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]);
}
}
/// <summary>
/// Initializes a new instance of the <see cref="UserGramSchmidt"/> class. This object creates an unitary matrix
/// using the modified Gram-Schmidt method.
/// </summary>
/// <param name="matrix">The matrix to factor.</param>
/// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception>
/// <exception cref="ArgumentException">If <paramref name="matrix"/> row count is less then column count</exception>
/// <exception cref="ArgumentException">If <paramref name="matrix"/> is rank deficient</exception>
public UserGramSchmidt(Matrix <Complex32> matrix)
{
if (matrix == null)
{
throw new ArgumentNullException("matrix");
}
if (matrix.RowCount < matrix.ColumnCount)
{
throw new ArgumentException(Resources.ArgumentMatrixDimensions);
}
MatrixQ = matrix.Clone();
MatrixR = matrix.CreateMatrix(matrix.ColumnCount, matrix.ColumnCount);
for (var k = 0; k < MatrixQ.ColumnCount; k++)
{
var norm = MatrixQ.Column(k).Norm(2).Real;
if (norm == 0.0f)
{
throw new ArgumentException(Resources.ArgumentMatrixNotRankDeficient);
}
MatrixR.At(k, k, norm);
for (var i = 0; i < MatrixQ.RowCount; i++)
{
MatrixQ.At(i, k, MatrixQ.At(i, k) / norm);
}
for (var j = k + 1; j < MatrixQ.ColumnCount; j++)
{
var dot = Complex32.Zero;
for (int i = 0; i < MatrixQ.RowCount; i++)
{
dot += MatrixQ.Column(k)[i].Conjugate() * MatrixQ.Column(j)[i];
}
MatrixR.At(k, j, dot);
for (var i = 0; i < MatrixQ.RowCount; i++)
{
var value = MatrixQ.At(i, j) - (MatrixQ.At(i, k) * dot);
MatrixQ.At(i, j, value);
}
}
}
}
public void Test_Matching_Pennies()
{
Debug.WriteLine("Matching Pennies");
var P1columns = new MatrixR(new double[, ] {
{ 1, -1, },
{ -1, 1, }
});
var P2rows = new MatrixR(new double[, ] {
{ -1, 1, },
{ 1, -1, }
});
var test = NashEq.FindNashEq(P1columns, P2rows);
foreach (var tuple in test)
{
Debug.WriteLine("P1 {0} - P2 {1} - Score {2}", tuple.Item1, tuple.Item2, tuple.Item3);
}
}
public void Test_Pigs_Game()
{
Debug.WriteLine("Pigs Game");
var P1columns = new MatrixR(new double[, ] {
{ 4, 2, },
{ 2, 3, }
});
var P2rows = new MatrixR(new double[, ] {
{ 6, 0, },
{ -1, 0, }
});
var test = NashEq.FindNashEq(P1columns, P2rows);
foreach (var tuple in test)
{
Debug.WriteLine("P1 {0} - P2 {1} - Score {2}", tuple.Item1, tuple.Item2, tuple.Item3);
}
}
public void Test_Hawk_Dove()
{
Debug.WriteLine("Hawk - Dove");
var P1columns = new MatrixR(new double[, ] {
{ 0, 1, },
{ 3, 2, }
});
var P2rows = new MatrixR(new double[, ] {
{ 0, 3, },
{ 1, 2, }
});
var test = NashEq.FindNashEq(P1columns, P2rows);
foreach (var tuple in test)
{
Debug.WriteLine("P1 {0} - P2 {1} - Score {2}", tuple.Item1, tuple.Item2, tuple.Item3);
}
}
public void Test_Prisoner_Dilemma()
{
Debug.WriteLine("Prisoner's Dilemma");
MatrixR P1columns = new MatrixR(new double[, ] {
{ 3, 0, },
{ 5, 1, }
});
MatrixR P2rows = new MatrixR(new double[, ] {
{ 3, 5, },
{ 0, 1, }
});
var test = NashEq.FindNashEq(P1columns, P2rows);
foreach (var tuple in test)
{
Debug.WriteLine("P1 {0} - P2 {1} - Score {2}", tuple.Item1, tuple.Item2, tuple.Item3);
}
}
/// <summary>
/// Initializes a new instance of the <see cref="UserGramSchmidt"/> class. This object creates an orthogonal matrix
/// using the modified Gram-Schmidt method.
