public void LinearAlgebraComplexMatrix()
{
//using DotNumerics.LinearAlgebra;
//using DotNumerics;
ComplexMatrix A = new ComplexMatrix(3, 3);
A[0, 0] = new Complex(3, 9); A[0, 1] = new Complex(4, 6); A[0, 2] = new Complex(1, 8);
A[1, 0] = new Complex(8, 3); A[1, 1] = new Complex(2, 4); A[1, 2] = new Complex(5, 5);
A[2, 0] = new Complex(2, 5); A[2, 1] = new Complex(7, 2); A[2, 2] = new Complex(5, 5);
EigenSystem es = new EigenSystem();
ComplexMatrix eigenvectors;
ComplexMatrix eigenvalues = es.GetEigenvalues(A, out eigenvectors);
//Ax-lX=0
Complex lambda = eigenvalues[0, 0];
ComplexVector X = eigenvectors.GetColumnVectors()[0];
ComplexMatrix AXmlambdaX = A * X - lambda * X;
ObjectDumper.Write("A=");
ObjectDumper.Write(A.MatrixToString("0.000"));
ObjectDumper.Write("Eigenvalues:");
ObjectDumper.Write(eigenvalues.MatrixToString("0.000"));
ObjectDumper.Write("Eigenvectors:");
ObjectDumper.Write(eigenvectors.MatrixToString("0.000"));
ObjectDumper.Write("A * X - lambda * X = ");
ObjectDumper.Write(AXmlambdaX.MatrixToString("0.000"));
}
public void LinearAlgebraEigenvaluesAndEigenvectors()
{
//using DotNumerics.LinearAlgebra;
//using DotNumerics;
Matrix A = new Matrix(3, 3);
A[0, 0] = 2; A[0, 1] = 5; A[0, 2] = 3;
A[1, 0] = 1; A[1, 1] = 5; A[1, 2] = 7;
A[2, 0] = 8; A[2, 1] = 2; A[2, 2] = 3;
EigenSystem es = new EigenSystem();
ComplexMatrix eigenvectors;
ComplexMatrix eigenvalues = es.GetEigenvalues(A, out eigenvectors);
//Ax-lX=0
Complex lambda = eigenvalues[0, 0];
ComplexVector X = eigenvectors.GetColumnVectors()[0];
ComplexMatrix AXmlambdaX = A.CopyToComplex() * X - lambda * X;
ObjectDumper.Write("A=");
ObjectDumper.Write(A.MatrixToString("0.000"));
ObjectDumper.Write("Eigenvalues:");
ObjectDumper.Write(eigenvalues.MatrixToString("0.000"));
ObjectDumper.Write("Eigenvectors:");
ObjectDumper.Write(eigenvectors.MatrixToString("0.000"));
ObjectDumper.Write("A * X - lambda * X = ");
ObjectDumper.Write(AXmlambdaX.MatrixToString("0.000"));
}
static void Main(string[] args)
{
GraphLoader loader = new GraphLoader("completPartite.xml");
loader.Init();
Graph graph = loader.GetGraph();
//graph.PrintVertex();
//graph.PrintEdge();
Matrix A = graph.GetAdjacentMatrix();
Matrix D = graph.GetDegreeMatrix();
Console.WriteLine("ADJACENT MATRIX:");
Console.WriteLine(A.MatrixToString());
Console.WriteLine("DEGREE MATRIX:");
Console.WriteLine(D.MatrixToString());
Matrix L = D.Subtract(A);
Console.WriteLine("LAPLACIAN MATRIX:");
Console.WriteLine(L.MatrixToString());
EigenSystem eigSys = new EigenSystem();
ComplexMatrix eigenVals = eigSys.GetEigenvalues(L);
Console.WriteLine("EIGENVALUES:");
Console.WriteLine(eigenVals.MatrixToString());
GraphPlotter plotter = new GraphPlotter(graph);
plotter.Draw();
return;
}
public void Schrodinger(double step, double range)
{
int size = (int)(range / step);
EkMatrix = new SymmetricBandMatrix(size, 1);
VMatrix = new SymmetricBandMatrix(size, 1);
HMatrix = new SymmetricBandMatrix(size, 1);
for (int i = 0; i < size; i++)
{
for (int j = 0; j < size; j++)
{
// EkMatrix
if (i == j)
{
EkMatrix[i, j] = -2 * C / (step * step * 1e-18);
}
else if (Math.Abs(i - j) == 1)
{
EkMatrix[i, j] = 1 * C / (step * step * 1e-18);
}
else
{
EkMatrix[i, j] = 0;
}
//VMatrix
if (i == j && (j < (size - Width / step) / 2 || j > (size + Width / step) / 2))
{
VMatrix[i, j] = BarrierHeight * e;
}
else
{
VMatrix[i, j] = 0;
}
}
}
HMatrix = EkMatrix + VMatrix;
EigenSystem eigenSystem = new EigenSystem();
eigenVals = eigenSystem.GetEigenvalues(HMatrix, out eigenVects);
eigenVals.MultiplyInplace(1 / e);
VMatrix.MultiplyInplace(1 / e);
EkMatrix.MultiplyInplace(1 / e);
HMatrix.MultiplyInplace(1 / e);
}
/// <summary>
/// Computes a 2D harmonic oscillator wavefunction with given quantum numbers.
