Question on virtual operator* on C++

I was trying to make virtual operator on C++

class Data
{
    virtual Matrix operator* (Matrix &_matrix);
    virtual Scalar operator* (Scalar &_scalar);
};

class Matrix : public Data
{
private:
    vector<vector<double>> data;
public:
    // ...
    Matrix operator* (Matrix &_matrix);
};

class Scalar : public Data
{
private:
    double data;
public:
    // ...
    Scalar operator* (Scalar &_scalar);
};

And the problem was, when I created Data* Array like below

Data* arr[10];
arr[0] = new Matrix(3,3);
arr[1] = new Matrix(3,3);

arr[0]->operator*(arr[1]);

I could not do multiplication between these 开发者_运维技巧two matrices, since I cannot pass Data as an argument. But the problem is, I cannot make the function's argument to take Data* type because, it will not be able to access private members of Matrix or Scalar objects.

How to deal with this kind of weird situation?

Class double dispatch problem - See Meyer's (forget which one). You need the operator to be virtual on both the lhs and rhs, so you need two virtual calls:

class Matrix;
class Scalar;

class Data
{
public:
    virtual Data* operator* (Data& data) = 0;
    virtual Data* operator* (Matrix &matrix) = 0;
    virtual Data* operator* (Scalar &scalar) = 0;
};

class Matrix : public Data
{
private:
    std::vector<std::vector<double>> data;

    // ...
public:
    Matrix* operator* (Matrix &_matrix)
    {
        // implement
    }
    Matrix* operator* (Scalar& scalar)
    {
        // implement
    }
    Data* operator* (Data &data)
    {
        // Magic here - *this is now Matrix, not Data
        return data * (*this);
    }
};

class Scalar : public Data
{
private:
    double data;
public:
    // ...
    Data* operator* (Data& data)
    {
        // Magic here - *this is now Scalar, not Data
        return data * (*this);
    }
    Scalar* operator* (Scalar &scalar)
    {
        // implement
    }

    Matrix* operator* (Matrix &matrix)
    {
        // Note how we need to allow for parameter reveral during the double dispatch
        Matrix& lhs = matrix;
        Matrix& rhs = *this;
        // Compute matrix product lhs * rhs
    }

};

I've glossed over the issue of the return type and memory management. As usual with operators, you might be better defining *= as the primitive. This can then return a reference to *this. The * operator can then defined in terms of *=. Once again, this is in "Effective C++".

The solution to this is called Double Dispatch which is a little strange in C++. The following code shows how this trick works:

#include <iostream>
#include <stdexcept>
#include <vector>


class Matrix;
class Scalar;

class Data {
public:
    virtual ~Data() {}
    virtual Data const& operator* (Data const& other) const = 0;
    virtual Data const& multiplyBy (Data const& other) const {
        throw std::runtime_error("bad function call");
    }
    virtual Data const& multiplyBy (Matrix const& other) const = 0;
    virtual Data const& multiplyBy (Scalar const& other) const = 0;
};

class Matrix : public Data {
private:
    std::vector< std::vector<double> > data;
public:
    virtual Data const& operator* (Data const& other) const {
        return other.multiplyBy(*this);
    }
    virtual Data const& multiplyBy (Matrix const& other) const {
        std::cout << "Matrix * Matrix" << std::endl;
        return *this;
    }
    virtual Data const& multiplyBy (Scalar const& other) const {
        std::cout << "Matrix * Scalar" << std::endl;
        return *this;
    }
};

class Scalar : public Data {
private:
    double data;
public:
    virtual Data const& operator* (Data const& other) const {
        return other.multiplyBy(*this);
    }
    virtual Data const& multiplyBy (Matrix const& other) const {
        std::cout << "Scalar * Matrix" << std::endl;
        return *this;
    }
    virtual Data const& multiplyBy (Scalar const& other) const {
        std::cout << "Scalar * Scalar" << std::endl;
        return *this;
    }
};

int
main() {
    Matrix m;
    Scalar s;
    Data* ary[] = { &m, &s };
    m * s;
    s * m;
    *(ary[0]) * *(ary[1]);
    *(ary[1]) * *(ary[0]);
    return 0;
}