The Computer Language
Benchmarks Game

spectral-norm Java program

source code

/* The Computer Language Benchmarks Game
 contributed by Java novice Jarkko Miettinen
 modified ~3 lines of the original C#-version 
 by Isaac Gouy
import java.text.DecimalFormat;
import java.text.NumberFormat; 

public class spectralnorm
   private static final NumberFormat formatter = new DecimalFormat("#.000000000");
   public static void main(String[] args) {
      int n = 100;
      if (args.length > 0) n = Integer.parseInt(args[0]);
      System.out.println(formatter.format(new spectralnorm().Approximate(n)));
   private final double Approximate(int n) {
      // create unit vector
      double[] u = new double[n];
      for (int i=0; i<n; i++) u[i] =  1;
      // 20 steps of the power method
      double[] v = new double[n];
      for (int i=0; i<n; i++) v[i] = 0;
      for (int i=0; i<10; i++) {
      // B=AtA         A multiplied by A transposed
      // v.Bv /(v.v)   eigenvalue of v
      double vBv = 0, vv = 0;
      for (int i=0; i<n; i++) {
         vBv += u[i]*v[i];
         vv  += v[i]*v[i];
      return Math.sqrt(vBv/vv);
   /* return element i,j of infinite matrix A */
   private final double A(int i, int j){
      return 1.0/((i+j)*(i+j+1)/2 +i+1);
   /* multiply vector v by matrix A */
   private final void MultiplyAv(int n, double[] v, double[] Av){
      for (int i=0; i<n; i++){
         Av[i] = 0;
         for (int j=0; j<n; j++) Av[i] += A(i,j)*v[j];
   /* multiply vector v by matrix A transposed */
   private final void MultiplyAtv(int n, double[] v, double[] Atv){
      for (int i=0;i<n;i++){
         Atv[i] = 0;
         for (int j=0; j<n; j++) Atv[i] += A(j,i)*v[j];
   /* multiply vector v by matrix A and then by matrix A transposed */
   private final void MultiplyAtAv(int n, double[] v, double[] AtAv){
      double[] u = new double[n];

notes, command-line, and program output

64-bit Ubuntu quad core
java version "1.8.0_121"
Java(TM) SE Runtime Environment (build 1.8.0_121-b13)
Java HotSpot(TM) 64-Bit Server VM (build 25.121-b13, mixed mode)

Mon, 06 Feb 2017 04:27:57 GMT

mv: '' and '' are the same file
/home/dunham/benchmarksgame/nanobench/makefiles/u64q.programs.Makefile:338: recipe for target 'spectralnorm.java_run' failed
make: [spectralnorm.java_run] Error 1 (ignored)
/usr/local/src/jdk1.8.0_121/bin/javac -d .
0.76s to complete and log all make actions

/usr/local/src/jdk1.8.0_121/bin/java   spectralnorm 5500