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/* |
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* Written by Doug Lea with assistance from members of JCP JSR-166 |
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* Expert Group and released to the public domain, as explained at |
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* http://creativecommons.org/publicdomain/zero/1.0/ |
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*/ |
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|
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//import jsr166y.*; |
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import java.util.concurrent.*; |
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|
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/** |
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* LU matrix decomposition demo |
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* Based on those in Cilk and Hood |
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*/ |
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public final class LU { |
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|
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/** for time conversion */ |
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static final long NPS = (1000L * 1000 * 1000); |
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|
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// granularity is hard-wired as compile-time constant here |
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static final int BLOCK_SIZE = 16; |
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static final boolean CHECK = false; // set true to check answer |
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|
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public static void main(String[] args) throws Exception { |
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|
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final String usage = "Usage: java LU <threads> <matrix size (must be a power of two)> [runs] \n For example, try java LU 2 512"; |
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|
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int procs = 0; |
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int n = 2048; |
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int runs = 5; |
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try { |
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if (args.length > 0) |
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procs = Integer.parseInt(args[0]); |
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if (args.length > 1) |
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n = Integer.parseInt(args[1]); |
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if (args.length > 2) |
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runs = Integer.parseInt(args[2]); |
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} catch (Exception e) { |
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System.out.println(usage); |
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return; |
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} |
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|
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if ( ((n & (n - 1)) != 0)) { |
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System.out.println(usage); |
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return; |
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} |
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ForkJoinPool pool = (procs == 0) ? new ForkJoinPool() : |
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new ForkJoinPool(procs); |
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System.out.println("procs: " + pool.getParallelism() + |
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" n: " + n + " runs: " + runs); |
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for (int run = 0; run < runs; ++run) { |
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double[][] m = new double[n][n]; |
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randomInit(m, n); |
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double[][] copy = null; |
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if (CHECK) { |
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copy = new double[n][n]; |
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for (int i = 0; i < n; ++i) { |
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for (int j = 0; j < n; ++j) { |
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copy[i][j] = m[i][j]; |
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} |
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} |
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} |
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Block M = new Block(m, 0, 0); |
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long start = System.nanoTime(); |
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pool.invoke(new LowerUpper(n, M)); |
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long time = System.nanoTime() - start; |
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double secs = ((double)time) / NPS; |
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System.out.printf("\tTime: %7.3f\n", secs); |
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|
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if (CHECK) check(m, copy, n); |
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} |
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System.out.println(pool.toString()); |
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pool.shutdown(); |
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} |
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|
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static void randomInit(double[][] M, int n) { |
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java.util.Random rng = new java.util.Random(); |
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for (int i = 0; i < n; ++i) |
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for (int j = 0; j < n; ++j) |
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M[i][j] = rng.nextDouble(); |
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// for compatibility with hood demo, force larger diagonals |
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for (int k = 0; k < n; ++k) |
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M[k][k] *= 10.0; |
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} |
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|
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static void check(double[][] LU, double[][] M, int n) { |
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double maxDiff = 0.0; // track max difference |
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for (int i = 0; i < n; ++i) { |
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for (int j = 0; j < n; ++j) { |
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double v = 0.0; |
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int k; |
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for (k = 0; k < i && k <= j; k++ ) v += LU[i][k] * LU[k][j]; |
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if (k == i && k <= j ) v += LU[k][j]; |
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double diff = M[i][j] - v; |
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if (diff < 0) diff = -diff; |
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if (diff > 0.001) { |
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System.out.println("large diff at[" + i + "," + j + "]: " + M[i][j] + " vs " + v); |
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} |
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if (diff > maxDiff) maxDiff = diff; |
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} |
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} |
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|
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System.out.println("Max difference = " + maxDiff); |
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} |
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|
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// Blocks record underlying matrix, and offsets into current block |
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static final class Block { |
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final double[][] m; |
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final int loRow; |
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final int loCol; |
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|
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Block(double[][] mat, int lr, int lc) { |
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m = mat; loRow = lr; loCol = lc; |
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} |
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} |
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|
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static final class Schur extends RecursiveAction { |
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final int size; |
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final Block V; |
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final Block W; |
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final Block M; |
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|
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Schur(int size, Block V, Block W, Block M) { |
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this.size = size; this.V = V; this.W = W; this.M = M; |
