c - C中如何用for循环计算中点法则黎曼和

Question

对于一项作业，我应该创建一个函数，使用四分之一圆的中点规则黎曼和来计算 PI。我无法获得正确的输出，因为我认为我的逻辑有问题。这是我的函数代码:

#include <math.h>

double circle_pi(int rectangles)
{
  int radius = 2;
  int i;
  int width = (double)radius / (double)rectangles;
  double rect_area = 0;

  for(i = 1; i<= rectangles; i++)
  {

    int midpoint = (double)width / 2;

    int height = sqrt((radius * radius) - (midpoint * midpoint));

    midpoint = midpoint + width;

    rect_area = (double)width * (double)height;

   }

  return rect_area;
}

这是主要功能:


#include <stdio.h> /* scanf, printf */

double circle_pi(int rectangles);  /* Calculates PI using a quarter circle */
double leibniz_pi(int iterations); /* Calculates PI using a series         */

int main(void)
{
  int i; /* loop counter */

    /* Print out table header */
  printf("Approximations for pi\n");
  printf("Iterations      Circle Method   Leibniz Method\n");
  printf("----------------------------------------------\n");

    /* Print out values for each set of numbers */
  for (i = 1; i <= 1000000; i *= 10)
  {
      /* Calculate PI with both methods */
    double pi_circle = circle_pi(i);
    double pi_leibniz = leibniz_pi(i);

      /* Print the results of the calculations */
    printf("%10i%20.12f%16.12f\n", i, pi_circle, pi_leibniz);
  }

  return 0; /* Return success to the OS */
}

这是预期的输出:

Approximations for pi
Iterations      Circle Method   Leibniz Method
----------------------------------------------
     1      3.464101615138  4.000000000000
    10      3.152411433262  3.041839618929
   100      3.141936857900  3.131592903559
  1000      3.141603544913  3.140592653840
 10000      3.141592998025  3.141492653590
100000      3.141592664482  3.141582653590
1000000      3.141592653934  3.141591653590

她是我从我的代码中得到的输出:

Approximations for pi
Iterations      Circle Method   Leibniz Method
----------------------------------------------
     1      2.000000000000  
    10      0.000000000000 
   100      0.000000000000
  1000      0.000000000000
 10000      0.000000000000
100000      0.000000000000
1000000      0.000000000000

(我还没有处理其他功能，这就是为什么它是空白的)

如果问题很明显，我真的很抱歉，但我是 C 的新手，很难适应它。任何帮助将不胜感激。谢谢。

Answer 1

正如 Iguananaut 已经提到的:您应该为 circle_pi 中的所有变量使用 double 数据类型，循环的迭代器除外。你真正的错误是你忘了最后总结一下

double circle_pi(int rectangles)
{
  double radius = 2.0;
  int i;
  double width = radius / (double)rectangles;
  double rect_area = 0.0;
  double midpoint, height;
  // set startvalue of mipoint
  midpoint = width / 2.0;

  for(i = 1; i <= rectangles; i++)
  {
    height = sqrt((radius * radius) - (midpoint * midpoint));
    midpoint = midpoint + width;
    rect_area = rect_area + width * height;
   }
  return rect_area;
}

这会产生预期的输出:

Approximations for pi
Iterations      Circle Method   Leibniz Method
----------------------------------------------
         1      3.464101615138
        10      3.152411433262
       100      3.141936857900
      1000      3.141603544913
     10000      3.141592998025
    100000      3.141592664486
   1000000      3.141592653923