Plotting a summation with two variables
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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
采纳的回答
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,:)])
10 个评论
Alice K
2023-4-6
Torsten
2023-4-6
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
2023-4-6
Alice K
2023-4-6
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
2023-4-6
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
2023-4-6
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