//Describe the rhs functions which depend on parameters X and
// u[0][j], u[1][j], ....u[T-1][j].
#include <iostream>
#include<fstream>
#include <cmath>
using namespace std;

int main()
{
   
ifstream in_stream_mu ; 
ifstream in_stream_k ; 
ifstream in_stream_Ks ;
ifstream in_stream_Y ;
in_stream_mu.open("parameters_mu.dat");
in_stream_k.open("parameters_k.dat");
in_stream_Ks.open("parameters_Ks.dat");
in_stream_Y.open("parameters_Y.dat");
double  mu[3], k[3], Ks[4], Y[6];
in_stream_mu >> mu[0] >> mu[1] >> mu[2] ;
in_stream_k  >> k[0] >> k[1] >> k[2] ;
in_stream_Ks  >> Ks[0] >> Ks[1] >> Ks[2] >> Ks[3];
in_stream_Y  >> Y[0] >> Y[1] >> Y[2] >> Y[3] >> Y[4] >>  Y[5];

double u[8][5];

for (int i =0; i<8; ++i)
    u[0][i] =0;
     
u[0][0] =6.25;
for (int i=0; i<2 ;++i)
	u[0][i+1] =0.4;
	
cout << "the initial condition for the states are declared here: "<< endl;
for (int i =0; i<8; ++i)
    {
cout << " \t "<< u[0][i] ;
     }
cout <<endl;
////////////////////////////////////////////////////

double F[8]={};
double sum_kh= (0.0001 + 0.00004 + 0.0175);
double su=1.0 ;
cout << "Right hand side formulation for the first time step t0 to t1!" <<endl;
/*
for (int i =0; i<8; ++i) // 
	{
cout << F[i] << "\t";
cout << endl; 
	} 
*/
F[0]  = -sum_kh*u[0][0];
F[1]  = ( (mu[0]*u[0][4])/(Ks[0] + u[0][4]) - k[0] )* u[0][1];
F[2]  = ( (mu[1]*u[0][5])/(Ks[1] + u[0][5]) - k[1] )* u[0][2];
F[3]  = ( su*(mu[2]*u[0][5])/((Ks[2] + u[0][5])*(su +Ks[3])) - k[2] )* u[0][3];
F[4]  = - F[0] - F[1];
F[5]  =   Y[3]*(1- Y[0])*mu[1]*u[0][4]/(Y[0]*(Ks[0] + u[0][4])) + Y[3]*k[0] ;
F[5] -=  su*(mu[2]*u[0][5])/((Ks[2] + u[0][5])*(su +Ks[3])); 
F[6]  =  Y[4]*((1- Y[1])*mu[1]*u[0][5]/(Y[0]*(Ks[1] + u[0][5]))   )*u[0][2] ;
F[6] -=  Y[4]*k[1]*u[0][2];
F[7]  = (1. -Y[4])*(1. - Y[0])*mu[0]*u[0][4]/(Y[0]*(Ks[0] + u[0][4]))*u[0][4] + (1. -Y[3])*k[0] *u[0][1];
F[7] +=	(1. -Y[5])*(1. - Y[1])*mu[1]*u[0][5]/(Y[1]*(Ks[1] + u[0][5]))*u[0][5] + (1. -Y[3])*k[1] *u[0][2];
F[7] +=	      Y[5]*(1. - Y[2])*mu[2]*u[0][5]/(Y[2]*(Ks[2] + u[0][5])*(su +Ks[3]))*u[0][5]*su + 
	      Y[5]*(1. -Y[3])*k[2]*u[0][3];			;
for (int i =0; i<8; ++i)
	{
cout << F[i] << "\t";
	}
cout << endl; 
	



//////////////////////////////////////////////////////
in_stream_mu.close(); 
in_stream_k.close(); 
in_stream_Ks.close(); 
in_stream_Y.close(); 

return 0 ;
}