private void GenerateSymmetries()
{
Symmetries = new SymmetryList();
Symmetries.Add(new Symmetry(Matrix.Identity(3)));
foreach (var sym in PrimitiveSymmetries)
{
Symmetries.Add(sym.Clone());
GenerateSymmetries(sym);
}
}
private static SymmetryList FindCompatibleSymmetries(int[] kgrid, SymmetryList syms)
{
SymmetryList compatSyms;
compatSyms = new SymmetryList();
Vector3 gridVector = new Vector3(kgrid[0], kgrid[1], kgrid[2]);
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);
}
}
return(compatSyms);
}
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);
}
static void Initialize()
{
if (init)
{
return;
}
init = true;
InitializeRegex();
string groups = Properties.Resources.spgroup;
using (StringReader r = new StringReader(groups))
{
for (; ;)
{
string groupName = r.ReadLine().Trim();
int number;
if (groupName.EndsWith("&"))
{
break;
}
if (int.TryParse(groupName.Substring(1, groupName.Length - 2), out number) == false)
{
throw new Exception();
}
SpaceGroup sp = new SpaceGroup();
sp.Number = number;
for (; ;)
{
if (r.Peek() == '/')
{
break;
}
string text = r.ReadLine();
int lastColon = text.IndexOf(":", 8);
var sym = ParseSymmetry(text);
sym.Name = text.Substring(lastColon + 1).Trim();
if (sym.Value.IsIdentity)
{
continue;
}
if (mPrimitiveSymmetries.Contains(sym) == false)
{
mPrimitiveSymmetries.Add(sym);
}
sp.PrimitiveSymmetries.Add(sym);
}
mGroups.Add(number, sp);
}
}
using (StringReader r = new StringReader(Properties.Resources.spnames))
{
for (; ;)
{
string text = r.ReadLine();
if (text == "&")
{
break;
}
string[] vals = text.Split('-');
int number = int.Parse(vals[0]);
string name = vals[1].Trim();
mGroups[number].Name = name;
}
}
}