TinyMatrix.hpp

#ifndef TINY_MATRIX_HPP
#define TINY_MATRIX_HPP

#include <algebra/TinyVector.hpp>
#include <utils/InvalidData.hpp>
#include <utils/NaNHelper.hpp>
#include <utils/PugsAssert.hpp>
#include <utils/PugsMacros.hpp>
#include <utils/Types.hpp>

#include <iostream>

template <size_t M, size_t N = M, typename T = double>
class [[nodiscard]] TinyMatrix
{
 public:
  inline static constexpr size_t Dimension       = M * N;
  inline static constexpr size_t NumberOfRows    = M;
  inline static constexpr size_t NumberOfColumns = N;

  using data_type = T;

 private:
  static_assert((M > 0), "TinyMatrix number of rows must be strictly positive");
  static_assert((N > 0), "TinyMatrix number of columns must be strictly positive");

  T m_values[M * N];

  PUGS_FORCEINLINE
  constexpr size_t
  _index(size_t i, size_t j) const noexcept   // LCOV_EXCL_LINE (due to forced inline)
  {
    return i * N + j;
  }

  template <typename... Args>
  PUGS_FORCEINLINE constexpr void
  _unpackVariadicInput(const T& t, Args&&... args) noexcept
  {
    m_values[M * N - 1 - sizeof...(args)] = t;
    if constexpr (sizeof...(args) > 0) {
      this->_unpackVariadicInput(std::forward<Args>(args)...);
    }
  }

  template <typename... Args>
  PUGS_FORCEINLINE constexpr void
  _unpackVariadicInput(const TinyVector<M, T>& t, Args&&... args) noexcept
  {
    for (size_t j = 0; j < M; ++j) {
      m_values[_index(j, N - 1 - sizeof...(args))] = t[j];
    }
    if constexpr (sizeof...(args) > 0) {
      this->_unpackVariadicInput(std::forward<Args>(args)...);
    }
  }

 public:
  [[nodiscard]] PUGS_INLINE constexpr bool
  isSquare() const noexcept
  {
    return M == N;
  }

  [[nodiscard]] PUGS_INLINE constexpr friend TinyMatrix<N, M, T>
  transpose(const TinyMatrix& A)
  {
    TinyMatrix<N, M, T> tA;
    for (size_t i = 0; i < M; ++i) {
      for (size_t j = 0; j < N; ++j) {
        tA(j, i) = A(i, j);
      }
    }
    return tA;
  }

  [[nodiscard]] PUGS_INLINE constexpr size_t
  dimension() const
  {
    return M * N;
  }

  [[nodiscard]] PUGS_INLINE constexpr size_t
  numberOfValues() const
  {
    return this->dimension();
  }

  [[nodiscard]] PUGS_INLINE constexpr size_t
  numberOfRows() const
  {
    return M;
  }

  [[nodiscard]] PUGS_INLINE constexpr size_t
  numberOfColumns() const
  {
    return N;
  }

  PUGS_INLINE constexpr TinyMatrix
  operator-() const
  {
    TinyMatrix opposite;
    for (size_t i = 0; i < M * N; ++i) {
      opposite.m_values[i] = -m_values[i];
    }
    return opposite;
  }

  PUGS_INLINE
  constexpr friend TinyMatrix
  operator*(const T& t, const TinyMatrix& A)
  {
    TinyMatrix B = A;
    return B *= t;
  }

  PUGS_INLINE
  constexpr friend TinyMatrix
  operator*(const T& t, TinyMatrix&& A)
  {
    return std::move(A *= t);
  }

  PUGS_INLINE
  constexpr TinyMatrix&
  operator*=(const T& t)
  {
    for (size_t i = 0; i < M * N; ++i) {
      m_values[i] *= t;
    }
    return *this;
  }

  [[nodiscard]] PUGS_INLINE constexpr friend T
  doubleDot(const TinyMatrix& A, const TinyMatrix& B)
  {
    T t = A.m_values[0] * B.m_values[0];
    for (size_t i = 1; i < M * N; ++i) {
      t += A.m_values[i] * B.m_values[i];
    }
    return t;
  }

  template <size_t P>
  PUGS_INLINE constexpr TinyMatrix<M, P, T>
  operator*(const TinyMatrix<N, P, T>& B) const
  {
    const TinyMatrix& A = *this;
    TinyMatrix<M, P, T> AB;
    for (size_t i = 0; i < M; ++i) {
      for (size_t j = 0; j < P; ++j) {
        T sum = A(i, 0) * B(0, j);
        for (size_t k = 1; k < N; ++k) {
          sum += A(i, k) * B(k, j);
        }
        AB(i, j) = sum;
      }
    }
    return AB;
  }

