matrix_t matrix_t::solve(matrix_t const &rhs) const
{
stack::fe_asserter dummy{};
// it appears as if dgesv works only for square matrices Oo
// --> if the matrix was rectangular, then they system would be over/under determined
// and we would need least squares instead (LAPACKE_dgels)
stack_assert(get_rows() == get_cols());
stack_assert(this->get_rows() == rhs.get_rows());
// TODO assert that this matrix is not singular
matrix_t A = this->clone(); // will be overwritten by LU factorization
matrix_t b = rhs.clone();
// thes solution is overwritten in b
vector_ll_t ipiv{A.get_rows()};
stack_assert(0 == LAPACKE_dgesv(LAPACK_COL_MAJOR,
A.get_rows(), rhs.get_cols()/*nrhs*/,
A.get_data(), A.ld(),
ipiv.get_data(),
b.get_data(), b.ld()));
return b;
}
vector_t /* user_factor */
est_factor(
vector_ll_t const & neighbors,
vector_t const & weights,
matrix_t const & P)
{
stack::fe_asserter dummy1{};
scoped_timer dummy(std::string(__func__));
vector_t user_factor{P.get_cols()};
for(int i = 0; i < neighbors.get_len(); i++)
user_factor += weights[i] * P.get_row_clone(neighbors[i]);
return user_factor.normalize_2();
}
matrix_t operator+(matrix_t const & X, diag_t const & D)
{
stack::fe_asserter fe{};
stack_assert(X.get_rows() == D.get_rows());
stack_assert(X.get_cols() == D.get_cols());
matrix_t ret = X.clone();
vector_t Xdiag = vector_t{
ret.get_data(),
ret.get_rows()/*it's a square matrix*/,
ret.get_rows() + 1, // diagonal entries of a square matrix
};
Xdiag += diag_clone(D);
return ret;
}
// mult X * D
matrix_t diag_t::left_mult(matrix_t const &X) const
{
stack::fe_asserter fe{};
stack_assert(diagonal.get_len() == X.get_cols());
matrix_t ret = X.clone();
if(ret.get_rows() < ret.get_cols())
for(size_t r = 0; r < ret.get_rows(); r++)
ret[r] *= diagonal;
else
for(size_t c = 0; c < ret.get_cols(); c++)
ret.get_col(c) *= diagonal[c];
return ret;
}
void most_similar(
index_t const user,
vector_ll_t /*out*/ neighbors,
vector_t /*out*/ weights,
matrix_t const sim)
{
stack_assert(neighbors.get_len() <= sim.get_rows());
stack_assert(weights.get_len() <= sim.get_rows());
stack_assert(neighbors.get_len() == weights.get_len());
stack_assert(sim.get_rows() == sim.get_cols());
// assert symmetric matrix; how ?
stack_assert(sim.get_rows() > user);
stack_assert(user >= 0); // always true if typeof(user) is unsigned.
stack::fe_asserter dummy1{};
// sort users by their similarity this this user
scoped_timer dummy(__func__);
vector_t sim_vec = sim.get_row_clone(user);
stack_assert(std::abs(boost::math::float_distance(sim_vec[user], 1.0)) <= 2);
// The previous assert won't hold when using perturbed similarity,
// However, we require it is set artificially to 1.
std::vector<index_t> all_others(sim.get_rows());
std::iota(std::begin(all_others), std::end(all_others), 0);
all_others.erase(std::begin(all_others) + user); // TODO could be optimized by doing iota is two steps
// top-k
// heapify(all_others.data(), sim_vec, neighbors.get_len());
// for (index_t i = 0; i < sim.get_rows(); i++)
// {
// // only consider unseen neighbors
// // this loop could be unnecessary given the next conditional, but be safe first then verify later
// if(i == user || std::find(std::begin(all_others), std::begin(all_others) + i, i) != std::begin(all_others) + i)
// continue;
// if (sim_vec[i] > sim_vec[all_others[0]] /*top of the heap: the min value of all similarities we have*/)
// {
// all_others[0] = i; // discards the old value
// sift_down(all_others.data(), sim_vec.get_data(), static_cast<index_t>(0), static_cast<index_t>(neighbors.get_len() - 1) /*end of heap - inclusive*/);
// }
// }
// I have to test my heap first. Be safe for now.
std::partial_sort(
std::begin(all_others),
std::begin(all_others) + neighbors.get_len(),
std::end(all_others),
[=](size_t a, size_t b)->bool
{
std::cout << "a = " << a << std::endl;
std::cout << "b = " << b << std::endl;
stack_assert(a < sim_vec.get_len());
stack_assert(b < sim_vec.get_len());
return sim_vec[a] >= sim_vec[b]; // descending order
});
// get weights of neighbors
all_others.resize(neighbors.get_len());
std::sort(std::begin(all_others), std::end(all_others));
{
size_t i = 0;
for(auto n : all_others)
{
neighbors[i] = n;
weights[i] = sim_vec[n];
stack_assert(weights[i] >= 0);
++i;
}
}
// normalize weights
// weights must be positive and sum to 1, normalize_1 will make them sum to 1
// and we have already verified they are positive
weights.normalize_1();
}