private static bool CenterOnGamma(Lattice lattice, ref KPoint qpt, KptList list)
{
double dist = qpt.Value.Magnitude;
double olddist = dist;
Vector3 newPt = qpt.Value;
bool retval = true;
double bs, bt;
list.GetPlaneST(qpt, out bs, out bt);
for (int k = -1; k <= 1; k++)
{
for (int j = -1; j <= 1; j++)
{
for (int i = -1; i <= 1; i++)
{
if (i == 0 && j == 0 && k == 0)
continue;
Vector3 pt = qpt.Value +
i * lattice.G1 +
j * lattice.G2 +
k * lattice.G3;
double s, t;
bool valid = list.GetPlaneST(new KPoint(pt), out s, out t);
if (!valid)
continue;
if (pt.Magnitude < dist - 1e-6)
{
if (list.allKpts.Any(x => Math.Abs((x.Value - pt).Magnitude) > 1e-6))
{
retval = false;
continue;
}
dist = pt.Magnitude;
newPt = pt;
}
}
}
}
if (olddist != dist)
retval = true;
if (retval == false)
return false;
qpt.Value = newPt;
return true;
}
public static KptList GeneratePlane(Lattice lattice, Vector3[] points, SymmetryList syms, KptList qmesh)
{
Vector3 diff_1 = points[1] - points[0];
Vector3 diff_2 = points[2] - points[0];
Vector3 norm = Vector3.CrossProduct(diff_1, diff_2);
KptList retval = new KptList();
retval.mesh = (int[])qmesh.mesh.Clone();
retval.shift = new int[3];
retval.gammaCentered = true;
retval.origin = points[0];
retval.sdir = diff_1;
retval.tdir = Vector3.CrossProduct(norm, diff_1);
NormalizeST(lattice, retval);
int zmax = qmesh.mesh[2] * 2;
int ymax = qmesh.mesh[1] * 2;
int xmax = qmesh.mesh[0] * 2;
int index = 0;
List<KPoint> planePoints = new List<KPoint>();
for (int i = 0; i < qmesh.AllKpts.Count; i++)
{
var qpt = qmesh.AllKpts[i];
Vector3 diff = qpt.Value - points[0];
double dot = Math.Abs(diff.DotProduct(norm));
if (dot < 1e-8)
{
double s, t;
retval.GetPlaneST(qpt, out s, out t);
planePoints.Add(qpt);
}
}
SortByDistanceFromGamma(planePoints);
for (int i = 0; i <planePoints.Count; i++)
{
var qpt = planePoints[i];
double s, t;
retval.GetPlaneST(qpt, out s, out t);
//if (CenterOnGamma(lattice, ref qpt, retval) == false)
// continue;
//retval.GetPlaneST(qpt, out news, out newt);
retval.allKpts.Add(qpt);
}
// now sort q-points to lay them in the s,t plane.
Comparison<KPoint> sorter = (x, y) =>
{
double s_x, s_y, t_x, t_y;
retval.GetPlaneST(x, out s_x, out t_x);
retval.GetPlaneST(y, out s_y, out t_y);
if (Math.Abs(t_x - t_y) > 1e-6)
return t_x.CompareTo(t_y);
else
return s_x.CompareTo(s_y);
};
retval.allKpts.Sort(sorter);
// now reduce points by symmetry.
for (int i = 0; i < retval.allKpts.Count; i++)
{
var qpt = retval.AllKpts[i];
int N = retval.KptToInteger(lattice, qpt);
int symN = N;
bool foundSym = false;
List<int> orbitals = null;
Vector3 pt = qpt.Value;
foreach (var symmetry in syms)
{
Vector3 Tpt = symmetry.Value * pt;
int newi, newj, newk;
retval.ReduceKpt(lattice, Tpt, out newi, out newj, out newk);
if (newi % 2 != 0 || newj % 2 != 0 || newk % 2 != 0)
continue;
symN = retval.KptToInteger(newi, newj, newk);
if (retval.Nvalues.ContainsKey(symN))
{
foundSym = true;
if (symmetry.OrbitalTransform.Count > 0)
{
orbitals = symmetry.OrbitalTransform;
}
}
if (foundSym)
break;
}
if (foundSym == false && retval.Nvalues.ContainsKey(N) == false)
{
retval.kpts.Add(qpt);
