protected void SetLattice(Lattice lattice)
{
this.lattice = lattice;
this.G[0] = lattice.G1;
this.G[1] = lattice.G2;
this.G[2] = lattice.G3;
}
private BZonePlane(KptPlane plane, Lattice lattice)
{
SetLattice(lattice);
Origin = plane.Origin;
Sdir = plane.Sdir;
Tdir = plane.Tdir;
List <Vector3> nearbyGammas = NearbyGammas();
double lastT = double.MinValue;
for (int i = 0; i < plane.Kpts.Count; i++)
{
var kpt = plane.Kpts[i];
this.Kpts.Add(new BZoneKPoint(kpt, i));
double s, t;
plane.GetPlaneST(kpt, out s, out t);
if (t != lastT)
{
lastT = t;
Vector3 closestGamma = ClosestGamma(nearbyGammas, kpt, lattice);
AddLeftBoundary(closestGamma, kpt, plane, lattice);
}
}
SortKpoints();
}
private BZonePlane(KptPlane plane, Lattice lattice)
{
SetLattice(lattice);
Origin = plane.Origin;
Sdir = plane.Sdir;
Tdir = plane.Tdir;
List<Vector3> nearbyGammas = NearbyGammas();
double lastT = double.MinValue;
for (int i = 0; i < plane.Kpts.Count; i++)
{
var kpt = plane.Kpts[i];
this.Kpts.Add(new BZoneKPoint(kpt, i));
double s, t;
plane.GetPlaneST(kpt, out s, out t);
if (t != lastT)
{
lastT = t;
Vector3 closestGamma = ClosestGamma(nearbyGammas, kpt, lattice);
AddLeftBoundary(closestGamma, kpt, plane, lattice);
}
}
SortKpoints();
}
private Vector3 ClosestGamma(List <Vector3> nearbyGammas, KPoint kpt, Lattice lattice)
{
if (nearbyGammas.Count == 0)
{
throw new ArgumentException();
}
double minDistance = double.MaxValue;
Vector3 closest = new Vector3();
Vector3 kptCart = lattice.ReciprocalExpand(kpt.Value);
foreach (var pt in nearbyGammas)
{
Vector3 gamma = lattice.ReciprocalExpand(pt);
double distance = (kptCart - gamma).Magnitude;
double s, t;
GetPlaneST(pt, out s, out t);
if (distance < minDistance)
{
minDistance = distance;
closest = pt;
}
}
return(closest);
}
private static void TranslateKptToNearGamma(Lattice lattice, ref Vector3 kptValue)
{
Vector3 newkpt = kptValue;
double newmag = newkpt.MagnitudeSquared;
for (int i = -1; i <= 1; i++)
{
for (int j = -1; j <= 1; j++)
{
for (int k = -1; k <= 1; k++)
{
if (i == j && j == k && k == 0)
{
continue;
}
Vector3 G = i * lattice.G1 + j * lattice.G2 + k * lattice.G3;
Vector3 kpt = kptValue + G;
double kmag = kpt.MagnitudeSquared;
if (kmag < newmag - 1e-6)
{
newkpt = kpt;
newmag = kmag;
}
}
}
}
kptValue = newkpt;
}
private void ReduceKpt(Lattice lattice, Vector3 pt, out int newi, out int newj, out int newk)
{
Vector3 red = lattice.ReducedCoords(pt, true);
newi = (int)Math.Round(mesh[0] * red.X * 2);
newj = (int)Math.Round(mesh[1] * red.Y * 2);
newk = (int)Math.Round(mesh[2] * red.Z * 2);
}
private int KptToInteger(Lattice lattice, Vector3 qpt)
{
int i, j, k;
ReduceKpt(lattice, qpt, out i, out j, out k);
return(KptToInteger(i, j, k));
}
private static Vector3 GammaInDirection(Lattice lattice, Vector3 direction)
{
Vector3 sred = lattice.ReducedCoords(direction);
sred /= SmallestNonzero(sred);
Vector3 retval = sred.X * lattice.G1 + sred.Y * lattice.G2 + sred.Z * lattice.G3;
return(retval);
}
public int AllKindex(Vector3 kpt, Lattice lattice)
{
int newi, newj, newk;
ReduceKpt(lattice, kpt, out newi, out newj, out newk);
int N = KptToInteger(newi, newj, newk);
return(AllNvalues[N]);
}
private static Vector3 GammaInDirection(Lattice lattice, Vector3 direction)
{
Vector3 sred = lattice.ReciprocalReduce(direction);
sred /= LargestNonzero(sred);
Vector3 retval = sred.X * lattice.G1 + sred.Y * lattice.G2 + sred.Z * lattice.G3;
return(retval);
}
public static KptPlane GeneratePlane(Lattice lattice, Vector3[] points, KptList qmesh)
{
Vector3 diff_1 = points[1] - points[0];
Vector3 diff_2 = points[2] - points[0];
Vector3 norm = Vector3.CrossProduct(diff_1, diff_2);
KptPlane retval = new KptPlane();
retval.SetLattice(lattice);
retval.mesh = (int[])qmesh.Mesh.Clone();
retval.shift = new int[3];
retval.origin = points[0];
retval.sdir = diff_1;
retval.tdir = diff_2;
NormalizeST(lattice, retval);
int zmax = qmesh.Mesh[2] * 2;
int ymax = qmesh.Mesh[1] * 2;
int xmax = qmesh.Mesh[0] * 2;
List <KPoint> planePoints = new List <KPoint>();
for (int i = 0; i < qmesh.Kpts.Count; i++)
{
var qpt = qmesh.Kpts[i];
Vector3 diff = lattice.ReciprocalExpand(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);
retval.AddKpt(qpt);
}
}
// now sort q-points to lay them in the s,t plane.
retval.SortKpoints();
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);
}
public static KptPlane GeneratePlane(Lattice lattice, Vector3[] points, KptList qmesh)
{
Vector3 diff_1 = points[1] - points[0];
Vector3 diff_2 = points[2] - points[0];
Vector3 norm = Vector3.CrossProduct(diff_1, diff_2);
KptPlane retval = new KptPlane();
retval.SetLattice(lattice);
retval.mesh = (int[])qmesh.Mesh.Clone();
retval.shift = new int[3];
retval.origin = points[0];
retval.sdir = diff_1;
retval.tdir = diff_2;
NormalizeST(lattice, retval);
int zmax = qmesh.Mesh[2] * 2;
int ymax = qmesh.Mesh[1] * 2;
int xmax = qmesh.Mesh[0] * 2;
List<KPoint> planePoints = new List<KPoint>();
for (int i = 0; i < qmesh.Kpts.Count; i++)
{
var qpt = qmesh.Kpts[i];
Vector3 diff = lattice.ReciprocalExpand(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);
retval.AddKpt(qpt);
}
}
// now sort q-points to lay them in the s,t plane.
retval.SortKpoints();
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 void NormalizeST(Lattice lattice, KptList retval)
{
retval.sdir /= retval.sdir.Magnitude;
retval.tdir /= retval.tdir.Magnitude;
retval.sdir /= GammaInDirection(lattice, retval.sdir).Magnitude;
retval.tdir /= GammaInDirection(lattice, retval.tdir).Magnitude;
// double them to make s and t 1 at the zone boundary, instead of 0.5.
retval.sdir *= 2;
retval.tdir *= 2;
}
public static KptList DefaultPath(Lattice l)
{
const int pts = 40;
KptList retval = new KptList();
retval.Kpts.Add(new KPoint(Vector3.Zero));
retval.AddPts(Vector3.Zero, l.G1 * Math.PI, pts);
retval.AddPts(l.G1 * Math.PI, (l.G1 + l.G2) * Math.PI, pts);
retval.AddPts((l.G1 + l.G2) * Math.PI, l.G2 * Math.PI, pts);
retval.AddPts(l.G2 * Math.PI, l.G3 * Math.PI, pts);
retval.AddPts(l.G3 * Math.PI, Vector3.Zero, pts);
return(retval);
}
public static KptList DefaultPath(Lattice l)
{
const int pts = 40;
KptList retval = new KptList();
retval.Kpts.Add(new KPoint(Vector3.Zero));
retval.AddPts(Vector3.Zero, l.G1 * Math.PI, pts);
retval.AddPts(l.G1 * Math.PI, (l.G1 + l.G2) * Math.PI, pts);
retval.AddPts((l.G1 + l.G2) * Math.PI, l.G2 * Math.PI, pts);
retval.AddPts(l.G2 * Math.PI, l.G3 * Math.PI, pts);
retval.AddPts(l.G3 * Math.PI, Vector3.Zero, pts);
return retval;
}
public int FindIndex(Lattice latt, Vector3 pos)
{
Vector3 reduced = latt.ReducedCoords(pos, true);
for (int i = 0; i < Count; i++)
{
Vector3 tr = latt.ReducedCoords(this[i].Location, true);
if ((reduced - tr).Magnitude < 1e-6)
{
return(i);
}
}
return(-1);
}
public int IrreducibleIndex(Vector3 kpt, Lattice lattice, SymmetryList symmetries, out List <int> orbitalMap)
{
for (int s = 0; s < symmetries.Count; s++)
{
int newi, newj, newk;
Vector3 newKpt = symmetries[s].Inverse * kpt;
ReduceKpt(lattice, newKpt, out newi, out newj, out newk);
int N = KptToInteger(newi, newj, newk);
if (Nvalues.ContainsKey(N))
{
int index = Nvalues[N];
orbitalMap = symmetries[s].OrbitalTransform;
return(index);
}
}
throw new Exception(string.Format("Could not find k-point {0}", kpt));
}
