Question

我尝试使用蒙特卡洛方法评估pi值。更准确地说，使用周长法。

最初，我编写了一个代码，该代码的迭代次数是固定的。现在，我试图在输入增加时模拟代码的行为。

为此，我编写了这段代码，但是它不起作用：

#define _XOPEN_SOURCE
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <mpi.h>

#define SEED time(NULL)

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

  int rank, size;
  unsigned int seed;
  double x, y, start, end;
  long long int i, j, all_point, points = 0, all_intern;

  long long int dim[] = {5, 50, 500, 5000, 50000, 500000, 5000000, 50000000};

  MPI_Init(&argc, &argv);
  start = MPI_Wtime();

  MPI_Comm_rank(MPI_COMM_WORLD, &rank);
  MPI_Comm_size(MPI_COMM_WORLD, &size);

  seed = SEED + rank;

  for ( j = 0; j < 8; j++ ) {
    for ( i = 0; i < dim[j]; i++ ) {
      x = (double) rand_r(&seed) / RAND_MAX;
      y = (double) rand_r(&seed) / RAND_MAX;

      if ( x * x + y * y <= 1.0 ) points++;
    }

    MPI_Reduce(&points, &all_intern, 1, MPI_LONG_LONG_INT, MPI_SUM, 0, MPI_COMM_WORLD);
    all_point = dim[j] * size;

    MPI_Barrier(MPI_COMM_WORLD);
    end = MPI_Wtime();

    if ( rank == 0 ) {
      printf("\u03C0 \u2248 %Lf\n", (long double) all_intern / all_point * 4.0);
      printf("Time elapsed: %.4f\n", end - start);
    }
  }

  MPI_Finalize();
  return 0;
}

Answer 1

问题在于points的值在每次迭代之间不会重置为零，而all_point仅计算当前迭代的总点数。因此，要么重置points的值，要么正确计算all_point。由于注释中不清楚，因此您可以在下面的代码中找到两个带有注释的变体，在其中进行了修改。由于不是MPI问题，因此我删除了所有MPI内容。

变量1：重置圆中的点数计数器

#define _XOPEN_SOURCE
#include <stdio.h>
#include <stdlib.h>
#include <time.h>

#define SEED time(NULL)

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

  unsigned int seed;
  double x, y, start, end;
  long long int i, j, all_point, points = 0, all_intern;

  long long int dim[] = {5, 50, 500, 5000,50000,500000,5000000,50000000};

  seed = SEED + 1;

  for ( j = 0; j < 8; j++ ) {
    // reset points to 0 here
    points=0;
    for ( i = 0; i < dim[j]; i++ ) {
      x = (double) rand_r(&seed) / RAND_MAX;
      y = (double) rand_r(&seed) / RAND_MAX;

      if ( x * x + y * y <= 1.0 ) points++;
    }

    all_point = dim[j];

    printf("\u03C0 \u2248 %Lf\n", (long double) points / all_point * 4.0);

  }

  return 0;
}

变量2：保留以前迭代的结果，但调整点的总数

#define _XOPEN_SOURCE
#include <stdio.h>
#include <stdlib.h>
#include <time.h>

#define SEED time(NULL)

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

  unsigned int seed;
  double x, y, start, end;
  long long int i, j, all_point, points = 0, all_intern;

  long long int dim[] = {5, 50, 500, 5000,50000,500000,5000000,50000000};

  seed = SEED + 1;

  for ( j = 0; j < 8; j++ ) {
    for ( i = 0; i < dim[j]; i++ ) {
      x = (double) rand_r(&seed) / RAND_MAX;
      y = (double) rand_r(&seed) / RAND_MAX;

      if ( x * x + y * y <= 1.0 ) points++;
    }
    // Correctly count the total of points used
    // since the beginning
    all_point=0;
    for ( int k = 0; k <= j; k++ ) {
        all_point += dim[k];
    }

    printf("\u03C0 \u2248 %Lf\n", (long double) points / all_point * 4.0);

  }

  return 0;
}

在两种情况下，输出都是相似且正确的。

获取输入数组返回错误结果

1 个答案: