Matrix.h

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#pragma once
#include "Random.h"
#include "vec/vec3.h"
#include <cassert>
#include <cmath>
#include <cstdlib>
#include <cstring>
#include <functional>
#include <initializer_list>
#include <iostream>
#include <memory>
#include <type_traits>
 
#include <signal.h>
 
 
struct MatrixDimension {
  size_t rows;
  size_t columns;
  size_t elemDim = 1;
};
template<typename T = double>
class Matrix
{
public:
  explicit Matrix(T val, size_t rowCount, size_t colCount, size_t elementDimension = 1) {
    Resize(rowCount, colCount, elementDimension);
    for(size_t i = 0; i < _rows * _columns * _element_size; ++i) { _data[i] = val; }
  }
 
  explicit Matrix(T* val, size_t colCount) {
    Resize(1, colCount);
    for(size_t j = 0; j < _columns; j++) { _data[GetIndex(0, j)] = val[j]; }
  }
 
  Matrix() { }
 
  Matrix(const std::initializer_list<std::initializer_list<T>>& lst) {
    int i = 0, j = 0;
    auto rows = lst.size();
    auto cols = lst.begin()->size();
    Resize(rows, cols);
    for(const auto& l : lst) {
      for(const auto& v : l) {
        _data[GetIndex(i, j)] = v;
        ++j;
      }
      j = 0;
      ++i;
    }
  }
 
  Matrix(const std::initializer_list<std::initializer_list<std::initializer_list<T>>>& lst) {
    int i = 0, j = 0, c = 0;
    auto rows  = lst.size();
    auto cols  = lst.begin()->size();
    auto elems = lst.begin()->begin()->size();
    Resize(rows, cols, elems);
    for(const auto& l : lst) {
      for(const auto& v : l) {
        for(const auto k : v) {
          _data[GetIndex(i, j, c)] = k;
          ++c;
        }
        c = 0;
        ++j;
      }
      j = 0;
      ++i;
    }
  }
 
  Matrix(Matrix const& other) {
    Resize(other._rows, other._columns, other._element_size);
    std::memcpy(this->_data, other._data, other._dataSize * sizeof(T));
    this->needsFree = true;
  };
 
  template<typename V>
  Matrix(const Matrix<V>& other) {
    Resize(other.rows(), other.columns(), other.elements());
    auto index_factor = _columns * _element_size;
    for(size_t i = 0; i < (_rows * _columns * _element_size); ++i) {
      _data[i] = static_cast<T>(other(i / (index_factor), i % (index_factor), i % _element_size));
    }
 
    this->needsFree = true;
  }
 
  ~Matrix() {
    if(needsFree) { free(_data); }
  }
 
  static Matrix
  Random(size_t rows, size_t columns, size_t element_size = 1, double minValue = 0.0, double maxValue = 1.0) {
    Matrix<T> matrix(0, rows, columns, element_size);
    for(size_t i = 0; i < rows * columns * element_size; ++i) { matrix._data[i] = Random::Get(minValue, maxValue); }
    return matrix;
  }
 
  static Matrix Normal(size_t rows, size_t columns, double mu, double sigma) {
    assert(columns % 2 == 0);
 
    constexpr double two_pi = 2.0 * M_PI;
    Matrix out;
    out.Resize(rows, columns);
    for(size_t i = 0; i < rows * columns; i += 2) {
      auto u1 = Random::Get();
      auto u2 = Random::Get();
 
      auto mag         = sigma * sqrt(-2.0 * log(u1));
      out._data[i]     = mag * cos(two_pi * u2) + mu;
      out._data[i + 1] = mag * sin(two_pi * u2) + mu;
    }
 
    return out;
  }
 
  [[nodiscard]] inline size_t rows() const { return _rows; }
  [[nodiscard]] inline size_t columns() const { return _columns; }
 
  [[nodiscard]] inline size_t elements() const { return _element_size; }
 
  [[nodiscard]] inline size_t elements_total() const {return _rows * _columns * _element_size; }
 