private int KptToInteger(Lattice lattice, Vector3 qpt)
{
int i, j, k;
ReduceKpt(lattice, qpt, out i, out j, out k);
return KptToInteger(i, j, k);
}
private static void TranslateKptToNearGamma(Lattice lattice, ref Vector3 kptValue)
{
Vector3 newkpt = kptValue;
double newmag = newkpt.MagnitudeSquared;
for (int i = -1; i <= 1; i++)
{
for (int j = -1; j <= 1; j++)
{
for (int k = -1; k <= 1; k++)
{
if (i == j && j == k && k == 0) continue;
Vector3 G = i * lattice.G1 + j * lattice.G2 + k * lattice.G3;
Vector3 kpt = kptValue + G;
double kmag = kpt.MagnitudeSquared;
if (kmag < newmag - 1e-6)
{
newkpt = kpt;
newmag = kmag;
}
}
}
}
kptValue = newkpt;
}
private static void NormalizeST(Lattice lattice, KptList retval)
{
retval.sdir /= retval.sdir.Magnitude;
retval.tdir /= retval.tdir.Magnitude;
retval.sdir /= GammaInDirection(lattice, retval.sdir).Magnitude;
retval.tdir /= GammaInDirection(lattice, retval.tdir).Magnitude;
// double them to make s and t 1 at the zone boundary, instead of 0.5.
retval.sdir *= 2;
retval.tdir *= 2;
}
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 KptPlane GeneratePlane(Lattice lattice, Vector3[] points, int[] qgrid, int[] qshift)
{
KptList qmesh = GenerateMesh(qgrid, qshift, true);
return GeneratePlane(lattice, points, qmesh);
}
public int AllKindex(Vector3 kpt, Lattice lattice)
{
int newi, newj, newk;
ReduceKpt(lattice, kpt, out newi, out newj, out newk);
int N = KptToInteger(newi, newj, newk);
return AllNvalues[N];
}
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;
}
public static BZonePlane CreateBZonePlane(KptPlane plane, Lattice lattice)
{
return new BZonePlane(plane, lattice);
}
public static KptList GenerateMesh(Lattice lattice, int[] kgrid, int[] shift, SymmetryList syms, bool includeEnds)
{
KptList retval = new KptList();
if (shift == null)
{
shift = new int[3];
}
for (int i = 0; i < 3; i++)
{
if (kgrid[i] == 1)
{
shift[i] = 1;
}
}
retval.mesh = (int[])kgrid.Clone();
retval.shift = (int[])shift.Clone();
retval.gammaCentered = true;
SymmetryList compatSyms = FindCompatibleSymmetries(kgrid, syms);
int index = 0;
for (int k = -kgrid[2] + shift[2]; k <= kgrid[2]; k += 2)
{
for (int j = -kgrid[1] + shift[1]; j <= kgrid[1]; j += 2)
{
for (int i = -kgrid[0] + shift[0]; i <= kgrid[0]; i += 2)
{
if (includeEnds == false)
{
if (k == kgrid[2])
{
break;
}
if (j == kgrid[1])
{
break;
}
if (i == kgrid[0])
{
break;
}
}
double dx = i * 0.5 / kgrid[0];
double dy = j * 0.5 / kgrid[1];
double dz = k * 0.5 / kgrid[2];
Vector3 kptValue = CalcK(lattice, dx, dy, dz);
int N = retval.KptToInteger(i, j, k);
int symN = N;
System.Diagnostics.Debug.Assert(!(retval.Nvalues.ContainsKey(N) && includeEnds == false));
List <int> orbitals = null;
bool foundSym = false;
foreach (var symmetry in compatSyms)
{
Vector3 Tpt = symmetry.Value * kptValue;
if (Tpt == kptValue)
{
continue;
}
int newi, newj, newk;
retval.ReduceKpt(lattice, Tpt, out newi, out newj, out newk);
if (Math.Abs(newi) % 2 != shift[0] ||
Math.Abs(newj) % 2 != shift[1] ||
Math.Abs(newk) % 2 != shift[2])
{
continue;
}
