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/licenses/publicdomain
 */

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


/**
 * 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 = 5;
        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) ? new ForkJoinPool() :
            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("\tTime: %7.3f\n", secs);

            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:	1.4
Committed:	Mon Nov 29 20:58:07 2010 UTC (13 years, 5 months ago) by jsr166
Branch:	MAIN
Changes since 1.3:	+1 -1 lines
Log Message:	consistent ternary operator style
#	User	Rev	Content
1	dl	1.1	/*
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/licenses/publicdomain
5			*/
6
7			//import jsr166y.*;
8			import java.util.concurrent.*;
9			import java.util.concurrent.TimeUnit;
10
11
12			/**
13			* LU matrix decomposition demo
14			* Based on those in Cilk and Hood
15	jsr166	1.3	*/
16	dl	1.1	public final class LU {
17
18			/** for time conversion */
19			static final long NPS = (1000L * 1000 * 1000);
20
21			// granularity is hard-wired as compile-time constant here
22	jsr166	1.2	static final int BLOCK_SIZE = 16;
23	dl	1.1	static final boolean CHECK = false; // set true to check answer
24
25			public static void main(String[] args) throws Exception {
26
27			final String usage = "Usage: java LU <threads> <matrix size (must be a power of two)> [runs] \n For example, try java LU 2 512";
28
29			int procs = 0;
30			int n = 2048;
31			int runs = 5;
32			try {
33			if (args.length > 0)
34			procs = Integer.parseInt(args[0]);
35			if (args.length > 1)
36			n = Integer.parseInt(args[1]);
37	jsr166	1.2	if (args.length > 2)
38	dl	1.1	runs = Integer.parseInt(args[2]);
39			} catch (Exception e) {
40			System.out.println(usage);
41			return;
42			}
43
44			if ( ((n & (n - 1)) != 0)) {
45			System.out.println(usage);
46			return;
47			}
48	jsr166	1.4	ForkJoinPool pool = (procs == 0) ? new ForkJoinPool() :
49	dl	1.1	new ForkJoinPool(procs);
50	jsr166	1.2	System.out.println("procs: " + pool.getParallelism() +
51	dl	1.1	" n: " + n + " runs: " + runs);
52			for (int run = 0; run < runs; ++run) {
53			double[][] m = new double[n][n];
54			randomInit(m, n);
55			double[][] copy = null;
56			if (CHECK) {
57			copy = new double[n][n];
58			for (int i = 0; i < n; ++i) {
59			for (int j = 0; j < n; ++j) {
60			copy[i][j] = m[i][j];
61			}
62			}
63			}
64			Block M = new Block(m, 0, 0);
65			long start = System.nanoTime();
66			pool.invoke(new LowerUpper(n, M));
67			long time = System.nanoTime() - start;
68			double secs = ((double)time) / NPS;
69			System.out.printf("\tTime: %7.3f\n", secs);
70
71			if (CHECK) check(m, copy, n);
72			}
73			System.out.println(pool.toString());
74			pool.shutdown();
75			}
76
77
78			static void randomInit(double[][] M, int n) {
79			java.util.Random rng = new java.util.Random();
80			for (int i = 0; i < n; ++i)
81			for (int j = 0; j < n; ++j)
82			M[i][j] = rng.nextDouble();
83			// for compatibility with hood demo, force larger diagonals
84			for (int k = 0; k < n; ++k)
85			M[k][k] *= 10.0;
86			}
87
88			static void check(double[][] LU, double[][] M, int n) {
89			double maxDiff = 0.0; // track max difference
90			for (int i = 0; i < n; ++i) {
91			for (int j = 0; j < n; ++j) {
92			double v = 0.0;
93			int k;
94			for (k = 0; k < i && k <= j; k++ ) v += LU[i][k] * LU[k][j];
95			if (k == i && k <= j ) v += LU[k][j];
96			double diff = M[i][j] - v;
97			if (diff < 0) diff = -diff;
98			if (diff > 0.001) {
99			System.out.println("large diff at[" + i + "," + j + "]: " + M[i][j] + " vs " + v);
100			}
101			if (diff > maxDiff) maxDiff = diff;
102			}
103			}
104
105			System.out.println("Max difference = " + maxDiff);
106			}
107
108
109			// Blocks record underlying matrix, and offsets into current block
110			static final class Block {
111			final double[][] m;
112			final int loRow;
