}
285	}
286	}
287
288	static final class LowerUpper extends RecursiveAction {
289	final int size;
290	final Block M;
291	LowerUpper(int size, Block M) {
292	this.size = size; this.M = M;
293	}
294
295	void lu() { // base case
296	for (int k = 0; k < BLOCK_SIZE; ++k) {
297	for (int i = k+1; i < BLOCK_SIZE; ++i) {
298	double b = M.m[k+M.loRow][k+M.loCol];
299	double a = M.m[i+M.loRow][k+M.loCol] / b;
300	M.m[i+M.loRow][k+M.loCol] = a;
301	double[] x = M.m[k+M.loRow];
302	double[] y = M.m[i+M.loRow];
303	int n = BLOCK_SIZE-k-1;
304	for (int p = n-1; p >= 0; --p) {
305	y[k+1+p+M.loCol] -= a * x[k+1+p+M.loCol];
306	}
307	}
308	}
309	}
310
311	public void compute() {
312	if (size == BLOCK_SIZE) {
313	lu();
314	}
315	else {
316	int h = size / 2;
317	Block M00 = new Block(M.m, M.loRow, M.loCol);
318	Block M01 = new Block(M.m, M.loRow, M.loCol+h);
319	Block M10 = new Block(M.m, M.loRow+h, M.loCol);
320	Block M11 = new Block(M.m, M.loRow+h, M.loCol+h);
321
322	new LowerUpper(h, M00).compute();
323	Lower sl = new Lower(h, M00, M01);
324	Upper su = new Upper(h, M00, M10);
325	su.fork();
326	sl.compute();
327	if (su.tryUnfork()) su.compute(); else su.join();
328	new Schur(h, M10, M01, M11).compute();
329	new LowerUpper(h, M11).compute();
330	}
331	}
332	}
333
334	static Seq2 seq(RecursiveAction task1,
335	RecursiveAction task2) {
336	return new Seq2(task1, task2);
337	}
338
339	static final class Seq2 extends RecursiveAction {
340	final RecursiveAction fst;
341	final RecursiveAction snd;
342	public Seq2(RecursiveAction task1, RecursiveAction task2) {
343	fst = task1;
344	snd = task2;
345	}
346	public void compute() {
347	fst.invoke();
348	snd.invoke();
349	}
350	}
351
352	static Seq3 seq(RecursiveAction task1,
353	RecursiveAction task2,
354	RecursiveAction task3) {
355	return new Seq3(task1, task2, task3);
356	}
357
358	static final class Seq3 extends RecursiveAction {
359	final RecursiveAction fst;
360	final RecursiveAction snd;
361	final RecursiveAction thr;
362	public Seq3(RecursiveAction task1,
363	RecursiveAction task2,
364	RecursiveAction task3) {
365	fst = task1;
366	snd = task2;
367	thr = task3;
368	}
369	public void compute() {
370	fst.invoke();
371	snd.invoke();
372	thr.invoke();
373	}
374	}
375	}