当运算符与操作数不匹配时，如何通过重载 * 运算符来将矩阵相乘？

Question

我有两个矩阵应该通过在构造函数类中重载 * 运算符来相乘，但这里的问题是没有 operator [] 匹配这些操作数。为什么？

我看了视频，问了我的同学多次，尝试了我自己的方法，但我无法做到。我只得到这个错误！

这是我遇到问题的代码：

构造函数代码：

我做了两种方法来使这段代码工作。结果应存储在单元矩阵或新矩阵中：

Matrix operator*(const Matrix &matrix1, const Matrix &matrix2)
  {
    if (matrix1.Cols != matrix2.Rows) {
        throw("Error");
    }
    cell.resize(matrix2.Cols); // one way to call 
    Matrix res(matrix1.Rows, matrix2.Cols, 1.0); // second way to call
    for (int i = 0; i < matrix1.Rows; i++) {
        cell[i].resize(matrix1.Rows);
        for (int j = 0; j < matrix2.Cols; j++) {
            double value_of_elements;
            for (int k = 0; k = matrix1.Cols; k++) {
                res[i][j] += matrix1[i][k] * matrix2[i][j];// 
   1. metod
                value_of_elements += matrix1[i][k] * 
    matrix2[i][j];// 2. metod
            }
            cell[i][j]+=value_of_elements;
        }
    }
    return res;
   }

标头代码：

除非需要进行一些修改，否则我通常没有标头代码。

friend Matrix operator*(const Matrix &matrix1, const Matrix &matrix2);

源代码：

这是测试代码的地方：

try {

        Matrix m1(3, 3, 1.0);
        Matrix m2(3, 4, 1.0);

        std::cout << "m1*m2:" << m1 * m2 << std::endl;// this si where the matrix should be multiplied here;

    }
    catch (std::exception &e) {
        std::cout << "Exception: " << e.what() << "!" << std::endl;
    }
    catch (...) {
        std::cout << "Unknown exception caught!" << std::endl;
    }
   system("pause");
   return 0;
}

结果：

结果应该是这样的：

m1*m2:[3, 3, 3, 3
3, 3, 3, 3
3, 3, 3, 3]

我得到的是一个错误；错误的原因是res[i][j]、matrix1[i][k] 等有操作符 [] 不能在这些操作数上工作：

Error   C2065   'cell': undeclared identifier 71  matrix.cpp
Error   C2065   'cell': undeclared identifier 74  matrix.cpp
Error   C2065   'cell': undeclared identifier 81  matrix.cpp
Error   C2088   '[': illegal for class 79   matrix.cpp 
Error   C2088   '[': illegal for class 78   matrix.cpp  
Error   C2676   binary '[': 'Matrix' does not define this operator or a conversion to a type acceptable to the predefined operator  78  matrix.cpp
Error   C2676   binary '[': 'const Matrix' does not define this operator or a conversion to a type acceptable to the predefined operator    78  matrix.cpp
Error   C2676   binary '[': 'const Matrix' does not define this operator or a conversion to a type acceptable to the predefined operator    79  matrix.cpp
Error (active)  E0020   identifier "cell" is undefined  71  Matrix.cpp
Error (active)  E0349   no operator "[]" matches these operands 78  Matrix.cpp
Error (active)  E0349   no operator "[]" matches these operands 78  Matrix.cpp
Error (active)  E0349   no operator "[]" matches these operands 78  Matrix.cpp
Error (active)  E0349   no operator "[]" matches these operands 79  Matrix.cpp
Error (active)  E0349   no operator "[]" matches these operands 79  Matrix.cpp  

Answer 1

假设类矩阵有一个成员vector<vector<double>> cell，这里是一个矩阵相乘的例子：

Matrix operator*(const Matrix &matrix1, const Matrix &matrix2)
  {
    if (matrix1.Cols != matrix2.Rows) {
        throw("Error");
    }
    Matrix res(matrix1.Rows, matrix2.Cols, 1.0);
    for (int i = 0; i < matrix1.Rows; i++) {
        for (int j = 0; j < matrix2.Cols; j++) {
            double value_of_elements=0;
            for (int k = 0; k = matrix1.Cols; k++)
                value_of_elements += matrix1.cell[i][k] * matrix2.cell[k][j];
            res.cell[i][j]=value_of_elements;
        }
    }
    return res;
}

有三个问题。首先Matrix 类没有运算符[]。通过直接访问成员cell 解决了该问题。其次，变量value_of_elements 未初始化，导致结果未定义。第三，矩阵乘法没有正确完成。您将来自matrix1 的一列与来自matrix2 的一列相乘，而您应该将一行乘以一列。

Answer 2

在这里得到我的答案：

Matrix operator*(const Matrix &matrix1, const Matrix &matrix2)
{
    if (matrix1.Cols != matrix2.Rows) {
        throw("Error");
    }
    Matrix res(matrix1.Rows, matrix2.Cols, 0.0);
    for (int i = 0; i < matrix1.Rows; i++) {
        for (int j = 0; j < matrix2.Cols; j++) {
            double value_of_elements;
            for (int k = 0; k < matrix1.Cols; k++) {
                res.cell[i][j] += matrix1.cell[i][k] * matrix2.cell[i][j];
            }
        }
    }
    return res;
}