I tried to do Monte Carlo simulation in MATLAB, but it cannot be run! Can anyone help me?

sigma=[2 1;1 3]   %statr simulation with matlab
mu=[1,2]
N=100
counter=0

function w=mcs(x,y,z) %run the simulation
for i=1:N
    x(i)=2*randn(1,N);
    y(i)=randn(1,N);
    z(i)= sqrt(1 - x.^2 - y.^2);
    if   w == x(i)*(x(i).^2 + y(i).^2 + Z(i).^2)  %check if occur
        counter=counter+1         %find the number of occurrence 
        plot3(x(i), y(i), z(i), '.r')
    else
        plot3(x(i), y(i), z(i), '.b')
    end
end
histogram(w)
histfit(w)
PDFNormal=normpdf(x,mu,sigma)
plot(w,PDFNormal)
gm = gmdistribution(mu,sigma)
pdf(gm,x)
fsurf(@(x,y)reshape(pdf(gm,[x(:),y(:)]),size(x)),[-10 10])
disp(['The estimated value is ' num2str(Probability)])
end

Answer 1

[Walter Roberson]

You define a function but do not invoke the function.

The function does not have access to any of the variables you define before the function.

In order for the function to have access to those variables without passing them in, you would need to be using nested functions.

[sogol bandekian]

how invoke the function?

nested functions for w you mean?

[Image Analyst]

If you put the code below in my Answer into an m-file then it sets up the parameters and invokes/calls the function. Just be sure to end your function with the "end" statement if it's going to be in the same m-file as the script that calls the function.

[Walter Roberson]

Here is the code using a nested function in order to have access to the shared variables that define sigma and so on.

I do not think there is any good reason to use a nested function with shared variables for this application, but you must have had some reason to divide the functionality like that,

You need to pass in x, y, and z values to this function.

As Image Analyst pointed out, you do not assign anything to w and that is a problem; as he also pointed out, using == bit-for-bit-identical comparison is very likely to also be a problem.

Your call to pdf(gm,x) is probably an error.

Your call to fsurf() should be supplying y limits as well as x limits.

Your code never assigns anything to Probability

making one plot3() call for each point is inefficient. It would be more efficient if you were to compute all of the x y z values first, and then after the loop use logical indexing to call plot3() once to plot the matching points, and once to plot the non-matching points.

function drive_mcs(x, y, z)

    %create shared variables
    sigma =[2 1;1 3];   %statr simulation with matlab
    mu =[1,2];
    N = 100;
    counter = 0;
    
    %invoke the function
    w = mcs(x, y, z);
    
    %define nested function
    
    function w = mcs(x,y,z) %run the simulation
        fig1 = figure();
        ax1 = axes(fig1);
        
        hold(ax1, 'on');
        
        for i=1:N
            x(i) = 2*randn(1,N);
            y(i) = randn(1,N);
            z(i) = sqrt(1 - x.^2 - y.^2);
            if w == x(i)*(x(i).^2 + y(i).^2 + Z(i).^2)  %check if occur
                counter = counter + 1;         %find the number of occurrence 
                plot3(ax1, x(i), y(i), z(i), '.r')
            else
                plot3(ax1, x(i), y(i), z(i), '.b')
            end
        end
        
        fig2 = figure();
        ax2 = axes(fig2);
        
        histogram(ax2, w)
        histfit(ax2, w)
        PDFNormal = normpdf(x,mu,sigma);
        plot(ax2, w,PDFNormal)
        gm = gmdistribution(mu,sigma);
        
        %caution, this calculates the pdf and dumps the result to
        %the display. It does not plot the pdf in any way.
        pdf(gm,x)
        
        fig3 = figure();
        ax3 = axes(fig3);
        
        fsurf(ax3, @(x,y)reshape(pdf(gm,[x(:),y(:)]),size(x)),[-10 10])
        disp(['The estimated value is ' num2str(Probability)])
    end
end

[sogol bandekian]

so with all of these I was wrong with writing these codes.how can I do the monte carlo similation other than examples in matlab??

[Walter Roberson]

Let us start with your w : your current code asks to output it, so logically it must not be a constant, but you have not given any formula for it.

My guess for the last thing I mentioned is

Probability = count ./ N;

Answer 2

[Image Analyst]

Try this:

sigma = [2 1; 1 3]   %statr simulation with matlab
mu = [1, 2]
N = 100
w = mcs(N, mu) % Run the simulation

function w = mcs(N, mu) %run the simulation
% CODE
end

In the function, this will never work

if   w == x(i)*(x(i).^2 + y(i).^2 + Z(i).^2)  %check if occur

for two reasons. One, you have not yet defined w, and two, you're going a floating point comparison trying for an exact match. See the FAQ and use a tolerance instead

https://matlab.fandom.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F

Finally, nowhere in the code do you compute (the badly-named) w. What the heck is it? You need a line of code that starts

    w =  something!!!

so that w will have a value. Otherwise there is nothing that the function can return.