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 = 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:	1.7
Committed:	Wed Dec 31 16:44:01 2014 UTC (9 years, 4 months ago) by jsr166
Branch:	MAIN
Changes since 1.6:	+0 -1 lines
Log Message:	remove unused imports
#	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	jsr166	1.5	* http://creativecommons.org/publicdomain/zero/1.0/
5	dl	1.1	*/
6
7			//import jsr166y.*;
8			import java.util.concurrent.*;
9
10
11			/**
12			* LU matrix decomposition demo
13			* Based on those in Cilk and Hood
14	jsr166	1.3	*/
15	dl	1.1	public final class LU {
16
17			/** for time conversion */
18			static final long NPS = (1000L * 1000 * 1000);
19
20			// granularity is hard-wired as compile-time constant here
21	jsr166	1.2	static final int BLOCK_SIZE = 16;
22	dl	1.1	static final boolean CHECK = false; // set true to check answer
23
24			public static void main(String[] args) throws Exception {
25
26			final String usage = "Usage: java LU <threads> <matrix size (must be a power of two)> [runs] \n For example, try java LU 2 512";
27
28			int procs = 0;
29			int n = 2048;
30			int runs = 5;
31			try {
32			if (args.length > 0)
33			procs = Integer.parseInt(args[0]);
34			if (args.length > 1)
35			n = Integer.parseInt(args[1]);
36	jsr166	1.2	if (args.length > 2)
37	dl	1.1	runs = Integer.parseInt(args[2]);
38			} catch (Exception e) {
39			System.out.println(usage);
40			return;
41			}
42
43			if ( ((n & (n - 1)) != 0)) {
44			System.out.println(usage);
45			return;
46			}
47	jsr166	1.4	ForkJoinPool pool = (procs == 0) ? new ForkJoinPool() :
48	dl	1.1	new ForkJoinPool(procs);
49	jsr166	1.2	System.out.println("procs: " + pool.getParallelism() +
50	dl	1.1	" n: " + n + " runs: " + runs);
51			for (int run = 0; run < runs; ++run) {
52			double[][] m = new double[n][n];
53			randomInit(m, n);
54			double[][] copy = null;
55			if (CHECK) {
56			copy = new double[n][n];
57			for (int i = 0; i < n; ++i) {
58			for (int j = 0; j < n; ++j) {
59			copy[i][j] = m[i][j];
60			}
61			}
62			}
63			Block M = new Block(m, 0, 0);
64			long start = System.nanoTime();
65			pool.invoke(new LowerUpper(n, M));
66			long time = System.nanoTime() - start;
67			double secs = ((double)time) / NPS;
68			System.out.printf("\tTime: %7.3f\n", secs);
69
70			if (CHECK) check(m, copy, n);
71			}
72			System.out.println(pool.toString());
73			pool.shutdown();
74			}
75
76
77			static void randomInit(double[][] M, int n) {
78			java.util.Random rng = new java.util.Random();
79			for (int i = 0; i < n; ++i)
80			for (int j = 0; j < n; ++j)
81			M[i][j] = rng.nextDouble();
82			// for compatibility with hood demo, force larger diagonals
83			for (int k = 0; k < n; ++k)
84			M[k][k] *= 10.0;
85			}
86
87			static void check(double[][] LU, double[][] M, int n) {
88			double maxDiff = 0.0; // track max difference
89			for (int i = 0; i < n; ++i) {
90			for (int j = 0; j < n; ++j) {
91			double v = 0.0;
92			int k;
93			for (k = 0; k < i && k <= j; k++ ) v += LU[i][k] * LU[k][j];
94			if (k == i && k <= j ) v += LU[k][j];
95			double diff = M[i][j] - v;
96			if (diff < 0) diff = -diff;
97			if (diff > 0.001) {
98			System.out.println("large diff at[" + i + "," + j + "]: " + M[i][j] + " vs " + v);
99			}
100			if (diff > maxDiff) maxDiff = diff;
101			}
102			}
103
104			System.out.println("Max difference = " + maxDiff);
105			}
106
107
108			// Blocks record underlying matrix, and offsets into current block
109			static final class Block {
110			final double[][] m;
111			final int loRow;
112			final int loCol;
113
114			Block(double[][] mat, int lr, int lc) {
115			m = mat; loRow = lr; loCol = lc;
116			}
117			}
118
119			static final class Schur extends RecursiveAction {
120			final int size;
121			final Block V;
