Javakurs/Übungsaufgaben/Lineare Funktionen/Musterlösung

public class LinearFunctions {

  public static void main( String args[] ) {

    double[] y= new double[21];

    System.out.println("Es wird ein 20 zelliges Array gefüllt mit "+
                       "Funktionswerten für f(x)= x * 2 - 5  für "+
                       " x in [0,20]");

    y= fillArray(y, 0, 2, -5);

    System.out.println("Es sind "+ biggerZero(y) +" Funktionswerte"+
                       " größer als 0.");

    System.out.println("");
    System.out.println("Flächenbetrag im Interval [0,5]: "+ 
                                               absArea(2, -5, 0, 5));
    System.out.println("Flächenbetrag im Interval [0,5]: "+ 
                                               absArea(2, -5,-2, 0));

    System.out.println("");
    makeFunction(0,   1, polynomial1(0, 2, -5),  
                         polynomial1(  1, 2, -5));
    System.out.println("");
    makeFunction(0, 2.5, polynomial1(0, 2, -5),  
                         polynomial1(2.5, 2, -5));
    System.out.println("");
    makeFunction(1,   3, polynomial1(1, 2, -5),  
                         polynomial1(  3, 2, -5));
    System.out.println("");
    makeFunction(3,   5, polynomial1(3, 2, -5),  
                         polynomial1(  5, 2, -5));


    System.out.println("");
    System.out.println("offset= 5: ");
    y= offset(y, 5);
    System.out.println("Es sind "+ biggerZero(y) +" Funktionswerte"+
                       " größer als 0.");

    System.out.println("");
    System.out.println("offset= -10: ");
    y= offset(y, -10);
    System.out.println("Es sind "+ biggerZero(y) +" Funktionswerte"+
                       " größer als 0.");

  }


  /* fills array with function values f(x) = x* m +n  beginning by
   * x= start iterated by one for each entry up to the end of the 
   * array
   */
  public static double[] fillArray( double y[], double start,
                                    double m, double n       )  {
    for(int i= 0; i < y.length; i++) {
      y[i]= polynomial1( start + i, m, n);
    }
  
    return y;
  }

  /* calculates y for function y= x * m + n, a polynomial of grade 
   * one
   */
  public static double polynomial1( double x, double m, double n ) {
    return (x*m + n);
  }

  /* counts number of entrys bigger zero */
  public static double biggerZero( double y[] ) { 
    int count= 0;

    for(int i= 0; i< y.length; i++) {
      if (y[i] > 0) {
        count++;
      }
    }

    return count;
  }

  /*moves graph along ordinate by given value*/
  public static double[] offset( double y[], double value ) {
    for (int i= 0; i< y.length; i++) {
      y[i]= y[i] + value;
    }
     return y;
  }

  /* calculates y for function y= x * m + n, a polynomial of grade 
   * one
   */
  public static double polynomial2( double x,double a, double b, 
                                    double c                    ) {
    return ( x * x * a + b * x + c );
  }

  /*calculates the area under the graph for f(x)= x*m + n, x in [a,b]*/
  public static double area(double m, double n, double start, 
                            double end                       ) {
    /* define coefficients for a polynomial of grade 2  so that it is
     * the antiderivative for  f(x)= x*m + n, thus F(x)= x^2 * m/2 + x*n
     */

    double a= m/2;

    double b= n;
    double c= 0;
  
    return ( polynomial2(end, a, b, c) -  polynomial2(start, a, b, c) );
  }

  /*calculates the absolut value of the area between the graph and 
   *the ordinate in an interval 
   */
  public static double absArea(double m, double n, double start,
                               double end                       ) {
    /*is there a root in the interval? */
    if ( polynomial1(start, m, n)*polynomial1(end, m, n) < 0 ) {

      /*There is a root. Calculate the area under the abscissa, take
       *its absolut value and add the area from above the abscissa.
       */

      /* find root, 0= x*m + n, x= -n/m */
      double root= -n/m;

      return ( area(m, n, start, root)*(-1) + area(m, n, root, end));
    } else {
      /*there is no spoon*/
      double result= area(m, n, start, end);
      if ( result < 0 ) {
        return result*(-1);
      } else {
        return result;
      }
    }    
  }

  public static void makeFunction( double x1, double x2, 
                                   double y1, double y2 ) {
    /*define gradient*/
    double m = (y2-y1) /(x2-x1);
    double n= y1- m*x1;

    System.out.println("x1: "+ x1 +" x2: "+ x2 +" y1: "+ y1 +
                       " y2: "+ y2);
    System.out.println("Funktion ist: y= x*"+ m + " +"+ n);
  }

}