  [[nodiscard]] inline T Determinant() const {
    if(!HasDet()) return 0;
 
    if(_rows == 3 && _columns == 3) {
      return (
      _data[GetIndex(0, 0)] * _data[GetIndex(1, 1)] * _data[GetIndex(2, 2)]
      + _data[GetIndex(0, 1)] * _data[GetIndex(1, 2)] * _data[GetIndex(2, 0)]
      + _data[GetIndex(0, 2)] * _data[GetIndex(1, 0)] * _data[GetIndex(2, 1)]
      - _data[GetIndex(0, 2)] * _data[GetIndex(1, 1)] * _data[GetIndex(2, 0)]
      - _data[GetIndex(0, 1)] * _data[GetIndex(1, 0)] * _data[GetIndex(2, 2)]
      - _data[GetIndex(0, 0)] * _data[GetIndex(1, 2)] * _data[GetIndex(2, 1)]);
    }
    if(_rows == 2 && _columns == 2) {
      return _data[GetIndex(0, 0)] * _data[GetIndex(1, 1)] - _data[GetIndex(0, 1)] * _data[GetIndex(1, 0)];
    }
 
    Matrix<T> submat(0.0, _rows - 1, _columns - 1);
    T d = 0;
    {
      for(size_t c = 0; c < _columns; c++) {
        size_t subi = 0; //sub-matrix's i value
        for(size_t i = 1; i < _rows; i++) {
          size_t subj = 0;
          for(size_t j = 0; j < _columns; j++) {
            if(j == c) continue;
            submat._data[submat.GetIndex(subi, subj)] = _data[GetIndex(i, j)];
            subj++;
          }
          subi++;
        }
        d = d + (std::pow(-1, c) * _data[GetIndex(0, c)] * submat.Determinant());
      }
    }
    return d;
  }
 
  [[nodiscard]] constexpr Matrix<T> Transpose() const {
    Matrix<T> res(0, _columns, _rows, _element_size);
    int index_factor = _rows * _element_size;
    for(size_t i = 0; i < (_rows * _columns * _element_size); ++i) {
      res._data[i] = _data[GetIndex(i % (index_factor), i / (index_factor), i % _element_size)];
    }
    return res;
  }
 
  Matrix<T> HorizontalConcat(const Matrix<T>& other) {
    assert(this->rows() == other.rows());
    auto result = new Matrix<T>(0, this->rows(), this->columns() + other.columns(), other.elements());
    for(size_t i = 0; i < rows(); ++i) {
      for(size_t j = 0; j < columns() + other.columns(); ++j) {
        for(size_t elem = 0; elem < _element_size; ++elem) {
          (*result)(i, j, elem) = j < columns() ? _data[GetIndex(i, j, elem)] : other(i, j - columns(), elem);
        }
      }
    }
    return *result;
  }
 
  // Comparison
 
  bool operator==(const Matrix<T>& rhs) const {
    // Just need to check element-wise
    // Dimensions handled by implementation.
    this->assertSize(rhs);
    return elementWiseCompare(rhs);
  }
  bool operator!=(const Matrix<T>& rhs) const {
    return !(rhs == *this); // NOLINT
  }
 
  bool operator<(const Matrix<T>& rhs) const {
    assertSize(rhs);
    for(size_t i = 0; i < _rows * _columns * _element_size; ++i) {
      if(_data[i] > rhs._data[i]) { return false; }
    }
    return true;
  }
 
  bool operator>(const Matrix<T>& rhs) const {
    assertSize(rhs);
    for(size_t i = 0; i < _rows * _columns * _element_size; ++i) {
      if(_data[i] < rhs._data[i]) { return false; }
    }
    return true;
  }
 
  [[nodiscard]] bool IsVector() const { return _columns == 1 || _rows == 1; }
 
  void assertSize(const Matrix<T>& other) const {
    assert(_columns == other.columns() && _rows == other.rows() && _element_size == other.elements());
  }
 
