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;
}
答案 0 :(得分:0)
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。