RDGeom::Transform3D *computeCanonicalTransform(const Conformer &conf,
const RDGeom::Point3D *center,
bool normalizeCovar,
bool ignoreHs) {
RDGeom::Point3D origin;
if (!center) {
origin = computeCentroid(conf, ignoreHs);
} else {
origin = (*center);
}
RDNumeric::DoubleSymmMatrix *covMat =
computeCovarianceMatrix(conf, origin, normalizeCovar, ignoreHs);
// find the eigen values and eigen vectors for the covMat
RDNumeric::DoubleMatrix eigVecs(3, 3);
RDNumeric::DoubleVector eigVals(3);
// if we have a single atom system we don't need to do anyhting other than
// setting translation
// translation
unsigned int nAtms = conf.getNumAtoms();
RDGeom::Transform3D *trans = new RDGeom::Transform3D;
// set the translation
origin *= -1.0;
// trans->SetTranslation(origin);
// if we have a single atom system we don't need to do anyhting setting
// translation is sufficient
if (nAtms > 1) {
RDNumeric::EigenSolvers::powerEigenSolver(3, *covMat, eigVals, eigVecs,
conf.getNumAtoms());
// deal with zero eigen value systems
unsigned int i, j, dim = 3;
for (i = 0; i < 3; ++i) {
if (fabs(eigVals.getVal(i)) < EIGEN_TOLERANCE) {
dim--;
}
}
CHECK_INVARIANT(dim >= 1, "");
if (dim < 3) {
RDGeom::Point3D first(eigVecs.getVal(0, 0), eigVecs.getVal(0, 1),
eigVecs.getVal(0, 2));
if (dim == 1) {
// pick an arbitrary eigen vector perpendicular to the first vector
RDGeom::Point3D second(first.getPerpendicular());
eigVecs.setVal(1, 0, second.x);
eigVecs.setVal(1, 1, second.y);
eigVecs.setVal(1, 2, second.z);
if (eigVals.getVal(0) > 1.0) {
eigVals.setVal(1, 1.0);
} else {
eigVals.setVal(1, eigVals.getVal(0) / 2.0);
}
}
RDGeom::Point3D second(eigVecs.getVal(1, 0), eigVecs.getVal(1, 1),
eigVecs.getVal(1, 2));
// pick the third eigen vector perpendicular to the first two
RDGeom::Point3D third = first.crossProduct(second);
eigVecs.setVal(2, 0, third.x);
eigVecs.setVal(2, 1, third.y);
eigVecs.setVal(2, 2, third.z);
if (eigVals.getVal(1) > 1.0) {
eigVals.setVal(2, 1.0);
} else {
eigVals.setVal(2, eigVals.getVal(1) / 2.0);
}
}
// now set the transformation
for (i = 0; i < 3; ++i) {
for (j = 0; j < 3; ++j) {
trans->setVal(i, j, eigVecs.getVal(i, j));
}
}
} // end of multiple atom system
trans->TransformPoint(origin);
trans->SetTranslation(origin);
delete covMat;
return trans;
}
double AlignPoints(const RDGeom::Point3DConstPtrVect &refPoints,
const RDGeom::Point3DConstPtrVect &probePoints,
RDGeom::Transform3D &trans, const DoubleVector *weights,
bool reflect, unsigned int maxIterations) {
unsigned int npt = refPoints.size();
PRECONDITION(npt == probePoints.size(), "Mismatch in number of points");
trans.setToIdentity();
const DoubleVector *wts;
double wtsSum;
bool ownWts;
if (weights) {
PRECONDITION(npt == weights->size(), "Mismatch in number of points");
wts = weights;
wtsSum = _sumOfWeights(*wts);
ownWts = false;
} else {
wts = new DoubleVector(npt, 1.0);
wtsSum = static_cast<double>(npt);
ownWts = true;
}
RDGeom::Point3D rptSum = _weightedSumOfPoints(refPoints, *wts);
RDGeom::Point3D pptSum = _weightedSumOfPoints(probePoints, *wts);
double rptSumLenSq = _weightedSumOfLenSq(refPoints, *wts);
double pptSumLenSq = _weightedSumOfLenSq(probePoints, *wts);
double covMat[3][3];
// compute the co-variance matrix
_computeCovarianceMat(refPoints, probePoints, *wts, covMat);
if (ownWts) {
delete wts;
wts = 0;
}
if (reflect) {
rptSum *= -1.0;
reflectCovMat(covMat);
}
// convert the covariance matrix to a 4x4 matrix that needs to be diagonalized
double quad[4][4];
_covertCovMatToQuad(covMat, rptSum, pptSum, wtsSum, quad);
// get the eigenVecs and eigenVals for the matrix
double eigenVecs[4][4], eigenVals[4];
jacobi(quad, eigenVals, eigenVecs, maxIterations);
// get the quaternion
double quater[4];
quater[0] = eigenVecs[0][0];
quater[1] = eigenVecs[1][0];
quater[2] = eigenVecs[2][0];
quater[3] = eigenVecs[3][0];
trans.SetRotationFromQuaternion(quater);
if (reflect) {
// put the flip in the rotation matrix
trans.Reflect();
}
// compute the SSR value
double ssr = eigenVals[0] - (pptSum.lengthSq() + rptSum.lengthSq()) / wtsSum +
rptSumLenSq + pptSumLenSq;
if ((ssr < 0.0) && (fabs(ssr) < TOLERANCE)) {
ssr = 0.0;
}
if (reflect) {
rptSum *= -1.0;
}
// set the translation
trans.TransformPoint(pptSum);
RDGeom::Point3D move = rptSum;
move -= pptSum;
move /= wtsSum;
trans.SetTranslation(move);
return ssr;
}