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} |
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|
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void schur() { // base case |
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for (int j = 0; j < BLOCK_SIZE; ++j) { |
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for (int i = 0; i < BLOCK_SIZE; ++i) { |
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double s = M.m[i+M.loRow][j+M.loCol]; |
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for (int k = 0; k < BLOCK_SIZE; ++k) { |
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s -= V.m[i+V.loRow][k+V.loCol] * W.m[k+W.loRow][j+W.loCol]; |
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} |
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M.m[i+M.loRow][j+M.loCol] = s; |
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} |
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} |
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} |
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|
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public void compute() { |
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if (size == BLOCK_SIZE) { |
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schur(); |
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} |
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else { |
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int h = size / 2; |
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|
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Block M00 = new Block(M.m, M.loRow, M.loCol); |
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Block M01 = new Block(M.m, M.loRow, M.loCol+h); |
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Block M10 = new Block(M.m, M.loRow+h, M.loCol); |
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Block M11 = new Block(M.m, M.loRow+h, M.loCol+h); |
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|
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Block V00 = new Block(V.m, V.loRow, V.loCol); |
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Block V01 = new Block(V.m, V.loRow, V.loCol+h); |
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Block V10 = new Block(V.m, V.loRow+h, V.loCol); |
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Block V11 = new Block(V.m, V.loRow+h, V.loCol+h); |
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|
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Block W00 = new Block(W.m, W.loRow, W.loCol); |
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Block W01 = new Block(W.m, W.loRow, W.loCol+h); |
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Block W10 = new Block(W.m, W.loRow+h, W.loCol); |
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Block W11 = new Block(W.m, W.loRow+h, W.loCol+h); |
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|
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Seq2 s3 = seq(new Schur(h, V10, W01, M11), |
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new Schur(h, V11, W11, M11)); |
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s3.fork(); |
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Seq2 s2 = seq(new Schur(h, V10, W00, M10), |
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new Schur(h, V11, W10, M10)); |
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s2.fork(); |
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Seq2 s1 = seq(new Schur(h, V00, W01, M01), |
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new Schur(h, V01, W11, M01)); |
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s1.fork(); |
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new Schur(h, V00, W00, M00).compute(); |
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new Schur(h, V01, W10, M00).compute(); |
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if (s1.tryUnfork()) s1.compute(); else s1.join(); |
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if (s2.tryUnfork()) s2.compute(); else s2.join(); |
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if (s3.tryUnfork()) s3.compute(); else s3.join(); |
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} |
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} |
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} |
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|
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static final class Lower extends RecursiveAction { |
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final int size; |
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final Block L; |
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final Block M; |
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Lower(int size, Block L, Block M) { |
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this.size = size; this.L = L; this.M = M; |
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} |
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|
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void lower() { // base case |
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for (int i = 1; i < BLOCK_SIZE; ++i) { |
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for (int k = 0; k < i; ++k) { |
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double a = L.m[i+L.loRow][k+L.loCol]; |
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double[] x = M.m[k+M.loRow]; |
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double[] y = M.m[i+M.loRow]; |
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int n = BLOCK_SIZE; |
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for (int p = n-1; p >= 0; --p) { |
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y[p+M.loCol] -= a * x[p+M.loCol]; |
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} |
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} |
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} |
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} |
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|
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public void compute() { |
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if (size == BLOCK_SIZE) { |
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lower(); |
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} |
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else { |
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int h = size / 2; |
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|
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Block M00 = new Block(M.m, M.loRow, M.loCol); |
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Block M01 = new Block(M.m, M.loRow, M.loCol+h); |
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Block M10 = new Block(M.m, M.loRow+h, M.loCol); |
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Block M11 = new Block(M.m, M.loRow+h, M.loCol+h); |
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|
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Block L00 = new Block(L.m, L.loRow, L.loCol); |
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Block L01 = new Block(L.m, L.loRow, L.loCol+h); |
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Block L10 = new Block(L.m, L.loRow+h, L.loCol); |
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Block L11 = new Block(L.m, L.loRow+h, L.loCol+h); |
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|
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Seq3 s1 = |
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seq(new Lower(h, L00, M00), |
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new Schur(h, L10, M00, M10), |
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new Lower(h, L11, M10)); |
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Seq3 s2 = |
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seq(new Lower(h, L00, M01), |
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new Schur(h, L10, M01, M11), |
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new Lower(h, L11, M11)); |
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s2.fork(); |
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s1.compute(); |
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if (s2.tryUnfork()) s2.compute(); else s2.join(); |
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} |
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} |
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} |
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|
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static final class Upper extends RecursiveAction { |
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final int size; |
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final Block U; |
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final Block M; |
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Upper(int size, Block U, Block M) { |
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this.size = size; this.U = U; this.M = M; |
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} |
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|
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void upper() { // base case |
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for (int i = 0; i < BLOCK_SIZE; ++i) { |
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for (int k = 0; k < BLOCK_SIZE; ++k) { |
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double a = M.m[i+M.loRow][k+M.loCol] / U.m[k+U.loRow][k+U.loCol]; |
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M.m[i+M.loRow][k+M.loCol] = a; |
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double[] x = U.m[k+U.loRow]; |
