test/bench/spectral-norm.c

/*
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    documentation and/or other materials provided with the distribution.

    * Neither the name of "The Computer Language Benchmarks Game" nor the
    name of "The Computer Language Shootout Benchmarks" nor the names of
    its contributors may be used to endorse or promote products derived
    from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED.  IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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*/

/* -*- mode: c -*-
 *
 * The Great Computer Language Shootout
 * http://shootout.alioth.debian.org/
 *
 * Contributed by Sebastien Loisel
 */

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

double eval_A(int i, int j) { return 1.0/((i+j)*(i+j+1)/2+i+1); }

void eval_A_times_u(int N, const double u[], double Au[])
{
  int i,j;
  for(i=0;i<N;i++)
    {
      Au[i]=0;
      for(j=0;j<N;j++) Au[i]+=eval_A(i,j)*u[j];
    }
}

void eval_At_times_u(int N, const double u[], double Au[])
{
  int i,j;
  for(i=0;i<N;i++)
    {
      Au[i]=0;
      for(j=0;j<N;j++) Au[i]+=eval_A(j,i)*u[j];
    }
}

void eval_AtA_times_u(int N, const double u[], double AtAu[])
{ double v[N]; eval_A_times_u(N,u,v); eval_At_times_u(N,v,AtAu); }

int main(int argc, char *argv[])
{
  int i;
  int N = ((argc == 2) ? atoi(argv[1]) : 2000);
  double u[N],v[N],vBv,vv;
  for(i=0;i<N;i++) u[i]=1;
  for(i=0;i<10;i++)
    {
      eval_AtA_times_u(N,u,v);
      eval_AtA_times_u(N,v,u);
    }
  vBv=vv=0;
  for(i=0;i<N;i++) { vBv+=u[i]*v[i]; vv+=v[i]*v[i]; }
  printf("%0.9f\n",sqrt(vBv/vv));
  return 0;
}