在 Visual Studio 中闲逛了一段时间，我想到了这个废话：
template<typename T>
class Matrix {
std::vector<size_t> dimensions;
std::unique_ptr<T[]> _data;
template<typename ... Dimensions>
size_t apply_dimensions(size_t dim, Dimensions&& ... dims) {
dimensions.emplace_back(dim);
return dim * apply_dimensions(std::forward<Dimensions>(dims)...);
}
size_t apply_dimensions(size_t dim) {
dimensions.emplace_back(dim);
return dim;
}
public:
Matrix(std::vector<size_t> dims) : dimensions(std::move(dims)) {
size_t size = flat_size();
_data = std::make_unique<T[]>(size);
}
template<typename ... Dimensions>
Matrix(size_t dim, Dimensions&&... dims) {
size_t size = apply_dimensions(dim, std::forward<Dimensions>(dims)...);
_data = std::make_unique<T[]>(size);
}
T & operator()(std::vector<size_t> const& indexes) {
if(indexes.size() != dimensions.size())
throw std::runtime_error("Incorrect number of parameters used to retrieve Matrix Data!");
return _data[get_flat_index(indexes)];
}
T const& operator()(std::vector<size_t> const& indexes) const {
if (indexes.size() != dimensions.size())
throw std::runtime_error("Incorrect number of parameters used to retrieve Matrix Data!");
return _data[get_flat_index(indexes)];
}
template<typename ... Indexes>
T & operator()(size_t idx, Indexes&& ... indexes) {
if (sizeof...(indexes)+1 != dimensions.size())
throw std::runtime_error("Incorrect number of parameters used to retrieve Matrix Data!");
size_t flat_index = get_flat_index(0, idx, std::forward<Indexes>(indexes)...);
return at(flat_index);
}
template<typename ... Indexes>
T const& operator()(size_t idx, Indexes&& ... indexes) const {
if (sizeof...(indexes)+1 != dimensions.size())
throw std::runtime_error("Incorrect number of parameters used to retrieve Matrix Data!");
size_t flat_index = get_flat_index(0, idx, std::forward<Indexes>(indexes)...);
return at(flat_index);
}
T & at(size_t flat_index) {
return _data[flat_index];
}
T const& at(size_t flat_index) const {
return _data[flat_index];
}
size_t dimension_size(size_t dim) const {
return dimensions[dim];
}
size_t num_of_dimensions() const {
return dimensions.size();
}
size_t flat_size() const {
size_t size = 1;
for (size_t dim : dimensions)
size *= dim;
return size;
}
private:
size_t get_flat_index(std::vector<size_t> const& indexes) const {
size_t dim = 0;
size_t flat_index = 0;
for (size_t index : indexes) {
flat_index += get_offset(index, dim++);
}
return flat_index;
}
template<typename ... Indexes>
size_t get_flat_index(size_t dim, size_t index, Indexes&& ... indexes) const {
return get_offset(index, dim) + get_flat_index(dim + 1, std::forward<Indexes>(indexes)...);
}
size_t get_flat_index(size_t dim, size_t index) const {
return get_offset(index, dim);
}
size_t get_offset(size_t index, size_t dim) const {
if (index >= dimensions[dim])
throw std::runtime_error("Index out of Bounds");
for (size_t i = dim + 1; i < dimensions.size(); i++) {
index *= dimensions[i];
}
return index;
}
};
我们来谈谈这段代码的作用。
//private:
template<typename ... Dimensions>
size_t apply_dimensions(size_t dim, Dimensions&& ... dims) {
dimensions.emplace_back(dim);
return dim * apply_dimensions(std::forward<Dimensions>(dims)...);
}
size_t apply_dimensions(size_t dim) {
dimensions.emplace_back(dim);
return dim;
}
public:
Matrix(std::vector<size_t> dims) : dimensions(std::move(dims)) {
size_t size = flat_size();
_data = std::make_unique<T[]>(size);
}
template<typename ... Dimensions>
Matrix(size_t dim, Dimensions&&... dims) {
size_t size = apply_dimensions(dim, std::forward<Dimensions>(dims)...);
_data = std::make_unique<T[]>(size);
}
这段代码使我们能够为该矩阵编写一个具有任意维数的初始值设定项。
int main() {
Matrix<int> mat{2, 2}; //Yields a 2x2 2D Rectangular Matrix
mat = Matrix<int>{4, 6, 5};//mat is now a 4x6x5 3D Rectangular Matrix
mat = Matrix<int>{9};//mat is now a 9-length 1D array.
mat = Matrix<int>{2, 3, 4, 5, 6, 7, 8, 9};//Why would you do this? (yet it compiles...)
}
如果维度的数量和大小仅在运行时已知，则此代码将解决该问题：
int main() {
std::cout << "Input the sizes of each of the dimensions.\n";
std::string line;
std::getline(std::cin, line);
std::stringstream ss(line);
size_t dim;
std::vector<size_t> dimensions;
while(ss >> dim)
dimensions.emplace_back(dim);
Matrix<int> mat{dimensions};//Voila.
}
然后，我们希望能够访问该矩阵的任意索引。此代码提供了两种方法来执行此操作：静态使用模板，或在运行时可变地使用模板。
//public:
T & operator()(std::vector<size_t> const& indexes) {
if(indexes.size() != dimensions.size())
throw std::runtime_error("Incorrect number of parameters used to retrieve Matrix Data!");
return _data[get_flat_index(indexes)];
}
T const& operator()(std::vector<size_t> const& indexes) const {
if (indexes.size() != dimensions.size())
throw std::runtime_error("Incorrect number of parameters used to retrieve Matrix Data!");
return _data[get_flat_index(indexes)];
}
template<typename ... Indexes>
T & operator()(size_t idx, Indexes&& ... indexes) {
if (sizeof...(indexes)+1 != dimensions.size())
throw std::runtime_error("Incorrect number of parameters used to retrieve Matrix Data!");
size_t flat_index = get_flat_index(0, idx, std::forward<Indexes>(indexes)...);
return at(flat_index);
}
template<typename ... Indexes>
T const& operator()(size_t idx, Indexes&& ... indexes) const {
if (sizeof...(indexes)+1 != dimensions.size())
throw std::runtime_error("Incorrect number of parameters used to retrieve Matrix Data!");
size_t flat_index = get_flat_index(0, idx, std::forward<Indexes>(indexes)...);
return at(flat_index);
}
然后，在实践中：
Matrix<int> mat{6, 5};
mat(5, 2) = 17;
//mat(5, 1, 7) = 24; //throws exception at runtime because of wrong number of dimensions.
mat = Matrix<int>{9, 2, 8};
mat(5, 1, 7) = 24;
//mat(5, 2) = 17; //throws exception at runtime because of wrong number of dimensions.
这对于运行时动态索引来说效果很好：
std::vector<size_t> indexes;
/*...*/
mat(indexes) = 54; //Will throw if index count is wrong, will succeed otherwise
这种对象可能还需要许多其他功能，例如resize方法，但选择如何实现它是一个高层设计决策。我还遗漏了大量其他可能有价值的实现细节（例如优化移动构造函数、比较运算符、复制构造函数），但这应该可以让您很好地了解如何开始。
EDIT:
如果您想完全避免使用模板，您可以削减此处提供的代码的一半，并且只需使用使用的方法/构造函数std::vector<size_t>提供尺寸/索引数据。如果您不需要在运行时动态适应维度数的能力，则可以删除std::vector<size_t>重载，甚至可能使维数成为类本身的模板参数（这将使您能够使用size_t[] or std::array[size_t, N]存储尺寸数据）。
