MATLAB学习笔记：随机模拟法计算数值积分

>> x=unifrnd(-2*pi,2*pi,10000,1);
>> f=(1-x.^2).*sin(5*x);
>> fmax=max(f)

fmax =

  34.711289618412117

随机模拟法求定积分：

数值积分：

>> f=inline('exp(x.^2+1)','x');
>> quad(f,0,1)

ans =

   3.975899680849105

随机模拟法：

xi=unifrnd(0,1,50000,1);
yi=9*rand(50000,1);
y=exp(xi.^2+1);
k=0;
for i=1:50000
    if yi(i)<=y(i)
        k=k+1;
    end
end
S=k/50000*9

S =

   3.985200000000000

数值积分：

>> f=@(x,y) exp(sqrt(1+x.^2+y.^2));
>> quad2d(f,0,1,1,4)

ans = 64.637437598359753

随机模拟法：

x=unifrnd(0,1,1000000,1);
y=unifrnd(1,4,1000000,1);
zi=unifrnd(0,70,1000000,1);
z=exp(sqrt(1+x.^2+y.^2));
k=0;
for i=1:1000000
    if zi(i)<=z(i)
        k=k+1;
    end
end
P=k/1000000*210

P =

  64.739639999999994