c++

如何在C++中实现矩阵类的加减乘除

小樊
89
2024-08-29 22:35:02
栏目: 编程语言

在C++中实现矩阵类的加减乘除,首先需要创建一个矩阵类(Matrix),然后为该类定义加减乘除的运算符重载函数。以下是一个简单的示例:

#include<iostream>
#include<vector>

class Matrix {
public:
    Matrix(int rows, int cols) : rows_(rows), cols_(cols), data_(rows * cols, 0) {}

    // 获取矩阵的行数
    int rows() const { return rows_; }

    // 获取矩阵的列数
    int cols() const { return cols_; }

    // 获取矩阵中指定位置的元素
    double& operator()(int row, int col) {
        return data_[row * cols_ + col];
    }

    // 获取矩阵中指定位置的元素(常量版本)
    double operator()(int row, int col) const {
        return data_[row * cols_ + col];
    }

    // 矩阵加法
    Matrix operator+(const Matrix& other) const;

    // 矩阵减法
    Matrix operator-(const Matrix& other) const;

    // 矩阵乘法
    Matrix operator*(const Matrix& other) const;

private:
    int rows_;
    int cols_;
    std::vector<double> data_;
};

// 矩阵加法
Matrix Matrix::operator+(const Matrix& other) const {
    if (rows_ != other.rows() || cols_ != other.cols()) {
        throw std::invalid_argument("Matrix dimensions do not match for addition.");
    }

    Matrix result(rows_, cols_);
    for (int i = 0; i< rows_; ++i) {
        for (int j = 0; j< cols_; ++j) {
            result(i, j) = (*this)(i, j) + other(i, j);
        }
    }
    return result;
}

// 矩阵减法
Matrix Matrix::operator-(const Matrix& other) const {
    if (rows_ != other.rows() || cols_ != other.cols()) {
        throw std::invalid_argument("Matrix dimensions do not match for subtraction.");
    }

    Matrix result(rows_, cols_);
    for (int i = 0; i< rows_; ++i) {
        for (int j = 0; j< cols_; ++j) {
            result(i, j) = (*this)(i, j) - other(i, j);
        }
    }
    return result;
}

// 矩阵乘法
Matrix Matrix::operator*(const Matrix& other) const {
    if (cols_ != other.rows()) {
        throw std::invalid_argument("Matrix dimensions do not match for multiplication.");
    }

    Matrix result(rows_, other.cols());
    for (int i = 0; i< rows_; ++i) {
        for (int j = 0; j< other.cols(); ++j) {
            for (int k = 0; k< cols_; ++k) {
                result(i, j) += (*this)(i, k) * other(k, j);
            }
        }
    }
    return result;
}

int main() {
    // 示例:创建两个矩阵并进行加减乘除运算
    Matrix A(2, 2);
    Matrix B(2, 2);

    A(0, 0) = 1; A(0, 1) = 2;
    A(1, 0) = 3; A(1, 1) = 4;

    B(0, 0) = 5; B(0, 1) = 6;
    B(1, 0) = 7; B(1, 1) = 8;

    Matrix C = A + B;
    Matrix D = A - B;
    Matrix E = A * B;

    // 输出结果
    std::cout << "A + B:\n";
    for (int i = 0; i < C.rows(); ++i) {
        for (int j = 0; j < C.cols(); ++j) {
            std::cout << C(i, j) << " ";
        }
        std::cout<< std::endl;
    }

    std::cout << "A - B:\n";
    for (int i = 0; i < D.rows(); ++i) {
        for (int j = 0; j < D.cols(); ++j) {
            std::cout << D(i, j) << " ";
        }
        std::cout<< std::endl;
    }

    std::cout << "A * B:\n";
    for (int i = 0; i < E.rows(); ++i) {
        for (int j = 0; j < E.cols(); ++j) {
            std::cout << E(i, j) << " ";
        }
        std::cout<< std::endl;
    }

    return 0;
}

这个示例中,我们创建了一个名为Matrix的矩阵类,并为其定义了加减乘除的运算符重载函数。在main函数中,我们创建了两个矩阵并进行了加减乘除运算,最后将结果输出到控制台。

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