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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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// Jacobi iteration on a mesh. Based loosely on a Filaments demo |
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|
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import java.util.concurrent.*; |
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|
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public class FJJacobi { |
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|
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// static final int DEFAULT_GRANULARITY = 4096; |
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static final int DEFAULT_GRANULARITY = 256; |
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|
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/** |
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* The maximum number of matrix cells |
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* at which to stop recursing down and instead directly update. |
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*/ |
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static final double EPSILON = 0.0001; // convergence criterion |
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|
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public static void main(String[] args) throws Exception { |
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int n = 2048; |
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int steps = 1000; |
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int granularity = DEFAULT_GRANULARITY; |
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|
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try { |
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if (args.length > 0) |
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n = Integer.parseInt(args[0]); |
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if (args.length > 1) |
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steps = Integer.parseInt(args[1]); |
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if (args.length > 2) |
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granularity = Integer.parseInt(args[2]); |
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} |
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|
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catch (Exception e) { |
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System.out.println("Usage: java FJJacobi <matrix size> <max steps> [<leafcells>]"); |
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return; |
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} |
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|
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ForkJoinPool fjp = new ForkJoinPool(); |
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|
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// allocate enough space for edges |
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int dim = n+2; |
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int ncells = dim * dim; |
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double[][] a = new double[dim][dim]; |
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double[][] b = new double[dim][dim]; |
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// Initialize interiors to small value |
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double smallVal = EPSILON; // 1.0/dim; |
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for (int i = 1; i < dim-1; ++i) { |
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for (int j = 1; j < dim-1; ++j) |
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a[i][j] = smallVal; |
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} |
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// Fill all edges with 1's. |
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for (int k = 0; k < dim; ++k) { |
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a[k][0] = 1.0; |
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a[k][n+1] = 1.0; |
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a[0][k] = 1.0; |
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a[n+1][k] = 1.0; |
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b[k][0] = 1.0; |
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b[k][n+1] = 1.0; |
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b[0][k] = 1.0; |
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b[n+1][k] = 1.0; |
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} |
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int nreps = 10; |
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for (int rep = 0; rep < nreps; ++rep) { |
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Driver driver = new Driver(a, b, 1, n, 1, n, steps, granularity); |
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|
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long startTime = System.currentTimeMillis(); |
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fjp.invoke(driver); |
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|
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long time = System.currentTimeMillis() - startTime; |
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double secs = ((double)time) / 1000.0; |
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|
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System.out.println("Compute Time: " + secs); |
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System.out.println(fjp); |
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} |
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} |
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|
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abstract static class MatrixTree extends RecursiveAction { |
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// maximum difference between old and new values |
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double maxDiff; |
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public final double directCompute() { |
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compute(); |
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return maxDiff; |
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} |
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public final double joinAndReinitialize(double md) { |
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if (tryUnfork()) |
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compute(); |
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else { |
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quietlyJoin(); |
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reinitialize(); |
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} |
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double m = maxDiff; |
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return (md > m) ? md : m; |
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} |
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|
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} |
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|
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static final class LeafNode extends MatrixTree { |
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final double[][] A; // matrix to get old values from |
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final double[][] B; // matrix to put new values into |
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|
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// indices of current submatrix |
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final int loRow; final int hiRow; |
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final int loCol; final int hiCol; |
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|
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int steps = 0; // track even/odd steps |
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|
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LeafNode(double[][] A, double[][] B, |
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int loRow, int hiRow, |
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int loCol, int hiCol) { |
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this.A = A; this.B = B; |
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this.loRow = loRow; this.hiRow = hiRow; |
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this.loCol = loCol; this.hiCol = hiCol; |
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} |
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|
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public void compute() { |
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boolean AtoB = (steps++ & 1) == 0; |
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double[][] a = AtoB ? A : B; |
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double[][] b = AtoB ? B : A; |
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|
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double md = 0.0; // local for computing max diff |
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|
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for (int i = loRow; i <= hiRow; ++i) { |