symN = retval.KptToInteger(newi, newj, newk);
if (symN < N)
{
foundSym = true;
if (symmetry.OrbitalTransform.Count > 0)
{
orbitals = symmetry.OrbitalTransform;
}
break;
}
}
if (includeEnds)
{
if (retval.AllNvalues.ContainsKey(N))
{
retval.allKpts.Add(new KPoint(kptValue));
continue;
}
}
retval.AllNvalues.Add(N, retval.allKpts.Count);
retval.allKpts.Add(new KPoint(kptValue));
if (foundSym == false)
{
retval.kpts.Add(new KPoint(kptValue));
retval.Nvalues.Add(N, index);
index++;
}
else
{
int newIndex = retval.Nvalues[symN];
retval.kpts[newIndex].Weight++;
retval.kpts[newIndex].AddOrbitalSymmetry(orbitals);
retval.Nvalues.Add(N, newIndex);
}
}
}
}
int count = kgrid[0] * kgrid[1] * kgrid[2];
for (int i = 0; i < retval.kpts.Count; i++)
{
retval.kpts[i].Weight /= count;
}
for (int i = 0; i < retval.allKpts.Count; i++)
{
retval.allKpts[i].Weight /= count;
}
return(retval);
}
private void AddLeftBoundary(Vector3 closestGamma, KPoint kpt, KptPlane plane, Lattice lattice)
{
double s, t;
plane.GetPlaneST(kpt, out s, out t);
double gs, gt;
plane.GetPlaneST(closestGamma, out gs, out gt);
if (gs == 0)
return;
double ratio = gt / gs;
// this is the solution to
// |S| = |S-P| where S is the target point, P is the nearby Gamma point
// and the y component of S is constrained to be the same as for the input.
double news = 0.5 * (gs + gt * ratio - 2 * t * ratio);
if (Math.Abs(news - s) < 1e-6)
return;
Kpts.Add(new BZoneKPoint(plane.ReduceST(news, t)));
}
public static BZonePlane CreateBZonePlane(KptPlane plane, Lattice lattice)
{
return(new BZonePlane(plane, lattice));
}
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);
}
public static KptList GeneratePlane(Lattice lattice, Vector3[] points, SymmetryList syms, int[] qgrid, int[] qshift)
{
KptList qmesh = GenerateMesh(lattice, qgrid, qshift, syms, true);
return(GeneratePlane(lattice, points, syms, qmesh));
}
internal Lattice Clone()
{
Lattice retval = new Lattice(a1, a2, a3);
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);
}
private static Vector3 GammaInDirection(Lattice lattice, Vector3 direction)
{
Vector3 sred = lattice.ReciprocalReduce(direction);
sred /= LargestNonzero(sred);
Vector3 retval = sred.X * lattice.G1 + sred.Y * lattice.G2 + sred.Z * lattice.G3;
return retval;
}
public static KptList oldGenerateMesh(Lattice lattice, int[] kgrid, int[] shift, SymmetryList syms, bool includeEnds)
{
bool centerGamma = false;
KptList retval = new KptList();
int zmax = kgrid[2] * 2;
int ymax = kgrid[1] * 2;
int xmax = kgrid[0] * 2;
if (shift == null)
shift = new int[3];
retval.mesh = (int[])kgrid.Clone();
retval.shift = (int[])shift.Clone();
retval.gammaCentered = centerGamma;
int index = 0;
Vector3 gridVector = new Vector3(kgrid[0], kgrid[1], kgrid[2]);
SymmetryList compatSyms = new SymmetryList();
foreach (var symmetry in syms)
{
Vector3 grid2 = symmetry.Value * gridVector;
for (int gi = 0; gi < 3; gi++)
grid2[gi] = Math.Abs(grid2[gi]);
if (grid2 == gridVector)
{
compatSyms.Add(symmetry);
}
}
for (int k = 0; k <= zmax; k += 2)
