// test_Big_inverse.java  tough matrix to invert accurately 

import java.math.BigDecimal;

public class test_Big_inverse
{
  final nbits = 332; // bits, 100 digits
  public test_Big_inverse()
  {
    int n;
    BigDecimal err;
    double time_start, now;

    System.out.println("test_Big_inverse.java on tough matrix to invert");
    n = 1;
    while(n < 256)
    {
      time_start = System.CurrentTimeMillis();
      n=n*2;
      System.out.println("initializing big matrix, n="+n+", n*n="+(n*n));
      BigDecimal AA[][] = new BigDecimal[n][n];
      BigDecimal AI[][] = new BigDecimal[n][n];
      BigDecimal II[][] = new BigDecimal[n][n];
      BigDecimal one = new BigDecimal(1.0);
      BigDecimal zero = new BigDecimal(0.0);

      one = one.setScale(nbits, BigDecimal.ROUND_DOWN);
      zero = zero.setScale(nbits, BigDecimal.ROUND_DOWN);
      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(nbits, BigDecimal.ROUND_DOWN);
        }
      }
      if(n<=4)
      {
        System.out.println("data");
        for(int i=0; i<n; i++)
        {
          for(int j=0; j<n; j++)
          {
            System.out.println("AA["+i+"]["+j+"]="+AA[i][j]);
          }
        }
      } 
      new Big_inverse(AA, AI);
      if(n<=4)
      {
        System.out.println("inverse");
        for(int i=0; i<n; i++)
        {
          for(int j=0; j<n; j++)
          {
            System.out.println("AI["+i+"]["+j+"]="+AI[i][j]);
          }
        }
      } 
      err = zero;
      for(int i=0; i<n; i++)
      {
        for(int j=0; j<n; j++)
        {
          II[i][j] = zero;
          for(int k=0; k<n; k++)
	  {
            II[i][j] = II[i][j].add(AA[i][k].multiply(AI[k][j]));
            II[i][j] = II[i][j].setScale(nbits, BigDecimal.ROUND_DOWN);
          }
          if(i == j)
            err = err.add((II[i][j].subtract(one)).abs());
          else
            err = err.add(II[i][j].abs());
        }
      }
      err = err.setScale(nbits, BigDecimal.ROUND_DOWN);
      System.out.println("AI["+n+"]["+n+"]="+AI[n-1][n-1]);
      System.out.println("sum of error="+err);
      err = (err.divide(new BigDecimal(n*n), BigDecimal.ROUND_DOWN));
      err = err.setScale(nbits, BigDecimal.ROUND_DOWN);
      System.out.println("avg error="+err);
      now = System.CurrentTimeMillis()-time_start;
      System.out.println("ran "+now+" seconds");
    }
    System.out.println("finished test_Big_inverse.java");
  } // end test_Big_inverse

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