113			final int loCol;
114
115			Block(double[][] mat, int lr, int lc) {
116			m = mat; loRow = lr; loCol = lc;
117			}
118			}
119
120			static final class Schur extends RecursiveAction {
121			final int size;
122			final Block V;
123			final Block W;
124			final Block M;
125
126			Schur(int size, Block V, Block W, Block M) {
127			this.size = size; this.V = V; this.W = W; this.M = M;
128			}
129
130			void schur() { // base case
131			for (int j = 0; j < BLOCK_SIZE; ++j) {
132			for (int i = 0; i < BLOCK_SIZE; ++i) {
133			double s = M.m[i+M.loRow][j+M.loCol];
134			for (int k = 0; k < BLOCK_SIZE; ++k) {
135			s -= V.m[i+V.loRow][k+V.loCol] * W.m[k+W.loRow][j+W.loCol];
136			}
137			M.m[i+M.loRow][j+M.loCol] = s;
138			}
139			}
140			}
141
142			public void compute() {
143			if (size == BLOCK_SIZE) {
144			schur();
145			}
146			else {
147			int h = size / 2;
148
149			Block M00 = new Block(M.m, M.loRow, M.loCol);
150			Block M01 = new Block(M.m, M.loRow, M.loCol+h);
151			Block M10 = new Block(M.m, M.loRow+h, M.loCol);
152			Block M11 = new Block(M.m, M.loRow+h, M.loCol+h);
153
154			Block V00 = new Block(V.m, V.loRow, V.loCol);
155			Block V01 = new Block(V.m, V.loRow, V.loCol+h);
156			Block V10 = new Block(V.m, V.loRow+h, V.loCol);
157			Block V11 = new Block(V.m, V.loRow+h, V.loCol+h);
158
159			Block W00 = new Block(W.m, W.loRow, W.loCol);
160			Block W01 = new Block(W.m, W.loRow, W.loCol+h);
161			Block W10 = new Block(W.m, W.loRow+h, W.loCol);
162			Block W11 = new Block(W.m, W.loRow+h, W.loCol+h);
163	jsr166	1.2
164	dl	1.1	Seq2 s3 = seq(new Schur(h, V10, W01, M11),
165			new Schur(h, V11, W11, M11));
166			s3.fork();
167			Seq2 s2 = seq(new Schur(h, V10, W00, M10),
168			new Schur(h, V11, W10, M10));
169			s2.fork();
170			Seq2 s1 = seq(new Schur(h, V00, W01, M01),
171			new Schur(h, V01, W11, M01));
172			s1.fork();
173			new Schur(h, V00, W00, M00).compute();
174			new Schur(h, V01, W10, M00).compute();
175			if (s1.tryUnfork()) s1.compute(); else s1.join();
176			if (s2.tryUnfork()) s2.compute(); else s2.join();
177			if (s3.tryUnfork()) s3.compute(); else s3.join();
178			}
179			}
180			}
181
182			static final class Lower extends RecursiveAction {
183			final int size;
184			final Block L;
185			final Block M;
186			Lower(int size, Block L, Block M) {
187			this.size = size; this.L = L; this.M = M;
188			}
189
190			void lower() { // base case
191			for (int i = 1; i < BLOCK_SIZE; ++i) {
192			for (int k = 0; k < i; ++k) {
193			double a = L.m[i+L.loRow][k+L.loCol];
194			double[] x = M.m[k+M.loRow];
195			double[] y = M.m[i+M.loRow];
196			int n = BLOCK_SIZE;
197			for (int p = n-1; p >= 0; --p) {
198			y[p+M.loCol] -= a * x[p+M.loCol];
199			}
200			}
201			}
202			}
203
204			public void compute() {
205			if (size == BLOCK_SIZE) {
206			lower();
207			}
208			else {
209			int h = size / 2;
210
211			Block M00 = new Block(M.m, M.loRow, M.loCol);
212			Block M01 = new Block(M.m, M.loRow, M.loCol+h);
213			Block M10 = new Block(M.m, M.loRow+h, M.loCol);
214			Block M11 = new Block(M.m, M.loRow+h, M.loCol+h);
215
216			Block L00 = new Block(L.m, L.loRow, L.loCol);
217			Block L01 = new Block(L.m, L.loRow, L.loCol+h);
218			Block L10 = new Block(L.m, L.loRow+h, L.loCol);
219			Block L11 = new Block(L.m, L.loRow+h, L.loCol+h);
220
221	jsr166	1.2
222			Seq3 s1 =
223	dl	1.1	seq(new Lower(h, L00, M00),
224			new Schur(h, L10, M00, M10),
225			new Lower(h, L11, M10));
226	jsr166	1.2	Seq3 s2 =
227	dl	1.1	seq(new Lower(h, L00, M01),
228			new Schur(h, L10, M01, M11),
229			new Lower(h, L11, M11));
230			s2.fork();
231			s1.compute();
232			if (s2.tryUnfork()) s2.compute(); else s2.join();
233			}
234			}
235			}
236
237
238			static final class Upper extends RecursiveAction {
239			final int size;
240			final Block U;
241			final Block M;
242			Upper(int size, Block U, Block M) {
243			this.size = size; this.U = U; this.M = M;
