/* 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; & CC Bordeianu, Univ Bucharest, 2007
   Support by National Science Foundation                              
*/
//  twodsol.c:  Solves SGE for 2D soliton   

#include<stdio.h>
#include<math.h> 
#define D 201

main() { 
	
	double u[D][D][3];
  int nint;
  void initial(double u[][D][3]);
  void solution(double u[][D][3], int nint);
	
                         //  Input +int proportional to viewing time
  printf(" Enter a positive integer from 1(initial time)\n");
  printf("to 1800 to get wave packet position at that time:\n");
  scanf("%d", &nint);
  initial(u);                    // Initializes constant values wave
  solution(u,nint);                                // Solve equation
}

void initial(double u[][D][3])  {             // Initialize function
  double dx, dy, dt, xx, yy, dts,time, tmp;
  int i,j;
  dx = 14./200.; dy = dx;
  dt = dx/sqrt(2.); dts = (dt/dx)*(dt/dx);
  yy = -7.; time = 0.;
  for (i = 0;i<= D-1;i++) {
    xx = -7.;
    for (j = 0;j<= D-1;j++) {
      tmp = 3.-sqrt(xx*xx+yy*yy);
      u[i][j][0] = 4.*atan(tmp);
      xx = xx+dx;       
		}
    yy = yy+dy;      
  } 
}

void solution(double u[][D][3], int nint)  {             // Solution
  double dx,dy,dt,time,a2,zz,dts,a1, tmp;
  int l,m,mm,k,j,i;
  FILE *pf;
  pf = fopen("2dsol.dat","w");
  dx = 14./200.;
  dy = dx;
  dt = dx/sqrt(2.);
  time = 0.;
  time = time+dt;
  dts = (dt/dx)*(dt/dx);
  tmp = 0.;
  for (m = 1;m<= D-2;m++)  {
      for (l = 1;l<= D-2;l++)  {
        a2 = u[m+1][l][0]+u[m-1][l][0]+u[m][l+1][0]+u[m][l-1][0];
        tmp = .25*a2;
        u[m][l][1] = .5*(dts*a2-dt*dt*sin(tmp));
    } 
  }
  for (mm = 1;mm<= D-2;mm++) {           // borders of 2nd iteration
    u[mm][0][1] = u[mm][1][1];
    u[mm][D-1][1] = u[mm][D-2][1];
    u[0][mm][1] = u[1][mm][1];
    u[D-1][mm][1] = u[D-2][mm][1]; 
	} 
  u[0][0][1] = u[1][0][1];                  // still undefined terms
  u[D-1][0][1] = u[D-2][0][1];
  u[0][D-1][1] = u[1][D-1][1];
  u[D-1][D-1][1] = u[D-2][D-1][1];
  tmp = 0.;                                    // 3rd etc iterations
  for (k = 0;k<= nint;k++) {
    for (m = 1;m<= D-2;m++) {
      for (l = 1;l<= D-2;l++) {
        a1 = u[m+1][l][1]+u[m-1][l][1]+u[m][l+1][1]+u[m][l-1][1];
        tmp = .25*a1;
        u[m][l][2] = -u[m][l][0]+dts*a1-dt*dt*sin(tmp);
        u[m][0][2] = u[m][1][2];
        u[m][D-1][2] = u[m][D-2][2];
      } 
		}
    for (mm = 1;mm<= D-2;mm++) {
      u[mm][0][2] = u[mm][1][2];
      u[mm][D-1][2] = u[mm][D-2][2];
      u[0][mm][2] = u[1][mm][2];
      u[D-1][mm][2] = u[D-2][mm][2];   
		}
    u[0][0][2] = u[1][0][2];
    u[D-1][0][2] = u[D-2][0][2];
    u[0][D-1][2] = u[1][D-1][2];
    u[D-1][D-1][2] = u[D-2][D-1][2];  
    for (l = 0;l<= D-1;l++)  {                              //recyle
      for (m = 0;m<= D-1;m++)  {
        u[l][m][0] = u[l][m][1];
        u[l][m][1] = u[l][m][2];
    } 
  }
  if (k == nint) {
    for (i = 0;i<= D-1;i = i+4) {
      for (j = 0;j<= D-1;j = j+4) 
      fprintf(pf,"%e\n",sin(u[i][j][2]/2.));
      fprintf(pf,"\n");
    }  
	}
  time = time+dt; 
  }
  fclose(pf);
}