行列ライブラリ
(matrix/matrix.hpp)

• View this file on GitHub
• Last update: 2023-12-22 19:57:12+09:00
• Include: #include "matrix/matrix.hpp"

Depends on

• matrix/gauss-elimination.hpp
• matrix/inverse-matrix.hpp

Required by

• P-recursiveの高速計算 (fps/find-p-recursive.hpp)
• 行列木定理(ラプラシアン行列) (matrix/matrix-tree.hpp)
• 多項式行列の行列式 (matrix/polynomial-matrix-determinant.hpp)
• 多項式行列のprefix product (matrix/polynomial-matrix-prefix-prod.hpp)

Verified with

• verify/verify-unit-test/bigint-gcd.test.cpp
• verify/verify-unit-test/debug.test.cpp
• verify/verify-unit-test/gauss-elimination.test.cpp
• verify/verify-unit-test/multipoint-binomial-sum.test.cpp
• verify/verify-unit-test/p-recursive.test.cpp
• verify/verify-unit-test/polynomial-matrix-prod.test.cpp
• verify/verify-yosupo-fps/yosupo-factorial-p-recursive.test.cpp
• verify/verify-yosupo-math/yosupo-determinant-matrixlib.test.cpp
• verify/verify-yuki/yuki-1303.test.cpp
• verify/verify-yuki/yuki-1533.test.cpp

Code

#pragma once

#include "inverse-matrix.hpp"

template <class T>
struct Matrix {
  vector<vector<T> > A;

  Matrix() = default;
  Matrix(int n, int m) : A(n, vector<T>(m, T())) {}
  Matrix(int n) : A(n, vector<T>(n, T())){};

  int H() const { return A.size(); }

  int W() const { return A[0].size(); }

  int size() const { return A.size(); }

  inline const vector<T> &operator[](int k) const { return A[k]; }

  inline vector<T> &operator[](int k) { return A[k]; }

  static Matrix I(int n) {
    Matrix mat(n);
    for (int i = 0; i < n; i++) mat[i][i] = 1;
    return (mat);
  }

  Matrix &operator+=(const Matrix &B) {
    int n = H(), m = W();
    assert(n == B.H() && m == B.W());
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++) (*this)[i][j] += B[i][j];
    return (*this);
  }

  Matrix &operator-=(const Matrix &B) {
    int n = H(), m = W();
    assert(n == B.H() && m == B.W());
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++) (*this)[i][j] -= B[i][j];
    return (*this);
  }

  Matrix &operator*=(const Matrix &B) {
    int n = H(), m = B.W(), p = W();
    assert(p == B.H());
    vector<vector<T> > C(n, vector<T>(m, T{}));
    for (int i = 0; i < n; i++)
      for (int k = 0; k < p; k++)
        for (int j = 0; j < m; j++) C[i][j] += (*this)[i][k] * B[k][j];
    A.swap(C);
    return (*this);
  }

  Matrix &operator^=(long long k) {
    Matrix B = Matrix::I(H());
    while (k > 0) {
      if (k & 1) B *= *this;
      *this *= *this;
      k >>= 1LL;
    }
    A.swap(B.A);
    return (*this);
  }

  Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); }

  Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); }

  Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); }

  Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); }

  bool operator==(const Matrix &B) const {
    assert(H() == B.H() && W() == B.W());
    for (int i = 0; i < H(); i++)
      for (int j = 0; j < W(); j++)
        if (A[i][j] != B[i][j]) return false;
    return true;
  }

  bool operator!=(const Matrix &B) const {
    assert(H() == B.H() && W() == B.W());
    for (int i = 0; i < H(); i++)
      for (int j = 0; j < W(); j++)
        if (A[i][j] != B[i][j]) return true;
    return false;
  }

  Matrix inverse() const {
    assert(H() == W());
    Matrix B(H());
    B.A = inverse_matrix(A);
    return B;
  }

  friend ostream &operator<<(ostream &os, const Matrix &p) {
    int n = p.H(), m = p.W();
    for (int i = 0; i < n; i++) {
      os << (i ? "   " : "") << "[";
      for (int j = 0; j < m; j++) {
        os << p[i][j] << (j + 1 == m ? "]\n" : ",");
      }
    }
    return (os);
  }

  T determinant() const {
    Matrix B(*this);
    assert(H() == W());
    T ret = 1;
    for (int i = 0; i < H(); i++) {
      int idx = -1;
      for (int j = i; j < W(); j++) {
        if (B[j][i] != 0) {
          idx = j;
          break;
        }
      }
      if (idx == -1) return 0;
      if (i != idx) {
        ret *= T(-1);
        swap(B[i], B[idx]);
      }
      ret *= B[i][i];
      T inv = T(1) / B[i][i];
      for (int j = 0; j < W(); j++) {
        B[i][j] *= inv;
      }
      for (int j = i + 1; j < H(); j++) {
        T a = B[j][i];
        if (a == 0) continue;
        for (int k = i; k < W(); k++) {
          B[j][k] -= B[i][k] * a;
        }
      }
    }
    return ret;
  }
};

/**
 * @brief 行列ライブラリ
 */

#line 2 "matrix/matrix.hpp"

#line 2 "matrix/inverse-matrix.hpp"

#line 2 "matrix/gauss-elimination.hpp"

#include <utility>
#include <vector>
using namespace std;

