How to sort a 2d Vector

I have a vector L containing vectors with 2 doubles each. I want to sort the vectors in L by their first element.

vector<vector<double>> L;

I tried to use the std::sort algorithm with a self-written compare function as follows:

    bool compare(const vector<double> &v1, const vector<double> &v2)
    {
        return v1[0] < v2[0];
    }

    void out_2d_vecotr_as_value_pairs(vector<vector<double>> &L)
    {
        L = sort(L.begin(), L.end(), compare);
            ...
    }

But I get this error I don't understand for the line calling the sort() function:

projet.cc:234:38: error: no match for ‘operator=’ (operand types are ‘std::vector<std::vector<double> >’ and ‘void’)

Thanks for your help