///
/// \return A new-and-improved Q matrix.
///
static matrix_type improve_q(
const genotype_matrix_type & g, ///< The G matrix.
const matrix_type & q, ///< The Q matrix.
const matrix_type & fa, ///< The F matrix.
const matrix_type & fb, ///< The 1-F matrix.
const matrix_type & qfa, ///< The Q*F matrix.
const matrix_type & qfb, ///< The Q*(1-F) matrix.
const forced_grouping_type * fg) ///< The force-grouping.
{
assert(verification_type::validate_gqf_sizes(g, q, fa));
assert(verification_type::validate_gqf_sizes(g, q, fb));
assert(verification_type::validate_q(q));
assert(verification_type::validate_f(fa));
const auto I = q.get_height();
const auto K = q.get_width();
matrix_type q_dst (I, K);
const std::vector<size_t> fixed_active_set { K + K };
matrix_type derivative_vec (K, 1);
matrix_type hessian_mat (K, K);
for (size_t i = 0; i < I; i++)
{
const auto q_row = q.copy_row(i);
g.compute_derivatives_q(
q,
fa,
fb,
qfa,
qfb,
i,
derivative_vec,
hessian_mat);
const auto coefficients_mat = _create_coefficients_mat(K, 1);
auto b_vec = _create_b_vec(q_row, 1);
if (nullptr != fg)
{
for (size_t k = 0; k < K; k++)
{
b_vec[k + 0] -= fg->get_min(i, k);
b_vec[k + K] += fg->get_max(i, k) - value_type(1);
}
}
std::vector<size_t> active_set { 0 };
matrix_type delta_vec (K, 1);
delta_vec[0] = -b_vec[0];
qpas_type::loop_over_active_set(
b_vec,
coefficients_mat,
hessian_mat,
derivative_vec,
fixed_active_set,
active_set,
delta_vec);
for (size_t k = 0; k < K; k++)
q_dst(i, k) = q_row[k] + delta_vec[k];
q_dst.clamp_row(i, min, max);
const auto sum = q_dst.get_row_sum(i);
q_dst.multiply_row(i, value_type(1) / sum);
}
return q_dst;
}
