Matrix
(math/Matrix.hpp)

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• Last update: 2023-06-25 16:21:20+09:00
• Include: #include "math/Matrix.hpp"

Depends on

• basic/template.hpp

Verified with

• test/yosupo/matrix_det.test.cpp
• test/yosupo/matrix_product.test.cpp

Code

#pragma once
#include "../basic/template.hpp"

template <class T, std::enable_if_t<
#if __cplusplus >= 201703L
					   std::is_same_v<decltype(T() / T()), T>
#else
					   std::is_same<decltype(T() / T()), T>::value
#endif
					   ,
					   std::nullptr_t> = nullptr>
class Matrix {
  protected:
	uint N, M;
	std::vector<std::vector<T>> elems;

  public:
	Matrix() = default;
	Matrix(uint N_, uint M_) : N(N_), M(M_), elems(N, std::vector<T>(M)) {}
	std::vector<T>& operator[](uint idx) { return elems[idx]; }
	const std::vector<T>& operator[](uint idx) const { return elems[idx]; }
	decltype(elems)& data() { return elems; }
	const decltype(elems)& data() const { return elems; }

	void resize(int N_, int M_) {
		elems.resize(N_);
		rep(i, N_) elems[i].resize(M_);
	}

	Matrix operator*(Matrix rhs) const {
		Matrix<T> res(N, rhs.M);
		rep(i, N) rep(j, M) rep(k, rhs.M) res[i][k] +=
			elems[i][j] * rhs.elems[j][k];
		return res;
	}
};

template <class T>
class SquareMatrix : public Matrix<T> {
	using Matrix<T>::N;
	using Matrix<T>::Matrix;
	using Matrix<T>::elems;

  public:
	SquareMatrix(uint N_) : Matrix<T>(N_, N_) {}
	SquareMatrix<T>& operator=(const Matrix<T>& rhs) {
		elems = rhs.data();
		return *this;
	}
	SquareMatrix<T>& operator=(Matrix<T>&& rhs) {
		elems = std::move(rhs.data());
		return *this;
	}
	SquareMatrix<T> operator*=(const SquareMatrix<T>& rhs) {
		*this = *this * rhs;
		return *this;
	}
	SquareMatrix<T> pow(lint p) const {
		SquareMatrix<T> res{N}, memo = *this;
		rep(i, N) res[i][i] = 1;
		while (p) {
			if (p & 1) res *= memo;
			p >>= 1;
			memo *= memo;
		}
		return res;
	}

	constexpr T determinant() const {
		SquareMatrix<T> tmp = *this;
		T res(1);
		rep(i, N) {
			if (tmp[i][i] == 0) {
				for (int j = i + 1; j < N; j++) {
					if (tmp[j][i]) {
						std::swap(tmp[i], tmp[j]);
						res = -res;
						break;
					}
				}
			}
			res *= tmp[i][i];
			for (int j = i + 1; j < N; j++) {
				T inv = T(1) / tmp[i][i];
				for (int k = i + 1; k < N; k++) {
					tmp[j][k] -= tmp[j][i] * inv * tmp[i][k];
				}
			}
		}
		return res;
	}
};

template <class T, uint N, uint M>
class FixedMatrix {
  protected:
	std::array<std::array<T, M>, N> elems;

  public:
	constexpr FixedMatrix() { rep(i, N) elems[i].fill(0); }
	constexpr FixedMatrix(std::initializer_list<T> init) {
		auto ite = init.begin();
		rep(i, N) rep(j, M) elems[i][j] = *ite++;
	}
	constexpr FixedMatrix(const FixedMatrix<T, N, M>& rhs) {
		elems = rhs.elems;
	}
	constexpr FixedMatrix(FixedMatrix<T, N, M>&& rhs) {
		elems = std::move(rhs.elems);
	}
	constexpr std::array<T, N>& operator[](uint idx) { return elems[idx]; }
	constexpr const std::array<T, N>& operator[](uint idx) const {
		return elems[idx];
	}
	constexpr decltype(elems)& data() { return elems; }
	constexpr const decltype(elems)& data() const { return elems; }

	constexpr FixedMatrix<T, N, M> operator=(const FixedMatrix<T, N, M>& rhs) {
		elems = rhs.elems;
		return *this;
	}
	constexpr FixedMatrix<T, N, M> operator=(FixedMatrix<T, N, M>&& rhs) {
		elems = std::move(rhs.elems);
		return *this;
	}

