Matrix (行列)
(math/algebra/matrix.hpp)

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• Last update: 2024-08-24 11:50:18+09:00
• Include: #include "math/algebra/matrix.hpp"

Depends on

• template/alias.hpp
• template/debug.hpp
• template/func.hpp
• template/macro.hpp
• template/template.hpp
• template/util.hpp

Verified with

• test/yosupo/matrix-det.test.cpp

Code

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

template <class T>
struct Matrix {
    vector<vector<T>> val;
    size_t height, width;

    Matrix(int n = 1, int m = 1, T v = 0) : val(n, vector<T>(m, v)), height(n), width(m) {}
    void init(int n, int m, T v = 0) {
        val.assign(n, vector<T>(m, v));
        height = n;
        width = m;
    }
    void resize(int n, int m) {
        val.resize(n);
        for (int i = 0; i < n; ++i) val[i].resize(m);
        height = n;
        width = m;
    }
    vector<T> &operator[](int i) { return val[i]; }
    const vector<T> &operator[](int i) const { return val[i]; }
    Matrix &operator=(const Matrix &A) {
        val = A.val;
        return *this;
    }
    Matrix &operator+=(const Matrix &r) {
        for (int i = 0; i < height; ++i)
            for (int j = 0; j < width; ++j)
                (*this)[i][j] += r[i][j];
        return (*this);
    }
    Matrix &operator-=(const Matrix &r) {
        for (int i = 0; i < height; ++i)
            for (int j = 0; j < width; ++j)
                (*this)[i][j] -= r[i][j];
        return (*this);
    }
    Matrix &operator*=(const Matrix &r) {
        vector<vector<T>> res(height, vector<T>(r.width));
        for (int i = 0; i < height; ++i)
            for (int j = 0; j < r.width; ++j)
                for (int k = 0; k < width; ++k)
                    res[i][j] += (*this)[i][k] * r[k][j];
        val.swap(res);
        return (*this);
    }
    Matrix operator+(const Matrix &r) { return Matrix(*this) += r; }
    Matrix operator-(const Matrix &r) { return Matrix(*this) -= r; }
    Matrix operator*(const Matrix &r) { return Matrix(*this) *= r; }
    friend Matrix<T> pow(const Matrix<T> &A, long long n) {
        Matrix<T> R(A.height, A.height);
        Matrix<T> B = A;
        for (int i = 0; i < A.height; ++i) R[i][i] = 1;
        while (n > 0) {
            if (n & 1) R = R * B;
            B = B * B;
            n >>= 1;
        }
        return R;
    }
    friend T det(Matrix<T> A) {
        T ret = 1;
        for (int i = 0; i < A.width; i++) {
            int idx = -1;
            for (int j = i; j < A.width; j++) {
                if (A[j][i] != 0) {
                    idx = j;
                    break;
                }
            }
            if (idx == -1) return T(0);
            if (i != idx) {
                ret *= T(-1);
                swap(A[i], A[idx]);
            }
            ret *= A[i][i];
            T tmp = A[i][i];
            for (int j = 0; j < A.width; j++) A[i][j] /= tmp;
            for (int j = i + 1; j < A.width; j++) {
                T now = A[j][i];
                for (int k = 0; k < A.width; k++) A[j][k] -= A[i][k] * now;
            }
        }
        return ret;
    }
};

#line 2 "template/template.hpp"
#include <bits/stdc++.h>
#line 3 "template/macro.hpp"

#define overload3(_1, _2, _3, name, ...) name
#define all1(v) std::begin(v), std::end(v)
#define all2(v, a) std::begin(v), std::begin(v) + a
#define all3(v, a, b) std::begin(v) + a, std::begin(v) + b
#define all(...) overload3(__VA_ARGS__, all3, all2, all1)(__VA_ARGS__)
#define rall1(v) std::rbegin(v), std::rend(v)
#define rall2(v, a) std::rbegin(v), std::rbegin(v) + a
#define rall3(v, a, b) std::rbegin(v) + a, std::rbegin(v) + b
#define rall(...) overload3(__VA_ARGS__, rall3, rall2, rall1)(__VA_ARGS__)
#define elif else if
#define updiv(N, X) (((N) + (X) - 1) / (X))
#define sigma(a, b) (((a) + (b)) * ((b) - (a) + 1) / 2)
#define INT(...)     \
    int __VA_ARGS__; \
    scan(__VA_ARGS__)
#define LL(...)     \
    ll __VA_ARGS__; \
    scan(__VA_ARGS__)
#define STR(...)        \
    string __VA_ARGS__; \
    scan(__VA_ARGS__)
#define CHR(...)      \
    char __VA_ARGS__; \
    scan(__VA_ARGS__)
#define DOU(...)        \
    double __VA_ARGS__; \
    scan(__VA_ARGS__)
#define LD(...)     \
    ld __VA_ARGS__; \
    scan(__VA_ARGS__)
#define pb push_back
#define eb emplace_back
#line 3 "template/alias.hpp"