122			final Block W;
123			final Block M;
124
125			Schur(int size, Block V, Block W, Block M) {
126			this.size = size; this.V = V; this.W = W; this.M = M;
127			}
128
129			void schur() { // base case
130			for (int j = 0; j < BLOCK_SIZE; ++j) {
131			for (int i = 0; i < BLOCK_SIZE; ++i) {
132			double s = M.m[i+M.loRow][j+M.loCol];
133			for (int k = 0; k < BLOCK_SIZE; ++k) {
134			s -= V.m[i+V.loRow][k+V.loCol] * W.m[k+W.loRow][j+W.loCol];
135			}
136			M.m[i+M.loRow][j+M.loCol] = s;
137			}
138			}
139			}
140
141			public void compute() {
142			if (size == BLOCK_SIZE) {
143			schur();
144			}
145			else {
146			int h = size / 2;
147
148			Block M00 = new Block(M.m, M.loRow, M.loCol);
149			Block M01 = new Block(M.m, M.loRow, M.loCol+h);
150			Block M10 = new Block(M.m, M.loRow+h, M.loCol);
151			Block M11 = new Block(M.m, M.loRow+h, M.loCol+h);
152
153			Block V00 = new Block(V.m, V.loRow, V.loCol);
154			Block V01 = new Block(V.m, V.loRow, V.loCol+h);
155			Block V10 = new Block(V.m, V.loRow+h, V.loCol);
156			Block V11 = new Block(V.m, V.loRow+h, V.loCol+h);
157
158			Block W00 = new Block(W.m, W.loRow, W.loCol);
159			Block W01 = new Block(W.m, W.loRow, W.loCol+h);
160			Block W10 = new Block(W.m, W.loRow+h, W.loCol);
161			Block W11 = new Block(W.m, W.loRow+h, W.loCol+h);
162	jsr166	1.2
163	dl	1.1	Seq2 s3 = seq(new Schur(h, V10, W01, M11),
164			new Schur(h, V11, W11, M11));
165			s3.fork();
166			Seq2 s2 = seq(new Schur(h, V10, W00, M10),
167			new Schur(h, V11, W10, M10));
168			s2.fork();
169			Seq2 s1 = seq(new Schur(h, V00, W01, M01),
170			new Schur(h, V01, W11, M01));
171			s1.fork();
172			new Schur(h, V00, W00, M00).compute();
173			new Schur(h, V01, W10, M00).compute();
174			if (s1.tryUnfork()) s1.compute(); else s1.join();
175			if (s2.tryUnfork()) s2.compute(); else s2.join();
176			if (s3.tryUnfork()) s3.compute(); else s3.join();
177			}
178			}
179			}
180
181			static final class Lower extends RecursiveAction {
182			final int size;
183			final Block L;
184			final Block M;
185			Lower(int size, Block L, Block M) {
186			this.size = size; this.L = L; this.M = M;
187			}
188
189			void lower() { // base case
190			for (int i = 1; i < BLOCK_SIZE; ++i) {
191			for (int k = 0; k < i; ++k) {
192			double a = L.m[i+L.loRow][k+L.loCol];
193			double[] x = M.m[k+M.loRow];
194			double[] y = M.m[i+M.loRow];
195			int n = BLOCK_SIZE;
196			for (int p = n-1; p >= 0; --p) {
197			y[p+M.loCol] -= a * x[p+M.loCol];
198			}
199			}
200			}
201			}
202
203			public void compute() {
204			if (size == BLOCK_SIZE) {
205			lower();
206			}
207			else {
208			int h = size / 2;
209
210			Block M00 = new Block(M.m, M.loRow, M.loCol);
211			Block M01 = new Block(M.m, M.loRow, M.loCol+h);
212			Block M10 = new Block(M.m, M.loRow+h, M.loCol);
213			Block M11 = new Block(M.m, M.loRow+h, M.loCol+h);
214
215			Block L00 = new Block(L.m, L.loRow, L.loCol);
216			Block L01 = new Block(L.m, L.loRow, L.loCol+h);
217			Block L10 = new Block(L.m, L.loRow+h, L.loCol);
218			Block L11 = new Block(L.m, L.loRow+h, L.loCol+h);
219
220	jsr166	1.2
221			Seq3 s1 =
222	dl	1.1	seq(new Lower(h, L00, M00),
223			new Schur(h, L10, M00, M10),
224			new Lower(h, L11, M10));
225	jsr166	1.2	Seq3 s2 =
226	dl	1.1	seq(new Lower(h, L00, M01),
227			new Schur(h, L10, M01, M11),
228			new Lower(h, L11, M11));
229			s2.fork();
230			s1.compute();
231			if (s2.tryUnfork()) s2.compute(); else s2.join();
232			}
233			}
234			}
235
236
237			static final class Upper extends RecursiveAction {
238			final int size;
239			final Block U;
240			final Block M;
241			Upper(int size, Block U, Block M) {
242			this.size = size; this.U = U; this.M = M;
243			}
244
245			void upper() { // base case
246			for (int i = 0; i < BLOCK_SIZE; ++i) {
