Tifa's CP Library

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

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#ifndef TIFALIBS_LALG_SHERMAN_MORRISON
#define TIFALIBS_LALG_SHERMAN_MORRISON

#include "../util/util.hpp"

namespace tifa_libs::math {

template <class Mat, class T = typename Mat::value_type>
requires std::same_as<T, typename Mat::value_type>
constexpr void sherman_morrison(Mat &inv_A, vec<T> const &u, vec<T> const &v) {
  u32 n = inv_A.row();
  assert(n == inv_A.col());
  vec<T> x(n), y(n);
  for (u32 i = 0; i < n; ++i)
    for (u32 j = 0; j < n; ++j)
      x[i] += inv_A(i, j) * u[j], y[j] += v[i] * inv_A(i, j);
  T sum = 1;
  for (u32 i = 0; i < n; ++i)
    for (u32 j = 0; j < n; ++j) sum += v[i] * inv_A(i, j) * u[j];
  for (u32 i = 0; i < n; ++i)
    for (u32 j = 0; j < n; ++j) inv_A(i, j) -= x[i] * y[j] / sum;
}

}  // namespace tifa_libs::math

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



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



#include <bits/stdc++.h>

template <class T>
constexpr T abs(T x) { return x < 0 ? -x : x; }

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>;

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

using namespace std::literals;

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

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

inline const auto fn_0 = [](auto&&...) {};


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

namespace tifa_libs::math {

template <class Mat, class T = typename Mat::value_type>
requires std::same_as<T, typename Mat::value_type>
constexpr void sherman_morrison(Mat &inv_A, vec<T> const &u, vec<T> const &v) {
  u32 n = inv_A.row();
  assert(n == inv_A.col());
  vec<T> x(n), y(n);
  for (u32 i = 0; i < n; ++i)
    for (u32 j = 0; j < n; ++j)
      x[i] += inv_A(i, j) * u[j], y[j] += v[i] * inv_A(i, j);
  T sum = 1;
  for (u32 i = 0; i < n; ++i)
    for (u32 j = 0; j < n; ++j) sum += v[i] * inv_A(i, j) * u[j];
  for (u32 i = 0; i < n; ++i)
    for (u32 j = 0; j < n; ++j) inv_A(i, j) -= x[i] * y[j] / sum;
}

}  // namespace tifa_libs::math


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