Tifa's CP Library

:heavy_check_mark: ge_basic_mat (src/code/lalg/ge_basic_mat.hpp)

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#ifndef TIFALIBS_LALG_GE_BASIC_MAT
#define TIFALIBS_LALG_GE_BASIC_MAT

#include "ge_swapr_mat_.hpp"

namespace tifa_libs::math {

template <class Mat, class Is0>
requires requires(Is0 is0, TPN Mat::value_type t) {
  { is0(t) } -> std::same_as<bool>;
}
CEXP i32 ge_basic(Mat& mat, Is0&& is0, bool clear_u = true) {
  using T = TPN Mat::value_type;
  u32 r_ = mat.row(), c_ = mat.col(), rk_max = min(r_, c_);
  u32 rk = 0;
  bool neg = false;
  for (u32 i = 0, now_row = 0, j_ = i; i < mat.row(); ++i) {
    neg ^= ge_impl_::swapr__(mat, now_row, rk, mat.row());
    j_ = max(j_, i);
    while (j_ < c_ && is0(mat(rk, j_))) ++j_;
    if (j_ == c_) break;
    for (u32 j = clear_u ? 0 : rk + 1; j < mat.row(); ++j) {
      if (j == rk || is0(mat(j, j_))) continue;
      T _ = mat(j, j_) / mat(rk, j_);
      mat(j, j_) = 0;
      for (u32 k = j_ + 1; k < c_; ++k) mat(j, k) -= mat(rk, k) * _;
    }
    if (++rk >= rk_max) break;
  }
  return neg ? -((i32)rk) : (i32)rk;
}

}  // namespace tifa_libs::math

#endif
#line 1 "src/code/lalg/ge_basic_mat.hpp"



#line 1 "src/code/lalg/ge_swapr_mat_.hpp"



#line 1 "src/code/util/util.hpp"



#include <bits/stdc++.h>

#define CEXP constexpr
#define TPN typename
#define CR const&

#define cT_(...) std::conditional_t<sizeof(__VA_ARGS__) <= sizeof(size_t), __VA_ARGS__, __VA_ARGS__ CR>
#define fle_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i <= i##e; ++i)
#define flt_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i < i##e; ++i)

#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif

using i8 = int8_t;
using i16 = int16_t;
using i32 = int32_t;
using i64 = int64_t;
using i128 = __int128_t;
using isz = ptrdiff_t;

using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using u128 = __uint128_t;
using usz = size_t;

using f32 = float;
using f64 = double;
using f128 = long double;

template <class T>
using ptt = std::pair<T, T>;
template <class T>
using pt3 = std::tuple<T, T, T>;
template <class T>
using pt4 = std::tuple<T, T, T, T>;

template <class T, usz N>
using arr = std::array<T, N>;
template <class T>
using vec = std::vector<T>;
template <class T>
using vvec = vec<vec<T>>;
template <class T>
using v3ec = vec<vvec<T>>;
template <class U, class T>
using vecp = vec<std::pair<U, T>>;
template <class U, class T>
using vvecp = vvec<std::pair<U, T>>;
template <class T>
using vecpt = vec<ptt<T>>;
template <class T>
using vvecpt = vvec<ptt<T>>;

template <class T, class C = std::less<T>>
using pq = std::priority_queue<T, vec<T>, C>;
template <class T>
using pqg = std::priority_queue<T, vec<T>, std::greater<T>>;

using strn = std::string;
using strnv = std::string_view;

using vecu = vec<u32>;
using vvecu = vvec<u32>;
using v3ecu = v3ec<u32>;
using vecu64 = vec<u64>;
using vecb = vec<bool>;
using vvecb = vvec<bool>;

using namespace std::literals;

CEXP i8 operator""_i8(unsigned long long x) { return (i8)x; }
CEXP i16 operator""_i16(unsigned long long x) { return (i16)x; }
CEXP i32 operator""_i32(unsigned long long x) { return (i32)x; }
CEXP i64 operator""_i64(unsigned long long x) { return (i64)x; }
CEXP isz operator""_iz(unsigned long long x) { return (isz)x; }

CEXP u8 operator""_u8(unsigned long long x) { return (u8)x; }
CEXP u16 operator""_u16(unsigned long long x) { return (u16)x; }
CEXP u32 operator""_u32(unsigned long long x) { return (u32)x; }
CEXP u64 operator""_u64(unsigned long long x) { return (u64)x; }
CEXP usz operator""_uz(unsigned long long x) { return (usz)x; }

inline const auto fn_0 = [](auto&&...) {};
inline const auto fn_is0 = [](auto x) { return x == 0; };

// std::sqrt(std::numeric_limits<FP>::epsilon())
template <std::floating_point FP>
CEXP inline FP eps_v = FP(1e-8L);
using std::numbers::pi_v;

namespace tifa_libs {
using std::min, std::max, std::swap;
template <class T>
constexpr T abs(T x) { return x < 0 ? -x : x; }
}  // namespace tifa_libs


#line 5 "src/code/lalg/ge_swapr_mat_.hpp"

namespace tifa_libs::math::ge_impl_ {

template <class Mat>
CEXP bool swapr__(Mat &mat, u32 &r_, u32 r_pre_, u32 r_end) {
  r_ = r_pre_;
  for (u32 j = r_ + 1; j < r_end; ++j)
    if (mat.data()[r_] < mat.data()[j]) r_ = j;
  if (r_ != r_pre_) {
    mat.swap_row(r_, r_pre_);
    return true;
  }
  return false;
}

}  // namespace tifa_libs::math::ge_impl_


#line 5 "src/code/lalg/ge_basic_mat.hpp"

namespace tifa_libs::math {

template <class Mat, class Is0>
requires requires(Is0 is0, TPN Mat::value_type t) {
  { is0(t) } -> std::same_as<bool>;
}
CEXP i32 ge_basic(Mat& mat, Is0&& is0, bool clear_u = true) {
  using T = TPN Mat::value_type;
  u32 r_ = mat.row(), c_ = mat.col(), rk_max = min(r_, c_);
  u32 rk = 0;
  bool neg = false;
  for (u32 i = 0, now_row = 0, j_ = i; i < mat.row(); ++i) {
    neg ^= ge_impl_::swapr__(mat, now_row, rk, mat.row());
    j_ = max(j_, i);
    while (j_ < c_ && is0(mat(rk, j_))) ++j_;
    if (j_ == c_) break;
    for (u32 j = clear_u ? 0 : rk + 1; j < mat.row(); ++j) {
      if (j == rk || is0(mat(j, j_))) continue;
      T _ = mat(j, j_) / mat(rk, j_);
      mat(j, j_) = 0;
      for (u32 k = j_ + 1; k < c_; ++k) mat(j, k) -= mat(rk, k) * _;
    }
    if (++rk >= rk_max) break;
  }
  return neg ? -((i32)rk) : (i32)rk;
}

}  // namespace tifa_libs::math


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