  [[nodiscard]] bool elementWiseCompare(const Matrix<T>& rhs) const {
    assertSize(rhs);
    for(size_t i = 0; i < _rows * _columns * _element_size; ++i) {
      if(_data[i] != rhs._data[i]) { return false; }
    }
    return true;
  }
 
 
  // Assignment
  Matrix<T> operator=(const Matrix<T>& other) {
    if(this != &other) {
      if((this == NULL) || (_rows != other.rows() || _columns != other.columns())) {
        Resize(other.rows(), other.columns(), other.elements());
      }
      for(size_t i = 0; i < _rows * _columns * _element_size; ++i) { _data[i] = other._data[i]; }
    }
    return *this;
  }
 
  Matrix<T> Apply(const std::function<T(T)>& fun) const {
    auto out = (*this);
    for(size_t i = 0; i < _rows * _columns * _element_size; ++i) { out._data[i] = fun(_data[i]); }
    return out;
  }
 
  // Math
 
  Matrix& HadamardMulti(const Matrix& other) {
    for(size_t i = 0; i < _rows * _columns * _element_size; ++i) { _data[i] *= other._data[i]; }
    return *this;
  }
 
  Matrix<T>& KroneckerMulti(const Matrix<T>& other) {
    assert(_element_size == other.elements());
    auto result = new Matrix<T>(0, rows() * other.rows(), columns() * other.columns(), _element_size);
    for(size_t m = 0; m < rows(); m++) {
      for(size_t n = 0; n < columns(); n++) {
        for(size_t p = 0; p < other.rows(); p++) {
          for(size_t q = 0; q < other.columns(); q++) {
            for(size_t elem = 0; elem < _element_size; ++elem) {
              (*result)(m * other.rows() + p, n * other.columns() + q, elem) =
              _data[GetIndex(m, n, elem)] * other(p, q, elem);
            }
          }
        }
      }
    }
    return *result;
  }
 
  T sumElements() const {
    T result = T(0.0);
    for(size_t i = 0; i < _rows * _columns * _element_size; ++i) { result += _data[i]; }
    return result;
  }
 
  Matrix<T> sum(size_t axis) const {
    Matrix<T> out(0, axis == 0 ? _rows : 1, axis == 1 ? _columns : 1);
    for(size_t i = 0; i < (axis == 0 ? _rows : _columns); ++i) {
      out(axis == 0 ? i : 0, axis == 1 ? i : 0) =
      GetSlice(axis == 0 ? i : 0, axis == 0 ? i : _rows - 1, axis == 1 ? i : 0, axis == 1 ? i : _columns - 1)
      .sumElements();
    }
    return out;
  }
 
  Matrix<T>& operator*=(T rhs) {
    (*this) = *this * rhs;
    return *this;
  }
 
  Matrix<T>& operator+=(const Matrix<T>& rhs) {
    (*this) = (*this) + rhs;
    return *this;
  }
  Matrix<T>& operator-=(const Matrix<T>& rhs) {
    (*this) = (*this) - rhs;
    return *this;
  }
 
  // Access
 
  T& operator()(size_t row, size_t column, size_t elem = 0) { return _data[GetIndex(row, column, elem)]; }
  T& operator()(size_t row, size_t column, size_t elem = 0) const { return _data[GetIndex(row, column, elem)]; }
 
  Matrix<T> operator()(size_t row) { return GetSlice(row, row, 0, _columns - 1); }
  Matrix<T> operator()(size_t row) const { return GetSlice(row, row, 0, _columns - 1); }
 
