C++ template matrix class - square matrix specialisation - c++

Question

I'm creating a simple C++ matrix template class, with the following definition:
template<uint n, uint m, typename T = double>
class Matrix {
private:
T data[n][m];
static Matrix<n, m, T> I;
public:
Matrix();
Matrix(std::initializer_list<T> l);
T& at(uint i, uint j); // one-based index
T& at_(uint i, uint j); // zero-based index
template<uint k> Matrix<n, k, T> operator*(Matrix<m, k, T>& rhs);
Matrix<m, n, T> transpose();
Matrix<n, m, T> operator+(const Matrix<n, m, T>& rhs);
Matrix<n, m, T>& operator+=(const Matrix<n, m, T>& rhs);
Matrix<n, m, T> operator-(const Matrix<n, m, T>& rhs);
Matrix<n, m, T>& operator-=(const Matrix<n, m, T>& rhs);
Matrix<n, m, T> operator*(const T& rhs);
Matrix<n, m, T>& operator*=(const T& rhs);
Matrix<n, m, T> operator/(const T& rhs);
Matrix<n, m, T>& operator/=(const T& rhs);
static Matrix<n, m, T> identity();
};
(uint is defined as an unsigned int)
The final function Matrix<n, m, T> identity() aims to return the static I member which is the identity matrix using a basic singleton pattern. Obviously the identity matrix is only defined for square matrices so I tried this:
template<uint n, typename T>
inline Matrix<n, n, T> Matrix<n, n, T>::identity() {
if (!I) {
I = Matrix<n, n, T>();
for (uint i = 0; i < n; ++i) {
I.at(i, i) = 1;
}
}
return I;
}
Which gives the error C2244 'Matrix<n,n,T>::identity': unable to match function definition to an existing declaration.
My impression was that I could do some sort of specialisation of the template where the number of columns and rows are equal. I'm not sure if this is even possible, but your help would be much appreciated.

Answer 1

Try this:
static Matrix<n, m> identity() {
static_assert(n == m, "Only square matrices have a identity");
return {}; //TODO
}
See: http://cpp.sh/7te2z

Answer 2

Partial specialization of a template class is allowed for the entire class, but not for its single member.
Members of partial specializations are not related to the members of the primary
template.
That is the reason behind your compilation error.
Of course, specializing the entire Matrix template for the square matrix case doesn't make sense. #tkausl has already answered how to make the identity() function available only for the square matrix types.
However, I would like to draw your attention toward a couple of issues in your implementation of Matrix:
The matrix data is a plain array (instead of a dynamically allocated array or std::vector). This has the following disadvantages:
sizeof(Matrix<N, M, T>) == sizeof(T)*N*M. Allocating large matrices on the stack may result in stack overflow.
Impossibility of taking advantage of move semantics (as the data is inseparable from the matrix object).
Though, if the matrix dimensions are fixed at compile time constants, then, most probably, they will be small numbers. If so, paying the cost of dynamic allocation may indeed be unjustified.
identity() returns its result by value (rather than by constant reference).
I (the identity matrix) is a static member of the class. It is better to make it a static variable inside the identity() function.