	constexpr FixedMatrix<T, N, M> operator+=(const FixedMatrix<T, N, M>& rhs) {
		rep(i, N) rep(j, M) elems[i][j] += rhs.elems[i][j];
		return *this;
	}

	constexpr FixedMatrix<T, N, M> operator+(
		const FixedMatrix<T, N, M>& rhs) const {
		FixedMatrix<T, N, M> res = *this;
		return res += rhs;
	}

	template <uint L>
	constexpr FixedMatrix<T, N, L> operator*(
		const FixedMatrix<T, M, L>& rhs) const {
		FixedMatrix<T, N, L> res;
		rep(i, N) rep(j, M) rep(k, L) res[i][k] +=
			elems[i][j] * rhs.elems[j][k];
		return res;
	}
};

template <class T, uint N>
class FixedSquareMatrix : public FixedMatrix<T, N, N> {
	using FixedMatrix<T, N, N>::FixedMatrix;
	using FixedMatrix<T, N, N>::elems;

  public:
	using FixedMatrix<T, N, N>::operator*;
	constexpr FixedSquareMatrix(const FixedMatrix<T, N, N>& obj)
		: FixedMatrix<T, N, N>(obj) {}
	constexpr FixedSquareMatrix(FixedMatrix<T, N, N>&& obj)
		: FixedMatrix<T, N, N>(obj) {}

	constexpr FixedSquareMatrix<T, N>& operator*=(
		const FixedSquareMatrix<T, N>& rhs) {
		*this = *this * rhs;
		return *this;
	}

	constexpr FixedSquareMatrix<T, N> pow(lint p) const {
		FixedSquareMatrix<T, N> res, memo = *this;
		rep(i, N) res[i][i] = 1;
		while (p) {
			if (p & 1) res *= memo;
			p >>= 1;
			memo *= memo;
		}
		return res;
	}

	constexpr T determinant() const {
		FixedSquareMatrix<T, N> tmp = *this;
		T res(1);
		rep(i, N) {
			if (tmp[i][i] == 0) {
				for (int j = i + 1; j < N; j++) {
					if (tmp[j][i]) {
						std::swap(tmp[i], tmp[j]);
						res = -res;
						break;
					}
				}
			}
			res *= tmp[i][i];
			for (int j = i + 1; j < N; j++) {
				T inv = T(1) / tmp[i][i];
				for (int k = i + 1; k < N; k++) {
					tmp[j][k] -= tmp[j][i] * inv * tmp[i][k];
				}
			}
		}
		return res;
	}

	constexpr static FixedSquareMatrix<T, N> ident() {
		FixedSquareMatrix<T, N> res;
		rep(i, N) res[i][i] = 1;
		return res;
	}
};

/**
 * @title Matrix
 */

#line 2 "basic/template.hpp"
#define _CRT_SECURE_NO_WARNINGS
#ifndef __clang__
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#endif
#include <string.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cfloat>
#include <chrono>
#include <climits>
#include <cmath>
#include <complex>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <memory>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#define rep(i, n) for (int i = 0; i < int(n); i++)
#define REP(i, n) for (int i = 1; i <= int(n); i++)
#define all(V) V.begin(), V.end()

using i128 = __int128_t;
using u128 = __uint128_t;
using uint = unsigned int;
using lint = long long;
using ulint = unsigned long long;
using IP = std::pair<int, int>;
using LP = std::pair<lint, lint>;

constexpr int INF = INT_MAX / 2;
constexpr lint LINF = LLONG_MAX / 2;
constexpr double eps = DBL_EPSILON * 10;
constexpr double PI = 3.141592653589793238462643383279;

