多个类的父类的部分特化

Question

我想对模板类使用部分专业化，以便该模板类的所有子级都将使用该专业化。让我用一个例子来解释它:)

template < typename T, unsigned int rows, unsigned int cols>
class BaseMatrix {...};

这个类将有指定矩阵结构的子类，如稀疏、密集、对角线等。

template < typename T, unsigned int rows, unsigned int cols>
class DiagonalMatrix : public BaseMatrix<T,rows,cols>{..}

然后这些类将再次有指定存储的子类：堆栈数组、向量、列表、队列，..

template < typename T, unsigned int rows, unsigned int cols>
class StackDiagonalMatrix : public DiagonalMatrix<T, rows, cols> {..}

然后是一个 Matrix 类，它提供了所有的数学功能。这个模板类实现了operator+、operator-等...

   template <typename T, 
             template<typename, unsigned, unsigned> class MatrixContainer,
             unsigned Rows, 
             unsigned Cols>
    class matrix;

对于最后一个类，我想编写这样的专业化：

template <typename T,unsigned Rows, unsigned Cols>
class matrix<T, BaseMatrix, Rows, Cols> {};

template <typename T,unsigned Rows, unsigned Cols>
class matrix<T, DiagonalMatrix, Rows, Cols>  {};

但是当我编写一个继承自DiagonalMatrix的StackDiagonalMatrix时，它没有找到DiagonalMatrix的专业化——它没有找到实际上根本就是一个专业。

error: aggregate ‘matrix<int, StackDenseMatrix, 3u, 2u> matrix’ has incomplete type and cannot be defined

现在这个问题有解决办法吗？您可以为多个模板类的父类编写专门化吗？

非常感谢！

涉及的完整来源：

    template <typename T, unsigned int rows, unsigned int cols>
    class BaseMatrix {
    protected:
        BaseMatrix(){};
        static const unsigned rowSize = rows;
        static const unsigned colSize = cols;
    };

    template <typename T, unsigned int rows, unsigned int cols>
    class DenseMatrix : public BaseMatrix<T, rows, cols> {
    protected:
        DenseMatrix(){};

    };

    template <typename T, unsigned int rows, unsigned int cols>
    class StackDenseMatrix : public DenseMatrix<T, rows, cols> {

    public:
        typedef T                                           value_type;

    private:
        value_type                                          grid[rows][cols];
        StackDenseMatrix();
    };

    template<typename value_type, unsigned int rows, unsigned int cols>
    StackDenseMatrix<value_type, rows,cols>::StackDenseMatrix () {
        for (unsigned int i = 0; i < this->rowSize; i++) {
            for (unsigned int j = 0; j < this->colSize; j++) {
                grid[i][j] = 0;
            }
        }
    }

    template <typename T, template<typename, unsigned, unsigned> class MatrixContainer ,unsigned Rows, unsigned Cols>
    class matrix;

    template <typename T,unsigned Rows, unsigned Cols>
    class matrix<T,BaseMatrix, Rows, Cols> {
         matrix(){};
};

int main () {
    matrix<int, StackDenseMatrix, 3, 2> matrix;
    return 0;
}

Answer 1

继承不适用于模板特化。当您调用matrix时，它会选择matrix的通用模板，因为第二个参数是StackDenseMatrix，而不是BaseMatrix。即使这些类通过继承相关，但没有任何区别，它们不是完全相同的类型，因此编译器不会选择matrix的特化。

为了解决你的问题，我认为继承在这种情况下不会给你带来任何好处。在泛型编程中，更合适的工具是类型特征、策略和概念。在这种情况下，您应该能够应用一些类型特征来实现类似的目标。我喜欢使用的一个技巧是默认模板参数依赖于先前的模板参数，然后进行部分特化。例如如下：

enum MatrixStorage {
  DenseMatrix,
  SparseMatrix
};

enum MatrixStructure {
  GeneralMatrix,
  SquareMatrix,
  DiagonalMatrix  //, ...
};

template <typename T, unsigned Rows, unsigned Cols>
class StackDenseMatrix {
  public: 
    typedef T value_type;
    static const MatrixStorage Storage = DenseMatrix;
    static const MatrixStructure Structure = GeneralMatrix;
  //..
};

//General template with default arguments:
template <typename T, 
          template <typename, unsigned, unsigned> class MatrixContainer,
          unsigned Rows, unsigned Cols, 
          MatrixStorage Storage = MatrixContainer<T,Rows,Cols>::Storage,
          MatrixStructure Structure = MatrixContainer<T,Rows,Cols>::Structure>
class matrix;

//Specialization with given arguments:
template <typename T, 
          template <typename, unsigned, unsigned> class MatrixContainer,
          unsigned Rows, unsigned Cols>
class matrix<T,MatrixContainer,Rows,Cols,DenseMatrix,GeneralMatrix> {
  //implementation of matrix for when the container is dense and has general structure...
};

int main() {
  matrix<int,StackDenseMatrix,3,2> M; //no extra arguments, and the right specialization will be selected based on the traits of StackDenseMatrix.
  return 0;
};

