library/numerical/matrix2.hpp

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• Last update: 2022-07-21 16:12:33-04:00
• Include: #include "library/numerical/matrix2.hpp"

Verified with

• verify/kattis/kattis-equationsolver.test.cpp
• verify/yosupo/yosupo-inverse_matrix.test.cpp

Code

#pragma once

namespace MatrixOperations {

template <class T> using Matrix = std::vector<std::vector<T>>;

template <class T> Matrix<T> make_matrix(int r, int c) { return Matrix<T>(r, std::vector<T>(c)); }

template <class T> Matrix<T>& operator+=(Matrix<T>& a, const Matrix<T>& b) {
	for (int i = 0; i < (int)a.size(); i++) {
		for (int j = 0; j < (int)a[0].size(); j++) {
			a[i][j] += b[i][j];
		}
	}
	return a;
}

template <class T> Matrix<T>& operator-=(Matrix<T>& a, const Matrix<T>& b) {
	for (int i = 0; i < (int)a.size(); i++) {
		for (int j = 0; j < (int)a[0].size(); j++) {
			a[i][j] -= b[i][j];
		}
	}
	return a;
}

template <class T> Matrix<T> operator*(const Matrix<T>& a, const Matrix<T>& b) {
	assert(a[0].size() == b.size());
	int x = (int)a.size();
	int y = (int)a[0].size();
	int z = (int)b[0].size();
	Matrix<T> c = make_matrix<T>(x, z);
	for (int i = 0; i < x; i++) {
		for (int j = 0; j < y; j++) {
			for (int k = 0; k < z; k++) {
				c[i][k] += a[i][j] * b[j][k];
			}
		}
	}
	return c;
}

template <class T> Matrix<T> operator+(Matrix<T> a, const Matrix<T>& b) { return a += b; }
template <class T> Matrix<T> operator-(Matrix<T> a, const Matrix<T>& b) { return a -= b; }
template <class T> Matrix<T>& operator*=(Matrix<T>& a, const Matrix<T>& b) { return a = a * b; }

template <class T> Matrix<T> pow(Matrix<T> m, long long p) {
	int n = (int)m.size();
	assert(n == (int)m[0].size() && p >= 0);
	Matrix<T> res = make_matrix<T>(n, n);
	for (int i = 0; i < n; i++) 
		res[i][i] = 1;
	for (; p; p >>= 1, m *= m) {
		if (p & 1) {
			res *= m;
		}
	}
	return res;
}

template <class T> int get_row(Matrix<T>& m, int r, int i, int nxt) {
	for (int j = nxt; j < r; j++) {
		if (m[j][i] != 0) {
			return j;
		}
	}
	return -1;
}

const long double EPS = 1e-12;

template <> int get_row<long double>(Matrix<long double>& m, int r, int i, int nxt) {
	std::pair<long double, int> best = {0, -1};
	for (int j = nxt; j < r; j++) {
		best = std::max(best, {abs(m[j][i]), j});
	}
	return best.first < EPS ? -1 : best.second;
}

// returns a pair of determinant, rank, while doing Gaussian elimination to m

template <class T> std::pair<T, int> gauss(Matrix<T>& m) {
	int r = (int)m.size();
	int c = (int)m[0].size();
	int rank = 0, nxt = 0;
	T prod = 1;
	for (int i = 0; i < r; i++) {
		int row = get_row(m, r, i, nxt);
		if (row == -1) {
			prod = 0;
			continue;
		}
		if (row != nxt) {
			prod *= -1;
			m[row].swap(m[nxt]);
		}
		prod *= m[nxt][i];
		rank++;
		T x = 1 / m[nxt][i];
		for (int k = i; k < c; k++) 
			m[nxt][k] *= x;
		for (int j = 0; j < r; j++) {
			if (j != nxt) {
				T v = m[j][i];
				if (v == 0) continue;
				for (int k = i; k < c; k++) {
					m[j][k] -= v * m[nxt][k];
				}
			}
		}
		nxt++;
	}
	return {prod, rank};
}

template <class T> Matrix<T> inv(Matrix<T> m) {
	int r = (int)m.size();
	assert(r == (int)m[0].size());
	Matrix<T> x = make_matrix<T>(r, 2 * r);
	for (int i = 0; i < r; i++) {
		x[i][i + r] = 1;
		for (int j = 0; j < r; j++) {
			x[i][j] = m[i][j];
		}
	}
	if (gauss(x).second != r) return Matrix<T>();
	Matrix<T> res = make_matrix<T>(r, r);
	for (int i = 0; i < r; i++) {
		for (int j = 0; j < r; j++) {
			res[i][j] = x[i][j + r];
		}
	}
	return res;
}

