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vector.hpp
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vector.hpp
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#ifndef CP_ALGO_LINALG_VECTOR_HPP
#define CP_ALGO_LINALG_VECTOR_HPP
#include "../random/rng.hpp"
#include "../math/modint.hpp"
#include <functional>
#include <algorithm>
#include <valarray>
#include <iostream>
#include <iterator>
#include <cassert>
namespace cp_algo::linalg {
template<class vec, typename base>
struct valarray_base: std::valarray<base> {
using Base = std::valarray<base>;
using Base::Base;
valarray_base(base const& t): Base(t, 1) {}
auto begin() {return std::begin(to_valarray());}
auto begin() const {return std::begin(to_valarray());}
auto end() {return std::end(to_valarray());}
auto end() const {return std::end(to_valarray());}
bool operator == (vec const& t) const {return std::ranges::equal(*this, t);}
bool operator != (vec const& t) const {return !(*this == t);}
vec operator-() const {return Base::operator-();}
static vec from_range(auto const& R) {
vec res(std::ranges::distance(R));
std::ranges::copy(R, res.begin());
return res;
}
Base& to_valarray() {return static_cast<Base&>(*this);}
Base const& to_valarray() const {return static_cast<Base const&>(*this);}
};
template<class vec, typename base>
vec operator+(valarray_base<vec, base> const& a, valarray_base<vec, base> const& b) {
return a.to_valarray() + b.to_valarray();
}
template<class vec, typename base>
vec operator-(valarray_base<vec, base> const& a, valarray_base<vec, base> const& b) {
return a.to_valarray() - b.to_valarray();
}
template<class vec, typename base>
struct vec_base: valarray_base<vec, base> {
using Base = valarray_base<vec, base>;
using Base::Base;
static vec ei(size_t n, size_t i) {
vec res(n);
res[i] = 1;
return res;
}
virtual void add_scaled(vec const& b, base scale, size_t i = 0) {
if(scale != base(0)) {
for(; i < size(*this); i++) {
(*this)[i] += scale * b[i];
}
}
}
virtual vec const& normalize() {
return static_cast<vec&>(*this);
}
virtual base normalize(size_t i) {
return (*this)[i];
}
void read() {
for(auto &it: *this) {
std::cin >> it;
}
}
void print() const {
std::ranges::copy(*this, std::ostream_iterator<base>(std::cout, " "));
std::cout << "\n";
}
static vec random(size_t n) {
vec res(n);
std::ranges::generate(res, random::rng);
return res;
}
// Concatenate vectors
vec operator |(vec const& t) const {
vec res(size(*this) + size(t));
res[std::slice(0, size(*this), 1)] = *this;
res[std::slice(size(*this), size(t), 1)] = t;
return res;
}
// Generally, vec shouldn't be modified
// after its pivot index is set
std::pair<size_t, base> find_pivot() {
if(pivot == size_t(-1)) {
pivot = 0;
while(pivot < size(*this) && normalize(pivot) == base(0)) {
pivot++;
}
if(pivot < size(*this)) {
pivot_inv = base(1) / (*this)[pivot];
}
}
return {pivot, pivot_inv};
}
void reduce_by(vec &t) {
auto [pivot, pinv] = t.find_pivot();
if(pivot < size(*this)) {
add_scaled(t, -normalize(pivot) * pinv, pivot);
}
}
private:
size_t pivot = -1;
base pivot_inv;
};
template<typename base>
struct vec: vec_base<vec<base>, base> {
using Base = vec_base<vec<base>, base>;
using Base::Base;
};
template<math::modint_type base>
struct vec<base>: vec_base<vec<base>, base> {
using Base = vec_base<vec<base>, base>;
using Base::Base;
void add_scaled(vec const& b, base scale, size_t i = 0) override {
if(scale != base(0)) {
for(; i < size(*this); i++) {
(*this)[i].add_unsafe(scale.getr() * b[i].getr());
}
if(++counter == 8) {
for(auto &it: *this) {
it.pseudonormalize();
}
counter = 0;
}
}
}
vec const& normalize() override {
for(auto &it: *this) {
it.normalize();
}
return *this;
}
base normalize(size_t i) override {
return (*this)[i].normalize();
}
private:
size_t counter = 0;
};
}
#endif // CP_ALGO_LINALG_VECTOR_HPP