//	Übung 4 - Aufgabe A  (dyanmische Arrays)
//	g++ -Wno-deprecated -Wall u4A.cc
//	icc -ansi -w2 -Wall u4A.cc

#include <iostream.h>
#include <math.h>			// sqrt, sin, M_PI

int main()
{
 double *u, *w, *z;		// Pointer fuer dynamische Arrays
    int n,			// Laenge von u und w
        i;
 double u_norm, w_norm, uw_prod,// Normen und inneres Produkt
        alpha, beta,		// skalare Groesse
        t4,ti,ui,wi;			// Hilfsgroessen

//			Datenberechnung und Speicherallokierung
 cout << " Eingabe n = "; cin >> n;

//			Speicher fuer u, w, z
 u = new double [n];
 w = new double [n];
 z = new double [2*n];

//			Berechnung u,w
 t4 = 4*M_PI/(n-1);
 for ( i=0; i<n; i++ )
   {
     ti     = 1.0/(i+1);
     u[i]   = ti*ti;
     *(w+i) = sin(t4*(i-1));
   }

//		Berechnung der Normen und des Produktes in  e i n e m  Durchlauf
 u_norm = w_norm = uw_prod = 0.0;
 for ( i=0; i<n; i++ )
   {
     ui       = u[i];
     wi       = *(w+i);
     u_norm  += ui*ui;		// bzw.:  u[i] * u[i]
     w_norm  += wi*wi;		// bzw.:  *(w+i) * *(w+i)
     uw_prod += wi*ui;		// bzw.:  *(w+i) * u[i]
   }
 u_norm = sqrt(u_norm);
 w_norm = sqrt(w_norm);

//		Berechnung alpha und beta
 alpha = uw_prod/u_norm;
 beta  = uw_prod/w_norm;

//		Berechnung von z
 for ( i=0; i<n; i++ )
   {
     z[2*i]   =         u[i] + beta * *(w+i);
     z[2*i+1] = alpha * u[i] +        *(w+i);
   }

//		Datenausgabe
 cout << endl << "  Datenausgabe z" << endl << endl;
 if ( n<=20 )
   {
     for ( i=0; i<2*n; i++)
       {
         cout << i << " : " << z[i] << endl;
       }
   }
 else
   {
     cout << 0     << " : " << z[0]     << endl;
     cout << 1     << " : " << z[1]     << endl;
     cout << 2*n-2 << " : " << z[2*n-2] << endl;
     cout << 2*n-1 << " : " << z[2*n-1] << endl;
   }
 cout << endl;
 cout << " alpha = " << alpha << "    beta = " << beta << endl << endl;

 cout << " || u || = " << u_norm << "    || w || = " << w_norm
      << "    < u,w > = " << uw_prod << endl;

//		Speicherfreigabe
 delete [] z;
 delete [] w;
 delete [] u;

}