/**
   This class implements nonnegative real vectors.
*/
public class NonNegativeVector{

    float[] coefficients;
    int dimension;
    /**
       Creates an <code>n</code> vector with <code>float</code>
       coordinates.
    */
    public NonNegativeVector(int n){
	coefficients=new float[n];
	dimension=n;
    }
    /**
       Computes the scalar product of the vector with
       the vector <code>y</code>.
    */
    public float scalarProduct(NonNegativeVector y){
	float s=0;
	for(int i=0;i<dimension;i++)
	    s+=coefficients[i]*y.coefficients[i];
	return s;
    }
    /**
       Divides all coordinates of the vector by the factor <code>r</code>.
    */
    public NonNegativeVector scale(float r){
	NonNegativeVector y=new NonNegativeVector(dimension);
	for(int i=0;i<dimension;i++)
	    y.coefficients[i]=r*coefficients[i];
	return y;
    }
    /**
       Creates the vector of dimension <code>n</code> with
       all coordinates equal to <code>1</code>..
    */
    static NonNegativeVector ones(int n){
	NonNegativeVector x=new NonNegativeVector(n);
	for(int i=0;i<n;i++)
	    x.coefficients[i]=1;
	return x;
    }

    public  String toString(){
	String s=""+coefficients[0];
	
	for(int i=1;i<dimension;i++)
	    s=s+","+coefficients[i];
	return s;
    }
}