* The row slices are determined by the pj.schedule property specified * on the command line; the default is to divide the rows evenly among the * processes (i.e. no load balancing). For further information about the * pj.schedule property, see class {@linkplain edu.rit.pj.PJProperties * PJProperties}. *
* Usage: java -Dpj.np=K [ -Dpj.schedule=schedule ]
* edu.rit.clu.fractal.MandelbrotSetClu3 width height
* xcenter ycenter resolution maxiter gamma
* filename
*
K = Number of parallel processes
*
schedule = Load balancing schedule
*
width = Image width (pixels)
*
height = Image height (pixels)
*
xcenter = X coordinate of center point
*
ycenter = Y coordinate of center point
*
resolution = Pixels per unit
*
maxiter = Maximum number of iterations
*
gamma = Used to calculate pixel hues
*
filename = PJG image file name
*
* If filename is specified as, for example, "image.pjg", then * the per-worker image files are named "image_0.pjg", * "image_1.pjg", and so on through K-1. *
* The program considers a rectangular region of the complex plane centered at * (xcenter,ycenter) of width pixels by height pixels, * where the distance between adjacent pixels is 1/resolution. The * program takes each pixel's location as a complex number c and performs * the following iteration: *
* z0 = 0
*
zi+1 = zi2 + c
*
* until zi's magnitude becomes greater than or equal * to 2, or i reaches a limit of maxiter. The complex numbers * c where i reaches a limit of maxiter are considered to * be in the Mandelbrot Set. (Actually, a number is in the Mandelbrot Set only * if the iteration would continue forever without zi * becoming infinite; the foregoing is just an approximation.) The program * creates an image with the pixels corresponding to the complex numbers * c and the pixels' colors corresponding to the value of i * achieved by the iteration. Following the traditional practice, points in the * Mandelbrot set are black, and the other points are brightly colored in a * range of colors depending on i. The exact hue of each pixel is * (i/maxiter)gamma. The image is stored in a * Parallel Java Graphics (PJG) file specified on the command line. *
* The computation is performed in parallel in multiple processors. The program
* measures the computation's running time, including the time to write the
* image file.
*
* @author Alan Kaminsky
* @version 26-Dec-2009
*/
public class MandelbrotSetClu3
{
// Prevent construction.
private MandelbrotSetClu3()
{
}
// Program shared variables.
// Communicator.
static Comm world;
static int size;
static int rank;
// Command line arguments.
static int width;
static int height;
static double xcenter;
static double ycenter;
static double resolution;
static int maxiter;
static double gamma;
static File filename;
// Initial pixel offsets from center.
static int xoffset;
static int yoffset;
// Image matrix.
static int[][] matrix;
static PJGColorImage image;
static PJGImage.Writer writer;
// Table of hues.
static int[] huetable;
// Number of chunks the worker computed.
static int chunkCount;
// Main program.
/**
* Mandelbrot Set main program.
*/
public static void main
(String[] args)
throws Exception
{
// Start timing.
long t1 = System.currentTimeMillis();
// Initialize middleware.
Comm.init (args);
world = Comm.world();
size = world.size();
rank = world.rank();
// Validate command line arguments.
if (args.length != 8) usage();
width = Integer.parseInt (args[0]);
height = Integer.parseInt (args[1]);
xcenter = Double.parseDouble (args[2]);
ycenter = Double.parseDouble (args[3]);
resolution = Double.parseDouble (args[4]);
maxiter = Integer.parseInt (args[5]);
gamma = Double.parseDouble (args[6]);
filename = new File (args[7]);
// Initial pixel offsets from center.
xoffset = -(width - 1) / 2;
yoffset = (height - 1) / 2;
// Allocate storage for pixel matrix row references only.
matrix = new int [height] [];
// Prepare to write image row slices to per-worker PJG image file.
image = new PJGColorImage (height, width, matrix);
writer =
image.prepareToWrite
(new BufferedOutputStream
(new FileOutputStream
(Files.fileForRank (filename, rank))));
// Create table of hues for different iteration counts.
huetable = new int [maxiter+1];
for (int i = 0; i < maxiter; ++ i)
{
huetable[i] = HSB.pack
(/*hue*/ (float) Math.pow (((double)i)/((double)maxiter),gamma),
/*sat*/ 1.0f,
/*bri*/ 1.0f);
}
huetable[maxiter] = HSB.pack (1.0f, 1.0f, 0.0f);
long t2 = System.currentTimeMillis();
// Compute pixels in parallel.
new WorkerTeam().execute (new WorkerRegion()
{
public void run() throws Exception
{
execute (0, height-1, new WorkerIntegerForLoop()
{
// Storage for row slice of pixels.
int[][] slice = new int [0] [];
// Compute chunk of pixels, rows lb .. ub.
public void run (int lb, int ub) throws Exception
{
// Count chunks.
++ chunkCount;
// Allocate storage for row slice if necessary.
int len = ub - lb + 1;
if (slice.length < len)
{
slice = new int [len] [width];
}
// Compute pixels.
for (int r = lb; r <= ub; ++ r)
{
int[] slice_r = slice[r-lb];
double y = ycenter + (yoffset - r) / resolution;
for (int c = 0; c < width; ++ c)
{
double x = xcenter + (xoffset + c) / resolution;
// Iterate until convergence.
int i = 0;
double aold = 0.0;
double bold = 0.0;
double a = 0.0;
double b = 0.0;
double zmagsqr = 0.0;
while (i < maxiter && zmagsqr <= 4.0)
{
++ i;
a = aold*aold - bold*bold + x;
b = 2.0*aold*bold + y;
zmagsqr = a*a + b*b;
aold = a;
bold = b;
}
// Record number of iterations for pixel.
slice_r[c] = huetable[i];
}
}
// Set full pixel matrix rows to refer to slice rows.
System.arraycopy (slice, 0, matrix, lb, len);
// Write row slice of full pixel matrix to image file.
writer.writeRowSlice (new Range (lb, ub));
}
});
}
});
long t3 = System.currentTimeMillis();
// Close image file.
writer.close();
// Stop timing.
long t4 = System.currentTimeMillis();
System.out.println (chunkCount + " chunks " + rank);
System.out.println ((t2-t1) + " msec pre " + rank);
System.out.println ((t3-t2) + " msec calc " + rank);
System.out.println ((t4-t3) + " msec post " + rank);
System.out.println ((t4-t1) + " msec total " + rank);
}
// Hidden operations.
/**
* Print a usage message and exit.
*/
private static void usage()
{
System.err.println ("Usage: java -Dpj.np=