/* From: "COMPUTATIONAL PHYSICS, 2nd Ed" 
   by RH Landau, MJ Paez, and CC Bordeianu 
   Copyright Wiley-VCH, 2007.
   Electronic Materials copyright: R Landau, Oregon State Univ, 2007;
   MJ Paez, Univ Antioquia, 2007; and CC Bordeianu, Univ Bucharest, 2007.
   Support by National Science Foundation                              
*/
// Tune4.java: matrix algebra program, basic optimization      

public class Tune4  {
    
    public static void main(String[] argv)  { 
			
      final int Ldim = 2051;   
      int i, j, iter = 0; 
      double [][] ham = new double [Ldim] [Ldim]; 
      double []   diag = new double [Ldim]; 
      double [] coef  = new double [Ldim]; 
      double [] sigma = new double [Ldim];   
      double err, ener, ovlp, ovlp1, ovlp2; 
      double step = 0., fact, time, t, t1, t2, u; 
			
      time = System.currentTimeMillis();        // Store initial time
			                                          // Set up Hamiltonian
      for ( i = 1;  i <= Ldim-1;  i++ )   {         
        for ( j = 1;  j <= Ldim-1;  j++ )  
          if (Math.abs(j-i) >10) ham[j][i] = 0. ; 
          else  ham[j][i] = Math.pow(0.3, Math.abs(j-i));    
        }   
                                          // Iterate towards solution
      for ( i=1;  i < Ldim-1;  i++ ) {        
        ham[i][i] = i ; 
        coef[i] = 0.;  
        diag[i] = ham [i][i]; 
      }
      coef[1] = 1.;  
      err = 1.;  
      iter = 0 ;  
      while (iter  < 15 && err > 1.e-6)  {
        iter = iter + 1; 
                                // compute current energy & normalize
        ener = 0. ; 
        ovlp1 = 0.;  
        ovlp2 = 0.; 
        for ( i= 1;  i <= Ldim-2;  i = i + 2  ) {   
          ovlp1 = ovlp1 + coef[i]*coef[i] ;   
          ovlp2 = ovlp2 + coef[i+1]*coef[i+1] ;   
          t1 = 0.; 
          t2 = 0.; 
          for ( j=1;  j <= Ldim-1;  j++ )  {
            t1 = t1 + coef[j]*ham[j][i]; 
            t2 = t2 + coef[j]*ham[j][i+1]; 
          }
          sigma[i] = t1;   
          sigma[i + 1] = t2;   
          ener = ener + coef[i]*t1 + coef[i+1]*t2 ; 
        }   
        ovlp = ovlp1 + ovlp2 ; 
        ener = ener/ovlp; 
        fact = 1./Math.sqrt(ovlp); 
        coef[1] = fact*coef[1]; 
        err = 0.;   
				                                       // Update & error norm
        for ( i = 2;  i <= Ldim-1;  i++ ) {        
          t = fact*coef[i]; 
          u = fact*sigma[i]-ener*t; 
          step = u/(ener-diag[i]) ;  
          coef[i] = t + step  ; 
          err = err +  step*step  ; 
        }  
        err = Math.sqrt(err) ;  
        System.out.println 
                  ("iter, ener, err "+iter+", " + ener + ", " + err);
      }   
      time = (System.currentTimeMillis() - time)/1000; 
      System.out.println("time = " + time + "s");     // Elapsed time
  }
}