template <class T>
class prique : public std::priority_queue<T, std::vector<T>, std::greater<T>> {};
int popcount(uint x) {
#if __cplusplus >= 202002L
	return std::popcount(x);
#else
#ifndef __clang__
	return __builtin_popcount(x);
#endif
#endif
	x = (x & 0x55555555) + (x >> 1 & 0x55555555);
	x = (x & 0x33333333) + (x >> 2 & 0x33333333);
	x = (x & 0x0f0f0f0f) + (x >> 4 & 0x0f0f0f0f);
	x = (x & 0x00ff00ff) + (x >> 8 & 0x00ff00ff);
	return (x & 0x0000ffff) + (x >> 16 & 0x0000ffff);
}
template <class F>
inline constexpr decltype(auto) lambda_fix(F&& f) {
	return [f = std::forward<F>(f)](auto&&... args) {
		return f(f, std::forward<decltype(args)>(args)...);
	};
}
template <class T>
constexpr std::vector<T> make_vec(size_t n) {
	return std::vector<T>(n);
}
template <class T, class... Args>
constexpr auto make_vec(size_t n, Args&&... args) {
	return std::vector<decltype(make_vec<T>(args...))>(n, make_vec<T>(std::forward<Args>(args)...));
}
template <class T, class U, class Stream>
Stream& operator>>(Stream& ist, std::pair<T, U>& x) {
	return ist >> x.first >> x.second;
}
template <class T, class U, class Stream>
Stream& operator<<(Stream& ost, const std::pair<T, U>& x) {
	return ost << x.first << " " << x.second;
}
template <class Container,
		  std::enable_if_t<!std::is_same<Container, std::string>::value, std::nullptr_t> = nullptr>
auto operator>>(std::istream& ist, Container& cont)
	-> decltype(typename Container::iterator(), std::cin)& {
	Container tmp;
	while (true) {
		typename Container::value_type t;
		ist >> t;
		tmp.emplace_back(t);
		if (getchar() == '\n') break;
	}
	cont = Container(std::move(tmp));
	return ist;
}
template <class Container, class Stream,
		  std::enable_if_t<!std::is_same<Container, std::string>::value, std::nullptr_t> = nullptr>
auto operator<<(Stream& ost, const Container& cont)
	-> decltype(typename Container::iterator(), ost)& {
	for (auto it = cont.begin(); it != cont.end(); it++) {
		if (it != cont.begin()) ost << ' ';
		ost << *it;
	}
	return ost;
}
template <class Container>
auto sum(const Container& cont) -> decltype(typename Container::iterator(), 0LL) {
	lint res = 0;
	for (auto it = cont.begin(); it != cont.end(); it++) res += *it;
	return res;
}
template <class T, class U>
constexpr inline bool chmax(T& lhs, const U& rhs) noexcept {
	if (lhs < rhs) {
		lhs = rhs;
		return true;
	}
	return false;
}
template <class T, class U>
constexpr inline bool chmin(T& lhs, const U& rhs) noexcept {
	if (lhs > rhs) {
		lhs = rhs;
		return true;
	}
	return false;
}
constexpr inline lint gcd(lint a, lint b) noexcept {
	while (b) {
		lint c = a;
		a = b;
		b = c % b;
	}
	return a;
}
inline lint lcm(lint a, lint b) noexcept { return a / gcd(a, b) * b; }
constexpr bool isprime(lint n) noexcept {
	if (n == 1) return false;
	for (int i = 2; i * i <= n; i++) {
		if (n % i == 0) return false;
	}
	return true;
}
template <class T>
constexpr T mypow(T a, lint b) noexcept {
	T res(1);
	while (true) {
		if (b & 1) res *= a;
		b >>= 1;
		if (!b) break;
		a *= a;
	}
	return res;
}
constexpr lint modpow(lint a, lint b, lint m) noexcept {
	a %= m;
	lint res(1);
	while (b) {
		if (b & 1) res *= a, res %= m;
		a *= a, a %= m, b >>= 1;
	}
	return res;
}
LP extGcd(lint a, lint b) noexcept {
	if (b == 0) return {1, 0};
	LP s = extGcd(b, a % b);
	std::swap(s.first, s.second);
	s.second -= a / b * s.first;
	return s;
}
LP ChineseRem(const lint& b1, const lint& m1, const lint& b2, const lint& m2) noexcept {
	auto p = extGcd(m1, m2);
	lint g = gcd(m1, m2), l = m1 / g * m2;
	lint tmp = (b2 - b1) / g * p.first % (m2 / g);
	lint r = (b1 + m1 * tmp + l) % l;
	return {r, l};
}
int LCS(const std::string& a, const std::string& b) {
	auto dp = make_vec<int>(a.size() + 1, b.size() + 1);
	rep(i, a.size()) {
		rep(j, b.size()) {
			chmax(dp[i + 1][j], dp[i][j]);
			chmax(dp[i][j + 1], dp[i][j]);
			if (a[i] == b[j]) chmax(dp[i + 1][j + 1], dp[i][j] + 1);
		}
		chmax(dp[i + 1][b.size()], dp[i][b.size()]);
	}
	rep(j, b.size()) chmax(dp[a.size()][j + 1], dp[a.size()][j]);
	return dp[a.size()][b.size()];
}
template <class T, std::enable_if_t<std::is_convertible<int, T>::value, std::nullptr_t> = nullptr>
void compress(std::vector<T>& vec) {
	auto tmp = vec;
	std::sort(all(tmp));
	tmp.erase(std::unique(all(tmp)), tmp.end());
	for (T& i : vec) i = std::lower_bound(all(tmp), i) - tmp.begin();
}
template <class T>
void compress(T* l, T* r) {
	std::vector<T> tmp(l, r);
	std::sort(all(tmp));
	tmp.erase(std::unique(all(tmp)), tmp.end());
	for (auto i = l; i < r; i++) {
		*i = std::lower_bound(all(tmp), *i) - tmp.begin();
	}
}
template <class InputIter>
void compress(InputIter l, InputIter r) {
	std::vector<typename InputIter::value_type> tmp(l, r);
	std::sort(all(tmp));
	tmp.erase(std::unique(all(tmp)), tmp.end());
	for (auto i = l; i < r; i++) {
		*i = std::lower_bound(all(tmp), *i) - tmp.begin();
	}
}
template <class InputIter,
		  std::enable_if_t<std::is_same<typename InputIter::value_type, std::pair<IP, int>>::value,
						   std::nullptr_t> = nullptr>
void mo_sort(InputIter l, InputIter r, int N) {
	const int M = std::max(1.0, std::sqrt(lint(N) * N / std::distance(l, r)));
	std::sort(l, r, [M](const auto& lhs, const auto& rhs) {
		if (lhs.first.first / M < rhs.first.first / M) return true;
		if (lhs.first.first / M == rhs.first.first / M) return lhs.first.second < rhs.first.second;
		return false;
	});
	int before = -1, cnt = 0;
	bool f = false;
	for (InputIter i = l; i != r; i++) {
		if (before != i->first.first / M) {
			if (f) std::reverse(i - cnt, i);
			f ^= true, before = i->first.first / M, cnt = 1;
		} else
			cnt++;
	}
	if (f) std::reverse(r - cnt, r);
}
template <class T>
std::vector<T> xor_bases(const std::vector<T>& vec) {
	std::vector<T> res;
	for (T i : vec) {
		for (T j : res) {
			chmin(i, i ^ j);
		}
		if (i) res.emplace_back(i);
	}
	return res;
}
#line 3 "math/Matrix.hpp"

