Generating random numbers

Question

Atakan 2012-1-22

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/26783-generating-random-numbers

I want to write a Matlab code for generating “m” numbers from N(0,1) using following algorithm. My code should be a general code for “m”, “mu” & “sigma”.

1.Generate u1, u2 from UNIF(0,1), then set y=tan(pi*(u1-1/2))

2.If u2 <= (sqrt(e)/2)*(1+y^2)*e^((-y^2)/2) then set x=y, otherwise go to step 1

3.Repeat 1-2 until you generate m numbers.

this is my code:

function [randnormal]=atakan(a,b,m) randnormal=[];

count=1;

while (count<=m) R = normrnd(a,b);

    u1=unifrnd(0,1);
    u2=unifrnd(0,1);
    y=tan(pi*(u1-1/2));
    if (u2<=((sqrt(exp(1))/2)*(1+y^2)*(exp(1)^(-y^2/2))))
        randnormal=[R;y];
    end
     count=count+1;
end

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Jan 2012-1-22

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Answer 1

Atakan 2012-1-24

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https://ww2.mathworks.cn/matlabcentral/answers/26783-generating-random-numbers#answer_35069

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function x = atakan(mu,sigmasqroot,m)

count=0; x=[]; y=[];

while (count<m)

    u1=rand;
    u2=rand;
    y=tan(pi*(u1-(1/2)));
    test=((sqrt(exp(1))/2)*(1+(y^2))*((exp(1)^((-y^2)/2))));
    if (u2<=test)  
        z=sqrt(sigmasqroot)*(y+mu); % if x~N(0,1) then sigma*(x+mu)~N(mu,sigma^2) then set x=y;
        x=[x; z];  
        count=count+1;
    end

end

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the cyclist 2012-1-24

Just so you know, "growing" your array x in this way is extremely inefficient, computationally, because MATLAB will need to continually reallocate memory for the ever-larger array. The method in my solution, in which I preallocate the memory before the while loop, will be stupendously faster for large values of m.

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Answer 2

the cyclist 2012-1-23

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https://ww2.mathworks.cn/matlabcentral/answers/26783-generating-random-numbers#answer_34964

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You were overwriting your random numbers, rather than storing all "m" of them, and you were not tracking the counting of successes properly. Does this work better? (I did not check any other part of your algorithm.)

function [randnormal]=atakan(a,b,m)
randnormal=zeros(2,m);
count=1;
while (count<=m)
      R = normrnd(a,b);
      u1=unifrnd(0,1);
      u2=unifrnd(0,1);
      y=tan(pi*(u1-1/2));
      if (u2<=((sqrt(exp(1))/2)*(1+y^2)*(exp(1)^(-y^2/2))))
          randnormal(:,count)=[R;y];
          count=count+1;
      end
end
end