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double[] y = M.m[i+M.loRow]; |
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int n = BLOCK_SIZE - k - 1; |
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for (int p = n - 1; p >= 0; --p) { |
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y[p+k+1+M.loCol] -= a * x[p+k+1+U.loCol]; |
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} |
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} |
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} |
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} |
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|
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public void compute() { |
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if (size == BLOCK_SIZE) { |
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upper(); |
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} |
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else { |
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int h = size / 2; |
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|
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Block M00 = new Block(M.m, M.loRow, M.loCol); |
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Block M01 = new Block(M.m, M.loRow, M.loCol+h); |
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Block M10 = new Block(M.m, M.loRow+h, M.loCol); |
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Block M11 = new Block(M.m, M.loRow+h, M.loCol+h); |
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|
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Block U00 = new Block(U.m, U.loRow, U.loCol); |
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Block U01 = new Block(U.m, U.loRow, U.loCol+h); |
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Block U10 = new Block(U.m, U.loRow+h, U.loCol); |
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Block U11 = new Block(U.m, U.loRow+h, U.loCol+h); |
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|
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Seq3 s1 = |
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seq(new Upper(h, U00, M00), |
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new Schur(h, M00, U01, M01), |
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new Upper(h, U11, M01)); |
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Seq3 s2 = |
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seq(new Upper(h, U00, M10), |
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new Schur(h, M10, U01, M11), |
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new Upper(h, U11, M11)); |
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s2.fork(); |
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s1.compute(); |
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if (s2.tryUnfork()) s2.compute(); else s2.join(); |
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} |
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} |
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} |
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|
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static final class LowerUpper extends RecursiveAction { |
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final int size; |
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final Block M; |
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LowerUpper(int size, Block M) { |
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this.size = size; this.M = M; |
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} |
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|
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void lu() { // base case |
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for (int k = 0; k < BLOCK_SIZE; ++k) { |
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for (int i = k+1; i < BLOCK_SIZE; ++i) { |
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double b = M.m[k+M.loRow][k+M.loCol]; |
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double a = M.m[i+M.loRow][k+M.loCol] / b; |
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M.m[i+M.loRow][k+M.loCol] = a; |
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double[] x = M.m[k+M.loRow]; |
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double[] y = M.m[i+M.loRow]; |
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int n = BLOCK_SIZE-k-1; |
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for (int p = n-1; p >= 0; --p) { |
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y[k+1+p+M.loCol] -= a * x[k+1+p+M.loCol]; |
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} |
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} |
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} |
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} |
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|
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public void compute() { |
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if (size == BLOCK_SIZE) { |
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lu(); |
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} |
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else { |
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int h = size / 2; |
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Block M00 = new Block(M.m, M.loRow, M.loCol); |
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Block M01 = new Block(M.m, M.loRow, M.loCol+h); |
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Block M10 = new Block(M.m, M.loRow+h, M.loCol); |
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Block M11 = new Block(M.m, M.loRow+h, M.loCol+h); |
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|
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new LowerUpper(h, M00).compute(); |
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Lower sl = new Lower(h, M00, M01); |
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Upper su = new Upper(h, M00, M10); |
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su.fork(); |
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sl.compute(); |
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if (su.tryUnfork()) su.compute(); else su.join(); |
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new Schur(h, M10, M01, M11).compute(); |
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new LowerUpper(h, M11).compute(); |
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} |
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} |
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} |
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|
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static Seq2 seq(RecursiveAction task1, |
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RecursiveAction task2) { |
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return new Seq2(task1, task2); |
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} |
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|
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static final class Seq2 extends RecursiveAction { |
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final RecursiveAction fst; |
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final RecursiveAction snd; |
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public Seq2(RecursiveAction task1, RecursiveAction task2) { |
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fst = task1; |
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snd = task2; |
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} |
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public void compute() { |
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fst.invoke(); |
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snd.invoke(); |
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} |
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} |
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|
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static Seq3 seq(RecursiveAction task1, |
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RecursiveAction task2, |
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RecursiveAction task3) { |
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return new Seq3(task1, task2, task3); |
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} |
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|
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static final class Seq3 extends RecursiveAction { |
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final RecursiveAction fst; |
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final RecursiveAction snd; |
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final RecursiveAction thr; |
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public Seq3(RecursiveAction task1, |
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RecursiveAction task2, |
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RecursiveAction task3) { |
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fst = task1; |
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snd = task2; |
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thr = task3; |
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} |
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public void compute() { |
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fst.invoke(); |
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snd.invoke(); |
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thr.invoke(); |
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} |
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} |
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} |