{
for (int j = 0; j <= ymax; j += 2)
{
for (int i = 0; i <= xmax; i += 2)
{
if (includeEnds == false)
{
if (k == zmax) break;
if (i == xmax) break;
if (j == ymax) break;
}
int N = retval.KptToInteger(i, j, k);
bool foundSym = false;
double dx = (i + shift[0]) / (double)xmax;
double dy = (j + shift[1]) / (double)ymax;
double dz = (k + shift[2]) / (double)zmax;
int symN = N;
List<int> orbitals = null;
if (centerGamma)
{
if (kgrid[0] > 1) dx -= 0.5;
if (kgrid[1] > 1) dy -= 0.5;
if (kgrid[2] > 1) dz -= 0.5;
}
Vector3 pt = CalcK(lattice, dx, dy, dz);
#if DEBUG
int testi, testj, testk;
retval.ReduceKpt(lattice, new Vector3(pt), out testi, out testj, out testk);
//System.Diagnostics.Debug.Assert(i == testi);
//System.Diagnostics.Debug.Assert(j == testj);
//System.Diagnostics.Debug.Assert(k == testk);
#endif
foreach (var symmetry in compatSyms)
{
Vector3 Tpt = symmetry.Value * pt;
if (Tpt == pt)
continue;
Vector3 red = lattice.ReducedCoords(Tpt, true);
int newi = (int)Math.Round(xmax * red.X - shift[0]);
int newj = (int)Math.Round(ymax * red.Y - shift[1]);
int newk = (int)Math.Round(zmax * red.Z - shift[2]);
if (newi % 2 != 0 || newj % 2 != 0 || newk % 2 != 0)
continue;
symN = retval.KptToInteger(newi, newj, newk);
if (symN < N)
{
foundSym = true;
if (symmetry.OrbitalTransform.Count > 0)
{
orbitals = symmetry.OrbitalTransform;
}
}
if (foundSym)
break;
}
Vector3 kptValue = CalcK(lattice, dx, dy, dz);
retval.allKpts.Add(new KPoint(kptValue));
if (retval.Nvalues.ContainsKey(N))
{
}
else if (foundSym == false)
{
retval.kpts.Add(new KPoint(kptValue));
retval.Nvalues.Add(N, index);
index++;
}
else
{
int newIndex = retval.Nvalues[symN];
retval.kpts[newIndex].Weight++;
retval.kpts[newIndex].AddOrbitalSymmetry(orbitals);
retval.Nvalues.Add(N, newIndex);
}
}
}
}
int count = kgrid[0] * kgrid[1] * kgrid[2];
for (int i = 0; i < retval.kpts.Count; i++)
{
retval.kpts[i].Weight /= count;
retval.allKpts[i].Weight /= count;
}
if (includeEnds)
{
retval.allKpts.Sort((x, y) => x.Value.Z.CompareTo(y.Value.Z));
List<int> removeThese = new List<int>();
List<int> equivKpt = new List<int>();
// read this value first, because the size of the array will change.
int kptCount = retval.AllKpts.Count;
for (int kindex = 0; kindex < kptCount; kindex++)
{
if (removeThese.Contains(kindex))
continue;
Vector3 kpt = retval.allKpts[kindex].Value;
double dist = kpt.Magnitude;
equivKpt.Clear();
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 = kpt +
i * lattice.G1 +
j * lattice.G2 +
k * lattice.G3;
double newDist = pt.Magnitude;
if (newDist < dist - 1e-6)
{
foreach (var value in equivKpt)
{
if (removeThese.Contains(value) == false)
removeThese.Add(value);
}
equivKpt.Clear();
int search = retval.AllKpts.FindIndex(x => (x.Value - pt).Magnitude < 1e-6);
if (search != -1)
{
if (removeThese.Contains(kindex) == false)
removeThese.Add(kindex);
// break out of the loop
k = 1; j = 1; i = 2;
}
else
{
retval.allKpts[kindex].Value = pt;
kpt = pt;
dist = newDist;
// reset variables since we updated this kpoint value.
