const Matrix<complex<double> >
gslMatrixSqrt( const Matrix<complex<double> >& mat ) {
if( mat.num_rows() != mat.num_cols() ) throw("Matrices not square");
Vector<double> eigVals( mat.num_rows() );
Matrix<complex<double> > eigVects = nan_to_zero(mat);
// eigVals = Hermitian_eigenvalue_solve( eigVects );
Matrix<complex<double> > tmpMat2 =
dagger(eigVects)*mat*eigVects;
const complex<double> zero(0.0,0.0);
Matrix<complex<double> > out(mat.num_rows(),
mat.num_rows(),
zero);
for (int i=1; i<=mat.num_rows(); i++ ) {
out(i,i) = sqrt( tmpMat2(i,i) );
}
return nan_to_zero(eigVects*out*dagger(eigVects));
}
const Vector<double> gslMatrixEigVals( const Matrix<complex<double> >& mat ) {
if( mat.num_rows() != mat.num_cols() ) throw("Matrices not square");
Vector<double> eigVals( mat.num_rows() );
Matrix<complex<double> > eigVects = nan_to_zero(mat);
// eigVals = Hermitian_eigenvalue_solve( eigVects );
return eigVals;
}
extern void printDiffs( ofstream& outFile,
const int iteration,
const Matrix<complex<double> >& mat1,
const Matrix<complex<double> >& mat2 ) {
// errbnds on Bures?
outFile << iteration
<< ' '
<< distBures(mat1,mat2)
<< ' ';
const Vector<double> eVals = eigVals(mat2);
// const double eValErrBnd = get_eps() *
// max( eVals[0], eVals[ eVals.size() - 1 ] );
// too small for now
for ( int i=eVals.size() -1; i>=0; i-- ) {
outFile << eVals[i]
<< ' ';
}
outFile << endl;
}
bool computeInitialCoords(const RDNumeric::SymmMatrix<double> &distMat,
RDGeom::PointPtrVect &positions,
RDKit::double_source_type &rng, bool randNegEig,
unsigned int numZeroFail) {
unsigned int N = distMat.numRows();
unsigned int nPt = positions.size();
CHECK_INVARIANT(nPt == N, "Size mismatch");
unsigned int dim = positions.front()->dimension();
const double *data = distMat.getData();
RDNumeric::SymmMatrix<double> sqMat(N), T(N, 0.0);
RDNumeric::DoubleMatrix eigVecs(dim, N);
RDNumeric::DoubleVector eigVals(dim);
double *sqDat = sqMat.getData();
unsigned int dSize = distMat.getDataSize();
double sumSqD2 = 0.0;
for (unsigned int i = 0; i < dSize; i++) {
sqDat[i] = data[i] * data[i];
sumSqD2 += sqDat[i];
}
sumSqD2 /= (N * N);
RDNumeric::DoubleVector sqD0i(N, 0.0);
double *sqD0iData = sqD0i.getData();
for (unsigned int i = 0; i < N; i++) {
for (unsigned int j = 0; j < N; j++) {
sqD0iData[i] += sqMat.getVal(i, j);
}
sqD0iData[i] /= N;
sqD0iData[i] -= sumSqD2;
if ((sqD0iData[i] < EIGVAL_TOL) && (N > 3)) {
return false;
}
}
for (unsigned int i = 0; i < N; i++) {
for (unsigned int j = 0; j <= i; j++) {
double val = 0.5 * (sqD0iData[i] + sqD0iData[j] - sqMat.getVal(i, j));
T.setVal(i, j, val);
}
}
unsigned int nEigs = (dim < N) ? dim : N;
RDNumeric::EigenSolvers::powerEigenSolver(nEigs, T, eigVals, eigVecs,
(int)(sumSqD2 * N));
double *eigData = eigVals.getData();
bool foundNeg = false;
unsigned int zeroEigs = 0;
for (unsigned int i = 0; i < dim; i++) {
if (eigData[i] > EIGVAL_TOL) {
eigData[i] = sqrt(eigData[i]);
} else if (fabs(eigData[i]) < EIGVAL_TOL) {
eigData[i] = 0.0;
zeroEigs++;
} else {
foundNeg = true;
}
}
if ((foundNeg) && (!randNegEig)) {
return false;
}
if ((zeroEigs >= numZeroFail) && (N > 3)) {
return false;
}
for (unsigned int i = 0; i < N; i++) {
RDGeom::Point *pt = positions[i];
for (unsigned int j = 0; j < dim; ++j) {
if (eigData[j] >= 0.0) {
(*pt)[j] = eigData[j] * eigVecs.getVal(j, i);
} else {
// std::cerr<<"!!! "<<i<<"-"<<j<<": "<<eigData[j]<<std::endl;
(*pt)[j] = 1.0 - 2.0 * rng();
}
}
}
return true;
}
