Question

I have a (basically completed) matrix class (later in this post). If the matrix is a 1×1 matrix, then I’d like to have an implicit conversion to the backing type (e.g. a 1×1 float matrix should convert to a float).

Is there a way to do that without creating a specialization and duplicating all the methods inside Matrix? (e.g. using something like std::enable_if?) I basically want to enable the implicit conversion if and only if ROWS == COLS == 1.

template <std::size_t ROWS, std::size_t COLS = 1, typename BackingType = float>
class Matrix
{
    BackingType data[ROWS][COLS];
public:
    Matrix()
    {
        for(std::size_t rdx = 0; rdx < ROWS; ++rdx)
        {
            for (std::size_t cdx = 0; cdx < COLS; ++cdx)
            {
                data[rdx][cdx] = 0;
            }
        }
    }
    const BackingType& Member(std::size_t index) const
    {
        assert(index < ROWS*COLS);
        return *(static_cast<BackingType*>(&data[0][0]) + index);
    }
    BackingType& Member(std::size_t index)
    {
        assert(index < ROWS*COLS);
        return *(static_cast<BackingType*>(&data[0][0]) + index);
    }
    const BackingType& Member(std::size_t rowIndex, std::size_t colIndex) const
    {
        assert(rowIndex < ROWS);
        assert(colIndex < COLS);
        return data[rowIndex][colIndex];
    }
    BackingType& Member(std::size_t rowIndex, std::size_t colIndex)
    {
        assert(rowIndex < ROWS);
        assert(colIndex < COLS);
        return data[rowIndex][colIndex];
    }
    Matrix<COLS, ROWS, BackingType> Transpose() const
    {
        Matrix<COLS, ROWS, BackingType> result;
        for(std::size_t rowIdx = 0; rowIdx < ROWS; rowIdx++)
        {
            for (std::size_t colIdx = 0; colIdx < COLS; ++colIdx)
            {
                result.Member(colIdx, rowIdx) = Member(rowIdx, colIdx);
            }
        }
        return result;
    }
    template <std::size_t otherRows, std::size_t otherCols>
    Matrix<ROWS + otherRows, COLS, BackingType> AugmentBelow(const Matrix<otherRows, otherCols, BackingType>& other)
    {
        static_assert(COLS == otherCols, "Columns must match for a vertical augmentation.");
        Matrix<ROWS + otherRows, COLS, BackingType> result;
        for (std::size_t curRow = 0; curRow < ROWS; ++curRow)
        {
            for (std::size_t curCol = 0; curCol < COLS; ++curCol)
            {
                result.Member(curRow, curCol) = Member(curRow, curCol);
            }
        }
        for (std::size_t curRow = ROWS; curRow < (ROWS + otherRows); ++curRow)
        {
            for (std::size_t curCol = 0; curCol < COLS; ++curCol)
            {
                result.Member(curRow, curCol) = other.Member(curRow - ROWS, curCol);
            }
        }
        return result;
    }
    template <std::size_t otherRows, std::size_t otherCols>
    Matrix<ROWS, COLS + otherCols, BackingType> AugmentRight(const Matrix<otherRows, otherCols, BackingType>& other)
    {
        static_assert(ROWS == otherRows, "Rows must match for a vertical augmentation.");
        Matrix<ROWS, COLS + otherCols, BackingType> result;
        for (std::size_t curRow = 0; curRow < ROWS; ++curRow)
        {
            for (std::size_t curCol = 0; curCol < COLS; ++curCol)
            {
                result.Member(curRow, curCol) = Member(curRow, curCol);
            }
            for (std::size_t curCol = COLS; curCol < (COLS + otherCols); ++curCol)
            {
                result.Member(curRow, curCol) = other.Member(curRow, curCol - COLS);
            }
        }
        return result;
    }
    static Matrix<ROWS, COLS, BackingType> Identity()
    {
        static_assert(ROWS == COLS, "Identity matrices are always square.");
        Matrix<ROWS, COLS, BackingType> result;
        for (std::size_t diagonal = 0; diagonal < ROWS; ++diagonal)
        {
            result.Member(diagonal, diagonal) = 1;
        }
        return result;
    }
};

template <std::size_t leftRows, std::size_t leftCols, std::size_t rightRows, std::size_t rightCols, typename BackingType>
inline Matrix<leftRows, rightCols, BackingType> operator*(const Matrix<leftRows, leftCols, BackingType>& left, const Matrix<rightRows, rightCols, BackingType>& right)
{
    static_assert(leftCols == rightRows, "Matrix multiplications require that the left column count and the right row count match.");
    Matrix<leftRows, rightCols, BackingType> result;
    for (std::size_t i = 0; i < leftRows; ++i)
    {
        for (std::size_t j = 0; j < rightCols; ++j)
        {
            BackingType curItem = 0;
            for (std::size_t k = 0; k < leftCols; ++k)
            {
                curItem += left.Member(i, k) * right.Member(k, j);
            }
            result.Member(i, j) = curItem;
        }
    }
    return result;
}

template <std::size_t rows, std::size_t cols, typename BackingType>
inline Matrix<rows, cols, BackingType> operator*(BackingType val, const Matrix<rows, cols, BackingType>& target)
{
    Matrix<rows, cols, BackingType> result = target;
    for (std::size_t i = 0; i < rows; ++i)
    {
        for (std::size_t j = 0; j < cols; ++j)
        {
            result *= val;
        }
    }
    return result;
}

Answer 1

Here’s a crude hackaround, using conditional rather than enable_if:

#include <functional>

template <typename T, int N, int M>
struct Matrix
{
  struct IncompleteType;

  T buf[N * M];
  operator typename std::conditional<N == 1 && M == 1, T, IncompleteType<T>>::type () const
  {
    return buf[0];
  }
};

With some work one could probably make the compiler error a bit more meaningful, too.