k = -1;
j = -1;
i = -2;
}
}
else if (Math.Abs(dist - newDist) < 1e-6)
{
int search = retval.AllKpts.FindIndex(x => (x.Value - pt).Magnitude < 1e-6);
if (search != -1)
{
if (removeThese.Contains(search))
{
k = 1; j = 1; i = 2;
removeThese.Add(kindex);
break;
}
equivKpt.Add(search);
continue;
}
equivKpt.Add(retval.allKpts.Count);
retval.allKpts.Add(new KPoint(pt));
}
}
}
}
}
// sort in reverse order
removeThese.Sort((x, y) => -x.CompareTo(y));
for (int i = 0; i < removeThese.Count; i++)
{
retval.allKpts.RemoveAt(removeThese[i]);
}
retval.allKpts.Sort((x, y) => x.Value.Z.CompareTo(y.Value.Z));
}
#if DEBUG
if (!includeEnds)
{
double check = 0;
for (int i = 0; i < retval.kpts.Count; i++)
check += retval.kpts[i].Weight;
System.Diagnostics.Debug.Assert(Math.Abs(check - 1) < 1e-8);
}
#endif
return retval;
}
private Vector3 ClosestGamma(List<Vector3> nearbyGammas, KPoint kpt, Lattice lattice)
{
if (nearbyGammas.Count == 0)
throw new ArgumentException();
double minDistance = double.MaxValue;
Vector3 closest = new Vector3();
Vector3 kptCart = lattice.ReciprocalExpand(kpt.Value);
foreach (var pt in nearbyGammas)
{
Vector3 gamma = lattice.ReciprocalExpand(pt);
double distance = (kptCart - gamma).Magnitude;
double s, t;
GetPlaneST(pt, out s, out t);
if (distance < minDistance)
{
minDistance = distance;
closest = pt;
}
}
return closest;
}
public static Vector3 CalcK(Lattice l, double dx, double dy, double dz)
{
return dx * l.G1 + dy * l.G2 + dz * l.G3;
}
private int KptToInteger(Lattice lattice, KPoint qpt)
{
return(KptToInteger(lattice, qpt.Value));
}
public int IrreducibleIndex(Vector3 kpt, Lattice lattice, SymmetryList symmetries, out List<int> orbitalMap)
{
for (int s = 0; s < symmetries.Count; s++)
{
int newi, newj, newk;
Vector3 newKpt = symmetries[s].Inverse * kpt;
ReduceKpt(lattice, newKpt, out newi, out newj, out newk);
int N = KptToInteger(newi, newj, newk);
if (Nvalues.ContainsKey(N))
{
int index = Nvalues[N];
orbitalMap = symmetries[s].OrbitalTransform;
return index;
}
}
throw new Exception(string.Format("Could not find k-point {0}", kpt));
}
internal Lattice Clone()
{
Lattice retval = new Lattice(a1, a2, a3);
return retval;
}
private static Vector3 GammaInDirection(Lattice lattice, Vector3 direction)
{
Vector3 sred = lattice.ReducedCoords(direction);
sred /= SmallestNonzero(sred);
Vector3 retval = sred.X * lattice.G1 + sred.Y * lattice.G2 + sred.Z * lattice.G3;
return retval;
}
public static KptList oldGenerateMesh(Lattice lattice, int[] kgrid, int[] shift, SymmetryList syms, bool includeEnds)
{
bool centerGamma = false;
KptList retval = new KptList();
int zmax = kgrid[2] * 2;
int ymax = kgrid[1] * 2;
int xmax = kgrid[0] * 2;
if (shift == null)
{
shift = new int[3];
}
retval.mesh = (int[])kgrid.Clone();
retval.shift = (int[])shift.Clone();
retval.gammaCentered = centerGamma;
int index = 0;
Vector3 gridVector = new Vector3(kgrid[0], kgrid[1], kgrid[2]);
SymmetryList compatSyms = new SymmetryList();
foreach (var symmetry in syms)
{
Vector3 grid2 = symmetry.Value * gridVector;
for (int gi = 0; gi < 3; gi++)
{
grid2[gi] = Math.Abs(grid2[gi]);
}
if (grid2 == gridVector)
{
compatSyms.Add(symmetry);
}
}
for (int k = 0; k <= zmax; k += 2)
{
for (int j = 0; j <= ymax; j += 2)
{
for (int i = 0; i <= xmax; i += 2)
{
if (includeEnds == false)
{
if (k == zmax)
{
break;
}
if (i == xmax)
{
break;
}
if (j == ymax)
{
break;
}
}
int N = retval.KptToInteger(i, j, k);
bool foundSym = false;
double dx = (i + shift[0]) / (double)xmax;
double dy = (j + shift[1]) / (double)ymax;
double dz = (k + shift[2]) / (double)zmax;
int symN = N;
List <int> orbitals = null;
if (centerGamma)
{
if (kgrid[0] > 1)
{
dx -= 0.5;
}
