Subsystem(MSRdr msRdr, String code, Matrix w) {
this.msRdr = msRdr;
this.code = code;
this.w = w;
d = w.getArray().length - 3;
}
private void setSymmetry(boolean setOperators) {
double[][] a;
// Part 1: Get sigma_nu
// van Smaalen, p. 92.
Logger.info("[subsystem " + code + "]");
Matrix winv = w.inverse();
Logger.info("w=" + w);
Logger.info("w_inv=" + winv);
// w33 w3d van Smaalen, p. 94, Eqn. 4.15
// w =
// wd3 wdd
Matrix w33 = w.getSubmatrix(0, 0, 3, 3);
Matrix wd3 = w.getSubmatrix(3, 0, d, 3);
Matrix w3d = w.getSubmatrix(0, 3, 3, d);
Matrix wdd = w.getSubmatrix(3, 3, d, d);
Matrix sigma = msRdr.getSigma();
// Eqn. 4.16
Matrix sigma_nu = wdd.mul(sigma).add(wd3).mul(w3d.mul(sigma).add(w33).inverse());
Matrix tFactor = wdd.sub(sigma_nu.mul(w3d));
Logger.info("sigma_nu = " + sigma_nu);
// Part 2: Get the new unit cell and symmetry operators
SymmetryInterface s0 = msRdr.cr.asc.getSymmetry();
V3[] vu43 = s0.getUnitCellVectors();
V3[] vr43 = reciprocalsOf(vu43);
// using full matrix math here:
//
// mar3 = just 3x3 matrix of ai* (a*, b*, c*)
// mard3 = full (3+d)x3 matrix of ai* (a*, b*, c*, x4*, x5*,....)
// = [ mard3 | sigma * mard3 ]
//
Matrix mard3 = new Matrix(null, 3 + d, 3);
Matrix mar3 = new Matrix(null, 3, 3);
double[][] mard3a = mard3.getArray();
double[][] mar3a = mar3.getArray();
for (int i = 0; i < 3; i++)
mard3a[i] = mar3a[i] = new double[] {vr43[i + 1].x, vr43[i + 1].y, vr43[i + 1].z};
Matrix sx = sigma.mul(mar3);
a = sx.getArray();
for (int i = 0; i < d; i++) mard3a[i + 3] = a[i];
a = w.mul(mard3).getArray();
// back to vector notation and direct lattice
V3[] uc_nu = new V3[4];
uc_nu[0] = vu43[0]; // origin
for (int i = 0; i < 3; i++)
uc_nu[i + 1] = V3.new3((float) a[i][0], (float) a[i][1], (float) a[i][2]);
uc_nu = reciprocalsOf(uc_nu);
symmetry =
((Symmetry) msRdr.cr.getInterface("org.jmol.symmetry.Symmetry"))
.getUnitCell(uc_nu, false, null);
modMatrices = new Matrix[] {sigma_nu, tFactor};
if (!setOperators) return;
isFinalized = true;
// Part 3: Transform the operators
//
Logger.info("unit cell parameters: " + symmetry.getUnitCellInfo());
symmetry.createSpaceGroup(-1, "[subsystem " + code + "]", new Lst<M4>());
int nOps = s0.getSpaceGroupOperationCount();
for (int iop = 0; iop < nOps; iop++) {
Matrix rv = s0.getOperationRsVs(iop);
Matrix r0 = rv.getRotation();
Matrix v0 = rv.getTranslation();
Matrix r = w.mul(r0).mul(winv);
Matrix v = w.mul(v0);
String code = this.code;
if (isMixed(r)) {
// This operator mixes x4,x5... into x1,x2,x3.
// It is not a pure operation. Instead, it correlates one
// subsystem with another. Our job is to find the other
// subsystem "j" that will satisfy the following condition:
//
// (Wj R Wi_inv).submatrix(0,3,3,d) == all_zeros
//
for (Entry<String, Subsystem> e : msRdr.htSubsystems.entrySet()) {
Subsystem ss = e.getValue();
if (ss == this) continue;
Matrix rj = ss.w.mul(r0).mul(winv);
if (!isMixed(rj)) {
// We have found the corresponding subsystem.
// The result of this operation will be in other system,
// and the operation itself will be used to rotate the modulation.
// ss.code will be used to mark any atom created by this operation as
// part of the other system.
r = rj;
v = ss.w.mul(v0);
code = ss.code;
break;
}
}
}
String jf = symmetry.addOp(code, r, v, sigma_nu);
Logger.info(
this.code + "." + (iop + 1) + (this.code.equals(code) ? " " : ">" + code + " ") + jf);
}
}
private boolean isMixed(Matrix r) {
double[][] a = r.getArray();
for (int i = 3; --i >= 0; ) for (int j = 3 + d; --j >= 3; ) if (a[i][j] != 0) return true;
return false;
}