spectral-norm Java program

/* The Computer Language Benchmarks Game
   https://salsa.debian.org/benchmarksgame-team/benchmarksgame/
 
 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++) {
         MultiplyAtAv(n,u,v);
         MultiplyAtAv(n,v,u);
      }
      
      // 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];
      MultiplyAv(n,v,u);
      MultiplyAtv(n,u,AtAv);
   }
}
    

NOTES:
64-bit Ubuntu quad core
openjdk 14 2020-03-17
OpenJDK Runtime Environment (build 14+36-1461)
OpenJDK 64-Bit Server VM (build 14+36-1461, mixed mode, sharing)


Tue, 05 May 2020 03:54:08 GMT

MAKE:
mv spectralnorm.java spectralnorm.java
mv: 'spectralnorm.java' and 'spectralnorm.java' are the same file
make: [/home/dunham/8000-benchmarksgame/nanobench/makefiles/u64q.programs.Makefile:239: spectralnorm.java_run] Error 1 (ignored)
/opt/src/openjdk-14/bin/javac -d .  spectralnorm.java

2.34s to complete and log all make actions

COMMAND LINE:
/opt/src/openjdk-14/bin/java   spectralnorm 5500

PROGRAM OUTPUT:
1.274224153