if (kgrid[1] > 1)
{
dy -= 0.5;
}
if (kgrid[2] > 1)
{
dz -= 0.5;
}
}
Vector3 pt = CalcK(lattice, dx, dy, dz);
#if DEBUG
int testi, testj, testk;
retval.ReduceKpt(lattice, new Vector3(pt), out testi, out testj, out testk);
//System.Diagnostics.Debug.Assert(i == testi);
//System.Diagnostics.Debug.Assert(j == testj);
//System.Diagnostics.Debug.Assert(k == testk);
#endif
foreach (var symmetry in compatSyms)
{
Vector3 Tpt = symmetry.Value * pt;
if (Tpt == pt)
{
continue;
}
Vector3 red = lattice.ReducedCoords(Tpt, true);
int newi = (int)Math.Round(xmax * red.X - shift[0]);
int newj = (int)Math.Round(ymax * red.Y - shift[1]);
int newk = (int)Math.Round(zmax * red.Z - shift[2]);
if (newi % 2 != 0 || newj % 2 != 0 || newk % 2 != 0)
{
continue;
}
symN = retval.KptToInteger(newi, newj, newk);
if (symN < N)
{
foundSym = true;
if (symmetry.OrbitalTransform.Count > 0)
{
orbitals = symmetry.OrbitalTransform;
}
}
if (foundSym)
{
break;
}
}
Vector3 kptValue = CalcK(lattice, dx, dy, dz);
retval.allKpts.Add(new KPoint(kptValue));
if (retval.Nvalues.ContainsKey(N))
{
}
else if (foundSym == false)
{
retval.kpts.Add(new KPoint(kptValue));
retval.Nvalues.Add(N, index);
index++;
}
else
{
int newIndex = retval.Nvalues[symN];
retval.kpts[newIndex].Weight++;
retval.kpts[newIndex].AddOrbitalSymmetry(orbitals);
retval.Nvalues.Add(N, newIndex);
}
}
}
}
int count = kgrid[0] * kgrid[1] * kgrid[2];
for (int i = 0; i < retval.kpts.Count; i++)
{
retval.kpts[i].Weight /= count;
retval.allKpts[i].Weight /= count;
}
if (includeEnds)
{
retval.allKpts.Sort((x, y) => x.Value.Z.CompareTo(y.Value.Z));
List <int> removeThese = new List <int>();
List <int> equivKpt = new List <int>();
// read this value first, because the size of the array will change.
int kptCount = retval.AllKpts.Count;
for (int kindex = 0; kindex < kptCount; kindex++)
{
if (removeThese.Contains(kindex))
{
continue;
}
Vector3 kpt = retval.allKpts[kindex].Value;
double dist = kpt.Magnitude;
equivKpt.Clear();
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 = kpt +
i * lattice.G1 +
j * lattice.G2 +
k * lattice.G3;
double newDist = pt.Magnitude;
if (newDist < dist - 1e-6)
{
foreach (var value in equivKpt)
{
if (removeThese.Contains(value) == false)
{
removeThese.Add(value);
}
}
equivKpt.Clear();
int search = retval.AllKpts.FindIndex(x => (x.Value - pt).Magnitude < 1e-6);
if (search != -1)
{
if (removeThese.Contains(kindex) == false)
{
removeThese.Add(kindex);
}
// break out of the loop
k = 1; j = 1; i = 2;
}
else
{
retval.allKpts[kindex].Value = pt;
kpt = pt;
dist = newDist;
// reset variables since we updated this kpoint value.
k = -1;
j = -1;
i = -2;
}
}
else if (Math.Abs(dist - newDist) < 1e-6)
{
int search = retval.AllKpts.FindIndex(x => (x.Value - pt).Magnitude < 1e-6);
if (search != -1)
{
if (removeThese.Contains(search))
{
k = 1; j = 1; i = 2;
removeThese.Add(kindex);
break;
}
equivKpt.Add(search);
continue;
}
equivKpt.Add(retval.allKpts.Count);
retval.allKpts.Add(new KPoint(pt));
}
}
}
}
}
// sort in reverse order
removeThese.Sort((x, y) => - x.CompareTo(y));
for (int i = 0; i < removeThese.Count; i++)
{
retval.allKpts.RemoveAt(removeThese[i]);
}
retval.allKpts.Sort((x, y) => x.Value.Z.CompareTo(y.Value.Z));
}
#if DEBUG
if (!includeEnds)
{
double check = 0;
for (int i = 0; i < retval.kpts.Count; i++)
{
check += retval.kpts[i].Weight;
}
System.Diagnostics.Debug.Assert(Math.Abs(check - 1) < 1e-8);
}
#endif
return(retval);
}
public static KptList GenerateMesh(Lattice lattice, int[] kgrid, int[] shift, SymmetryList syms, bool includeEnds)
{
KptList retval = new KptList();
if (shift == null)
shift = new int[3];
for (int i = 0; i < 3; i++)
if (kgrid[i] == 1)
shift[i] = 1;