/// </summary>
public static WaveFunction2D1P GetSHOWaveFunction(
int gridSizeX, int gridSizeY, float latticeSpacing, float mass,
Vec2 packetCenter, float sigma, int N, int Lz, bool multiThread = true)
{
// Check the input
if ((N < 0) || (Lz > N) || (Lz < -N) || ((N + Lz) % 2) != 0)
{
throw new ArgumentException("Invalid (N,m) in WaveFunctionUtils.GetSHOWaveFunction.");
}
EigenSystem hamX = Diagonalized1dShoHamiltonian(mass, sigma, packetCenter.X, latticeSpacing, gridSizeX);
EigenSystem hamY = Diagonalized1dShoHamiltonian(mass, sigma, packetCenter.Y, latticeSpacing, gridSizeY);
Vector eivcX0 = hamX.EigenVector(0);
Vector eivcY0 = hamY.EigenVector(0);
WaveFunction2D1P result;
if ((N == 0) && (Lz == 0))
{
result = DirectProduct(hamX.EigenVector(0), hamY.EigenVector(0), latticeSpacing);
}
else if ((N == 1) && (Lz == 1))
{
WaveFunction2D1P psi_10 = DirectProduct(hamX.EigenVector(1), hamY.EigenVector(0), latticeSpacing);
WaveFunction2D1P psi_01 = DirectProduct(hamX.EigenVector(0), hamY.EigenVector(1), latticeSpacing);
result = psi_10 + Complex.I * psi_01;
}
else if ((N == 2) && (Lz == 0))
{
WaveFunction2D1P psi_20 = DirectProduct(hamX.EigenVector(2), hamY.EigenVector(0), latticeSpacing);
WaveFunction2D1P psi_02 = DirectProduct(hamX.EigenVector(0), hamY.EigenVector(2), latticeSpacing);
result = psi_20 + psi_02;
}
else if ((N == 2) && (Lz == 2))
{
WaveFunction2D1P psi_11 = DirectProduct(hamX.EigenVector(1), hamY.EigenVector(1), latticeSpacing);
WaveFunction2D1P psi_20 = DirectProduct(hamX.EigenVector(2), hamY.EigenVector(0), latticeSpacing);
WaveFunction2D1P psi_02 = DirectProduct(hamX.EigenVector(0), hamY.EigenVector(2), latticeSpacing);
result = psi_20 - psi_02 + (Math.Sqrt(2) * Complex.I) * psi_11;
}
else
{
throw new ArgumentException("Invalid (N,Lz) in WaveFunctionUtils.GetSHOWaveFunction.");
}
result.Normalize();
return(result);
}
public void LinearAlgebraEigenvalues()
{
//using DotNumerics.LinearAlgebra;
//using DotNumerics;
Matrix A = new Matrix(3, 3);
A[0, 0] = 2; A[0, 1] = 5; A[0, 2] = 3;
A[1, 0] = 1; A[1, 1] = 5; A[1, 2] = 7;
A[2, 0] = 8; A[2, 1] = 2; A[2, 2] = 3;
EigenSystem es = new EigenSystem();
ComplexMatrix eigenvalues = es.GetEigenvalues(A);
ObjectDumper.Write("A=");
ObjectDumper.Write(A.MatrixToString("0.000"));
ObjectDumper.Write("Eigenvalues:");
ObjectDumper.Write(eigenvalues.MatrixToString("0.000"));
}