// this is multiplication in the matrix sense
template <typename T, typename X> void permutation_matrix<T, X>::multiply_by_permutation_from_right(permutation_matrix<T, X> & p) {
auto clone = clone_m_permutation();
lean_assert(p.size() == size());
unsigned i = size();
while (i-- > 0) {
set_val(i, p[clone[i]]); // we have m(P)*m(Q) = m(QP), where m is the matrix of the permutation
}
delete [] clone;
}
inline unsigned number_of_inversions(permutation_matrix<T, X> & p) {
unsigned ret = 0;
unsigned n = p.size();
for (unsigned i = 0; i < n; i++) {
for (unsigned j = i + 1; j < n; j++) {
if (p[i] > p[j]) {
ret++;
}
}
}
return ret;
}
void swap_columns(permutation_matrix const& P, matrix_expression<M>& A) {
for(std::size_t i = 0; i != P.size(); ++i)
swap_columns(A(),i,P(i));
}
void swap_rows_inverted(permutation_matrix const& P, matrix_expression<M>& A) {
for(std::size_t i = P.size(); i != 0; --i) {
swap_rows(A(),i-1,P(i-1));
}
}
void swap_rows(permutation_matrix const& P, vector_expression<V>& v) {
for (std::size_t i = 0; i != P.size(); ++ i)
std::swap(v()(i),v()(P(i)));
}