I cannot think of the proper wording for this, but I am trying to have my code run a loop that will input a value of X into an initial condition variable. This variable is then inputted into the heat equation to be plotted. From the code I want to choose a value which is at X(i=51) and plot it as T(x,T1). As i said before I don't know the proper wording to search for a possible solution. Any advice would be great!
clear;
clc;
% initialize given variables
A= 0.25;
L= pi;
Nx=101; Nt=10^(-4);
dx=L/(Nx-1);
T1=zeros(1,Nx);
x=linspace(0, L, Nx); %x distance
%Initial condition
%T1 will be the "new" T value and To will be the old
T1= x.*(pi-x);
%For plotting, time starts at 0.
t=0;
for n=1:50
To=T1;
t=t+1;
for i=2:Nx-1
T1(i)=To(i)+Nt *A*((To(i+1)-2*To(i)+To(i-1))/(dx^2))+ sin(5*x(i));
end
%B.C given than # T(0,t) & T(L,t) = 0
T1(1)=0; T1(end)=0;
figure(1)
plot(x,T1); set(gca, 'ylim',[-110 110]);
ylabel('Temperature along the Rod');
xlabel('Location on the Rod of length Pi');
title(sprintf('Time = %f seconds', t));
pause(0.001);
end
The expected out put that I want to plot is plot(x(i=51),T1) which would show an image just like this. For this plot I ran my code and altered i to =50:51 to get the needed values for the heat equation. I am trying to have this be plotted in the code shown and not have to rewrite my code over and over to get different plots because I change values such as i or time ect...
You want to plot a consistent value of x, specifically x(51), for every n.
This can be done a couple of ways
First, as individual points with hold on:
for n = 1:50
% ... calculation ...
hold on
plot( x(51), T1(51), '.' );
hold off
end
You could update the plot, this will be quicker to compute and has the advantage of showing a line plot
x_51 = NaN( 50, 1 );
T1_51 = NaN( 50, 1 );
p = plot( [], [] );
for n = 1:50
% ... calculation ...
x_51(n) = x(51);
T1_51(n) = T1(51);
set( p, 'XData', x_51, 'YData', T1_51 );
end
Related
I need to plot population growth model with different values of b
where b>d
and b=d
using for loops. Both results should be visible on the same graph with different colors.
Here is my function and intial value, but I am not getting how to get the plot .
[T,Y]=ode45(H,[0:1:time],[N0]);
Intitial value
b= 0.1 0.001
d=0.001
N0=400````
I need two line for each b on the same plot.
```***
Intitial value
b= 0.1 0.001;
d=0.001;
N0=400;
H=#(t,N)[b*N-d*N];
[T,Y]=ode45(H,[0:1:time],[N0]);
plot(T,Y)
***```
First, you need to put the code in a proper format, now you copied the initial value block twice (I guess you had some issue putting the code format. I hope you can focus on that when asking new questions.
The current code gives an error on the definition of b as you did not define it as a vector. To have two lines, it is best to store the output Y as a matrix of two columns (each column being one vector). MATLAB then outputs each column as a line in the plot.
The following code solves your issue:
% Initial value
b = [0.1, 0.001];
d = 0.001;
N0= 400;
simTime = 0:1:300;
% Preallocate output for the loop
Y = zeros(length(simTime), length(b));
% Run for loop
for i = 1:length(b)
b_i = b(i);
H=#(t,N)[b_i*N-d*N];
[T,y]=ode45(H, simTime, [N0]);
Y(:,i) = y;
end
% Plot output
plot(T,Y)
My goal output is to have four plots displaying (time, dist_a), (time, speed_a), (time, dist_b), and (time, speed_b) when looping through a multidimensional array. However, I am displaying only 2 blanked plots.
Here is my code:
time = rand(10, 1)
dist_a = rand(10,1)
dist_b = rand(10,1)
speed_a = rand(10,1)
speed_b = rand(10,1)
dist = cat(2, dist_a, dist_b);
speed = cat(2, speed_a, speed_b);
for k = 1:2
figure;
plot(time, dist(k));
plot(time, speed(k));
end
Your problems were two-fold. Firstly, you were only plotting a single point as opposed to a vector, changing dist(k) to dist(:,k) for example fixes this. Secondly, if you want four figures with a loop that executes twice, you need to include another figure command before the second plot. The following should do what you asked for, I also added in some formatting to make the plots looks nicer
for k = 1:2
figure
plot(time, dist(:,k),'o','LineWidth',2);
xlabel('time')
ylabel('distance')
box on
grid on
figure
plot(time, speed(:,k),'o','LineWidth',2);
xlabel('time')
ylabel('speed')
box on
grid on
end
which gives:
I am trying to plot variables dynamically in MATLAB. I have an array (set of states) that needs to be plotted with time. I tried plot(time,theta), where theta is a 1*5 array. With this command, I get an error saying that theta should be a scalar because time is a scalar. I then tried using for-loop to plot(time,theta(i)). The problem with this is that I get data points at discrete time intervals on my plot. However I need a continuous plot. I wonder how this can be done.