retval.Nvalues.Add(N, index);
index++;
}
else if (retval.Nvalues.ContainsKey(N) == false)
{
int newIndex = retval.Nvalues[symN];
retval.kpts[newIndex].AddOrbitalSymmetry(orbitals);
retval.Nvalues.Add(N, newIndex);
}
else
{ } // skip points which are already in there. This should only happen for zone edge points
}
retval.kpts.Sort(sorter);
Vector3 sd = retval.sdir / SmallestNonzero(retval.sdir);
Vector3 td = retval.tdir / SmallestNonzero(retval.tdir);
Output.WriteLine("Plane horizontal direction: {0}", sd);
Output.WriteLine("Plane vertical direction: {0}", td);
Output.WriteLine("Plane horizontal vector: {0}", retval.sdir);
Output.WriteLine("Plane vertical vector: {0}", retval.tdir);
return retval;
}
private static bool CenterOnGamma(Lattice lattice, ref KPoint qpt, KptList list)
{
double dist = qpt.Value.Magnitude;
double olddist = dist;
Vector3 newPt = qpt.Value;
bool retval = true;
double bs, bt;
list.GetPlaneST(qpt, out bs, out bt);
for (int k = -1; k <= 1; k++)
{
for (int j = -1; j <= 1; j++)
{
for (int i = -1; i <= 1; i++)
{
if (i == 0 && j == 0 && k == 0)
{
continue;
}
Vector3 pt = qpt.Value +
i * lattice.G1 +
j * lattice.G2 +
k * lattice.G3;
double s, t;
bool valid = list.GetPlaneST(new KPoint(pt), out s, out t);
if (!valid)
{
continue;
}
if (pt.Magnitude < dist - 1e-6)
{
if (list.allKpts.Any(x => Math.Abs((x.Value - pt).Magnitude) > 1e-6))
{
retval = false;
continue;
}
dist = pt.Magnitude;
newPt = pt;
}
}
}
}
if (olddist != dist)
{
retval = true;
}
if (retval == false)
{
return(false);
}
qpt.Value = newPt;
return(true);
}
public static KptList GeneratePlane(Lattice lattice, Vector3[] points, SymmetryList syms, KptList qmesh)
{
Vector3 diff_1 = points[1] - points[0];
Vector3 diff_2 = points[2] - points[0];
Vector3 norm = Vector3.CrossProduct(diff_1, diff_2);
KptList retval = new KptList();
retval.mesh = (int[])qmesh.mesh.Clone();
retval.shift = new int[3];
retval.gammaCentered = true;
retval.origin = points[0];
retval.sdir = diff_1;
retval.tdir = Vector3.CrossProduct(norm, diff_1);
NormalizeST(lattice, retval);
int zmax = qmesh.mesh[2] * 2;
int ymax = qmesh.mesh[1] * 2;
int xmax = qmesh.mesh[0] * 2;
int index = 0;
List <KPoint> planePoints = new List <KPoint>();
for (int i = 0; i < qmesh.AllKpts.Count; i++)
{
var qpt = qmesh.AllKpts[i];
Vector3 diff = qpt.Value - points[0];
double dot = Math.Abs(diff.DotProduct(norm));
if (dot < 1e-8)
{
double s, t;
retval.GetPlaneST(qpt, out s, out t);
planePoints.Add(qpt);
}
}
SortByDistanceFromGamma(planePoints);
for (int i = 0; i < planePoints.Count; i++)
{
var qpt = planePoints[i];
double s, t;
retval.GetPlaneST(qpt, out s, out t);
//if (CenterOnGamma(lattice, ref qpt, retval) == false)
// continue;
//retval.GetPlaneST(qpt, out news, out newt);
retval.allKpts.Add(qpt);
}
// now sort q-points to lay them in the s,t plane.
Comparison <KPoint> sorter = (x, y) =>
{
double s_x, s_y, t_x, t_y;
retval.GetPlaneST(x, out s_x, out t_x);
retval.GetPlaneST(y, out s_y, out t_y);
if (Math.Abs(t_x - t_y) > 1e-6)
{
return(t_x.CompareTo(t_y));
}
else
{
return(s_x.CompareTo(s_y));
}
};
retval.allKpts.Sort(sorter);
// now reduce points by symmetry.
