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, 8 months ago) by dl
Branch:	MAIN
CVS Tags:	HEAD
Changes since 1.8:	+4 -3 lines
Log Message:	Use commonPool
#	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			* LU matrix decomposition demo
12			* Based on those in Cilk and Hood
13	jsr166	1.3	*/
14	dl	1.1	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	jsr166	1.2	static final int BLOCK_SIZE = 16;
21	dl	1.1	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	dl	1.9	int runs = 32;
30	dl	1.1	try {
31			if (args.length > 0)
32			procs = Integer.parseInt(args[0]);
33			if (args.length > 1)
34			n = Integer.parseInt(args[1]);
35	jsr166	1.2	if (args.length > 2)
36	dl	1.1	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	dl	1.9	ForkJoinPool pool = (procs == 0) ? ForkJoinPool.commonPool() :
47	dl	1.1	new ForkJoinPool(procs);
48	jsr166	1.2	System.out.println("procs: " + pool.getParallelism() +
49	dl	1.1	" 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	dl	1.9	System.out.printf("Time: %7.3f ", secs);
68			if ((run & 3) == 3) System.out.println();
69	dl	1.1
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	jsr166	1.2
161	dl	1.1	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	jsr166	1.2	Seq3 s1 =
219	dl	1.1	seq(new Lower(h, L00, M00),
220			new Schur(h, L10, M00, M10),
221			new Lower(h, L11, M10));
222	jsr166	1.2	Seq3 s2 =
223	dl	1.1	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	jsr166	1.2	Seq3 s1 =
274	dl	1.1	seq(new Upper(h, U00, M00),
275			new Schur(h, M00, U01, M01),
276			new Upper(h, U11, M01));
277	jsr166	1.2	Seq3 s2 =
278	dl	1.1	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	jsr166	1.2
288	dl	1.1	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	jsr166	1.2	static Seq2 seq(RecursiveAction task1,
335			RecursiveAction task2) {
336			return new Seq2(task1, task2);
337	dl	1.1	}
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	jsr166	1.2	static Seq3 seq(RecursiveAction task1,
353	dl	1.1	RecursiveAction task2,
354	jsr166	1.2	RecursiveAction task3) {
355			return new Seq3(task1, task2, task3);
356	dl	1.1	}
357
358			static final class Seq3 extends RecursiveAction {
359			final RecursiveAction fst;
360			final RecursiveAction snd;
361			final RecursiveAction thr;
362	jsr166	1.2	public Seq3(RecursiveAction task1,
363	dl	1.1	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			}