How to resolve, "Nonscalar arrays of function handles are not allowed; use cell arrays instead."

Hey everyone,

I know this question is asked a lot but I'm still having troubles trying to resolve the issue. I have a working code for this, so the homework problem is done. However, I have a pet peeve where I always try to make things look as nice as possible. The original problem was to expand a function into a Fourier Series and plot it. I was able to do that manually by computing 21 different integrals (-10 to 10) and then adding them all up.

However since I wanted it to look pretty, I wanted to try to do it in a for loop since that seemed like the best option in order to have full control over how many coefficients I want to use to show how accuracy increases or decreases as the number of coefficients increases or decreases respectively.

This is my current code:

%Methods For Loop
close all
C=1;
V=5;
R=4;
t=linspace(0,20,22);
%-------------------------------------------------------------------------%
%Original Function - (V*C*(1-exp(-t/((R*C)))))
%Integrand - (V*C*(1-exp(-t/((R*C)))))*(exp((-1i*4*n*pi*t)/(R*C))))
for n=1:21
  Coeff=@(t) (V.*C.*(1-exp(-t/((R.*C))))).*(exp((-1i.*4.*(n-11).*pi.*t)/(R.*C)));
 I(n)= (2/(R*C))*integral(Coeff,0,2);
E(n)=@(t) exp((4*1i*(n-11)*pi*t)/(R*C));
end
CN=I*E
end

I cannot for the life of me seem to resolve this issue. I would greatly appreciate if anyone could offer any insight!

Answer 1

[Guillaume]

An alternative to Walter's solution that avoids the TCN recursion:

C=1;
V=5;
R=4;
t=linspace(0,20,22);
for n = 1:21
   Coeff=@(t) (V.*C.*(1-exp(-t/((R.*C))))).*(exp((-1i.*4.*(n-11).*pi.*t)/(R.*C)));
   I(n) = (2/(R*C))*integral(Coeff,0,2);
   E{n} = @(t) exp((4*1i*(n-11)*pi*t)/(R*C));
   CN{n} = @(t) I(n) * E{n}(t);
end
%sum of the first n CN{i}:
TCN = @(n, t) sum(cell2mat(arrayfun(@(i) CN{i}(t), (1:n)', 'UniformOutput', false)));  
%obviously, the maximum value for n is 21, since you calculated 21 CN

%at this point you can plot individual CN{i}
%e.g, to plot the first n CN:
n = 5; %for example
figure; hold on;
arrayfun(@(i) plot(t, CN{i}(t), 'DisplayName', sprintf('CN{%d}', i)), 1:n);
%and the sum of the first n CN:
plot(t, TCN(n, t), 'DisplayName', 'TCN')
legend('show');

[Cody Stein]

I'm having trouble understanding exactly what you did. Also when I plot it, it doesn't seem to plot the correct plot, it should look something like this screen shot, however it is all wonky when I tried that code on my computer. Do you know why? Thank you!

[Guillaume]

I and E are exactly the same as your original code, except E is a cell array since, as you found out, you can't put function handles in a plain array. CN is just a cell array of function handles, each the respective product of I and E.

If the CN do not plot properly, then the problem is with your original formula.

TCN is a function handle that:

• concatenate vertically the first n CN(t) vectors.
• sum the columns of the vectors

SO TCN(n, t) is basically the sum of the first n CN applied to the t vector.

My guess is that there's something wrong in the Coeff, I or E formula.

Answer 2

[Walter Roberson]

in the loop

E{n} = @(t) exp((4*1i*(n-11)*pi*t)/(R*C));
CN{n} = @(t) I(n) * E{n}(t);

and remove the CN = I*E after the loop.

I do not know why you are wanting to construct E as function handles. When you do, your CN has to be function handles too as you are multiplying I (numeric) by E (a function handle)

And I do not see any summation. I also do not see any place that you apply your function handles to the actual t values you have defined.

[Cody Stein]

It was just the angle I was working at to get the for loop to work as a way of doing a Fourier expansion of any length. Do you have another suggestion on a way I should do it.

When CN=I*E was evaluated, it ended up as an expression where it had Cn1+Cn2+....

Thank you for your prompt response!

[Walter Roberson]

C=1;
V=5;
R=4;
t=linspace(0,20,22);
%-------------------------------------------------------------------------%
%Original Function - (V*C*(1-exp(-t/((R*C)))))
%Integrand - (V*C*(1-exp(-t/((R*C)))))*(exp((-1i*4*n*pi*t)/(R*C))))

TCN = @(t) 0;

for n=1:21
  Coeff=@(t) (V.*C.*(1-exp(-t/((R.*C))))).*(exp((-1i.*4.*(n-11).*pi.*t)/(R.*C)));
  I(n) = (2/(R*C))*integral(Coeff,0,2);
  E{n} = @(t) exp((4*1i*(n-11)*pi*t)/(R*C));
  CN{n} = @(t) I(n) * E{n}(t);
  TCN = @(t) TCN(t) + CN{n}(t);
end

This will be functional, but it will not be pretty.

[Cody Stein]

How would I go about plotting this against t?

[Walter Roberson]

plot(t, TCN(t))