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#include <stdio.h>
#include <unsupported/Eigen/MatrixFunctions>
#include <iostream>
#include <math.h>
#include <conio.h>//define getch
#include <iomanip>
#include <fstreaM>
#include <string>
#include <map>
#include <random>
#include <chrono>
#include <vector>
//#define KMAX 2
//#define M ((KMAX+1)*(KMAX+2))/2
#define m 10
using namespace std;
using namespace Eigen;
void main()
{
int k = 1, L = 0, A = 0, i, j, e,max,M;
int z = 1, R = 0, C = 0; //variable for Q
int B = 0, T = 0, c = 1, q = 1, n = 0, H = 0,o = 0,u = 0,t=24,F; // variable for diagonal
//double P[KMAX];
//double Q[KMAX];
//double S[KMAX];
//double E[M][M];
//double Matrix[M + 1][M + 1];
//double I[M + 1][M + 1];
int a[m];
//double MX[M][M];
double p = 0.95;
double a1 = 20.79, a2 = 0.005;
int Vmax = 3, KM = 5;
cout.setf(ios::fixed);
cout.precision(3);
//////////////////////////////////////////////////////////////////////////////////////////
//value of X-axis
/////////////////////////////////////////////////////////////////////////////////////////
double X_axis[m];
for (i = 1; i <= m; i++)
{
X_axis[i] = ((i - 1) / 4.0);
cout << " " << X_axis[i] << endl;
}
///////////////////////////////////////////////////////////////////////////////////////
//random number follow poisson distribution
//////////////////////////////////////////////////////////////////////////////////////
cout << "some Poisson-distributed results:" << endl;
unsigned seed = std::chrono::system_clock::now().time_since_epoch().count();
std::default_random_engine generator(seed);
std::poisson_distribution<int> distribution(2*X_axis[m]);
int KMAX;
for (int i = 0; i < m; ++i)
{
a[i] = distribution(generator);
std::cout << a[i] << " " << endl;
}
////////////////////////////////////////////////////////////////////////////////////
//maximum number of DSB
///////////////////////////////////////////////////////////////////////////////////
max=a[1];
for (int i = 0; i < m; ++i)
{
if (max <= a[i])
max = a[i];
KMAX = max;
}
cout << "maximum number is " << KMAX << endl;
unsigned short int size = KMAX;
std::vector<int> vec(size);
std::cout << "Size of vector is: " << vec.size() << '\n';
for (int i = 0; i < vec.size(); i++)
{
double P = (p*Vmax*i) / (KM + i);
double Q = (1 - p)*Vmax*i / (KM + i);
cout << "P[" << i << "] = " << P << "\t" << "Q[" << i << "] = " << Q << endl;
}
/////////////////////////////////////////////////////////////////////////////////////////
//matrix
////////////////////////////////////////////////////////////////////////////////////////
int M=((KMAX + 1)*(KMAX + 2)) / 2;
for (i = 0; i <= M; i++)//matrix 0
for (j = 0; j <= M; j++);
MX[M][M]=0;
for (i = KMAX; i >= 1; i--)// position P in matrix
{
for (j = 1; j <= i; j++)
{
MX[j - 1 + L][KMAX + k] = P[A + 1];
//cout <<"MX["<<j-1+L<<"]["<<KMAX+k<<"] = " <<MX[j-1+L][KMAX+k]<<endl;
k++;
}
//cout<<endl;
L = k + A;
A++;
}
for (i = KMAX; i >= 1; i--)// position Q in matrix
{
for (j = 1; j <= i; j++)
{
MX[j + R][KMAX + z] = Q[C + 1];
//cout <<"MX["<<j+R<<"]["<<KMAX+z<<"] = " <<MX[j+R][KMAX+z]<<endl;
z++;
}
//cout<<endl;
R = z + C;
C++;
}
for (i = KMAX + 1; i >= 1; i--)// calculation for diagonal
{
for (j = 1; j <= i; j++)
{
MX[B + c - q][B + c - q] = -(a1*double(j - 1) + a2*double(B)*double(B)) - ((Vmax*double(B)) / (KM + double(B)));
//cout <<"MX["<<B+c-q<<"]["<<B+c-q<<"] = "<< MX[B+c-q][B+c-q] << endl;
c++;
}
q++;
B++;
}
cout << "Here is the matrix:" << endl; //double array matrix
for (i = 0; i < M; i++)
{
for (j = 0; j < M; j++)
{
// cout << setw(7) << MX[i][j] << " ";
}
//cout << endl;
}
////////////////////////////////////////////////////////////////////////////////
//solve matrix exponential
///////////////////////////////////////////////////////////////////////////////
MatrixXd result(M, M); //apply eigen matrix
for (int i = 0; i < M; i++)
for (int j = 0; j < M; j++)
result(i,j)=MX[i][j]*t;
cout << " " << result << endl;
EigenSolver<MatrixXd> es(result);
MatrixXd D = es.pseudoEigenvalueMatrix();
MatrixXd V = es.pseudoEigenvectors();
cout << "The pseudo-eigenvalue matrix D is:" << endl << D << endl;
cout << "The pseudo-eigenvector matrix V is:" << endl << V << endl;
cout << "Finally, V * D * V^(-1) = " << endl << V * D * V.inverse() << endl;*/
_getch();
}
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