retval.mesh = (int[])kgrid.Clone();
retval.shift = (int[])shift.Clone();
retval.gammaCentered = true;
SymmetryList compatSyms = FindCompatibleSymmetries(kgrid, syms);
int index = 0;
for (int k = -kgrid[2] + shift[2]; k <= kgrid[2]; k += 2)
{
for (int j = -kgrid[1] + shift[1]; j <= kgrid[1]; j += 2)
{
for (int i = -kgrid[0] + shift[0]; i <= kgrid[0]; i += 2)
{
if (includeEnds == false)
{
if (k == kgrid[2]) break;
if (j == kgrid[1]) break;
if (i == kgrid[0]) break;
}
double dx = i * 0.5 / kgrid[0];
double dy = j * 0.5 / kgrid[1];
double dz = k * 0.5 / kgrid[2];
Vector3 kptValue = CalcK(lattice, dx, dy, dz);
int N = retval.KptToInteger(i, j, k);
int symN = N;
System.Diagnostics.Debug.Assert(!(retval.Nvalues.ContainsKey(N) && includeEnds == false));
List<int> orbitals = null;
bool foundSym = false;
foreach (var symmetry in compatSyms)
{
Vector3 Tpt = symmetry.Value * kptValue;
if (Tpt == kptValue)
continue;
int newi, newj, newk;
retval.ReduceKpt(lattice, Tpt, out newi, out newj, out newk);
if (Math.Abs(newi) % 2 != shift[0] ||
Math.Abs(newj) % 2 != shift[1] ||
Math.Abs(newk) % 2 != shift[2])
continue;
symN = retval.KptToInteger(newi, newj, newk);
if (symN < N)
{
foundSym = true;
if (symmetry.OrbitalTransform.Count > 0)
{
orbitals = symmetry.OrbitalTransform;
}
break;
}
}
if (includeEnds)
{
if (retval.AllNvalues.ContainsKey(N))
{
retval.allKpts.Add(new KPoint(kptValue));
continue;
}
}
retval.AllNvalues.Add(N, retval.allKpts.Count);
retval.allKpts.Add(new KPoint(kptValue));
if (foundSym == false)
{
retval.kpts.Add(new KPoint(kptValue));
retval.Nvalues.Add(N, index);
index++;
}
else
{
int newIndex = retval.Nvalues[symN];
retval.kpts[newIndex].Weight++;
retval.kpts[newIndex].AddOrbitalSymmetry(orbitals);
retval.Nvalues.Add(N, newIndex);
}
}
}
}
int count = kgrid[0] * kgrid[1] * kgrid[2];
for (int i = 0; i < retval.kpts.Count; i++)
{
retval.kpts[i].Weight /= count;
}
for (int i = 0; i < retval.allKpts.Count; i++)
{
retval.allKpts[i].Weight /= count;
}
return retval;
}
public static Vector3 CalcK(Lattice l, double dx, double dy, double dz)
{
return(dx * l.G1 + dy * l.G2 + dz * l.G3);
}
private int KptToInteger(Lattice lattice, KPoint qpt)
{
return KptToInteger(lattice, qpt.Value);
}
public static KptPlane GeneratePlane(Lattice lattice, Vector3[] points, int[] qgrid, int[] qshift)
{
KptList qmesh = GenerateMesh(qgrid, qshift, true);
return(GeneratePlane(lattice, points, qmesh));
}
private void ReduceKpt(Lattice lattice, Vector3 pt, out int newi, out int newj, out int newk)
{
Vector3 red = lattice.ReducedCoords(pt, true);
newi = (int)Math.Round(mesh[0] * red.X * 2);
newj = (int)Math.Round(mesh[1] * red.Y * 2);
newk = (int)Math.Round(mesh[2] * red.Z * 2);
}
public static KptList GeneratePlane(Lattice lattice, Vector3[] points, SymmetryList syms, int[] qgrid, int[] qshift)
{
KptList qmesh = GenerateMesh(lattice, qgrid, qshift, syms, true);
return GeneratePlane(lattice, points, syms, qmesh);
}
protected void SetLattice(Lattice lattice)
{
this.lattice = lattice;
this.G[0] = lattice.G1;
this.G[1] = lattice.G2;
this.G[2] = lattice.G3;
}
private void AddLeftBoundary(Vector3 closestGamma, KPoint kpt, KptPlane plane, Lattice lattice)
{
double s, t;
plane.GetPlaneST(kpt, out s, out t);
double gs, gt;
plane.GetPlaneST(closestGamma, out gs, out gt);
if (gs == 0)
{
return;
}
double ratio = gt / gs;
// this is the solution to
// |S| = |S-P| where S is the target point, P is the nearby Gamma point
// and the y component of S is constrained to be the same as for the input.
double news = 0.5 * (gs + gt * ratio - 2 * t * ratio);
if (Math.Abs(news - s) < 1e-6)
{
return;
}
Kpts.Add(new BZoneKPoint(plane.ReduceST(news, t)));
}
