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