InterfaceConsiderations

/**
 * Basic vector interface.
 */
public interface VectorInterface {
  
  /**
   * @return size of the vector
   */
  public int size();

  /**
   * @param index
   * @return v(index)
   */
  public double get(int index); 
  
  /**
   * v(index) = value
   *  
   * @param index
   * @param value
   */
  public void set(int index, double value);
  
  /**
   * @param v
   * @return x = v 
   */
  public Vector set(Vector v);

  /**
   * v(index) += value
   *  
   * @param index
   * @param value
   */
  public void add(int index, double value);
  
  /**
   * @param alpha
   * @param v
   * @return  x = alpha*v + x
   */
  public boolean add(double alpha, Vector v);

  /**
   * @param v
   * @return x = v + x
   */
  public Vector add(Vector v);
  
  /**
   * @param v
   * @return x dot v
   */
  public double dot(Vector v);

  /**
   * Computes the given norm of the vector
   * 
   * @param type
   * @return norm of the vector
   */
  public double norm(Vector.Norm type);
}

/**
 * Basic matrix interface.
 */
public interface MatrixInterface {

  /**
   * @param i ith row of the matrix
   * @param j jth column of the matrix
   * @return A(i, j)
   */
  public double get(int i, int j);

  /**
   * Get a number of row of the matrix
   * 
   * @return a number of rows of the matrix
   */
  public int getRows();

  /**
   * Get a number of column of the matrix
   * 
   * @return a number of columns of the matrix
   */
  public int getColumns();

  /**
   * A(i, j) = value
   * 
   * @param i ith row of the matrix
   * @param j jth column of the matrix
   * @param value the value of entry
   */
  public void set(int i, int j, double value);

  /**
   * A=alpha*B
   * 
   * @param alpha
   * @param B
   * @return A
   */
  public Matrix set(double alpha, Matrix B);

  /**
   * A=B
   * 
   * @param B
   * @return A
   */
  public Matrix set(Matrix B);

  /**
   * A(row,column) += value
   * 
   * @param row
   * @param column
   * @param value
   */
  public void add(int row, int column, double value);

  /**
   * A = B + A
   * 
   * @param B
   * @return
   */
  public Matrix add(Matrix B);

  /**
   * A = alpha*B + A
   * 
   * @param alpha
   * @param B
   * @return A
   */
  public Matrix add(double alpha, Matrix B);

  /**
   * C = A*B
   * 
   * @param B
   * @return C
   */
  public Matrix mult(Matrix B);

  /**
   * Computes the given norm of the matrix
   * 
   * @param type
   * @return norm of the matrix
   */
  public double norm(Matrix.Norm type);
}