c++利用类重载矩阵加减乘除

好的，我可以通过类重载运算符来实现矩阵的加减乘除。下面是一个简单的示例代码：

#include <iostream>
using namespace std;

class Matrix {
private:
    int rows;
    int cols;
    double* data;

public:
    Matrix(int m, int n) : rows(m), cols(n), data(new double[m*n]) {}
    Matrix(const Matrix& mat) : rows(mat.rows), cols(mat.cols), data(new double[mat.rows * mat.cols]) {
        for (int i = 0; i < rows * cols; i++) {
            data[i] = mat.data[i];
        }
    }
    ~Matrix() { delete[] data; }

    double& operator()(int i, int j) {
        return data[i*cols + j];
    }

    const double& operator()(int i, int j) const {
        return data[i*cols + j];
    }

    Matrix& operator=(const Matrix& mat) {
        if (this != &mat) {
            delete[] data;
            rows = mat.rows;
            cols = mat.cols;
            data = new double[rows * cols];
            for (int i = 0; i < rows * cols; i++) {
                data[i] = mat.data[i];
            }
        }
        return *this;
    }

    Matrix operator+(const Matrix& mat) const {
        Matrix result(rows, cols);
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                result(i, j) = (*this)(i, j) + mat(i, j);
            }
        }
        return result;
    }

    Matrix operator-(const Matrix& mat) const {
        Matrix result(rows, cols);
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                result(i, j) = (*this)(i, j) - mat(i, j);
            }
        }
        return result;
    }

    Matrix operator*(const Matrix& mat) const {
        if (cols != mat.rows) {
            throw runtime_error("Matrix dimensions do not match for multiplication.");
        }
        Matrix result(rows, mat.cols);
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < mat.cols; j++) {
                double sum = 0;
                for (int k = 0; k < cols; k++) {
                    sum += (*this)(i, k) * mat(k, j);
                }
                result(i, j) = sum;
            }
        }
        return result;
    }

    Matrix operator/(const Matrix& mat) const {
        if (mat.rows != mat.cols || rows != cols || mat.rows != rows) {
            throw runtime_error("Matrix dimensions do not match for division.");
        }

        Matrix result(rows, cols);
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                result(i, j) = (*this)(i, j) / mat(i, j);
            }
        }
        return result;
    }

    friend ostream& operator<<(ostream& os, const Matrix& mat) {
        for (int i = 0; i < mat.rows; i++) {
            for (int j = 0; j < mat.cols; j++) {
                os << mat(i, j) << " ";
            }
            os << endl;
        }
        return os;
    }
};

int main() {
    Matrix A(2, 3);
    A(0, 0) = 1;
    A(0, 1) = 2;
    A(0, 2) = 3;
    A(1, 0) = 4;
    A(1, 1) = 5;
    A(1, 2) = 6;
    cout << "Matrix A:" << endl;
    cout << A << endl;

    Matrix B(3, 2);
    B(0, 0) = 1;
    B(0, 1) = 4;
    B(1, 0) = 2;
    B(1, 1) = 5;
    B(2, 0) = 3;
    B(2, 1) = 6;
    cout << "Matrix B:" << endl;
    cout << B << endl;

    Matrix C = A + B;
    cout << "A + B:" << endl;
    cout << C << endl;

    Matrix D = A - B;
    cout << "A - B:" << endl;
    cout << D << endl;

    Matrix E = A * B;
    cout << "A * B:" << endl;
    cout << E << endl;

    Matrix F(2, 3);
    F(0, 0) = 2;
    F(0, 1) = 4;
    F(0, 2) = 6;
    F(1, 0) = 8;
    F(1, 1) = 10;
    F(1, 2) = 12;
    cout << "Matrix F:" << endl;
    cout << F << endl;

    Matrix G = A / F;
    cout << "A / F:" << endl;
    cout << G << endl;

    return 0;
}

在这个示例中，我们定义了一个 `Matrix` 类，并重载了 `operator+`、`operator-`、`operator*` 和 `operator/` 运算符。这些运算符可以用来执行矩阵加减乘除运算。我们还重载了括号运算符 `()`，以方便访问矩阵元素。

在 `main` 函数中，我们创建了两个矩阵 `A` 和 `B`，并演示了如何使用重载运算符来执行矩阵加减乘除运算。