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for (int j = loCol; j <= hiCol; ++j) { |
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double v = 0.25 * (a[i-1][j] + a[i][j-1] + |
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a[i+1][j] + a[i][j+1]); |
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b[i][j] = v; |
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|
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double diff = v - a[i][j]; |
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if (diff < 0) diff = -diff; |
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if (diff > md) md = diff; |
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} |
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} |
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|
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maxDiff = md; |
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} |
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} |
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|
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static final class FourNode extends MatrixTree { |
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final MatrixTree q1; |
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final MatrixTree q2; |
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final MatrixTree q3; |
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final MatrixTree q4; |
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FourNode(MatrixTree q1, MatrixTree q2, |
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MatrixTree q3, MatrixTree q4) { |
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this.q1 = q1; this.q2 = q2; this.q3 = q3; this.q4 = q4; |
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} |
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|
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public void compute() { |
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q4.fork(); |
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q3.fork(); |
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q2.fork(); |
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double md = q1.directCompute(); |
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md = q2.joinAndReinitialize(md); |
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md = q3.joinAndReinitialize(md); |
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md = q4.joinAndReinitialize(md); |
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maxDiff = md; |
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} |
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} |
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|
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static final class TwoNode extends MatrixTree { |
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final MatrixTree q1; |
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final MatrixTree q2; |
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|
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TwoNode(MatrixTree q1, MatrixTree q2) { |
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this.q1 = q1; this.q2 = q2; |
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} |
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|
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public void compute() { |
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q2.fork(); |
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maxDiff = q2.joinAndReinitialize(q1.directCompute()); |
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} |
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|
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} |
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|
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static final class Driver extends RecursiveAction { |
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MatrixTree mat; |
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double[][] A; double[][] B; |
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int firstRow; int lastRow; |
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int firstCol; int lastCol; |
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final int steps; |
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final int leafs; |
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int nleaf; |
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|
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Driver(double[][] A, double[][] B, |
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int firstRow, int lastRow, |
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int firstCol, int lastCol, |
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int steps, int leafs) { |
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this.A = A; |
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this.B = B; |
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this.firstRow = firstRow; |
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this.firstCol = firstCol; |
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this.lastRow = lastRow; |
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this.lastCol = lastCol; |
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this.steps = steps; |
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this.leafs = leafs; |
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mat = build(A, B, firstRow, lastRow, firstCol, lastCol, leafs); |
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System.out.println("Using " + nleaf + " segments"); |
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|
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} |
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|
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MatrixTree build(double[][] a, double[][] b, |
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int lr, int hr, int lc, int hc, int leafs) { |
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int rows = (hr - lr + 1); |
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int cols = (hc - lc + 1); |
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|
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int mr = (lr + hr) >>> 1; // midpoints |
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int mc = (lc + hc) >>> 1; |
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|
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int hrows = (mr - lr + 1); |
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int hcols = (mc - lc + 1); |
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|
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if (rows * cols <= leafs) { |
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++nleaf; |
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return new LeafNode(a, b, lr, hr, lc, hc); |
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} |
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else if (hrows * hcols >= leafs) { |
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return new FourNode(build(a, b, lr, mr, lc, mc, leafs), |
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build(a, b, lr, mr, mc+1, hc, leafs), |
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build(a, b, mr+1, hr, lc, mc, leafs), |
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build(a, b, mr+1, hr, mc+1, hc, leafs)); |
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} |
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else if (cols >= rows) { |
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return new TwoNode(build(a, b, lr, hr, lc, mc, leafs), |
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build(a, b, lr, hr, mc+1, hc, leafs)); |
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} |
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else { |
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return new TwoNode(build(a, b, lr, mr, lc, hc, leafs), |
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build(a, b, mr+1, hr, lc, hc, leafs)); |
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|
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} |
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} |
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|
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static void doCompute(MatrixTree m, int s) { |
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for (int i = 0; i < s; ++i) { |
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m.invoke(); |
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m.reinitialize(); |
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} |
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} |
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|
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public void compute() { |
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doCompute(mat, steps); |
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double md = mat.maxDiff; |
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System.out.println("max diff after " + steps + " steps = " + md); |
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} |
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} |
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} |
