for

计算圆周率

1. 使用无穷级数展开式

   y = 0;
   g = -1;
   n = input('n = ?  ');
   for i = 1 : n
    g = -g;
    y = y + g/(2*i-1);
   end
   pai = 4*y

   用向量表示更直观，符合MATLAB的特点

   n = input('n = ?  ');
   x = 1 : 2 : (2 * n - 1);
   y = (-1).^(2 : n+1)./ x;
   pai = sum(y) * 4

2. 使用定积分求

a = 0;
b = 1;
n = input('n=?  ');
h = (b - a) / n;
x = a : h : b;
f = sqrt(1-x.*x);
s = [];
for k = 1 : n
    s1 = (f(k) + f(k+1))*h /2;
    s = [s, s1];
end
pai = 4 * sum(s)

1. 蒙特卡洛法

   s = 0;
   n = input('n = ');
   for i = 1 : n
    x = rand(1);
    y = rand(1);
    if x * x + y * y <= 1
        s = s + 1;
    end
   end
   pai = s / n * 4

   for更一般的格式

while

while语句