// {rank, det(非正方行列の場合は未定義)} を返す
// 型が double や Rational でも動くはず？(未検証)
//
// pivot 候補 : [0, pivot_end)
template <typename T>
std::pair<int, T> GaussElimination(vector<vector<T>> &a, int pivot_end = -1,
                                   bool diagonalize = false) {
  int H = a.size(), W = a[0].size(), rank = 0;
  if (pivot_end == -1) pivot_end = W;
  T det = 1;
  for (int j = 0; j < pivot_end; j++) {
    int idx = -1;
    for (int i = rank; i < H; i++) {
      if (a[i][j] != T(0)) {
        idx = i;
        break;
      }
    }
    if (idx == -1) {
      det = 0;
      continue;
    }
    if (rank != idx) det = -det, swap(a[rank], a[idx]);
    det *= a[rank][j];
    if (diagonalize && a[rank][j] != T(1)) {
      T coeff = T(1) / a[rank][j];
      for (int k = j; k < W; k++) a[rank][k] *= coeff;
    }
    int is = diagonalize ? 0 : rank + 1;
    for (int i = is; i < H; i++) {
      if (i == rank) continue;
      if (a[i][j] != T(0)) {
        T coeff = a[i][j] / a[rank][j];
        for (int k = j; k < W; k++) a[i][k] -= a[rank][k] * coeff;
      }
    }
    rank++;
  }
  return make_pair(rank, det);
}
#line 4 "matrix/inverse-matrix.hpp"

template <typename mint>
vector<vector<mint>> inverse_matrix(const vector<vector<mint>>& a) {
  int N = a.size();
  assert(N > 0);
  assert(N == (int)a[0].size());

  vector<vector<mint>> m(N, vector<mint>(2 * N));
  for (int i = 0; i < N; i++) {
    copy(begin(a[i]), end(a[i]), begin(m[i]));
    m[i][N + i] = 1;
  }

  auto [rank, det] = GaussElimination(m, N, true);
  if (rank != N) return {};

  vector<vector<mint>> b(N);
  for (int i = 0; i < N; i++) {
    copy(begin(m[i]) + N, end(m[i]), back_inserter(b[i]));
  }
  return b;
}
#line 4 "matrix/matrix.hpp"

template <class T>
struct Matrix {
  vector<vector<T> > A;

  Matrix() = default;
  Matrix(int n, int m) : A(n, vector<T>(m, T())) {}
  Matrix(int n) : A(n, vector<T>(n, T())){};

  int H() const { return A.size(); }

  int W() const { return A[0].size(); }

  int size() const { return A.size(); }

  inline const vector<T> &operator[](int k) const { return A[k]; }

  inline vector<T> &operator[](int k) { return A[k]; }

  static Matrix I(int n) {
    Matrix mat(n);
    for (int i = 0; i < n; i++) mat[i][i] = 1;
    return (mat);
  }

  Matrix &operator+=(const Matrix &B) {
    int n = H(), m = W();
    assert(n == B.H() && m == B.W());
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++) (*this)[i][j] += B[i][j];
    return (*this);
  }

  Matrix &operator-=(const Matrix &B) {
    int n = H(), m = W();
    assert(n == B.H() && m == B.W());
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++) (*this)[i][j] -= B[i][j];
    return (*this);
  }

  Matrix &operator*=(const Matrix &B) {
    int n = H(), m = B.W(), p = W();
    assert(p == B.H());
    vector<vector<T> > C(n, vector<T>(m, T{}));
    for (int i = 0; i < n; i++)
      for (int k = 0; k < p; k++)
        for (int j = 0; j < m; j++) C[i][j] += (*this)[i][k] * B[k][j];
    A.swap(C);
    return (*this);
  }

  Matrix &operator^=(long long k) {
    Matrix B = Matrix::I(H());
    while (k > 0) {
      if (k & 1) B *= *this;
      *this *= *this;
      k >>= 1LL;
    }
    A.swap(B.A);
    return (*this);
  }

  Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); }

  Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); }

  Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); }

  Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); }

  bool operator==(const Matrix &B) const {
    assert(H() == B.H() && W() == B.W());
    for (int i = 0; i < H(); i++)
      for (int j = 0; j < W(); j++)
        if (A[i][j] != B[i][j]) return false;
    return true;
  }

  bool operator!=(const Matrix &B) const {
    assert(H() == B.H() && W() == B.W());
    for (int i = 0; i < H(); i++)
      for (int j = 0; j < W(); j++)
        if (A[i][j] != B[i][j]) return true;
    return false;
  }

  Matrix inverse() const {
    assert(H() == W());
    Matrix B(H());
    B.A = inverse_matrix(A);
    return B;
  }

  friend ostream &operator<<(ostream &os, const Matrix &p) {
    int n = p.H(), m = p.W();
    for (int i = 0; i < n; i++) {
      os << (i ? "   " : "") << "[";
      for (int j = 0; j < m; j++) {
        os << p[i][j] << (j + 1 == m ? "]\n" : ",");
      }
    }
    return (os);
  }

  T determinant() const {
    Matrix B(*this);
    assert(H() == W());
    T ret = 1;
    for (int i = 0; i < H(); i++) {
      int idx = -1;
      for (int j = i; j < W(); j++) {
        if (B[j][i] != 0) {
          idx = j;
          break;
        }
      }
      if (idx == -1) return 0;
      if (i != idx) {
        ret *= T(-1);
        swap(B[i], B[idx]);
      }
      ret *= B[i][i];
      T inv = T(1) / B[i][i];
      for (int j = 0; j < W(); j++) {
        B[i][j] *= inv;
      }
      for (int j = i + 1; j < H(); j++) {
        T a = B[j][i];
        if (a == 0) continue;
        for (int k = i; k < W(); k++) {
          B[j][k] -= B[i][k] * a;
        }
      }
    }
    return ret;
  }
};

/**
 * @brief 行列ライブラリ
 */

Back to top page