247			for (int k = 0; k < BLOCK_SIZE; ++k) {
248			double a = M.m[i+M.loRow][k+M.loCol] / U.m[k+U.loRow][k+U.loCol];
249			M.m[i+M.loRow][k+M.loCol] = a;
250			double[] x = U.m[k+U.loRow];
251			double[] y = M.m[i+M.loRow];
252			int n = BLOCK_SIZE - k - 1;
253			for (int p = n - 1; p >= 0; --p) {
254			y[p+k+1+M.loCol] -= a * x[p+k+1+U.loCol];
255			}
256			}
257			}
258			}
259
260
261			public void compute() {
262			if (size == BLOCK_SIZE) {
263			upper();
264			}
265			else {
266			int h = size / 2;
267
268			Block M00 = new Block(M.m, M.loRow, M.loCol);
269			Block M01 = new Block(M.m, M.loRow, M.loCol+h);
270			Block M10 = new Block(M.m, M.loRow+h, M.loCol);
271			Block M11 = new Block(M.m, M.loRow+h, M.loCol+h);
272
273			Block U00 = new Block(U.m, U.loRow, U.loCol);
274			Block U01 = new Block(U.m, U.loRow, U.loCol+h);
275			Block U10 = new Block(U.m, U.loRow+h, U.loCol);
276			Block U11 = new Block(U.m, U.loRow+h, U.loCol+h);
277
278	jsr166	1.2	Seq3 s1 =
279	dl	1.1	seq(new Upper(h, U00, M00),
280			new Schur(h, M00, U01, M01),
281			new Upper(h, U11, M01));
282	jsr166	1.2	Seq3 s2 =
283	dl	1.1	seq(new Upper(h, U00, M10),
284			new Schur(h, M10, U01, M11),
285			new Upper(h, U11, M11));
286			s2.fork();
287			s1.compute();
288			if (s2.tryUnfork()) s2.compute(); else s2.join();
289			}
290			}
291			}
292	jsr166	1.2
293	dl	1.1
294			static final class LowerUpper extends RecursiveAction {
295			final int size;
296			final Block M;
297			LowerUpper(int size, Block M) {
298			this.size = size; this.M = M;
299			}
300
301			void lu() { // base case
302			for (int k = 0; k < BLOCK_SIZE; ++k) {
303			for (int i = k+1; i < BLOCK_SIZE; ++i) {
304			double b = M.m[k+M.loRow][k+M.loCol];
305			double a = M.m[i+M.loRow][k+M.loCol] / b;
306			M.m[i+M.loRow][k+M.loCol] = a;
307			double[] x = M.m[k+M.loRow];
308			double[] y = M.m[i+M.loRow];
309			int n = BLOCK_SIZE-k-1;
310			for (int p = n-1; p >= 0; --p) {
311			y[k+1+p+M.loCol] -= a * x[k+1+p+M.loCol];
312			}
313			}
314			}
315			}
316
317			public void compute() {
318			if (size == BLOCK_SIZE) {
319			lu();
320			}
321			else {
322			int h = size / 2;
323			Block M00 = new Block(M.m, M.loRow, M.loCol);
324			Block M01 = new Block(M.m, M.loRow, M.loCol+h);
325			Block M10 = new Block(M.m, M.loRow+h, M.loCol);
326			Block M11 = new Block(M.m, M.loRow+h, M.loCol+h);
327
328			new LowerUpper(h, M00).compute();
329			Lower sl = new Lower(h, M00, M01);
330			Upper su = new Upper(h, M00, M10);
331			su.fork();
332			sl.compute();
333			if (su.tryUnfork()) su.compute(); else su.join();
334			new Schur(h, M10, M01, M11).compute();
335			new LowerUpper(h, M11).compute();
336			}
337			}
338			}
339
340	jsr166	1.2	static Seq2 seq(RecursiveAction task1,
341			RecursiveAction task2) {
342			return new Seq2(task1, task2);
343	dl	1.1	}
344
345			static final class Seq2 extends RecursiveAction {
346			final RecursiveAction fst;
347			final RecursiveAction snd;
348			public Seq2(RecursiveAction task1, RecursiveAction task2) {
349			fst = task1;
350			snd = task2;
351			}
352			public void compute() {
353			fst.invoke();
354			snd.invoke();
355			}
356			}
357
358	jsr166	1.2	static Seq3 seq(RecursiveAction task1,
359	dl	1.1	RecursiveAction task2,
360	jsr166	1.2	RecursiveAction task3) {
361			return new Seq3(task1, task2, task3);
362	dl	1.1	}
363
364			static final class Seq3 extends RecursiveAction {
365			final RecursiveAction fst;
366			final RecursiveAction snd;
367			final RecursiveAction thr;
368	jsr166	1.2	public Seq3(RecursiveAction task1,
369	dl	1.1	RecursiveAction task2,
370			RecursiveAction task3) {
371			fst = task1;
372			snd = task2;
373			thr = task3;
374			}
375			public void compute() {
376			fst.invoke();
377			snd.invoke();
378			thr.invoke();
379			}
380			}
381			}