  PUGS_INLINE
  constexpr TinyVector<M, T>
  operator*(const TinyVector<N, T>& x) const
  {
    const TinyMatrix& A = *this;
    TinyVector<M, T> Ax;
    for (size_t i = 0; i < M; ++i) {
      T sum = A(i, 0) * x[0];
      for (size_t j = 1; j < N; ++j) {
        sum += A(i, j) * x[j];
      }
      Ax[i] = sum;
    }
    return Ax;
  }

  PUGS_INLINE
  constexpr friend std::ostream&
  operator<<(std::ostream& os, const TinyMatrix& A)
  {
    os << '[';
    for (size_t i = 0; i < M; ++i) {
      if (i > 0) {
        os << ',';
      }
      os << '[' << NaNHelper(A(i, 0));
      for (size_t j = 1; j < N; ++j) {
        os << ',' << NaNHelper(A(i, j));
      }
      os << ']';
    }
    os << ']';

    return os;
  }

  [[nodiscard]] PUGS_INLINE constexpr bool
  operator==(const TinyMatrix& A) const
  {
    for (size_t i = 0; i < M * N; ++i) {
      if (m_values[i] != A.m_values[i])
        return false;
    }
    return true;
  }

  [[nodiscard]] PUGS_INLINE constexpr bool
  operator!=(const TinyMatrix& A) const
  {
    return not this->operator==(A);
  }

  PUGS_INLINE
  constexpr TinyMatrix
  operator+(const TinyMatrix& A) const
  {
    TinyMatrix sum;
    for (size_t i = 0; i < M * N; ++i) {
      sum.m_values[i] = m_values[i] + A.m_values[i];
    }
    return sum;
  }

  PUGS_INLINE
  constexpr TinyMatrix
  operator+(TinyMatrix&& A) const
  {
    A += *this;
    return std::move(A);
  }

  PUGS_INLINE
  constexpr TinyMatrix
  operator-(const TinyMatrix& A) const
  {
    TinyMatrix difference;
    for (size_t i = 0; i < M * N; ++i) {
      difference.m_values[i] = m_values[i] - A.m_values[i];
    }
    return difference;
  }

  PUGS_INLINE
  constexpr TinyMatrix
  operator-(TinyMatrix&& A) const
  {
    for (size_t i = 0; i < M * N; ++i) {
      A.m_values[i] = m_values[i] - A.m_values[i];
    }
    return std::move(A);
  }

  PUGS_INLINE
  constexpr TinyMatrix&
  operator+=(const TinyMatrix& A)
  {
    for (size_t i = 0; i < M * N; ++i) {
      m_values[i] += A.m_values[i];
    }
    return *this;
  }

  PUGS_INLINE
  constexpr TinyMatrix&
  operator-=(const TinyMatrix& A)
  {
    for (size_t i = 0; i < M * N; ++i) {
      m_values[i] -= A.m_values[i];
    }
    return *this;
  }

  [[nodiscard]] PUGS_INLINE constexpr T&
  operator()(size_t i, size_t j) noexcept(NO_ASSERT)
  {
    Assert((i < M) and (j < N));
    return m_values[_index(i, j)];
  }

  [[nodiscard]] PUGS_INLINE constexpr const T&
  operator()(size_t i, size_t j) const noexcept(NO_ASSERT)
  {
    Assert((i < M) and (j < N));
    return m_values[_index(i, j)];
  }

  PUGS_INLINE constexpr TinyMatrix&
  operator=(ZeroType) noexcept
  {
    static_assert(std::is_arithmetic<T>(), "Cannot assign 'zero' value for non-arithmetic types");
    for (size_t i = 0; i < M * N; ++i) {
      m_values[i] = 0;
    }
    return *this;
  }

  PUGS_INLINE
  constexpr TinyMatrix&
  operator=(IdentityType) noexcept
  {
    static_assert(std::is_arithmetic<T>(), "Cannot assign 'identity' value for non-arithmetic types");
    for (size_t i = 0; i < M; ++i) {
      for (size_t j = 0; j < N; ++j) {
        m_values[_index(i, j)] = (i == j) ? 1 : 0;
      }
    }
    return *this;
  }

  PUGS_INLINE
  constexpr TinyMatrix& operator=(const TinyMatrix& A) noexcept = default;

  PUGS_INLINE
  constexpr TinyMatrix& operator=(TinyMatrix&& A) noexcept = default;

  template <typename... Args>
  PUGS_INLINE explicit constexpr TinyMatrix(const T& t, Args&&... args) noexcept
  {
    static_assert(sizeof...(args) == M * N - 1, "wrong number of parameters");
    this->_unpackVariadicInput(t, std::forward<Args>(args)...);
  }

  template <typename... Args>
  PUGS_INLINE explicit constexpr TinyMatrix(const TinyVector<M, T>& t, Args&&... args) noexcept
  {
    static_assert(sizeof...(args) == N - 1, "wrong number of parameters");
    this->_unpackVariadicInput(t, std::forward<Args>(args)...);
  }

