Normalizing a vector to length one, normalizing a data point into a distribution of mean zero and standard deviation of one, and generating a vector by a normal distribution. Different operations that are named similarly and might be confusion.

normalize.java

 //makes a vector of length one
public static void normalize(double a[]){
  double scale = 0 ;
  for(int k=0;k<a.length;k++){
    scale+=a[k]*a[k];
  }
  scale = 1/Math.sqrt(scale);
  for(int k=0;k<a.length;k++){
    a[k]*=scale ;
  }
}
 
//scales points with the given mean and standard deviation to have mean of zero and deviation of one
public static void normalize(double a[], double mean[], double deviation[]){
  for(int k=0;k<a.length;k++){
    a[k] = (a[k]-mean[k])/deviation[k];
  }
}

 //returns a normally distributed random vector using the box muller transform
public static double[] normaldistribution(int dim, Random rand){
 double[] axis = new double[dim];
 //generate a normally distributed random vector using the Box-Muller transform to guarantee even distrubtion of directions
 for (int k = 0; k < dim; k++){
  axis[k] = Math.sqrt(-2 * Math.log(rand.nextDouble())) * Math.sin(2 * Math.PI * rand.nextDouble());
 }
 return axis;
}