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// Licensed to the .NET Foundation under one or more agreements.
// The .NET Foundation licenses this file to you under the MIT license.
// See the LICENSE file in the project root for more information.
// Adapted from spectral-norm C# .NET Core program
// http://benchmarksgame.alioth.debian.org/u64q/program.php?test=spectralnorm&lang=csharpcore&id=1
// Best-scoring single-threaded C# .NET Core version as of 2017-09-01
/* The Computer Language Benchmarks Game
http://benchmarksgame.alioth.debian.org/
contributed by Isaac Gouy
*/
using System;
namespace BenchmarksGame
{
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);
}
}
}
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