编写梯形积分法的mpi程序实验

A：以下是梯形积分法的MPI程序实验:

#include <stdio.h>
#include <math.h>
#include "mpi.h"

double func(double x) {
   return sin(x);
}

double trap(double local_a, double local_b, int local_n, double h) {
   double integral;
   double x;
   int i;

   integral = (func(local_a) + func(local_b))/2.0;
   x = local_a;
   for (i = 1; i <= local_n-1; i++) {
      x = x + h;
      integral = integral + func(x);
   }
   integral = integral*h;

   return integral;
}

int main(int argc, char** argv) {
   int my_rank;
   int p;
   double a = 0.0;
   double b = 3.14159;
   int n = 1024;
   double h;
   double local_a;
   double local_b;
   int local_n;
   double integral;
   double total_integral;
   int source;
   int dest = 0;
   int tag = 0;
   MPI_Status status;

   MPI_Init(&argc, &argv);

   MPI_Comm_rank(MPI_COMM_WORLD, &my_rank);
   MPI_Comm_size(MPI_COMM_WORLD, &p);

   h = (b-a)/n;
   local_n = n/p;
   local_a = a + my_rank*local_n*h;
   local_b = local_a + local_n*h;
   integral = trap(local_a, local_b, local_n, h);

   if (my_rank == 0) {
      total_integral = integral;
      for (source = 1; source < p; source++) {
         MPI_Recv(&integral, 1, MPI_DOUBLE, source, tag, MPI_COMM_WORLD, &status);
         total_integral = total_integral + integral;
      }
   } else {
      MPI_Send(&integral, 1, MPI_DOUBLE, dest, tag, MPI_COMM_WORLD);
   }

   if (my_rank == 0) {
      printf("With n = %d trapezoids, our estimate\n", n);
      printf("of the integral from %f to %f = %f\n", a, b, total_integral);
   }

   MPI_Finalize();
}

该程序使用了梯形积分法来计算 $sin(x)$ 的从0到$\pi$的积分。程序中首先定义了一个函数func，用于计算被积函数的值。接下来，定义了一个 trap 函数，用于计算局部积分的值。该函数接受了局部区间的起点local_a，终点local_b，局部区间内划分的梯形数量local_n和步长h，并使用梯形积分法计算该区间的局部积分。最后，程序使用MPI_Init来初始化MPI环境，调用MPI_Comm_rank和MPI_Comm_size来获取当前进程的排名和进程总数，计算局部积分并发送/接收各进程的积分值，使用Master进程将所有进程的积分值汇总计算总积分值并输出结果，并通过MPI_Finalize结束MPI环境。