template <class T, std::enable_if_t<
#if __cplusplus >= 201703L
					   std::is_same_v<decltype(T() / T()), T>
#else
					   std::is_same<decltype(T() / T()), T>::value
#endif
					   ,
					   std::nullptr_t> = nullptr>
class Matrix {
  protected:
	uint N, M;
	std::vector<std::vector<T>> elems;

  public:
	Matrix() = default;
	Matrix(uint N_, uint M_) : N(N_), M(M_), elems(N, std::vector<T>(M)) {}
	std::vector<T>& operator[](uint idx) { return elems[idx]; }
	const std::vector<T>& operator[](uint idx) const { return elems[idx]; }
	decltype(elems)& data() { return elems; }
	const decltype(elems)& data() const { return elems; }

	void resize(int N_, int M_) {
		elems.resize(N_);
		rep(i, N_) elems[i].resize(M_);
	}

	Matrix operator*(Matrix rhs) const {
		Matrix<T> res(N, rhs.M);
		rep(i, N) rep(j, M) rep(k, rhs.M) res[i][k] +=
			elems[i][j] * rhs.elems[j][k];
		return res;
	}
};

template <class T>
class SquareMatrix : public Matrix<T> {
	using Matrix<T>::N;
	using Matrix<T>::Matrix;
	using Matrix<T>::elems;

  public:
	SquareMatrix(uint N_) : Matrix<T>(N_, N_) {}
	SquareMatrix<T>& operator=(const Matrix<T>& rhs) {
		elems = rhs.data();
		return *this;
	}
	SquareMatrix<T>& operator=(Matrix<T>&& rhs) {
		elems = std::move(rhs.data());
		return *this;
	}
	SquareMatrix<T> operator*=(const SquareMatrix<T>& rhs) {
		*this = *this * rhs;
		return *this;
	}
	SquareMatrix<T> pow(lint p) const {
		SquareMatrix<T> res{N}, memo = *this;
		rep(i, N) res[i][i] = 1;
		while (p) {
			if (p & 1) res *= memo;
			p >>= 1;
			memo *= memo;
		}
		return res;
	}