  // One does not use the '=default' constructor to avoid (unexpected)
  // performances issues
  PUGS_INLINE
  constexpr TinyMatrix() noexcept
  {
#ifndef NDEBUG
    for (size_t i = 0; i < M * N; ++i) {
      m_values[i] = invalid_data_v<T>;
    }
#endif   // NDEBUG
  }

  PUGS_INLINE
  constexpr TinyMatrix(ZeroType) noexcept
  {
    static_assert(std::is_arithmetic<T>(), "Cannot construct from 'zero' value "
                                           "for non-arithmetic types");
    for (size_t i = 0; i < M * N; ++i) {
      m_values[i] = 0;
    }
  }

  PUGS_INLINE
  constexpr TinyMatrix(IdentityType) noexcept
  {
    static_assert(std::is_arithmetic<T>(), "Cannot construct from 'identity' "
                                           "value for non-arithmetic types");
    for (size_t i = 0; i < M; ++i) {
      for (size_t j = 0; j < N; ++j) {
        m_values[_index(i, j)] = (i == j) ? 1 : 0;
      }
    }
  }

  PUGS_INLINE
  constexpr TinyMatrix(const TinyMatrix&) noexcept = default;

  PUGS_INLINE
  TinyMatrix(TinyMatrix&& A) noexcept = default;

  PUGS_INLINE
  ~TinyMatrix() = default;
};

template <size_t M, size_t N, typename T>
[[nodiscard]] PUGS_INLINE constexpr TinyMatrix<M, N, T>
tensorProduct(const TinyVector<M, T>& x, const TinyVector<N, T>& y)
{
  TinyMatrix<M, N, T> A;
  for (size_t i = 0; i < M; ++i) {
    for (size_t j = 0; j < N; ++j) {
      A(i, j) = x[i] * y[j];
    }
  }
  return A;
}

template <size_t N, typename T>
[[nodiscard]] PUGS_INLINE constexpr T
det(const TinyMatrix<N, N, T>& A)
{
  static_assert(std::is_arithmetic<T>::value, "determinant is not defined for non-arithmetic types");
  static_assert(std::is_floating_point<T>::value, "determinant for arbitrary dimension N is defined for floating "
                                                  "point types only");
  TinyMatrix B = A;

  TinyVector<N, size_t> index;
  for (size_t i = 0; i < N; ++i) {
    index[i] = i;
  }

  T determinent = 1;
  for (size_t i = 0; i < N; ++i) {
    for (size_t j = i; j < N; ++j) {
      size_t l       = j;
      const size_t J = index[j];
      for (size_t k = j + 1; k < N; ++k) {
        if (std::abs(B(index[k], i)) > std::abs(B(J, i))) {
          l = k;
        }
      }
      if (l != j) {
        std::swap(index[l], index[j]);
        determinent *= -1;
      }
    }
    const size_t I = index[i];
    const T Bii    = B(I, i);
    if (Bii != 0) {
      const T inv_Bii = 1. / B(I, i);
      for (size_t k = i + 1; k < N; ++k) {
        const size_t K = index[k];
        const T factor = B(K, i) * inv_Bii;
        for (size_t l = i + 1; l < N; ++l) {
          B(K, l) -= factor * B(I, l);
        }
      }
    } else {
      return 0;
    }
  }

  for (size_t i = 0; i < N; ++i) {
    determinent *= B(index[i], i);
  }
  return determinent;
}

template <typename T>
[[nodiscard]] PUGS_INLINE constexpr T
det(const TinyMatrix<1, 1, T>& A)
{
  static_assert(std::is_arithmetic<T>::value, "determinent is not defined for non-arithmetic types");
  return A(0, 0);
}

template <typename T>
[[nodiscard]] PUGS_INLINE constexpr T
det(const TinyMatrix<2, 2, T>& A)
{
  static_assert(std::is_arithmetic<T>::value, "determinent is not defined for non-arithmetic types");
  return A(0, 0) * A(1, 1) - A(1, 0) * A(0, 1);
}

template <typename T>
[[nodiscard]] PUGS_INLINE constexpr T
det(const TinyMatrix<3, 3, T>& A)
{
  static_assert(std::is_arithmetic<T>::value, "determinent is not defined for non-arithmetic types");
  return A(0, 0) * (A(1, 1) * A(2, 2) - A(2, 1) * A(1, 2)) - A(1, 0) * (A(0, 1) * A(2, 2) - A(2, 1) * A(0, 2)) +
         A(2, 0) * (A(0, 1) * A(1, 2) - A(1, 1) * A(0, 2));
}

