How can I plot graph with lines of different color each using for loop?

Hello,

I draw the graph v vs t using for loop and graph should include multiple line for different dt. I try to let each lines have different color and add legend, but I got same color line and legend for last loop only. Code I write is:

%initial condition
uold=0;
dt=0.01;
i=0;%count
j=1;
frhs=@(t,v) (1/1000)*(1064*t*exp(-0.95*v)-135*v^2)-9.81;
dt=[0.001, 0.005, 0.01, 0.05, 0.1, 0.3];
for j=1:length(dt)
for told=0:dt:60
    i=i+1;
    [unew] = RK4(told,uold,frhs,dt(j));
    uold=unew;
    x(i)=told;
    y(i)=unew;
end
fprintf('v(60) = %f when dt = %f \n',unew,dt(j))
plot(x,y,'color',rand(1,3))
legend(sprintf('dt=%f',dt(j)))
end
xlabel('time')
ylabel('vertical velocity')

I would like to get graph which different color line with each dt and legend to show which color is which dt.

When I run the code, color is random every time I run, but all lines are same color and legend has only for dt=0.3.

Answer 1

[sai charan sampara]

Hi Szu,

Firstly there are some errors to be corrercted. The variable "i" needs to be intialized to zero every time the outer loop runs. "uold" might also be neede to be intialized to zero for each iteration of outer loop. Since the arrays "x" and "y" are being overwritten they need to be cleared at the end of each iteration of outer loop to remove the values from previous iteration. Also for the inner "for" loop the step value must be "dt(j)" instead of "dt". Making those corrections will give desired output as follows:

uold=0;
%dt=0.01;
i=0;%count
%j=1;
frhs=@(t,v) (1/1000)*(1064*t*exp(-0.95*v)-135*v^2)-9.81;
dt=[0.001, 0.005, 0.01, 0.05, 0.1, 0.3];

fig=figure;
hold on
for j=1:length(dt)
    i=0;
    uold=0;
for told=0:dt(j):60
    i=i+1;
    [unew] = told+uold+dt(j);%Some random function for verifying
    uold=unew;
    x(i)=told;
    y(i)=unew;
end
fprintf('v(60) = %f when dt = %f \n',unew,dt(j))
plot(x,y,'color',rand(1,3))
clear("x","y");

end

v(60) = 1800090.000999 when dt = 0.001000 
v(60) = 360090.005000 when dt = 0.005000 
v(60) = 180090.010000 when dt = 0.010000 
v(60) = 36090.050000 when dt = 0.050000 
v(60) = 18090.100000 when dt = 0.100000 
v(60) = 6090.300000 when dt = 0.300000 

hold off
xlabel('time')
ylabel('vertical velocity')
legend(["dt1","dt2","dt3","dt4","dt5","dt6"]);

[Szu Yu Chew]

Thank you its working!

Answer 2

[Dyuman Joshi]

You are over-writing the figure in each iteration, thus you only get the plot for a single iteration (i.e. the last one).

Call a figure before your for loop and retain the plots using hold on -

fig = figure;
hold on
for xyz
for abc
    ...
    ...
end
end
hold off

Remove the hold after the loops are completed.

[Szu Yu Chew]

I added figure, hold on and off at outside of all for loop but still all lines are same colour and legend show only last one, and color of line and legend is different now.

[Dyuman Joshi]

Please share your whole code so that I can check it and reproduce the issue.

Use the paperclip button to attach.

[Szu Yu Chew]

code edited is :

%initial condition
uold=0;
dt=0.01;
i=0;%count
j=1;
frhs=@(t,v) (1/1000)*(1064*t*exp(-0.95*v)-135*v^2)-9.81;
dt=[0.001, 0.005, 0.01, 0.05, 0.1, 0.3];

fig=figure;
hold on
for j=1:length(dt)
for told=0:dt:60
    i=i+1;
    [unew] = RK4(told,uold,frhs,dt(j));
    uold=unew;
    x(i)=told;
    y(i)=unew;
end
fprintf('v(60) = %f when dt = %f \n',unew,dt(j))
plot(x,y,'color',rand(1,3))
legend(sprintf('dt=%f',dt(j)))

end
xlabel('time')
ylabel('vertical velocity')
hold off

and result is:

[Dyuman Joshi]

Try this -

%initial condition
uold=0;
i=0;%count
j=1;
frhs=@(t,v) (1/1000)*(1064*t*exp(-0.95*v)-135*v^2)-9.81;
dt=[0.001, 0.005, 0.01, 0.05, 0.1, 0.3];

fig=figure;
hold on
for j=1:length(dt)
    vec = 0:dt(j):60;
    %preallocate accordingly
    x = zeros(size(vec));
    y = zeros(size(vec));
    for told=vec
        i=i+1;
        [unew] = RK4(told,uold,frhs,dt(j));
        uold=unew;
        x(i)=told;
        y(i)=unew;
    end
    fprintf('v(60) = %f when dt = %f \n',unew,dt(j))
    plot(x,y,'color',rand(1,3),'DisplayName',sprintf('dt=%f',dt(j)))
end
xlabel('time')
ylabel('vertical velocity')
hold off

legend()

[Szu Yu Chew]

I fixed initial conditions and can get different colours with the code. Thank you!

[Dyuman Joshi]

@Szu Yu Chew, I would suggest you to -

1) Not use clear() as done in the other answer and preallocate variables instead.

See - https://in.mathworks.com/help/matlab/matlab_prog/techniques-for-improving-performance.html#buwj1nn

https://in.mathworks.com/help/matlab/ref/clear.html#btd0uqt-4

for reference as to why.

2) Not define legend() dynamically as done in the other answer.

You can refer to the method I have used or utilize strings like this -

str = "dt" + 1:numel(dt);
legend(str);