spectral-norm Java -Xint program

source code

```/* 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, command-line, and program output

```NOTES:
java 22 2024-03-19
Java HotSpot(TM) 64-Bit Server VM
(build 22+36-2370,
interpreted mode, sharing)

Sat, 25 May 2024 03:29:32 GMT

MAKE:
mv spectralnorm.javaxint spectralnorm.java
/opt/src/jdk-22/bin/javac -d . -cp . spectralnorm.java

1.59s to complete and log all make actions

COMMAND LINE:
/opt/src/jdk-22/bin/java -Xint  -cp . spectralnorm 5500

PROGRAM OUTPUT:
1.274224153
```