source code
/* The Computer Language Benchmarks Game
https://salsa.debian.org/benchmarksgame-team/benchmarksgame/
contributed by Isaac Gouy
*/
using System;
class SpectralNorm
{
public static void Main(String[] args) {
int n = 100;
if (args.Length > 0) n = Int32.Parse(args[0]);
Console.WriteLine("{0:f9}", new SpectralNorm().Approximate(n));
}
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 */
double A(int i, int j){
return 1.0/((i+j)*(i+j+1)/2 +i+1);
}
/* multiply vector v by matrix A */
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 */
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 */
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:
64-bit Ubuntu quad core
.NET SDK 8.0.200
Host Version: 8.0.2
Commit: 1381d5ebd2
<ServerGarbageCollection>true
<PublishAot>true
Mon, 01 Apr 2024 20:23:47 GMT
MAKE:
cp spectralnorm.csharpaot Program.cs
cp Include/csharpaot/tmp.csproj .
mkdir obj
cp Include/csharpaot/project.assets.json ./obj
/usr/bin/dotnet publish -c Release -r linux-x64
MSBuild version 17.9.6+a4ecab324 for .NET
Determining projects to restore...
Restored /home/dunham/all-benchmarksgame/benchmarksgame_i53330/spectralnorm/tmp/tmp.csproj (in 894 ms).
tmp -> /home/dunham/all-benchmarksgame/benchmarksgame_i53330/spectralnorm/tmp/bin/Release/net8.0/linux-x64/tmp.dll
Generating native code
tmp -> /home/dunham/all-benchmarksgame/benchmarksgame_i53330/spectralnorm/tmp/bin/Release/net8.0/linux-x64/publish/
17.92s to complete and log all make actions
COMMAND LINE:
./bin/Release/net8.0/linux-x64/publish/tmp 5500
PROGRAM OUTPUT:
1.274224153