	constexpr T determinant() const {
		SquareMatrix<T> tmp = *this;
		T res(1);
		rep(i, N) {
			if (tmp[i][i] == 0) {
				for (int j = i + 1; j < N; j++) {
					if (tmp[j][i]) {
						std::swap(tmp[i], tmp[j]);
						res = -res;
						break;
					}
				}
			}
			res *= tmp[i][i];
			for (int j = i + 1; j < N; j++) {
				T inv = T(1) / tmp[i][i];
				for (int k = i + 1; k < N; k++) {
					tmp[j][k] -= tmp[j][i] * inv * tmp[i][k];
				}
			}
		}
		return res;
	}
};

template <class T, uint N, uint M>
class FixedMatrix {
  protected:
	std::array<std::array<T, M>, N> elems;

  public:
	constexpr FixedMatrix() { rep(i, N) elems[i].fill(0); }
	constexpr FixedMatrix(std::initializer_list<T> init) {
		auto ite = init.begin();
		rep(i, N) rep(j, M) elems[i][j] = *ite++;
	}
	constexpr FixedMatrix(const FixedMatrix<T, N, M>& rhs) {
		elems = rhs.elems;
	}
	constexpr FixedMatrix(FixedMatrix<T, N, M>&& rhs) {
		elems = std::move(rhs.elems);
	}
	constexpr std::array<T, N>& operator[](uint idx) { return elems[idx]; }
	constexpr const std::array<T, N>& operator[](uint idx) const {
		return elems[idx];
	}
	constexpr decltype(elems)& data() { return elems; }
	constexpr const decltype(elems)& data() const { return elems; }

	constexpr FixedMatrix<T, N, M> operator=(const FixedMatrix<T, N, M>& rhs) {
		elems = rhs.elems;
		return *this;
	}
	constexpr FixedMatrix<T, N, M> operator=(FixedMatrix<T, N, M>&& rhs) {
		elems = std::move(rhs.elems);
		return *this;
	}

	constexpr FixedMatrix<T, N, M> operator+=(const FixedMatrix<T, N, M>& rhs) {
		rep(i, N) rep(j, M) elems[i][j] += rhs.elems[i][j];
		return *this;
	}

	constexpr FixedMatrix<T, N, M> operator+(
		const FixedMatrix<T, N, M>& rhs) const {
		FixedMatrix<T, N, M> res = *this;
		return res += rhs;
	}

	template <uint L>
	constexpr FixedMatrix<T, N, L> operator*(
		const FixedMatrix<T, M, L>& rhs) const {
		FixedMatrix<T, N, L> res;
		rep(i, N) rep(j, M) rep(k, L) res[i][k] +=
			elems[i][j] * rhs.elems[j][k];
		return res;
	}
};

template <class T, uint N>
class FixedSquareMatrix : public FixedMatrix<T, N, N> {
	using FixedMatrix<T, N, N>::FixedMatrix;
	using FixedMatrix<T, N, N>::elems;

  public:
	using FixedMatrix<T, N, N>::operator*;
	constexpr FixedSquareMatrix(const FixedMatrix<T, N, N>& obj)
		: FixedMatrix<T, N, N>(obj) {}
	constexpr FixedSquareMatrix(FixedMatrix<T, N, N>&& obj)
		: FixedMatrix<T, N, N>(obj) {}

	constexpr FixedSquareMatrix<T, N>& operator*=(
		const FixedSquareMatrix<T, N>& rhs) {
		*this = *this * rhs;
		return *this;
	}

	constexpr FixedSquareMatrix<T, N> pow(lint p) const {
		FixedSquareMatrix<T, N> res, memo = *this;
		rep(i, N) res[i][i] = 1;
		while (p) {
			if (p & 1) res *= memo;
			p >>= 1;
			memo *= memo;
		}
		return res;
	}

	constexpr T determinant() const {
		FixedSquareMatrix<T, N> tmp = *this;
		T res(1);
		rep(i, N) {
			if (tmp[i][i] == 0) {
				for (int j = i + 1; j < N; j++) {
					if (tmp[j][i]) {
						std::swap(tmp[i], tmp[j]);
						res = -res;
						break;
					}
				}
			}
			res *= tmp[i][i];
			for (int j = i + 1; j < N; j++) {
				T inv = T(1) / tmp[i][i];
				for (int k = i + 1; k < N; k++) {
					tmp[j][k] -= tmp[j][i] * inv * tmp[i][k];
				}
			}
		}
		return res;
	}

	constexpr static FixedSquareMatrix<T, N> ident() {
		FixedSquareMatrix<T, N> res;
		rep(i, N) res[i][i] = 1;
		return res;
	}
};

/**
 * @title Matrix
 */

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