static double innprod(double[] c, double[] x){  //Innen-Produkt c^T x
    double sum = 0;
    for (int i=0; i<c.length; i++) sum += c[i]*x[i];
    return sum;
  }

  static void rang1kor(int s, double[] w, double[][] Bi){  //Rang-1-Korrektur in Bi
    int m = Bi.length;
    double q = w[s];
    for (int j=0; j<m; j++) Bi[s][j] = Bi[s][j]/q;
    for (int i=0; i<m; i++) if (i!=s) {
      for (int j=0; j<m; j++) Bi[i][j] -= w[i]*Bi[s][j];
    }
  }

  static double[] mvmul(double[][] B, double[] x){ //Matrix-Vektorprodukt B*x
    int m = B.length;
    double[] y = new double[m];
    double sum=0;
    for (int i=0; i<m; i++){
      for (int j=0; j<m; j++) sum += B[i][j]*x[j];
      y[i] = sum;
      sum = 0;
    }
    return y;
  }

  static double[] vmmul(double[][] B, double[] x){ //Vektor-Matrixprodukt x^T*B
    int m = B.length;
    double[] y = new double[m];
    double sum=0;
    for (int j=0; j<m; j++){
      for (int i=0; i<m; i++) sum += x[i]*B[i][j];
      y[j] = sum;
      sum = 0;
    }
    return y;
  }