for (int i = 0; i < retval.allKpts.Count; i++)
{
var qpt = retval.AllKpts[i];
int N = retval.KptToInteger(lattice, qpt);
int symN = N;
bool foundSym = false;
List <int> orbitals = null;
Vector3 pt = qpt.Value;
foreach (var symmetry in syms)
{
Vector3 Tpt = symmetry.Value * pt;
int newi, newj, newk;
retval.ReduceKpt(lattice, Tpt, out newi, out newj, out newk);
if (newi % 2 != 0 || newj % 2 != 0 || newk % 2 != 0)
{
continue;
}
symN = retval.KptToInteger(newi, newj, newk);
if (retval.Nvalues.ContainsKey(symN))
{
foundSym = true;
if (symmetry.OrbitalTransform.Count > 0)
{
orbitals = symmetry.OrbitalTransform;
}
}
if (foundSym)
{
break;
}
}
if (foundSym == false && retval.Nvalues.ContainsKey(N) == false)
{
retval.kpts.Add(qpt);
retval.Nvalues.Add(N, index);
index++;
}
else if (retval.Nvalues.ContainsKey(N) == false)
{
int newIndex = retval.Nvalues[symN];
retval.kpts[newIndex].AddOrbitalSymmetry(orbitals);
retval.Nvalues.Add(N, newIndex);
}
else
{
} // skip points which are already in there. This should only happen for zone edge points
}
retval.kpts.Sort(sorter);
Vector3 sd = retval.sdir / SmallestNonzero(retval.sdir);
Vector3 td = retval.tdir / SmallestNonzero(retval.tdir);
Output.WriteLine("Plane horizontal direction: {0}", sd);
Output.WriteLine("Plane vertical direction: {0}", td);
Output.WriteLine("Plane horizontal vector: {0}", retval.sdir);
Output.WriteLine("Plane vertical vector: {0}", retval.tdir);
return(retval);
}
private void WriteGreenFunctionPlane(TightBindingSuite.TightBinding tb, Matrix[] green, KptList kmesh)
{
Console.WriteLine("Output as a plane.");
Console.WriteLine();
Console.WriteLine("Enter vectors as a series of three numbers, like: 1 1 0");
Console.WriteLine("Only integer values need be used.");
Console.WriteLine();
Console.Write("Enter first vector: ");
string first = Console.ReadLine();
if (string.IsNullOrEmpty(first))
return;
Console.Write("Enter second vector: ");
string second = Console.ReadLine();
Vector3 sdir = Vector3.Parse(first);
Vector3 tdir = Vector3.Parse(second);
Vector3 udir = Vector3.CrossProduct(sdir, tdir);
Console.Write("Enter origin point: ");
string origin = Console.ReadLine();
Vector3 orig = Vector3.Parse(origin);
Vector3 closestKpt = Vector3.Zero;
double closestDistance = 999999999;
foreach (var kpt in kmesh.AllKpts)
{
double distance = (kpt.Value - orig).MagnitudeSquared;
if (distance < closestDistance)
{
closestKpt = kpt.Value;
closestDistance = distance;
}
}
if (closestDistance > 1e-6)
{
Console.WriteLine("Using closest k-point to specified origin: {0}.", closestKpt);
orig = closestKpt;
sdir += closestKpt;
tdir += closestKpt;
}
KptList plane = KptList.GeneratePlane(
tb.Lattice, new Vector3[] { orig, sdir, tdir }, tb.Symmetries, kmesh);
string tr_filename = string.Format("green.tr.pln");
StreamWriter tr = new StreamWriter(tr_filename);
double lastt = double.MinValue;
for (int k = 0; k < plane.AllKpts.Count; k++)
{
Complex trValue = new Complex();
for (int i = 0; i < green[k].Rows; i++)
{
trValue += green[k][i, i];
}
Vector3 kpt = plane.AllKpts[k].Value;
List<int> orbitalMap;
double s, t;
plane.GetPlaneST(plane.AllKpts[k], out s, out t);
int kindex = kmesh.IrreducibleIndex(kpt, tb.Lattice, tb.Symmetries, out orbitalMap);
if (Math.Abs(t - lastt) > 1e-6)
{
tr.WriteLine();
lastt = t;
}
tr.WriteLine("{0}\t{1}\t{2}", s, t, -trValue.ImagPart);
}
tr.Close();
for (int i = 0; i < green[0].Rows; i++)
{
for (int j = 0; j < green[0].Columns; j++)
{
string re_filename = string.Format("green.re.{0}.{1}.pln", i,j);
string im_filename = string.Format("green.im.{0}.{1}.pln", i, j);
string mag_filename = string.Format("green.mag.{0}.{1}.pln", i, j);
StreamWriter rew = new StreamWriter(re_filename);
StreamWriter imw = new StreamWriter(im_filename);
StreamWriter mag = new StreamWriter(mag_filename);
try
{
lastt = double.MaxValue;
for (int k = 0; k < plane.AllKpts.Count; k++)
{
Vector3 kpt = plane.AllKpts[k].Value;
List<int> orbitalMap;
double s, t;
plane.GetPlaneST(plane.AllKpts[k], out s, out t);
int kindex = kmesh.IrreducibleIndex(kpt, tb.Lattice, tb.Symmetries, out orbitalMap);
if (Math.Abs(t - lastt) > 1e-6)
{
rew.WriteLine();
imw.WriteLine();
mag.WriteLine();
lastt = t;
}
rew.WriteLine("{0}\t{1}\t{2}", s, t, green[kindex][i, j].RealPart);
imw.WriteLine("{0}\t{1}\t{2}", s, t, -green[kindex][i, j].ImagPart);
mag.WriteLine("{0}\t{1}\t{2}", s, t, green[kindex][i, j].Magnitude);
}
}
finally
{
rew.Dispose();
imw.Dispose();
mag.Dispose();
}
}
}
}