/// </summary>
/// <param name="matrix">The matrix to factor.</param>
/// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception>
/// <exception cref="ArgumentException">If <paramref name="matrix"/> row count is less then column count</exception>
/// <exception cref="ArgumentException">If <paramref name="matrix"/> is rank deficient</exception>
public UserGramSchmidt(Matrix <float> matrix)
{
if (matrix == null)
{
throw new ArgumentNullException("matrix");
}
if (matrix.RowCount < matrix.ColumnCount)
{
throw new ArgumentException(Resources.ArgumentMatrixDimensions);
}
MatrixQ = matrix.Clone();
MatrixR = matrix.CreateMatrix(matrix.ColumnCount, matrix.ColumnCount);
for (var k = 0; k < MatrixQ.ColumnCount; k++)
{
var norm = MatrixQ.Column(k).Norm(2);
if (norm == 0.0)
{
throw new ArgumentException(Resources.ArgumentMatrixNotRankDeficient);
}
MatrixR.At(k, k, norm);
for (var i = 0; i < MatrixQ.RowCount; i++)
{
MatrixQ.At(i, k, MatrixQ.At(i, k) / norm);
}
for (var j = k + 1; j < MatrixQ.ColumnCount; j++)
{
var dot = MatrixQ.Column(k).DotProduct(MatrixQ.Column(j));
MatrixR.At(k, j, dot);
for (var i = 0; i < MatrixQ.RowCount; i++)
{
var value = MatrixQ.At(i, j) - (MatrixQ.At(i, k) * dot);
MatrixQ.At(i, j, value);
}
}
}
}
/// <summary>
/// Solves a system of linear equations, <b>Ax = b</b>, with A QR factorized.
/// </summary>
/// <param name="input">The right hand side vector, <b>b</b>.</param>
/// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>x</b>.</param>
public override void Solve(Vector <double> input, Vector <double> result)
{
if (input == null)
{
throw new ArgumentNullException("input");
}
if (result == null)
{
throw new ArgumentNullException("result");
}
// Ax=b where A is an m x n matrix
// Check that b is a column vector with m entries
if (MatrixR.RowCount != input.Count)
{
throw new ArgumentException(Resources.ArgumentVectorsSameLength);
}
// Check that x is a column vector with n entries
if (MatrixR.ColumnCount != result.Count)
{
throw Matrix.DimensionsDontMatch <ArgumentException>(MatrixR, result);
}
var inputCopy = input.Clone();
// Compute Y = transpose(Q)*B
var column = new double[MatrixR.RowCount];
for (var k = 0; k < MatrixR.RowCount; k++)
{
column[k] = inputCopy[k];
}
for (var i = 0; i < MatrixR.RowCount; i++)
{
double s = 0;
for (var k = 0; k < MatrixR.RowCount; k++)
{
s += MatrixQ.At(k, i) * column[k];
}
inputCopy[i] = s;
}
// Solve R*X = Y;
for (var k = MatrixR.ColumnCount - 1; k >= 0; k--)
{
inputCopy[k] /= MatrixR.At(k, k);
for (var i = 0; i < k; i++)
{
inputCopy[i] -= inputCopy[k] * MatrixR.At(i, k);
}
}
for (var i = 0; i < MatrixR.ColumnCount; i++)
{
result[i] = inputCopy[i];
}
}
/// <summary>
/// Solves a system of linear equations, <b>AX = B</b>, with A QR factorized.
/// </summary>
/// <param name="input">The right hand side <see cref="Matrix{T}"/>, <b>B</b>.</param>
/// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>X</b>.</param>
public override void Solve(Matrix <double> input, Matrix <double> result)
{
// Check for proper arguments.
if (input == null)
{
throw new ArgumentNullException("input");
}
if (result == null)
{
throw new ArgumentNullException("result");
}
// The solution X should have the same number of columns as B
if (input.ColumnCount != result.ColumnCount)
{
throw new ArgumentException(Resources.ArgumentMatrixSameColumnDimension);
}
// The dimension compatibility conditions for X = A\B require the two matrices A and B to have the same number of rows
if (MatrixR.RowCount != input.RowCount)
{
throw new ArgumentException(Resources.ArgumentMatrixSameRowDimension);
}
// The solution X row dimension is equal to the column dimension of A
if (MatrixR.ColumnCount != result.RowCount)
{
throw new ArgumentException(Resources.ArgumentMatrixSameColumnDimension);
}
var inputCopy = input.Clone();
// Compute Y = transpose(Q)*B
var column = new double[MatrixR.RowCount];
for (var j = 0; j < input.ColumnCount; j++)
{
for (var k = 0; k < MatrixR.RowCount; k++)
{
column[k] = inputCopy.At(k, j);
}
for (var i = 0; i < MatrixR.RowCount; i++)
{
double s = 0;
for (var k = 0; k < MatrixR.RowCount; k++)
{
s += MatrixQ.At(k, i) * column[k];
}
inputCopy.At(i, j, s);
}
}
// Solve R*X = Y;
for (var k = MatrixR.ColumnCount - 1; k >= 0; k--)
{
for (var j = 0; j < input.ColumnCount; j++)
{
inputCopy.At(k, j, inputCopy.At(k, j) / MatrixR.At(k, k));
}
for (var i = 0; i < k; i++)
{
for (var j = 0; j < input.ColumnCount; j++)
{
inputCopy.At(i, j, inputCopy.At(i, j) - (inputCopy.At(k, j) * MatrixR.At(i, k)));
}
}
}
for (var i = 0; i < MatrixR.ColumnCount; i++)
{
for (var j = 0; j < inputCopy.ColumnCount; j++)
{
result.At(i, j, inputCopy.At(i, j));
}
}
}
