#include <cstddef> /* needed for std::size_t */
#include <cstdio> /* needed for printf */
#include <cassert> /* needed for assert */

enum class StorageOrder {ColMajor, RowMajor};

template<typename T>
struct Matrix {
   const std::size_t m; /* number of rows */
   const std::size_t n; /* number of columns */
   const std::size_t incRow;
   const std::size_t incCol;
   T* data;

   Matrix(std::size_t m, std::size_t n, StorageOrder order) :
	 m(m), n(n),
	 incRow(order == StorageOrder::ColMajor? 1: n),
	 incCol(order == StorageOrder::RowMajor? 1: m),
	 data(new T[m*n]) {
   }

   ~Matrix() {
      delete[] data;
   }

   const T& operator()(std::size_t i, std::size_t j) const {
      assert(i < m && j < n);
      return data[i*incRow + j*incCol];
   }
   
   T& operator()(std::size_t i, std::size_t j) {
      assert(i < m && j < n);
      return data[i*incRow + j*incCol];
   }
};

template<typename T>
struct MatrixView {
   const std::size_t m; /* number of rows */
   const std::size_t n; /* number of columns */
   const std::size_t incRow;
   const std::size_t incCol;
   T* data;

   MatrixView(std::size_t m, std::size_t n,
	    T* data,
	    std::size_t incRow, std::size_t incCol) :
	 m(m), n(n), 
	 incRow(incRow), incCol(incCol),
	 data(data) {
   }

   const T& operator()(std::size_t i, std::size_t j) const {
      assert(i < m && j < n);
      return data[i*incRow + j*incCol];
   }
   
   T& operator()(std::size_t i, std::size_t j) {
      assert(i < m && j < n);
      return data[i*incRow + j*incCol];
   }
};

template<typename T>
void init_matrix(Matrix<T>& A) {
   for (std::size_t i = 0; i < A.m; ++i) {
      for (std::size_t j = 0; j < A.n; ++j) {
	 A(i, j) = j * A.n + i + 1;
      }
   }
}

template<typename Matrix>
void print_matrix(const Matrix& A) {
   for (std::size_t i = 0; i < A.m; ++i) {
      std::printf("  ");
      for (std::size_t j = 0; j < A.n; ++j) {
	 /* be careful here, printf is not polymorph */
	 std::printf(" %4.1lf", (double) A(i, j));
      }
      std::printf("\n");
   }
}

int main() {
   Matrix<double> A(7, 8, StorageOrder::ColMajor);
   MatrixView<double> B(3, 3, &A(2, 2), A.incRow, A.incCol);

   init_matrix(A);
   B(1, 1) = 0;
   std::printf("A =\n"); print_matrix(A);
   std::printf("B =\n"); print_matrix(B);
}