  T& operator*() { return _data[0]; }
  T& operator*() const { return _data[0]; }
 
  void SetColumn(size_t index, const Matrix<T>& other) {
    bool isInColumns = other.columns() > other.rows();
    auto rowCount    = isInColumns ? other.columns() : other.rows();
    assert(rowCount == _rows);
    assert(_element_size == other.elements());
    for(size_t i = 0; i < rowCount; ++i) {
      for(size_t elem = 0; elem < elements(); ++elem) {
        _data[GetIndex(i, index, elem)] = other(isInColumns ? 0 : i, isInColumns ? i : 0, elem);
      }
    }
  }
 
  void SetRow(size_t index, const Matrix<T>& other) {
    bool isInColumns = other.columns() > other.rows();
    auto colCount    = isInColumns ? other.columns() : other.rows();
    assert(colCount == _columns);
    assert(_element_size == other.elements());
    for(size_t i = 0; i < colCount; ++i) {
      for(size_t elem = 0; elem < elements(); ++elem) {
        _data[GetIndex(index, i, elem)] = other(isInColumns ? 0 : i, isInColumns ? i : 0, elem);
      }
    }
  }
 
  friend std::ostream& operator<<(std::ostream& ostr, const Matrix& m) {
    ostr.precision(17);
    ostr << "[\n";
    for(size_t row = 0; row < m.rows(); row++) {
      ostr << '\t';
      for(size_t col = 0; col < m.columns(); col++) {
        if(m.elements() > 1) { ostr << "( "; }
        for(size_t elem = 0; elem < m.elements(); elem++) {
          ostr << m._data[m.GetIndex(row, col, elem)];
          if(elem < m.elements() - 1) ostr << ", ";
        }
        if(m.elements() > 1) { ostr << " )"; }
        if(col < m.columns() - 1) ostr << ", ";
      }
      ostr << "\n";
    }
    ostr << "]\n";
    return ostr;
  }
 
  void Resize(size_t rows, size_t cols, size_t elementSize = 1) {
    _rows         = rows;
    _columns      = cols;
    _element_size = elementSize;
    if(_data != nullptr || needsFree) {
      _data = (T*)realloc(_data, rows * cols * elementSize * sizeof(T));
    } else {
      _data = (T*)malloc(rows * cols * elementSize * sizeof(T));
    }
    _dataSize = rows * cols * elementSize;
    needsFree = true;
  }
 
  [[nodiscard]] inline int GetIndex(size_t row, size_t col, size_t elem = 0) const {
    //        assert(row < _rows && col < _columns && elem < _element_size);
    return elem + col * _element_size + row * _columns * _element_size;
  }
  [[nodiscard]] inline Matrix GetSlice(size_t rowStart) const { return GetSlice(rowStart, rowStart, 0, _columns - 1); }
  [[nodiscard]] inline Matrix GetSlice(size_t rowStart, size_t rowEnd) const {
    return GetSlice(rowStart, rowEnd, 0, _columns - 1);
  }
  [[nodiscard]] inline Matrix GetSlice(size_t rowStart, size_t rowEnd, size_t colStart) const {
    return GetSlice(rowStart, rowEnd, colStart, _columns - 1);
  }
  [[nodiscard]] inline Matrix GetSlice(size_t rowStart, size_t rowEnd, size_t colStart, size_t colEnd) const {
    size_t numRows = (rowEnd - rowStart) + 1;
    size_t numCols = (colEnd - colStart) + 1;
 
    Matrix out(0, numRows, numCols, _element_size);
 
    for(size_t i = 0; i < numRows; ++i) {
      for(size_t j = 0; j < numCols; ++j) {
        for(size_t elem = 0; elem < _element_size; ++elem) {
          out(i, j, elem) = _data[GetIndex(rowStart + i, colStart + j, elem)];
        }
      }
    }
    return out;
  }
 
  void SetSlice(
  const size_t& row_start,
  const size_t& row_end,
  const size_t& col_start,
  const size_t& col_end,
  const Matrix<T>& slice) {
    size_t numRows = (row_end - row_start) + 1;
    size_t numCols = (col_end - col_start) + 1;
    assert(numRows == slice.rows());
    assert(numCols == slice.columns());
 
    for(size_t i = 0; i < numRows; ++i) {
      for(size_t j = 0; j < numCols; ++j) { _data[GetIndex(row_start + i, col_start + j)] = slice(i, j); }
    }
  }
 
 
  void SetSlice(const size_t& row_start, const Matrix<T>& slice) {
    return SetSlice(row_start, row_start + slice.rows() - 1, 0, slice.columns() - 1, slice);
  }
 
