// time_Big_simeq.java  tough simultaneous equations to solv accurately 

import java.math.BigDecimal;

public class time_Big_simeq
{
  int nbit = 100; // bits precision being timed 

  public time_Big_simeq()
  {
    int n;
    BigDecimal err = new BigDecimal(0.0);
    double t1, t2;
    BigDecimal one = new BigDecimal(1.0);
    BigDecimal zero = new BigDecimal(0.0);
    BigDecimal tmp = new BigDecimal(0.0);
    BigDecimal sol = new BigDecimal(0.0);

    one = one.setScale(nbit, BigDecimal.ROUND_DOWN);  
    zero = zero.setScale(nbit, BigDecimal.ROUND_DOWN);

    System.out.println("time_Big_simeq.java on tough equations to solve");

    for(nbit=100; nbit<=350; nbit+=50)
    {    
      n = 16;
      while(n <= 32)
      {
        n=n*2;
        System.out.println("initializing Big matrix, n="+n+", n*n="+(n*n));
        BigDecimal AA[][] = new BigDecimal[n][n];
        BigDecimal Y[] = new BigDecimal[n];
        BigDecimal X[] = new BigDecimal[n];

        for(int i=0; i<n; i++)
        {
          for(int j=0; j<n; j++)
          {
            AA[i][j] = one.divide(new BigDecimal((i+1)+(j+1)),
                                  BigDecimal.ROUND_DOWN);
            AA[i][j] = AA[i][j].setScale(nbit, BigDecimal.ROUND_DOWN);
          }
        }
        for(int i=0; i<n; i++)
        {
	  tmp = zero;
          for(int j=0; j<n; j++)
          {
	    sol = new BigDecimal(j+1);
            tmp = tmp.add(sol.multiply(AA[i][j]));
          }
          Y[i] = tmp;
        }

	t1 = System.currentTimeMillis();
        new Big_simeq(AA, Y, X, nbit);
	t2 = System.currentTimeMillis();

        err = zero;
        for(int i=0; i<n; i++)
        {
	    err = err.add((X[i].subtract(new BigDecimal(i+1))).abs());
        }
        err = err.setScale(nbit, BigDecimal.ROUND_DOWN);
        System.out.println("nbit= "+nbit+", sum of error="+err.doubleValue());
        if(n==64)
          System.out.println("time="+((t2-t1)/8000.0)+" seconds/8");
        else
          System.out.println("time="+((t2-t1)/1000.0)+" seconds");
      }
    }
    System.out.println("finished time_Big_simeq.java");
  } // end time_Big_simeq

  public static void main (String[] args)
  {
    new time_Big_simeq();
  } // end main of time_Big_simeq.java
} // end class time_Big_simeq