} // namespace MatrixOperations

namespace MatrixOperations {

template <class T> using Matrix = std::vector<std::vector<T>>;

template <class T> Matrix<T> make_matrix(int r, int c) { return Matrix<T>(r, std::vector<T>(c)); }

template <class T> Matrix<T>& operator+=(Matrix<T>& a, const Matrix<T>& b) {
	for (int i = 0; i < (int)a.size(); i++) {
		for (int j = 0; j < (int)a[0].size(); j++) {
			a[i][j] += b[i][j];
		}
	}
	return a;
}

template <class T> Matrix<T>& operator-=(Matrix<T>& a, const Matrix<T>& b) {
	for (int i = 0; i < (int)a.size(); i++) {
		for (int j = 0; j < (int)a[0].size(); j++) {
			a[i][j] -= b[i][j];
		}
	}
	return a;
}

template <class T> Matrix<T> operator*(const Matrix<T>& a, const Matrix<T>& b) {
	assert(a[0].size() == b.size());
	int x = (int)a.size();
	int y = (int)a[0].size();
	int z = (int)b[0].size();
	Matrix<T> c = make_matrix<T>(x, z);
	for (int i = 0; i < x; i++) {
		for (int j = 0; j < y; j++) {
			for (int k = 0; k < z; k++) {
				c[i][k] += a[i][j] * b[j][k];
			}
		}
	}
	return c;
}

template <class T> Matrix<T> operator+(Matrix<T> a, const Matrix<T>& b) { return a += b; }
template <class T> Matrix<T> operator-(Matrix<T> a, const Matrix<T>& b) { return a -= b; }
template <class T> Matrix<T>& operator*=(Matrix<T>& a, const Matrix<T>& b) { return a = a * b; }

template <class T> Matrix<T> pow(Matrix<T> m, long long p) {
	int n = (int)m.size();
	assert(n == (int)m[0].size() && p >= 0);
	Matrix<T> res = make_matrix<T>(n, n);
	for (int i = 0; i < n; i++) 
		res[i][i] = 1;
	for (; p; p >>= 1, m *= m) {
		if (p & 1) {
			res *= m;
		}
	}
	return res;
}

template <class T> int get_row(Matrix<T>& m, int r, int i, int nxt) {
	for (int j = nxt; j < r; j++) {
		if (m[j][i] != 0) {
			return j;
		}
	}
	return -1;
}

const long double EPS = 1e-12;

template <> int get_row<long double>(Matrix<long double>& m, int r, int i, int nxt) {
	std::pair<long double, int> best = {0, -1};
	for (int j = nxt; j < r; j++) {
		best = std::max(best, {abs(m[j][i]), j});
	}
	return best.first < EPS ? -1 : best.second;
}

// returns a pair of determinant, rank, while doing Gaussian elimination to m

template <class T> std::pair<T, int> gauss(Matrix<T>& m) {
	int r = (int)m.size();
	int c = (int)m[0].size();
	int rank = 0, nxt = 0;
	T prod = 1;
	for (int i = 0; i < r; i++) {
		int row = get_row(m, r, i, nxt);
		if (row == -1) {
			prod = 0;
			continue;
		}
		if (row != nxt) {
			prod *= -1;
			m[row].swap(m[nxt]);
		}
		prod *= m[nxt][i];
		rank++;
		T x = 1 / m[nxt][i];
		for (int k = i; k < c; k++) 
			m[nxt][k] *= x;
		for (int j = 0; j < r; j++) {
			if (j != nxt) {
				T v = m[j][i];
				if (v == 0) continue;
				for (int k = i; k < c; k++) {
					m[j][k] -= v * m[nxt][k];
				}
			}
		}
		nxt++;
	}
	return {prod, rank};
}

template <class T> Matrix<T> inv(Matrix<T> m) {
	int r = (int)m.size();
	assert(r == (int)m[0].size());
	Matrix<T> x = make_matrix<T>(r, 2 * r);
	for (int i = 0; i < r; i++) {
		x[i][i + r] = 1;
		for (int j = 0; j < r; j++) {
			x[i][j] = m[i][j];
		}
	}
	if (gauss(x).second != r) return Matrix<T>();
	Matrix<T> res = make_matrix<T>(r, r);
	for (int i = 0; i < r; i++) {
		for (int j = 0; j < r; j++) {
			res[i][j] = x[i][j + r];
		}
	}
	return res;
}

} // namespace MatrixOperations

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