  Matrix<T> GetComponents(const size_t& index) const {
    assert(index < _element_size);
    Matrix<T> out(0, _rows, _columns, 1);
    for(size_t i = 0; i < _rows; ++i) {
      for(size_t j = 0; j < _columns; ++j) { out(i, j, 0) = _data[GetIndex(i, j, index)]; }
    }
    return out;
  }
 
  inline Matrix<T> GetSlicesByIndex(const Matrix<size_t>& indices) const {
    assert(indices.IsVector());
    auto _indices = indices.rows() > indices.columns() ? indices : indices.Transpose();
    Matrix<T> out(0, _indices.rows(), _columns, _element_size);
    for(size_t i = 0; i < _indices.rows(); ++i) {
      auto idx   = _indices(i, 0);
      auto slice = GetSlice(idx);
      out.SetSlice(i, slice);
    }
    return out;
  }
 
private:
  [[nodiscard]] bool HasDet() const { return _columns > 1 && _rows > 1 && _element_size == 1; }
 
  size_t _rows = 0;
  size_t _columns = 0;
  size_t _element_size = 0;
 
  T* _data = nullptr;
  size_t _dataSize = 0;
  bool needsFree = false;
};
 
template<typename T>
inline Matrix<T> operator+(const Matrix<T>& lhs, const Matrix<T>& rhs) {
  if(rhs.IsVector() && !lhs.IsVector()) {
    bool row_wise = rhs.rows() > rhs.columns();
    if(row_wise) {
      assert(rhs.rows() == lhs.rows());
    } else {
      assert(rhs.columns() == lhs.columns());
    }
    auto result = Matrix<T>(0, lhs.rows(), lhs.columns(), lhs.elements());
    for(size_t i = 0; i < lhs.rows(); i++) {
      for(size_t j = 0; j < lhs.columns(); j++) {
        for(size_t elem = 0; elem < lhs.elements(); elem++) {
          result(i, j, elem) = lhs(i, j, elem) + rhs(row_wise ? i : 0, row_wise ? 0 : j, elem);
        }
      }
    }
    return result;
  }
 
  lhs.assertSize(rhs);
  auto result = Matrix<T>(0, lhs.rows(), lhs.columns(), lhs.elements());
  for(size_t i = 0; i < lhs.rows(); i++) {
    for(size_t j = 0; j < lhs.columns(); j++) { result(i, j) = lhs(i, j) + rhs(i, j); }
  }
  return result;
}
template<typename T>
inline Matrix<T> operator-(const Matrix<T>& lhs, const Matrix<T>& rhs) {
  if(rhs.IsVector() && !lhs.IsVector()) {
    // Matrix-Vector substraction
    // substracts vector row/column wise from given lhs matrix
    // similar to numpy.
    auto result = Matrix<T>(0, lhs.rows(), lhs.columns(), lhs.elements());
    for(size_t i = 0; i < lhs.rows(); i++) {
      for(size_t j = 0; j < lhs.columns(); j++) {
        for(size_t elem = 0; elem < lhs.elements(); elem++) {
          result(i, j, elem) =
          lhs(i, j, elem) - rhs(rhs.rows() > rhs.columns() ? i : 0, rhs.rows() > rhs.columns() ? 0 : j, elem);
        }
      }
    }
    return result;
  }
  lhs.assertSize(rhs);
  auto result = Matrix<T>(0, lhs.rows(), lhs.columns(), lhs.elements());
  for(size_t i = 0; i < lhs.rows(); i++) {
    for(size_t j = 0; j < lhs.columns(); j++) {
      for(size_t elem = 0; elem < lhs.elements(); elem++) { result(i, j, elem) = lhs(i, j, elem) - rhs(i, j, elem); }
    }
  }
  return result;
}
template<typename T, typename U>
inline Matrix<T> operator/(U lhs, const Matrix<T>& rhs) {
  auto result = Matrix<T>(0.0, rhs.rows(), rhs.columns(), rhs.elements());
  for(size_t i = 0; i < rhs.rows(); i++) {
    for(size_t j = 0; j < rhs.columns(); j++) {
      for(size_t elem = 0; elem < rhs.elements(); elem++) { result(i, j, elem) = lhs / rhs(i, j, elem); }
    }
  }
  return result;
}
template<typename T, typename U>
inline Matrix<T> operator/(const Matrix<T>& lhs, const U& rhs) {
  auto result = Matrix<T>(0.0, lhs.rows(), lhs.columns(), lhs.elements());
  for(size_t i = 0; i < lhs.rows(); i++) {
    for(size_t j = 0; j < lhs.columns(); j++) {
      for(size_t elem = 0; elem < lhs.elements(); elem++) { result(i, j, elem) = lhs(i, j, elem) / rhs; }
    }
  }
  return result;
}
 
