c++ - 使用 MPI 环形拓扑通过比较每个处理器的局部最大值来找到函数的全局最大值

Question

我希望使用 MPI 环形拓扑，将每个处理器的最大值传递给环，比较局部最大值，然后为所有处理器输出全局最大值。 我正在使用 10 维蒙特卡洛积分函数。我的第一个想法是用每个处理器的局部最大值制作一个数组，然后传递该值，比较并输出最大值。但是我无法优雅地编写一个数组，该数组仅采用每个处理器的最大值并将其存储在对应于处理器等级的位置，这样我还可以跟踪哪个处理器获得了全局最大值。

我还没有完成我的代码，现在我有兴趣看看是否可以创建一个具有来自处理器的局部最大值的数组。我编码的方式非常耗时，如果有很多处理器，那么我每次都必须声明它们，但我无法生成我正在寻找的数组。 我在这里分享代码:

#include <iostream>
#include <fstream>
#include <iomanip>
#include <cmath>
#include <cstdlib>
#include <ctime>
#include <mpi.h>
using namespace std;


//define multivariate function F(x1, x2, ...xk)            

double f(double x[], int n)
{
    double y;
    int j;
    y = 0.0;

    for (j = 0; j < n-1; j = j+1)
      {
         y = y + exp(-pow((1-x[j]),2)-100*(pow((x[j+1] - pow(x[j],2)),2)));

      }     

    y = y;
    return y;
}

//define function for Monte Carlo Multidimensional integration

double int_mcnd(double(*fn)(double[],int),double a[], double b[], int n, int m)

{
    double r, x[n], v;
    int i, j;
    r = 0.0;
    v = 1.0;
    // initial seed value (use system time) 
    //srand(time(NULL)); 


    // step 1: calculate the common factor V
    for (j = 0; j < n; j = j+1)
      {
         v = v*(b[j]-a[j]);
      } 

    // step 2: integration
    for (i = 1; i <= m; i=i+1)
    {
        // calculate random x[] points
        for (j = 0; j < n; j = j+1)
        {
            x[j] = a[j] +  (rand()) /( (RAND_MAX/(b[j]-a[j])));
        }         
        r = r + fn(x,n);
    }
    r = r*v/m;

    return r;
}




double f(double[], int);
double int_mcnd(double(*)(double[],int), double[], double[], int, int); 



int main(int argc, char **argv)
{    

    int rank, size;

    MPI_Init (&argc, &argv);      // initializes MPI
    MPI_Comm_rank (MPI_COMM_WORLD, &rank); // get current MPI-process ID. O, 1, ...
    MPI_Comm_size (MPI_COMM_WORLD, &size); // get the total number of processes


    /* define how many integrals */
    const int n = 10;       

    double b[n] = {5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0,5.0};                    
    double a[n] = {-5.0, -5.0, -5.0, -5.0, -5.0, -5.0, -5.0, -5.0, -5.0,-5.0};  

    double result, mean;
    int m;

    const unsigned int N = 5;
    double max = -1;
    double max_store[4];

    cout.precision(6);
    cout.setf(ios::fixed | ios::showpoint); 


    srand(time(NULL) * rank);  // each MPI process gets a unique seed

    m = 4;                // initial number of intervals

    // convert command-line input to N = number of points
    //N = atoi( argv[1] );


    for (unsigned int  i=0; i <=N; i++)
    {
        result = int_mcnd(f, a, b, n, m);
        mean = result/(pow(10,10));

        if( mean > max) 
        {
         max = mean;
        }

        //cout << setw(10)  << m << setw(10) << max << setw(10) << mean << setw(10) << rank << setw(10) << size <<endl;
        m = m*4; 
    }

