Plotting Summation Function in matlab

Hi There,

I am trying to plot my function to see the expected behavior but I am running into trouble. It says the arrays dont match but I cant figure out why. Could someone please help me with this? I think my approach is right but I could be making it more complicated than it needs to be

%% Graphing mathematical model %%

clear all 


t = 0:1000;



plot(t,f(t),'--')
hold off
grid

title('Release')
legend('Theoretical')
xlabel('Time (sec)') 
ylabel('Concentration (mg/mL)') 


function Cal = f(t)
n = 0:250; % Number of summations
Cao = 22.4; 
L = 0.01; 
Vp = 1*1*2*L; 
Dab = .000000468;
Vl = 40; 

%Belows is the concentration profile 
sum_parts = ((3.*(2.*n+1).*pi.*sin(((2.*n+1).*pi)./2))./(((2.*n+1).*pi)+sin((2.*n+1).*pi))) .* exp(-(((2.*n+1).^2).*(pi.^2).*Dab.*t)/(4.*(L.^2))) .* (sin(((2.*n+1).*pi))./((2.*n+1).*pi)); %Summation
Cal = ((Cao.*Vp)./Vl).*(1-(2./L).*sum(sum_parts,2)); %Final Function
end

Any help is greatly appreciated!!!

-Daniel

Answer 1

[Walter Roberson]

t = 0:1000;

t is a row vector

n = 0:250; % Number of summations

n is a row vector that is a different size than t.

sum_parts = ((3.*(2.*n+1).*pi.*sin(((2.*n+1).*pi)./2))./(((2.*n+1).*pi)+sin((2.*n+1).*pi))) .* exp(-(((2.*n+1).^2).*(pi.^2).*Dab.*t)/(4.*(L.^2))) .* (sin(((2.*n+1).*pi))./((2.*n+1).*pi)); %Summation

That involves row vector n and row vector t, and uses .* between expressions that are length(n) and expressions that are length(t) . With those being different lengths, those are incompatible.

Cal = ((Cao.*Vp)./Vl).*(1-(2./L).*sum(sum_parts,2)); %Final Function

The sum,2 implies you are expecting sum_parts to be either a row vector or else a 2D array. If it were a row vector then sum,2 would give a scalar. If sum_parts is a 2D array then whether the result is length(n) or length(t) depends on whether the array is t x n or n x t.

You plot f(t) versus t, which tells us that you expect the sum to be a vector of length t, either 1 x length(t) or length(t) x 1. And with you having summed sum_parts over the second dimension, we can predict that you intended sum_parts to be length(t) x length(n) and that you want to sum over the different n values.

To have that happen in the context of your code... make t a column vector instead of a row vector, at least inside your function. Such as if you used

t = t(:);

[Daniel Alejandro Diaz]

Thank you it worked! I really appreciate you for your detailed response. It really helped me understand the issue and more about matlab.

Thanks again!!

Answer 2

[Chandler Hall]

Does adding the line:

[n, t] = meshgrid(n, t);
sum_parts = ...

produce the desired output?