 
template<typename T>
inline Matrix<T> operator/(const Matrix<T>& lhs, const Matrix<T>& rhs) {
  auto result = Matrix<T>(0.0, lhs.rows(), lhs.columns(), lhs.elements());
  if(rhs.IsVector()) {
    bool row_wise = rhs.rows() > rhs.columns();
    for(size_t i = 0; i < lhs.rows(); i++) {
      for(size_t j = 0; j < lhs.columns(); j++) {
        for(size_t elem = 0; elem < lhs.elements(); elem++) {
          result(i, j, elem) = lhs(i, j, elem) / rhs(row_wise ? i : 0, row_wise ? 0 : j, elem);
        }
      }
    }
    return result;
  }
 
  return lhs * (1.0 / rhs);
}
 
template<typename T, typename U>
inline Matrix<T> operator*(const Matrix<T>& lhs, const U& rhs) {
  auto result = Matrix<T>(0.0, lhs.rows(), lhs.columns(), lhs.elements());
  for(size_t i = 0; i < lhs.rows(); i++) {
    for(size_t j = 0; j < lhs.columns(); j++) {
      for(size_t elem = 0; elem < lhs.elements(); elem++) { result(i, j, elem) = lhs(i, j, elem) * rhs; }
    }
  }
  return result;
}
template<typename T, typename U>
inline Matrix<T> operator*(U lambda, const Matrix<T>& A) {
  auto result = Matrix<T>(0.0, A.rows(), A.columns(), A.elements());
  for(size_t i = 0; i < A.rows(); i++) {
    for(size_t j = 0; j < A.columns(); j++) {
      for(size_t elem = 0; elem < A.elements(); elem++) { result(i, j, elem) = A(i, j, elem) * lambda; }
    }
  }
  return result;
}
 
template<typename T>
inline Matrix<T> operator*(const Matrix<T>& lhs, const Matrix<T>& rhs) {
  if(lhs.columns() == rhs.rows() && lhs.elements() == rhs.elements()) {
    auto result = Matrix<T>(0.0, lhs.rows(), rhs.columns(), rhs.elements());
    for(size_t i = 0; i < lhs.rows(); i++) {
      for(size_t j = 0; j < rhs.columns(); j++) {
        for(size_t k = 0; k < rhs.rows(); k++) {
          for(size_t elem = 0; elem < rhs.elements(); elem++) {
            result(i, j, elem) += (T)(lhs(i, k, elem) * rhs(k, j, elem));
          }
        }
      }
    }
    return result;
  }
  assert(rhs.IsVector() && !lhs.IsVector());
 
  auto row_wise = rhs.rows() > rhs.columns();
  auto result   = Matrix<T>(0.0, lhs.rows(), lhs.columns(), lhs.elements());
  for(size_t i = 0; i < lhs.rows(); i++) {
    for(size_t j = 0; j < lhs.columns(); j++) {
      for(size_t k = 0; k < lhs.elements(); k++) {
        result(i, j, k) = (T)(lhs(i, j, k) * rhs(row_wise ? i : 0, row_wise ? 0 : j, k));
      }
    }
  }
  return result;
}