如何创建C++矩阵运算程序 二维数组与基本矩阵操作

#include <iostream>
#include <vector>
#include <stdexcept> // 用于异常处理

// 打印矩阵
void printMatrix(const std::vector<std::vector<int>>& matrix) {
    if (matrix.empty()) {
        std::cout << "空矩阵" << std::endl;
        return;
    }
    for (const auto& row : matrix) {
        for (int val : row) {
            std::cout << val << "\t";
        }
        std::cout << std::endl;
    }
}

// 矩阵加法
std::vector<std::vector<int>> addMatrices(
    const std::vector<std::vector<int>>& A,
    const std::vector<std::vector<int>>& B) {

    if (A.empty() || B.empty() || A.size() != B.size() || A[0].size() != B[0].size()) {
        throw std::invalid_argument("矩阵尺寸不匹配，无法执行加法。");
    }

    int rows = A.size();
    int cols = A[0].size();
    std::vector<std::vector<int>> result(rows, std::vector<int>(cols));

    for (int i = 0; i < rows; ++i) {
        for (int j = 0; j < cols; ++j) {
            result[i][j] = A[i][j] + B[i][j];
        }
    }
    return result;
}

// 矩阵减法
std::vector<std::vector<int>> subtractMatrices(
    const std::vector<std::vector<int>>& A,
    const std::vector<std::vector<int>>& B) {

    if (A.empty() || B.empty() || A.size() != B.size() || A[0].size() != B[0].size()) {
        throw std::invalid_argument("矩阵尺寸不匹配，无法执行减法。");
    }

    int rows = A.size();
    int cols = A[0].size();
    std::vector<std::vector<int>> result(rows, std::vector<int>(cols));

    for (int i = 0; i < rows; ++i) {
        for (int j = 0; j < cols; ++j) {
            result[i][j] = A[i][j] - B[i][j];
        }
    }
    return result;
}

// 矩阵乘法
std::vector<std::vector<int>> multiplyMatrices(
    const std::vector<std::vector<int>>& A,
    const std::vector<std::vector<int>>& B) {

    if (A.empty() || B.empty() || A[0].empty() || B[0].empty()) {
        throw std::invalid_argument("矩阵不能为空。");
    }
    if (A[0].size() != B.size()) {
        throw std::invalid_argument("矩阵A的列数必须等于矩阵B的行数，无法执行乘法。");
    }

    int rowsA = A.size();
    int colsA = A[0].size(); // 也是B的行数
    int colsB = B[0].size();

    std::vector<std::vector<int>> result(rowsA, std::vector<int>(colsB, 0));

    for (int i = 0; i < rowsA; ++i) {
        for (int j = 0; j < colsB; ++j) {
            for (int k = 0; k < colsA; ++k) { // colsA 也可以是 rowsB
                result[i][j] += A[i][k] * B[k][j];
            }
        }
    }
    return result;
}

// 矩阵转置
std::vector<std::vector<int>> transposeMatrix(
    const std::vector<std::vector<int>>& matrix) {

    if (matrix.empty()) {
        return {}; // 空矩阵转置后还是空矩阵
    }

    int rows = matrix.size();
    int cols = matrix[0].size();
    std::vector<std::vector<int>> result(cols, std::vector<int>(rows));

    for (int i = 0; i < rows; ++i) {
        for (int j = 0; j < cols; ++j) {
            result[j][i] = matrix[i][j];
        }
    }
    return result;
}

// 示例用法
int main() {
    std::vector<std::vector<int>> matrixA = {
        {1, 2, 3},
        {4, 5, 6}
    };

    std::vector<std::vector<int>> matrixB = {
        {7, 8, 9},
        {10, 11, 12}
    };

    std::vector<std::vector<int>> matrixC = {
        {1, 2},
        {3, 4},
        {5, 6}
    };

    std::cout << "Matrix A:" << std::endl;
    printMatrix(matrixA);
    std::cout << "\nMatrix B:" << std::endl;
    printMatrix(matrixB);
    std::cout << "\nMatrix C (for multiplication):" << std::endl;
    printMatrix(matrixC);

    try {
        std::cout << "\nMatrix A + B:" << std::endl;
        printMatrix(addMatrices(matrixA, matrixB));

        std::cout << "\nMatrix A - B:" << std::endl;
        printMatrix(subtractMatrices(matrixA, matrixB));

        std::cout << "\nMatrix A * C:" << std::endl;
        printMatrix(multiplyMatrices(matrixA, matrixC));

        std::cout << "\nTranspose of Matrix A:" << std::endl;
        printMatrix(transposeMatrix(matrixA));

    } catch (const std::invalid_argument& e) {
        std::cerr << "错误: " << e.what() << std::endl;
    }

    // 尝试一个错误的乘法
    try {
        std::cout << "\n尝试 Matrix A * B (错误尺寸):" << std::endl;
        printMatrix(multiplyMatrices(matrixA, matrixB));
    } catch (const std::invalid_argument& e) {
        std::cerr << "错误: " << e.what() << std::endl;
    }

    return 0;
}