// sigma_error.java  show error for different methods 

public class sigma_error
{
  public sigma_error()
  {
    float sigma1, sigma2;
    float x[] = new float[100];
    int n, i;
    n = 100;
    System.out.println("sigma_error.java running, n="+ n);

    for(i=0; i<n; i++)
      x[i] = 1.0f+(float)i;
    System.out.println("x 1 .. 100 ");

    sigma1 = stddeva(n, x);
    System.out.println("sum x^2 - (sum x)^2/n  sigma1 = "+ sigma1);

    sigma2 = stddevb(n, x);
    System.out.println("sum(x-mean)2/n  sigma2 ="+ sigma2);

    for(i=0; i<n; i++)
      x[i] = 1.0f+10.0f*(float)i;
    System.out.println("x 10 .. 1000 ");

    sigma1 = stddeva(n, x);
    System.out.println("sum x^2 - (sum x)^2/n  sigma1 ="+ sigma1);

    sigma2 = stddevb(n, x);
    System.out.println("sum(x-mean)2/n  sigma2 ="+ sigma2);

    for(i=0; i<n; i++)
      x[i] = 1.0f+100.0f*(float)i;
    System.out.println("x 100 .. 10000 ");

    sigma1 = stddeva(n, x);
    System.out.println("sum x^2 - (sum x)^2/n  sigma1 ="+ sigma1);

    sigma2 = stddevb(n, x);
    System.out.println("sum(x-mean)2/n  sigma2 ="+ sigma2);

    for(i=0; i<n; i++)
      x[i] = 1.0f+1000.0f*(float)i;
    System.out.println("x 1000 .. 100000 ");

    sigma1 = stddeva(n, x);
    System.out.println("sum x^2 - (sum x)^2/n  sigma1 ="+ sigma1);

    sigma2 = stddevb(n, x);
    System.out.println("sum(x-mean)2/n  sigma2 ="+ sigma2);

    for(i=0; i<n; i++)
      x[i] = 1.0f+10000.0f*(float)i;
    System.out.println("x 10000 .. 1000000 ");

    sigma1 = stddeva(n, x);
    System.out.println("sum x^2 - (sum x)^2/n  sigma1 ="+ sigma1);

    sigma2 = stddevb(n, x);
    System.out.println("sum(x-mean)2/n  sigma2 ="+ sigma2);

    for(i=0; i<n; i++)
      x[i] = 1.0f+10000.0f+(float)i;
    System.out.println("x 10001 .. 10100 ");

    sigma1 = stddeva(n, x);
    System.out.println("sum x^2 - (sum x)^2/n  sigma1 ="+ sigma1);

    sigma2 = stddevb(n, x);
    System.out.println("sum(x-mean)2/n  sigma2 ="+ sigma2);
  } // end constructor sigma_error

  float stddeva(int n, float x[])
  {
    float sdev, sumx2, sumx, rn;
    int i;

    rn = (float)n;
    sumx2 = 0.0f;
    sumx = 0.0f;
    for(i=0; i<n; i++)
    {
      sumx = sumx + x[i];
      sumx2 = sumx2 + x[i]*x[i];
    }
    sdev = (float)Math.sqrt((sumx2 - sumx*sumx/rn)/rn);
    return sdev;
  } // end stddeva

  float stddevb(int n, float x[])
  {
    float sdev, mean, sum2, rn;
    int i;

    rn = (float)n;
    mean = 0.0f;
    sum2 = 0.0f;
    for(i=0; i<n; i++)
      mean = mean + x[i];
    mean = mean/rn;
    for(i=0; i<n; i++)
      sum2 = sum2 +(x[i]-mean)*(x[i]-mean);
    sdev = (float)Math.sqrt(sum2/rn);
    return sdev;
  } // end stddevb

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