244			}
245
246			void upper() { // base case
247			for (int i = 0; i < BLOCK_SIZE; ++i) {
248			for (int k = 0; k < BLOCK_SIZE; ++k) {
249			double a = M.m[i+M.loRow][k+M.loCol] / U.m[k+U.loRow][k+U.loCol];
250			M.m[i+M.loRow][k+M.loCol] = a;
251			double[] x = U.m[k+U.loRow];
252			double[] y = M.m[i+M.loRow];
253			int n = BLOCK_SIZE - k - 1;
254			for (int p = n - 1; p >= 0; --p) {
255			y[p+k+1+M.loCol] -= a * x[p+k+1+U.loCol];
256			}
257			}
258			}
259			}
260
261
262			public void compute() {
263			if (size == BLOCK_SIZE) {
264			upper();
265			}
266			else {
267			int h = size / 2;
268
269			Block M00 = new Block(M.m, M.loRow, M.loCol);
270			Block M01 = new Block(M.m, M.loRow, M.loCol+h);
271			Block M10 = new Block(M.m, M.loRow+h, M.loCol);
272			Block M11 = new Block(M.m, M.loRow+h, M.loCol+h);
273
274			Block U00 = new Block(U.m, U.loRow, U.loCol);
275			Block U01 = new Block(U.m, U.loRow, U.loCol+h);
276			Block U10 = new Block(U.m, U.loRow+h, U.loCol);
277			Block U11 = new Block(U.m, U.loRow+h, U.loCol+h);
278
279	jsr166	1.2	Seq3 s1 =
280	dl	1.1	seq(new Upper(h, U00, M00),
281			new Schur(h, M00, U01, M01),
282			new Upper(h, U11, M01));
283	jsr166	1.2	Seq3 s2 =
284	dl	1.1	seq(new Upper(h, U00, M10),
285			new Schur(h, M10, U01, M11),
286			new Upper(h, U11, M11));
287			s2.fork();
288			s1.compute();
289			if (s2.tryUnfork()) s2.compute(); else s2.join();
290			}
291			}
292			}
293	jsr166	1.2
294	dl	1.1
295			static final class LowerUpper extends RecursiveAction {
296			final int size;
297			final Block M;
298			LowerUpper(int size, Block M) {
299			this.size = size; this.M = M;
300			}
301
302			void lu() { // base case
303			for (int k = 0; k < BLOCK_SIZE; ++k) {
304			for (int i = k+1; i < BLOCK_SIZE; ++i) {
305			double b = M.m[k+M.loRow][k+M.loCol];
306			double a = M.m[i+M.loRow][k+M.loCol] / b;
307			M.m[i+M.loRow][k+M.loCol] = a;
308			double[] x = M.m[k+M.loRow];
309			double[] y = M.m[i+M.loRow];
310			int n = BLOCK_SIZE-k-1;
311			for (int p = n-1; p >= 0; --p) {
312			y[k+1+p+M.loCol] -= a * x[k+1+p+M.loCol];
313			}
314			}
315			}
316			}
317
318			public void compute() {
319			if (size == BLOCK_SIZE) {
320			lu();
321			}
322			else {
323			int h = size / 2;
324			Block M00 = new Block(M.m, M.loRow, M.loCol);
325			Block M01 = new Block(M.m, M.loRow, M.loCol+h);
326			Block M10 = new Block(M.m, M.loRow+h, M.loCol);
327			Block M11 = new Block(M.m, M.loRow+h, M.loCol+h);
328
329			new LowerUpper(h, M00).compute();
330			Lower sl = new Lower(h, M00, M01);
331			Upper su = new Upper(h, M00, M10);
332			su.fork();
333			sl.compute();
334			if (su.tryUnfork()) su.compute(); else su.join();
335			new Schur(h, M10, M01, M11).compute();
336			new LowerUpper(h, M11).compute();
337			}
338			}
339			}
340
341	jsr166	1.2	static Seq2 seq(RecursiveAction task1,
342			RecursiveAction task2) {
343			return new Seq2(task1, task2);
344	dl	1.1	}
345
346			static final class Seq2 extends RecursiveAction {
347			final RecursiveAction fst;
348			final RecursiveAction snd;
349			public Seq2(RecursiveAction task1, RecursiveAction task2) {
350			fst = task1;
351			snd = task2;
352			}
353			public void compute() {
354			fst.invoke();
355			snd.invoke();
356			}
357			}
358
359	jsr166	1.2	static Seq3 seq(RecursiveAction task1,
360	dl	1.1	RecursiveAction task2,
361	jsr166	1.2	RecursiveAction task3) {
362			return new Seq3(task1, task2, task3);
363	dl	1.1	}
364
365			static final class Seq3 extends RecursiveAction {
366			final RecursiveAction fst;
367			final RecursiveAction snd;
368			final RecursiveAction thr;
369	jsr166	1.2	public Seq3(RecursiveAction task1,
370	dl	1.1	RecursiveAction task2,
371			RecursiveAction task3) {
372			fst = task1;
373			snd = task2;
374			thr = task3;
375			}
376			public void compute() {
377			fst.invoke();
378			snd.invoke();
379			thr.invoke();
380			}
381			}
382
383
384
385			}
386	jsr166	1.2