# spectral-norm C# .NET program

## 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:
.NET SDK 8.0.301
Host Version: 8.0.6
Commit: 3b8b000a0e

<OutputType>Exe
<TargetFramework>net8.0
<ImplicitUsings>enable
<Nullable>enable
<AllowUnsafeBlocks>true
<ServerGarbageCollection>true
<ConcurrentGarbageCollection>true
<PublishAot>false
<OptimizationPreference>Speed
<IlcInstructionSet>native

Wed, 29 May 2024 21:57:52 GMT

MAKE:
cp spectralnorm.csharpcore Program.cs
cp Include/csharpcore/program.csproj .
mkdir obj
cp Include/csharpcore/project.assets.json ./obj
~/dotnet/dotnet build -c Release --use-current-runtime
Determining projects to restore...
Restored /home/dunham/all-benchmarksgame/benchmarksgame_i53330/spectralnorm/tmp/program.csproj (in 849 ms).
program -> /home/dunham/all-benchmarksgame/benchmarksgame_i53330/spectralnorm/tmp/bin/Release/net8.0/linux-x64/program.dll

Build succeeded.
0 Warning(s)
0 Error(s)

Time Elapsed 00:00:05.16

6.88s to complete and log all make actions

COMMAND LINE:
./bin/Release/net8.0/linux-x64/program 5500

PROGRAM OUTPUT:
1.274224153
```