/// This function is not provided by AutoDiffBlock, so we must add it here.
inline CollOfScalar sqrt(const CollOfScalar& x)
{
// d(sqrt(x))/dy = 1/(2*sqrt(x)) * dx/dy
const auto& xjac = x.derivative();
if (xjac.empty()) {
return CollOfScalar(sqrt(x.value()));
}
const int num_blocks = xjac.size();
std::vector<CollOfScalar::M> jac(num_blocks);
const auto sqrt_x = sqrt(x.value());
const CollOfScalar::M one_over_two_sqrt_x((0.5/sqrt_x).matrix().asDiagonal());
for (int block = 0; block < num_blocks; ++block) {
jac[block] = one_over_two_sqrt_x * xjac[block];
}
return CollOfScalar::ADB::function(sqrt_x, jac);
}
CollOfVector EquelleRuntimeCPU::centroid(const CollOfCell& cells) const
{
const int n = cells.size();
const int dim = grid_.dimensions;
Eigen::Array<double, Eigen::Dynamic, Eigen::Dynamic, Eigen::ColMajor> c(n, dim);
for (int i = 0; i < n; ++i) {
const double* fc = grid_.cell_centroids + dim * cells[i].index;
for (int d = 0; d < dim; ++d) {
c(i, d) = fc[d];
}
}
CollOfVector centroids(dim);
for (int d = 0; d < dim; ++d) {
centroids.col(d) = CollOfScalar(c.col(d));
}
return centroids;
}
CollOfVector EquelleRuntimeCPU::normal(const CollOfFace& faces) const
{
const int n = faces.size();
const int dim = grid_.dimensions;
Eigen::Array<double, Eigen::Dynamic, Eigen::Dynamic, Eigen::ColMajor> nor(n, dim);
for (int i = 0; i < n; ++i) {
const double* fn = grid_.face_normals + dim * faces[i].index;
for (int d = 0; d < dim; ++d) {
nor(i, d) = fn[d];
}
}
// Since the UnstructuredGrid uses the unorthodox convention that face
// normals are scaled with the face areas, we must renormalize them.
nor.colwise() /= nor.matrix().rowwise().norm().array();
CollOfVector normals(dim);
for (int d = 0; d < dim; ++d) {
normals.col(d) = CollOfScalar(nor.col(d));
}
return normals;
}