public static List <Tuple <int, int, double> > FindNashEq(MatrixR P1, MatrixR P2)
{
int columnCount = P1.GetCols();
int rowCount = P1.GetCols();
var best_payouts = new List <Tuple <int, int, double> >
{
//new Tuple<int,int>(1,1),
};
var best_payout_labels = new List <Tuple <int, int, double> >
{
//new Tuple<int,int>(1,1),
};
// column then row
for (int c = 0; c < rowCount; c++)
{
// get max_payout per column
double max_payout = double.NegativeInfinity;
for (int r = 0; r < columnCount; r++)
{
//Console.WriteLine(P1[r,c]);
if (P1[r, c] > max_payout)
{
max_payout = P1[r, c];
}
}
for (int r = 0; r < columnCount; r++)
{
if (P1[r, c] == max_payout)
{
best_payouts.Add(new Tuple <int, int, double>(r, c, max_payout));
}
}
}
// row then column
for (int r = 0; r < rowCount; r++)
{
double max_payout = double.NegativeInfinity;
for (int c = 0; c < columnCount; c++)
{
//Console.WriteLine(P2[r,c]);
if (P2[r, c] > max_payout)
{
max_payout = P2[r, c];
}
}
for (int c = 0; c < columnCount; c++)
{
if (P2[r, c] == max_payout)
{
var item = best_payouts.Find(x => x.Item1 == r && x.Item2 == c);
if (item != null)
{
best_payout_labels.Add(item);
}
}
}
}
return(best_payout_labels);
}
public static void TestTridiagonalEigenvalues()
{
MatrixR A = new MatrixR(new double[, ] {
{ 5, 1, 2, 2, 4 },
{ 1, 1, 2, 1, 0 },
{ 2, 2, 0, 2, 1 },
{ 2, 1, 2, 1, 2 },
{ 4, 0, 1, 2, 4 }
});
int nn = 5;
MatrixR xx = new MatrixR(A.GetCols(), nn);
MatrixR V = Eigenvalue.Tridiagonalize(A);
double[] lambda = Eigenvalue.TridiagonalEigenvalues(nn);
for (int i = 0; i < nn; i++)
{
double s = lambda[i] * 1.001;
double lam;
VectorR x = Eigenvalue.TridiagonalEigenvector(s, 1e-8, out lam);
for (int j = 0; j < A.GetCols(); j++)
{
xx[j, i] = x[j];
}
}
xx = V * xx;
Console.WriteLine("\n Results from the tridiagonalization method:");
Console.WriteLine("\n Eigenvalues: \n ({0,10:n6} {1,10:n6} {2,10:n6} {3,10:n6} {4,10:n6})", lambda[0], lambda[1], lambda[2], lambda[3], lambda[4]);
Console.WriteLine("\n Eigenvectors:");
for (int i = 0; i < 5; i++)
{
Console.WriteLine(" ({0,10:n6} {1,10:n6} {2,10:n6} {3,10:n6} {4,10:n6})", xx[i, 0], xx[i, 1], xx[i, 2], xx[i, 3], xx[i, 4]);
}
A = new MatrixR(new double[, ] {
{ 5, 1, 2, 2, 4 },
{ 1, 1, 2, 1, 0 },
{ 2, 2, 0, 2, 1 },
{ 2, 1, 2, 1, 2 },
{ 4, 0, 1, 2, 4 }
});
MatrixR xm;
VectorR lamb;
Eigenvalue.Jacobi(A, 1e-8, out xm, out lamb);
Console.WriteLine("\n\n Results from the Jacobi method:");
Console.WriteLine("\n Eigenvalues: \n ({0,10:n6} {1,10:n6} {2,10:n6} {3,10:n6} {4,10:n6})", lamb[4], lamb[3], lamb[2], lamb[1], lamb[0]);
Console.WriteLine("\n Eigenvectors:");
for (int i = 0; i < 5; i++)
{
Console.WriteLine(" ({0,10:n6} {1,10:n6} {2,10:n6} {3,10:n6} {4,10:n6})", xm[i, 4], xm[i, 3], xm[i, 2], xm[i, 1], xm[i, 0]);
}
}