The Computer Language
Benchmarks Game

spectral-norm Dart #5 program

source code

// The Computer Language Benchmarks Game
// http://benchmarksgame.alioth.debian.org/
//
// contributed by Jos Hirth
// based on the JavaScript version by Ian Osgood with modifications by Isaac Gouy

import 'dart:math' as math;
import 'dart:typed_data';

const int maxSmi32 = 0x3FFFFFFF;

double A(int i, int j) {
  int div = ((i + j) * (i + j + 1) >> 1) + i + 1;
  return 1.0 / div;
}

void Au(Float64List u, Float64List w) {
  int len = u.length & maxSmi32;
  for (int i = 0; i < len; ++i) {
    double t = 0.0;
    for (int j = 0; j < len; ++j) {
      t += A(i, j) * u[j];
    }
    w[i] = t;
  }
}

void Atu(Float64List w, Float64List v) {
  int len = w.length & maxSmi32;
  for (int i = 0; i < len; ++i) {
    double t = 0.0;
    for (int j = 0; j < len; ++j) {
      t += A(j, i) * w[j];
    }
    v[i] = t;
  }
}

void AtAu(Float64List u, Float64List v, Float64List w) {
  Au(u, w);
  Atu(w, v);
}

double spectralNorm(n) {
  var u = new Float64List(n)..fillRange(0, n, 1.0),
      v = new Float64List(n),
      w = new Float64List(n),
      vv = 0.0,
      vBv = 0.0;

  for (int i = 0; i < 10; ++i) {
    AtAu(u, v, w);
    AtAu(v, u, w);
  }
  for (int i = 0; i < n; ++i) {
    vBv += u[i] * v[i];
    vv += v[i] * v[i];
  }
  return math.sqrt(vBv / vv);
}

void main(args) {
  int n = args.length > 0 ? int.parse(args[0]) : 100;
  print(spectralNorm(n).toStringAsFixed(9));
}
    

notes, command-line, and program output

NOTES:
64-bit Ubuntu quad core
Dart VM version: 1.22.1 (Tue Feb 21 14:27:26 2017) on "linux_x64"


Sat, 15 Apr 2017 05:41:59 GMT

MAKE:
make: 'spectralnorm.dart-5.dart_run' is up to date.
0.03s to complete and log all make actions

COMMAND LINE:
/usr/local/src/dart-sdk/bin/dart  spectralnorm.dart-5.dart 5500

PROGRAM OUTPUT:
1.274224153