using ll = long long;
using ld = long double;
using pii = std::pair<int, int>;
using pll = std::pair<ll, ll>;
constexpr int inf = 1 << 30;
constexpr ll INF = 1LL << 60;
constexpr int dx[8] = {1, 0, -1, 0, 1, -1, 1, -1};
constexpr int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1};
constexpr int mod = 998244353;
constexpr int MOD = 1e9 + 7;
#line 3 "template/func.hpp"

template <typename T>
inline bool chmax(T& a, T b) { return ((a < b) ? (a = b, true) : (false)); }
template <typename T>
inline bool chmin(T& a, T b) { return ((a > b) ? (a = b, true) : (false)); }
template <typename T, typename U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) {
    os << p.first << " " << p.second;
    return os;
}
template <typename T, typename U>
std::istream &operator>>(std::istream &is, std::pair<T, U> &p) {
    is >> p.first >> p.second;
    return is;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &v) {
    for (auto it = std::begin(v); it != std::end(v);) {
        os << *it << ((++it) != std::end(v) ? " " : "");
    }
    return os;
}
template <typename T>
std::istream &operator>>(std::istream &is, std::vector<T> &v) {
    for (T &in : v) {
        is >> in;
    }
    return is;
}
inline void scan() {}
template <class Head, class... Tail>
inline void scan(Head &head, Tail &...tail) {
    std::cin >> head;
    scan(tail...);
}
template <class T>
inline void print(const T &t) { std::cout << t << '\n'; }
template <class Head, class... Tail>
inline void print(const Head &head, const Tail &...tail) {
    std::cout << head << ' ';
    print(tail...);
}
template <class... T>
inline void fin(const T &...a) {
    print(a...);
    exit(0);
}
#line 3 "template/util.hpp"

struct IOSetup {
    IOSetup() {
        std::cin.tie(nullptr);
        std::ios::sync_with_stdio(false);
        std::cout.tie(0);
        std::cout << std::fixed << std::setprecision(12);
        std::cerr << std::fixed << std::setprecision(12);
    }
} IOSetup;
#line 3 "template/debug.hpp"

#ifdef LOCAL
#include <dump.hpp>
#else
#define debug(...)
#endif
#line 8 "template/template.hpp"
using namespace std;
#line 3 "math/algebra/matrix.hpp"

template <class T>
struct Matrix {
    vector<vector<T>> val;
    size_t height, width;

    Matrix(int n = 1, int m = 1, T v = 0) : val(n, vector<T>(m, v)), height(n), width(m) {}
    void init(int n, int m, T v = 0) {
        val.assign(n, vector<T>(m, v));
        height = n;
        width = m;
    }
    void resize(int n, int m) {
        val.resize(n);
        for (int i = 0; i < n; ++i) val[i].resize(m);
        height = n;
        width = m;
    }
    vector<T> &operator[](int i) { return val[i]; }
    const vector<T> &operator[](int i) const { return val[i]; }
    Matrix &operator=(const Matrix &A) {
        val = A.val;
        return *this;
    }
    Matrix &operator+=(const Matrix &r) {
        for (int i = 0; i < height; ++i)
            for (int j = 0; j < width; ++j)
                (*this)[i][j] += r[i][j];
        return (*this);
    }
    Matrix &operator-=(const Matrix &r) {
        for (int i = 0; i < height; ++i)
            for (int j = 0; j < width; ++j)
                (*this)[i][j] -= r[i][j];
        return (*this);
    }
    Matrix &operator*=(const Matrix &r) {
        vector<vector<T>> res(height, vector<T>(r.width));
        for (int i = 0; i < height; ++i)
            for (int j = 0; j < r.width; ++j)
                for (int k = 0; k < width; ++k)
                    res[i][j] += (*this)[i][k] * r[k][j];
        val.swap(res);
        return (*this);
    }
    Matrix operator+(const Matrix &r) { return Matrix(*this) += r; }
    Matrix operator-(const Matrix &r) { return Matrix(*this) -= r; }
    Matrix operator*(const Matrix &r) { return Matrix(*this) *= r; }
    friend Matrix<T> pow(const Matrix<T> &A, long long n) {
        Matrix<T> R(A.height, A.height);
        Matrix<T> B = A;
        for (int i = 0; i < A.height; ++i) R[i][i] = 1;
        while (n > 0) {
            if (n & 1) R = R * B;
            B = B * B;
            n >>= 1;
        }
        return R;
    }
    friend T det(Matrix<T> A) {
        T ret = 1;
        for (int i = 0; i < A.width; i++) {
            int idx = -1;
            for (int j = i; j < A.width; j++) {
                if (A[j][i] != 0) {
                    idx = j;
                    break;
                }
            }
            if (idx == -1) return T(0);
            if (i != idx) {
                ret *= T(-1);
                swap(A[i], A[idx]);
            }
            ret *= A[i][i];
            T tmp = A[i][i];
            for (int j = 0; j < A.width; j++) A[i][j] /= tmp;
            for (int j = i + 1; j < A.width; j++) {
                T now = A[j][i];
                for (int k = 0; k < A.width; k++) A[j][k] -= A[i][k] * now;
            }
        }
        return ret;
    }
};

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