multiplying matrices of variable sizes - c++

Question

I have built a class that declares a m, n matrix with elements of different types.
template<typename T>
class Matrix {
public:
int m, n;
T *elements;
How would I now go about overloading an operator to multiply two matrices?
I am mostly confused about dealing with matrices that can take on a variety of sizes.
I know that I will need this line but I am not sure what to do after:
Matrix<T> operator*(Matrix<T> const &b)

Answer 1

The following code is untested, but it should give you an idea of how to do matrix multiplication.
I would suggest defining the operator* as a free function rather than a member function.
template<typename T>
class Matrix
{
public:
Matrix(int r, int c)
: rows(r)
, cols(c)
, elements.resize(rows * cols)
{ }
int rows = 0, cols = 0;
T& operator()(int i, int j) { return elements[i * ncols + j]; }
std::vector<T> elements;
};
template<typename T>
Matrix<T> operator*(Matrix<T> const& a, Matrix<T> const& b)
{
assert(a.cols == b.rows);
Matrix<T> c(a.rows, b.cols);
for (int output_row = 0; output_row < a.rows; ++output_row)
{
for (int output_col = 0; output_col < b.cols; ++output_col)
{
double sum = 0.0;
for (int i = 0; i < a.cols; ++i)
sum += a(output_row, i) * b(i, output_col);
c(output_row, output_col) = sum;
}
}
return c;
}