Plotting a summation with two variables

Hi All,

I need to plot a summation but I keep getting a blank plot,

Any help you can give would be great.

Here is my summation:

Here is the code I have tried:

t = linspace(0,0.01,1);

x = linspace(0,0.01,1);

n = 100;

for k = 0:1:n

y = (6/(pi+6*k*pi))*sin(k*x)*exp((-(pi/6+k*pi)^2)*t);

end

plot(v,t)

Thanks

Alice

Answer 1

[Torsten]

t = linspace(0,0.1,100);
x = linspace(0,1,100).';
n = 1000;
f = @(t) sum(6./(pi+6*(0:n)*pi).*sin(x.*(0:n)).*exp(-(pi/6+(0:n)*pi).^2*t),2);
for j = 1:numel(t)
  F(:,j) = f(t(j));
end
figure(1)
plot(x,[F(:,1),F(:,10),F(:,15),F(:,20),F(:,100)])

figure(2)
plot(t,[F(1,:);F(10,:);F(15,:);F(20,:);F(100,:)])

[Alice K]

That looks great thank you, but can you explain it please I don't fully understand what gets plotted.

[Torsten]

Figure 1 shows y over x for t = t(1), t(10), t(15), t(20), t(100).

Figure 2 shows y over t for x = x(1), x(10), x(15), x(20), x(100).

[Alice K]

Okay, that makes sense, just one last question is there a way to set the line colours? I can get the lines to be all of one colour but not different, I need the colours not to contain green.

[Torsten]

What ? Green is nature - you don't like green ?

plot(x,F(:,1),'r',x,F(:,10),'b',...

r = red

b = blue

...

[Alice K]

Brilliant thank you, not the biggest fan of green

[Alice K]

Sorry two last questions (i think)

is this line f = @(t) sum(6./(pi+6*(0:n)*pi).*sin(x.*(0:n)).*exp(-(pi/6+(0:n)*pi).^2*t),2);

what is the 2 aftter the comma at the end, and how would I get it to plot when t = 0, it is just plotting a blank plot.

Thank you for all your help.

[Torsten]

Summation of the matrix

6./(pi+6*(0:n)*pi).*sin(x.*(0:n)).*exp(-(pi/6+(0:n)*pi).^2*t)

over its columns (sum(.,1) would be summation over its rows).

For a better understanding, I think it would be a good exercise if you tried to solve this problem by a threefold loop:

for i = 1:numel(x)
    xv = x(i);
    for j = 1:numel(t)
        tv = t(j);
        F(i,j) = 0.0;
        for k = 0:n
            F(i,j) = F(i,j) + 6/(pi+6*k*pi)*sin(xv*k)*exp(-(pi/6+k*pi)^2*tv);
        end
    end
end

I guess this is somehow what you had in mind with your code.

Instead of the loop

for j = 1:numel(t)
    F(:,j) = f(t(j));
end

in the above code, you can also directly use

F = cell2mat(arrayfun(@(t)f(t),t,'UniformOutput',0));

[Alice K]

I am a bit lost, where would I put this code or what does it replace?

F = cell2mat(arrayfun(@(t)f(t),t,'UniformOutput',0));

and would I do the same if i wanted to plot this:

g = @(t) sum(6./(pi+6*(0:n)*pi).*sin(x.*(pi./6+(0:n)*pi)),2)

[Torsten]

You can use

t = linspace(0,0.1,100);
x = linspace(0,1,100).';
n = 1000;
f = @(t) sum(6./(pi+6*(0:n)*pi).*sin(x.*(0:n)).*exp(-(pi/6+(0:n)*pi).^2*t),2);
for j = 1:numel(t)
    F(:,j) = f(t(j));
end

or

t = linspace(0,0.1,100);
x = linspace(0,1,100).';
n = 1000;
f = @(t) sum(6./(pi+6*(0:n)*pi).*sin(x.*(0:n)).*exp(-(pi/6+(0:n)*pi).^2*t),2);
F = cell2mat(arrayfun(@(t)f(t),t,'UniformOutput',0));

or

t = linspace(0,0.1,100);
x = linspace(0,1,100).';
n = 1000;
F = zeros(numel(x),numel(t));
for i = 1:numel(x)
    xv = x(i);
    for j = 1:numel(t)
        tv = t(j);
        for k = 0:n
            F(i,j) = F(i,j) + 6/(pi+6*k*pi)*sin(xv*k)*exp(-(pi/6+k*pi)^2*tv);
        end
    end
end

F should be the same for all three codes, but I think for beginners, the last code is the easiest to understand.

[Alice K]

amazing, thank you so much for all you help