template <size_t M, size_t N, typename T>
[[nodiscard]] PUGS_INLINE constexpr TinyMatrix<M - 1, N - 1, T>
getMinor(const TinyMatrix<M, N, T>& A, size_t I, size_t J)
{
  static_assert(M >= 2 and N >= 2, "minor calculation requires at least 2x2 matrices");
  Assert((I < M) and (J < N));
  TinyMatrix<M - 1, N - 1, T> m;
  for (size_t i = 0; i < I; ++i) {
    for (size_t j = 0; j < J; ++j) {
      m(i, j) = A(i, j);
    }
    for (size_t j = J + 1; j < N; ++j) {
      m(i, j - 1) = A(i, j);
    }
  }
  for (size_t i = I + 1; i < M; ++i) {
    for (size_t j = 0; j < J; ++j) {
      m(i - 1, j) = A(i, j);
    }
    for (size_t j = J + 1; j < N; ++j) {
      m(i - 1, j - 1) = A(i, j);
    }
  }
  return m;
}

template <size_t N, typename T>
[[nodiscard]] PUGS_INLINE T
trace(const TinyMatrix<N, N, T>& A)
{
  static_assert(std::is_arithmetic<T>::value, "trace is not defined for non-arithmetic types");

  T t = A(0, 0);
  for (size_t i = 1; i < N; ++i) {
    t += A(i, i);
  }
  return t;
}

template <size_t M, size_t N, typename T>
[[nodiscard]] PUGS_INLINE constexpr decltype(std::sqrt(std::declval<T>()))
frobeniusNorm(const TinyMatrix<M, N, T>& A)
{
  static_assert(std::is_arithmetic<T>::value, "norm is not defined for non-arithmetic types");
  static_assert(std::is_floating_point<T>::value, "Frobenius norm is defined for floating point types only");

  return std::sqrt(doubleDot(A, A));
}

template <size_t N, typename T>
[[nodiscard]] PUGS_INLINE constexpr TinyMatrix<N, N, T> inverse(const TinyMatrix<N, N, T>& A);

template <typename T>
[[nodiscard]] PUGS_INLINE constexpr TinyMatrix<1, 1, T>
inverse(const TinyMatrix<1, 1, T>& A)
{
  static_assert(std::is_arithmetic<T>::value, "inverse is not defined for non-arithmetic types");
  static_assert(std::is_floating_point<T>::value, "inverse is defined for floating point types only");

  TinyMatrix<1, 1, T> A_1(1. / A(0, 0));
  return A_1;
}

template <size_t N, typename T>
[[nodiscard]] PUGS_INLINE constexpr T
cofactor(const TinyMatrix<N, N, T>& A, size_t i, size_t j)
{
  static_assert(std::is_arithmetic<T>::value, "cofactor is not defined for non-arithmetic types");
  const T sign = ((i + j) % 2) ? -1 : 1;

  return sign * det(getMinor(A, i, j));
}

template <typename T>
[[nodiscard]] PUGS_INLINE constexpr TinyMatrix<2, 2, T>
inverse(const TinyMatrix<2, 2, T>& A)
{
  static_assert(std::is_arithmetic<T>::value, "inverse is not defined for non-arithmetic types");
  static_assert(std::is_floating_point<T>::value, "inverse is defined for floating point types only");

  const T determinent     = det(A);
  const T inv_determinent = 1. / determinent;

  TinyMatrix<2, 2, T> A_cofactors_T(A(1, 1), -A(0, 1), -A(1, 0), A(0, 0));
  return A_cofactors_T *= inv_determinent;
}

template <typename T>
[[nodiscard]] PUGS_INLINE constexpr TinyMatrix<3, 3, T>
inverse(const TinyMatrix<3, 3, T>& A)
{
  static_assert(std::is_arithmetic<T>::value, "inverse is not defined for non-arithmetic types");
  static_assert(std::is_floating_point<T>::value, "inverse is defined for floating point types only");

  const T determinent = det(A);

  TinyMatrix<3, 3, T> A_cofactors_T(cofactor(A, 0, 0), cofactor(A, 1, 0), cofactor(A, 2, 0), cofactor(A, 0, 1),
                                    cofactor(A, 1, 1), cofactor(A, 2, 1), cofactor(A, 0, 2), cofactor(A, 1, 2),
                                    cofactor(A, 2, 2));

  return A_cofactors_T *= 1. / determinent;
}

#endif   // TINYMATRIX_HPP