The approximation error of Monte-Carlo method

Question

Mingxuan 2022-11-10

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1848218-the-approximation-error-of-monte-carlo-method

回答： Image Analyst 2022-11-10

Define the in-script function calc_pi(n) which inplements the Monte-Carlo method to approximate pi with n points generated.

the code I have is follows:

function value = calc_pi(n)
    x = rand(N,1);
    y = rand(N,1);
    r = x.^2+y.^2;
    inside = r<=1;
    outside = r>1;
end

I am not too sure if I got the function right or not for the Monte-Carlo method.

then we need to create row vector N from 1e3 to 1e6 with stepsize 1e3. and use a for loop to create a row vector err such that the i-th element of err(i) is the absolute error to approxiamte pi with N(i) points.

N = [1e3:1e3:1e6];
err = [];
for i = 1:length(N)
    err(i) = abs(calc_pi( ? ); 
end

I'm stuck on what to put after the calc_pi which is in the question mark area.

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Image Analyst 2022-11-10

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1848218-the-approximation-error-of-monte-carlo-method#answer_1096688

在 MATLAB Online 中打开

Here's some fixes. Not done but you can continue with your homework until it's done.

N = 1e3 : 1e3 : 1e6;
err = zeros(length(N), 1);
for k = 1:length(N)
    n = N(k);
    if rem(k, 50) == 0
        fprintf('On iteration %d.\n', k)
    end
    err(k) = abs(calc_pi(n)); 
end
plot(err, 'b-', 'LineWidth', 2);
xlabel('n')
ylabel('Error')
grid on;
%============================================================
function value = calc_pi(n)
x = rand(n,1);
y = rand(n,1);
r = x.^2+y.^2;
inside = sum(r <= 1);
outside = r>1;
% TO DO  assign value.
value = 20;
end