Questions about how to plot a summation function with two variables

Hello, I am trying to plot a summation function with two variables (x and y) shown in the figure. My code is:

[x,y] = meshgrid(1:1:40,1:1:5);
z=fun(x,y);
surf(x,y,z);
function [z] = fun(x,y)
z=0;
for i=1:x
z=z+(0.5.^((i-1)./x)-0.5.^(i./x)).*(1-(exp(y)-1)./(exp(y).*0.5.^(i./x)-0.5.^((i-1)./x)));
end
end

But the results are only valid for i=1, not for i=1:x. I can not find the errors, so I need help from all of you. Thanks in advance.

Answer 1

[James Tursa]

From the formula image, it appears you need fun( ) to create a matrix z where each element corresponds to the formula for a particular x and y pair. E.g., since you are passing in matrices

function z = fun(X,Y)
z = zeros(size(X));
for x = X
    for y = Y
        % insert your for-loop here to update z(x,y)
    end
end

[the cyclist]

I was just typing up something similar, so I'll just append this thought here.

@Yao Zhao, if you look at your function, you have x, which is a 5x40 matrix. You write a for loop that

for i = 1:x
    
end

but what does that mean? What does it mean for i to vary from [1] to [5x40 matrix]?

James and I are making the same point: You need to deal with the matrix nature of x and y.

[Yao Zhao]

Hi, James and cyclist, thanks for your replies. I realize the error has something to do with the x in "i=1:x". I misunderstood x was a scalar and wanted i to increase from 1 to x. This is to say, I wish to have the summation of values from i=1 to i=x. Here, x is a variable and changes from 1 to 40. This question is a little complicated for me. I tried James's method, but it still not work.

[James Tursa]

What have you tried? Basically all you needed to do was use the code I posted and insert your for-loop using z(x,y) instead of z.

[Yao Zhao]

[X,Y] = meshgrid(1:1:40,1:1:5);

z=fun(X,Y);

surf(X,Y,z);

function z = fun(X,Y)

z = zeros(size(X));

for x=X

for y=Y

for i=1:x

z(x,y)=z+(0.5.^((i-1)./x)-0.5.^(i./x)).*(1-(exp(y)-1)./(exp(y).*0.5.^(i./x)-0.5.^((i-1)./x)));

end

end

end

end

I tried this one. It says "Unable to perform assignment because the size of the left side is 5-by-5 and the size of the right side is 5-by-40."

[James Tursa]

Sorry. I forgot how for-loops act on matrices used for indexing (they do it by entire columns at once). Try this instead:

for m = 1:size(z,1)
    for n = 1:size(z,2)
        x = X(m,n);
        y = Y(m,n);
        for i=1:x
            z(m,n) = z(m,n) + etc.

[Yao Zhao]

Thank you very much, James. This problem is solved!