#ifndef MATRIX_HPP
#define MATRIX_HPP

#include <cmath>
#include <cassert>
#include <iostream>

class Matrix {
private:
  int height;
  int width;
  double* coeff;

public:
  //konstruktor, destruktor, zuweisung

  Matrix();
  Matrix(int height_new, int width_new, double init=0);
  Matrix(const Matrix&);
  ~Matrix();
  Matrix& operator=(const Matrix&);

  //size of zurueckgeben
  int rows() const;
  int columns() const;

  //lesen und schreiben von matrix eintraegen A(j, k)
  const double& operator()(int j, int k) const;
  double& operator()(int j, int k);

  //speichervektoren lesen und schreiben A[ell]
  const double& operator[](int ell) const;
  double& operator[](int ell);

  //norm berechnen
  double norm() const;
};


class SqMatrix : public Matrix {
  //keine neue elemente, nur neue methoden
public:
  SqMatrix();
  SqMatrix(int dim, double init=0);
  SqMatrix(const Matrix&); //type cast Matrix to SqMatrix

  int dimension() const;
};




//matrix-matrix summe und produkt

const Matrix operator+(const Matrix&, const Matrix&);
const Matrix operator*(const Matrix&, const Matrix&);

//print via output stream

std::ostream& operator<<(std::ostream& output, const Matrix&);



#endif