    //cout << setw(30)  << m << setw(30) << result << setw(30) << mean <<endl; 
    printf("Process %d of %d mean = %1.5e\n and local max = %1.5e\n", rank, size, mean, max );
    if (rank==0)
        {
         max_store[0] = max;
        }
        else if (rank==1)
        {
         max_store[1] = max;
        }
        else if (rank ==2)
        {
         max_store[2] = max;
        }
        else if (rank ==3)
        {
         max_store[3] = max;
        }
    for( int k = 0; k < 4; k++ )
    {
     printf( "%1.5e\n", max_store[k]);
    }


    //double max_store[4] = {4.43095e-02, 5.76586e-02, 3.15962e-02, 4.23079e-02}; 

    double send_junk = max_store[0];
    double rec_junk;
    MPI_Status status;


  // This next if-statment implemeents the ring topology
  // the last process ID is size-1, so the ring topology is: 0->1, 1->2, ... size-1->0
  // rank 0 starts the chain of events by passing to rank 1
  if(rank==0) {
    // only the process with rank ID = 0 will be in this block of code.
    MPI_Send(&send_junk, 1, MPI_DOUBLE, 1, 0, MPI_COMM_WORLD); //  send data to process 1
    MPI_Recv(&rec_junk, 1, MPI_DOUBLE, size-1, 0, MPI_COMM_WORLD, &status); // receive data from process size-1
  }
  else if( rank == size-1) { 
    MPI_Recv(&rec_junk, 1, MPI_DOUBLE, rank-1, 0, MPI_COMM_WORLD, &status); // recieve data from process rank-1 (it "left" neighbor")
    MPI_Send(&send_junk, 1, MPI_DOUBLE, 0, 0, MPI_COMM_WORLD); // send data to its "right neighbor", rank 0
  }
  else {
    MPI_Recv(&rec_junk, 1, MPI_DOUBLE, rank-1, 0, MPI_COMM_WORLD, &status); // recieve data from process rank-1 (it "left" neighbor")
    MPI_Send(&send_junk, 1, MPI_DOUBLE, rank+1, 0, MPI_COMM_WORLD); // send data to its "right neighbor" (rank+1)
  }
  printf("Process %d send %1.5e\n and recieved %1.5e\n", rank, send_junk, rec_junk ); 


  MPI_Finalize(); // programs should always perform a "graceful" shutdown
    return 0;
}

编译:

mpiCC -o gd test_code.cpp
 mpirun -np 4 ./gd

我很感激你的建议:

1. 是否有更优雅的方法来制作局部最大值数组？
2. 如何在环中传递值时比较局部最大值并确定全局最大值？

也可以随意修改代码，为我提供更好的示例。我将不胜感激任何建议。谢谢。

Answer 1

对于这类事情，最好使用 MPI_Reduce() 或 MPI_Allreduce() 和 MPI_MAX 作为运算符。前者将计算所有进程公开的值的最大值，并将结果仅提供给“根”进程，而后者将执行相同的操作，但将结果提供给所有进程。

// Only process of rank 0 get the global max
MPI_Reduce( &local_max, &global_max, 1, MPI_DOUBLE, MPI_MAX, 0, MPI_COMM_WORLD );
// All processes get the global max
MPI_Allreduce( &local_max, &global_max, 1, MPI_DOUBLE, MPI_MAX, MPI_COMM_WORLD );
// All processes get the global max, stored in place of the local max
// after the call ends - this might be the most interesting one for you
MPI_Allreduce( MPI_IN_PLACE, &max, 1, MPI_DOUBLE, MPI_MAX, MPI_COMM_WORLD );

如您所见，您只需将第三个示例插入到您的代码中即可解决您的问题。

顺便说一句，不相关的评论，但这伤害了我的眼睛:

if (rank==0)
    {
     max_store[0] = max;
    }
    else if (rank==1)
    {
     max_store[1] = max;
    }
    else if (rank ==2)
    {
     max_store[2] = max;
    }
    else if (rank ==3)
    {
     max_store[3] = max;
    }

像这样的事情怎么样:

if ( rank < 4 && rank >= 0 ) {
    max_store[rank] = max;
}