Simultaneous linear equations (Floating point number)
(Mylib/LinearAlgebra/simultaneous_linear_equations_float.cpp)

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• Last update: 2021-04-23 23:44:44+09:00

Operations

Requirements

Notes

Problems

References

Verified with

• test/aoj/2171/main.test.cpp

Code

#pragma once
#include <optional>
#include <utility>
#include <vector>

namespace haar_lib {
  namespace float_simultaneous_linear_equations_impl {
    template <typename T>
    struct result {
      int rank, dim;
      std::vector<T> solution;
    };
  }  // namespace float_simultaneous_linear_equations_impl

  template <typename T>
  auto float_simultaneous_linear_equations(std::vector<std::vector<T>> a, std::vector<T> b, T eps) {
    using result = float_simultaneous_linear_equations_impl::result<T>;
    std::optional<result> ret;

    const int n = a.size(), m = a[0].size();
    int rank = 0;

    for (int j = 0; j < m; ++j) {
      int pivot = -1;

      double M = eps;
      for (int i = rank; i < n; ++i) {
        if (std::abs(a[i][j]) > M) {
          M     = std::abs(a[i][j]);
          pivot = i;
        }
      }

      if (pivot == -1) continue;

      std::swap(a[pivot], a[rank]);
      std::swap(b[pivot], b[rank]);

      {
        double d = a[rank][j];
        for (int k = 0; k < m; ++k) a[rank][k] /= d;
        b[rank] /= d;
      }

      for (int i = 0; i < n; ++i) {
        if (i == rank or std::abs(a[i][j]) <= eps) continue;
        double d = a[i][j];
        for (int k = 0; k < m; ++k) {
          a[i][k] -= a[rank][k] * d;
        }
        b[i] -= b[rank] * d;
      }

      ++rank;
    }

    for (int i = rank; i < n; ++i) {
      if (std::abs(b[i]) > eps) {
        return ret;
      }
    }

    const int dim = m - rank;

    std::vector<T> solution(m);
    for (int i = 0; i < rank; ++i) solution[i] = b[i];

    ret = result({rank, dim, solution});
    return ret;
  }
}  // namespace haar_lib

#line 2 "Mylib/LinearAlgebra/simultaneous_linear_equations_float.cpp"
#include <optional>
#include <utility>
#include <vector>

namespace haar_lib {
  namespace float_simultaneous_linear_equations_impl {
    template <typename T>
    struct result {
      int rank, dim;
      std::vector<T> solution;
    };
  }  // namespace float_simultaneous_linear_equations_impl

  template <typename T>
  auto float_simultaneous_linear_equations(std::vector<std::vector<T>> a, std::vector<T> b, T eps) {
    using result = float_simultaneous_linear_equations_impl::result<T>;
    std::optional<result> ret;

    const int n = a.size(), m = a[0].size();
    int rank = 0;

    for (int j = 0; j < m; ++j) {
      int pivot = -1;

      double M = eps;
      for (int i = rank; i < n; ++i) {
        if (std::abs(a[i][j]) > M) {
          M     = std::abs(a[i][j]);
          pivot = i;
        }
      }

      if (pivot == -1) continue;

      std::swap(a[pivot], a[rank]);
      std::swap(b[pivot], b[rank]);

      {
        double d = a[rank][j];
        for (int k = 0; k < m; ++k) a[rank][k] /= d;
        b[rank] /= d;
      }

      for (int i = 0; i < n; ++i) {
        if (i == rank or std::abs(a[i][j]) <= eps) continue;
        double d = a[i][j];
        for (int k = 0; k < m; ++k) {
          a[i][k] -= a[rank][k] * d;
        }
        b[i] -= b[rank] * d;
      }

      ++rank;
    }

    for (int i = rank; i < n; ++i) {
      if (std::abs(b[i]) > eps) {
        return ret;
      }
    }

    const int dim = m - rank;

    std::vector<T> solution(m);
    for (int i = 0; i < rank; ++i) solution[i] = b[i];

    ret = result({rank, dim, solution});
    return ret;
  }
}  // namespace haar_lib

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