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)));
}
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();
}
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 Matrix GetValue(int index, KptPlane plane, MatrixValueGetter getter, params object[] args)
{
BZoneKPoint kpt = (BZoneKPoint)base.Kpts[index];
if (kpt.TargetIndex != -1)
{
return getter(kpt.TargetIndex, args);
}
else
return Matrix.Zero(4);
}
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 KptPlane CreateIrreduciblePlane(SymmetryList symmetries)
{
KptPlane p = new KptPlane();
p.origin = origin;
p.tdir = tdir;
p.sdir = sdir;
FillIrreducibleMesh(symmetries, p);
return(p);
}
protected override KptList CloneImpl()
{
KptPlane retval = new KptPlane();
base.CloneBaseImpl(retval);
retval.sdir = sdir;
retval.tdir = tdir;
retval.origin = origin;
return(retval);
}
private static void NormalizeST(Lattice lattice, KptPlane retval)
{
retval.sdir /= retval.sdir.Magnitude;
retval.tdir /= retval.tdir.Magnitude;
retval.sdir /= GammaInDirection(lattice, retval.sdir).DotProduct(retval.sdir);
retval.tdir /= GammaInDirection(lattice, retval.tdir).DotProduct(retval.tdir);
// double them to make s and t 1 at the zone boundary, instead of 0.5.
retval.sdir *= 2;
retval.tdir *= 2;
}
public Matrix GetValue(int index, KptPlane plane, MatrixValueGetter getter, params object[] args)
{
BZoneKPoint kpt = (BZoneKPoint)base.Kpts[index];
if (kpt.TargetIndex != -1)
{
return(getter(kpt.TargetIndex, args));
}
else
{
return(Matrix.Zero(4));
}
}
public static BZonePlane CreateBZonePlane(KptPlane plane, Lattice lattice)
{
return(new BZonePlane(plane, lattice));
}
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);
}
private static void NormalizeST(Lattice lattice, KptPlane retval)
{
retval.sdir /= retval.sdir.Magnitude;
retval.tdir /= retval.tdir.Magnitude;
retval.sdir /= GammaInDirection(lattice, retval.sdir).DotProduct(retval.sdir);
retval.tdir /= GammaInDirection(lattice, retval.tdir).DotProduct(retval.tdir);
// double them to make s and t 1 at the zone boundary, instead of 0.5.
retval.sdir *= 2;
retval.tdir *= 2;
}
protected override KptList CloneImpl()
{
KptPlane retval = new KptPlane();
base.CloneBaseImpl(retval);
retval.sdir = sdir;
retval.tdir = tdir;
retval.origin = origin;
return retval;
}
public KptPlane CreateIrreduciblePlane(SymmetryList symmetries)
{
KptPlane p = new KptPlane();
p.origin = origin;
p.tdir = tdir;
p.sdir = sdir;
FillIrreducibleMesh(symmetries, p);
return p;
}
