Method backpropagate

Core/Variational/expression.cpp:138–166

}

void expression::backpropagate(std::unordered_map<var, MatrixXd>& leaves){
    std::queue<var> q;
    std::unordered_map<var, MatrixXd> derivatives;
    std::unordered_map<var, size_t> explored;
    q.push(root);
    derivatives[root] = ones_like(root);
    
    while(!q.empty()){
        var v = q.front();
        q.pop();
        std::vector<var>& children = v.getChildren();
        std::vector<MatrixXd> child_derivs = v._back(derivatives[v]);
        for(size_t i = 0; i < children.size(); i++){
            auto child = children[i];
            if(explored.find(child) == explored.end())
                explored[child] = child.getParents().size();
            explored[child]--;
            if(derivatives.find(child) == derivatives.end())
                derivatives.emplace(child, zeros_like(child));
            derivatives[child] = derivatives[child].array() + child_derivs[i].array();
            if(children[i].getOp() != op_type::none && explored[child] == 0)
                q.push(child); 
        }
    }
   
    for(auto& iter : leaves){
        iter.second = derivatives[iter.first]; 
    } 
}

void expression::backpropagate(std::unordered_map<var, MatrixXd>& leaves, 
        const std::vector<var>& nonconsts){