利用OpenMP并行化傅里叶变换 用两种并行化方法实现代码

下面是使用OpenMP并行化傅里叶变换的两种方法的示例代码：

方法一：使用数据并行化

#include <iostream>
#include <cmath>
#include <complex>
#include <omp.h>

void parallel_fft(std::complex<double>* data, int size) {
    if (size <= 1) {
        return;
    }

    std::complex<double>* even = new std::complex<double>[size/2];
    std::complex<double>* odd = new std::complex<double>[size/2];

    // Divide the data into even and odd indices
    #pragma omp parallel for
    for (int i = 0; i < size/2; i++) {
        even[i] = data[2*i];
        odd[i] = data[2*i + 1];
    }

    // Perform FFT on even and odd indices recursively
    parallel_fft(even, size/2);
    parallel_fft(odd, size/2);

    // Combine the results of even and odd indices
    #pragma omp parallel for
    for (int k = 0; k < size/2; k++) {
        std::complex<double> t = std::polar(1.0, -2*M_PI*k/size) * odd[k];
        data[k] = even[k] + t;
        data[k + size/2] = even[k] - t;
    }

    delete[] even;
    delete[] odd;
}

int main() {
    const int size = 8;
    std::complex<double> data[size] = {1, 2, 3, 4, 5, 6, 7, 8};

    parallel_fft(data, size);

    for (int i = 0; i < size; i++) {
        std::cout << data[i] << " ";
    }
    std::cout << std::endl;

    return 0;
}

方法二：使用任务并行化

#include <iostream>
#include <cmath>
#include <complex>
#include <omp.h>

void parallel_fft(std::complex<double>* data, int size) {
    if (size <= 1) {
        return;
    }

    std::complex<double>* even = new std::complex<double>[size/2];
    std::complex<double>* odd = new std::complex<double>[size/2];

    // Divide the data into even and odd indices
    #pragma omp parallel sections
    {
        #pragma omp section
        {
            for (int i = 0; i < size/2; i++) {
                even[i] = data[2*i];
            }
        }

        #pragma omp section
        {
            for (int i = 0; i < size/2; i++) {
                odd[i] = data[2*i + 1];
            }
        }
    }

    // Perform FFT on even and odd indices recursively
    #pragma omp parallel sections
    {
        #pragma omp section
        {
            parallel_fft(even, size/2);
        }
        
        #pragma omp section
        {
            parallel_fft(odd, size/2);
        }
    }

    // Combine the results of even and odd indices
    #pragma omp parallel for
    for (int k = 0; k < size/2; k++) {
        std::complex<double> t = std::polar(1.0, -2*M_PI*k/size) * odd[k];
        data[k] = even[k] + t;
        data[k + size/2] = even[k] - t;
    }

    delete[] even;
    delete[] odd;
}

int main() {
    const int size = 8;
    std::complex<double> data[size] = {1, 2, 3, 4, 5, 6, 7, 8};

    parallel_fft(data, size);

    for (int i = 0; i < size; i++) {
        std::cout << data[i] << " ";
    }
    std::cout << std::endl;

    return 0;
}

这两种方法都使用递归算法来实现傅里叶变换，并通过OpenMP的并行化特性来加速计算。方法一使用数据并行化，将数据的操作分配给不同的线程并行执行。方法二使用任务并行化，将递归过程中的不同任务分配给不同的线程并行执行。两种方法的具体效果取决于实际的硬件和数据规模