使用Jacobi迭代，多线程并行计算二维卷积C++代码，不使用OpenMP和MPI

以下是使用Jacobi迭代，多线程并行计算二维卷积的C++代码，不使用OpenMP和MPI：

#include <iostream>
#include <thread>
#include <vector>

using namespace std;

const int N = 1000; // 矩阵大小
const int K = 3; // 卷积核大小
const int P = (K - 1) / 2; // 边界填充大小
const int num_threads = 4; // 线程数

// 边界填充
void padding(float in[N][N], float pad[N + 2 * P][N + 2 * P]) {
    for (int i = 0; i < N + 2 * P; ++i) {
        for (int j = 0; j < N + 2 * P; ++j) {
            if (i < P || i >= N + P || j < P || j >= N + P) {
                pad[i][j] = 0;
            } else {
                pad[i][j] = in[i - P][j - P];
            }
        }
    }
}

// 卷积核计算
void conv(float pad[N + 2 * P][N + 2 * P], float out[N][N], int i, int j) {
    float sum = 0;
    for (int u = -P; u <= P; ++u) {
        for (int v = -P; v <= P; ++v) {
            sum += pad[i + P + u][j + P + v];
        }
    }
    out[i][j] = sum / (K * K);
}

// Jacobi迭代
void jacobi(float in[N][N], float out[N][N], int start, int end) {
    float pad[N + 2 * P][N + 2 * P];
    padding(in, pad);
    for (int i = start; i < end; ++i) {
        for (int j = 0; j < N; ++j) {
            conv(pad, out, i, j);
        }
    }
}

int main() {
    float in[N][N], out[N][N];
    // 初始化输入矩阵
    for (int i = 0; i < N; ++i) {
        for (int j = 0; j < N; ++j) {
            in[i][j] = i * j;
        }
    }

    vector<thread> threads;
    int block_size = N / num_threads;
    // 创建线程
    for (int t = 0; t < num_threads; ++t) {
        int start = t * block_size;
        int end = (t + 1) * block_size;
        if (t == num_threads - 1) {
            end = N;
        }
        threads.emplace_back(jacobi, in, out, start, end);
    }
    // 等待线程结束
    for (auto &t : threads) {
        t.join();
    }

    // 输出结果矩阵
    for (int i = 0; i < N; ++i) {
        for (int j = 0; j < N; ++j) {
            cout << out[i][j] << " ";
        }
        cout << endl;
    }

    return 0;
}