我有自己的矩阵库，它严重依赖于模板元编程和通用编程技术，按照上面的示例，为不同类型的矩阵结构和存储提供矩阵运算的特殊实现，并且它非常有效好这样。我曾经对不同的矩阵类型使用继承，但现在我转而仅依赖类型特征、概念、策略和 Sfinae 开关，这是一个更实用的解决方案。

Answer 2

为了解决您的问题，您可以使用基于策略的设计。例如，您可以创建存储和形状的策略类。

class Diagonal  {
public:
    // the default storage facility of a Diagonal matrix
    typedef Stack default_storage;
};

template <typename T, typename Shape = DefaultShape, typename Storage = DefaultStorage, unsigned Row, unsigned Col>
class Matrix : public Storage, Shape {   // policy classes Storage and Shape
public:
    template <typename T1, typename Shape1, typename Storage1, unsigned Row1, unsigned Col1>
    friend Matrix<T1,Shape1,Storage1,Row1,Col1>& operator += (Matrix<T1,Shape1,Storage1,Row1,Col1> matrix1,Matrix<T,Shape,Storage,Row,Col> matrix2);

    template <typename T1, typename Shape1, typename Storage1, unsigned Row1, unsigned Col1>
    friend Matrix<T1,Diagonal,Storage1,Row1,Col1>& operator += (Matrix<T1,Diagonal,Storage1,Row1,Col1> matrix1,Matrix<T,Diagonal,Storage,Row,Col> matrix2);

    template <typename T1, typename Shape1, typename Storage1, unsigned Row1, unsigned Col1>
    friend Matrix<T,Shape,Storage,Row,Col>& operator + (Matrix<T,Shape,Storage,Row,Col> matrix1, Matrix<T,Shape,Storage,Row,Col> matrix2);

    template <typename T1, typename Shape1, typename Storage1, unsigned Row1, unsigned Col1>
    friend Matrix<T,Diagonal,Storage,Row,Col>& operator + (Matrix<T,Diagonal,Storage,Row,Col> matrix1, Matrix<T,Diagonal,Storage,Row,Col> matrix2);

// general template function
template <typename T, typename Shape, typename Storage, unsigned Row, unsigned Col>
Matrix<T,Shape,Storage,Row,Col>& operator + (Matrix<T,Shape,Storage,Row,Col> matrix1, Matrix<T,Shape,Storage,Row,Col> matrix2) {
    Matrix<T,Shape,Storage,Row,Col>* result = new Matrix<T,Shape,Storage,Row,Col>();
    for (unsigned i = 0; i < matrix1.getRowSize(); i++) {           // getRowSize is a member function of policy class Storage
        for (unsigned j = 0; j < matrix1.getRowSize(); j++) {
            (*result)(i,j) = matrix1.getValue(i,j) + matrix2.getValue(i,j);
        }
    }
    return *result;
}

// overloaded template function
template <typename T, typename Shape, typename Storage, unsigned Row, unsigned Col>
Matrix<T,Diagonal,Storage,Row,Col>& operator + (Matrix<T,Diagonal,Storage,Row,Col> matrix1, Matrix<T,Diagonal,Storage,Row,Col> matrix2) {
    Matrix<T,Shape,Storage,Row,Col>* result = new Matrix<T,Shape,Storage,Row,Col>();
    for (unsigned i = 0; i < matrix1.getRowSize(); i++) {
        (*result)(i,i) = matrix1.getValue(i,i) + matrix2.getValue(i,i);
    }
    return *result;
}

// general template function
template <typename T, typename Shape, typename Storage, unsigned Row, unsigned Col>
Matrix<T,Shape,Storage,Row,Col>& operator += (Matrix<T,Shape,Storage,Row,Col> matrix1,Matrix<T,Shape,Storage,Row,Col> matrix2)  {
    Matrix<T,Shape,Storage,Row,Col>* result = new Matrix<T,Shape,Storage,Row,Col>(matrix1); // copy constructor
    for (unsigned i = 0; i < matrix1.getRowSize(); i++) {
        for (unsigned j = 0; j < matrix1.getRowSize(); j++) {
            (*result)(i,j) = matrix1.getValue(i,j) + matrix2.getValue(i,j);
        }
    }
    return *result;
}

// overloaded template function
template <typename T, typename Shape, typename Storage, unsigned Row, unsigned Col>
Matrix<T,Diagonal,Storage,Row,Col>& operator += (Matrix<T,Diagonal,Storage,Row,Col> matrix1,Matrix<T,Diagonal,Storage,Row,Col> matrix2) {
    Matrix<T,Shape,Storage,Row,Col>* result = new Matrix<T,Shape,Storage,Row,Col>(matrix1); // copy constructor
    for (unsigned i = 0; i < matrix1.getRowSize(); i++) {
        (*result)(i,i) = matrix1.getValue(i,i) + matrix2.getValue(i,i);
    }
    return *result;
}

此处使用基于策略的设计的主要优点是您的用户可以轻松提供自己的存储设施和形状操作。您需要做的就是给他们一个清晰的界面，以便他们知道如何制作自己的存储设施和形状操作。