You need to use hold on when plotting.
For example:
time = 1;
theta = [1:100];
figure
for i=1:100
plot(time, theta(i),'r.')
hold on %--> Keeps the previous data in your plot
time = time + 1;
end
Let's see if I get this straight. Time is updated at every step, and theta are five different variables that also get updated. This should work for you:
% Use your own time variable
time = 1:100;
figure; hold on;
h = cell(5,1); % Handles of animated lines
colors = 'rgbkm'; % Colors of lines
for t = time
theta = randn(5,1);
if isempty(h{1})
% Initialize plot
for k = 1 : 5
h{k} = animatedline(t , theta(k) , 'LineStyle' , '-' , 'Color' , colors(k));
end
else
% Update plot with new data
for k = 1 : 5
addpoints(h{k}, t , theta(k));
end
end
% Update plot
drawnow
end
The object animatedline was introduced in R2014b. You can still do something similar with a conventional plot and updating the XData and YData properties of the lines at each loop.
I find that data points that lie on or near the axes are difficult to see. The obvious fix, of course, is to simply change the plot area using axis([xmin xmax ymin ymax]), but this is not preferable in all cases; for example, if the x axis is time, then moving the minimum x value to -1 to show activity at 0 does not make sense.
Instead, I was hoping to simply move the x and y axes away from the plot area, like I have done here:
left: MATLAB generated, right: desired (image editing software)
Is there a way to automatically do this in MATLAB? I thought there might be a way to do it by using the outerposition axes property (i.e., set it to [0 0 0.9 0.9] and drawing new axes where they originally were?), but I didn't get anywhere with that strategy.
The answers here already show you most of the way - here is the last step to separate the x and y axle as per the example you put together.
f = figure ( 'color', 'white' );
% create the axes and set some properties
ax = axes ( 'parent', f, 'box', 'off', 'nextplot', 'add', 'XMinorTick', 'on', 'YMinorTick', 'on' );
% plot some data
plot ( ax, 0:10, [0:10].^2, 'rx-' )
% modify the x and y limits to below the data (by a small amount)
ax.XLim(1) = ax.XLim(1)-(ax.XTick(2)-ax.XTick(1))/4;
ax.YLim(1) = ax.YLim(1)-(ax.YTick(2)-ax.YTick(1))/4;
% Set the tick direction
ax.TickDir = 'out';
% draw the plot to generate the undocumented vertex data var
drawnow()
%% R2015a
% X, Y and Z row of the start and end of the individual axle.
ax.XRuler.Axle.VertexData(1,1) = 0;
ax.YRuler.Axle.VertexData(2,1) = 0;
%% R2015b
% extract the x axis vertext data
% X, Y and Z row of the start and end of the individual axle.
vd = get(ax.XAxis.Axle,'VertexData');
% reset the zero value
vd(1,1) = 0;
% Update the vertex data
set(ax.XAxis.Axle,'VertexData',vd);
% repeat for Y (set 2nd row)
vd = get(ax.YAxis.Axle,'VertexData');
vd(2,1) = 0;
set(ax.YAxis.Axle,'VertexData',vd);
Edit: The vertex is something that Matlab recreates whenever the axes/figure changes size or if you zoom or pan for example.
You can try to counteract this (remember you are using undocumented features here) by adding a listener to attempt to capture this. We can use the MarkedClean event which is called quite a lot of times.
addlistener ( ax, 'MarkedClean', #(obj,event)resetVertex(ax) );
Where you resetVertex function is something like: (R2015b shown only)
Edit 2 added the code to turn off the minor ticks below 0.
function resetVertex ( ax )
% extract the x axis vertext data
% X, Y and Z row of the start and end of the individual axle.
ax.XAxis.Axle.VertexData(1,1) = 0;
% repeat for Y (set 2nd row)
ax.YAxis.Axle.VertexData(2,1) = 0;
% You can modify the minor Tick values by modifying the vertex data
% for them, e.g. remove any minor ticks below 0
ax.XAxis.MinorTickChild.VertexData(:,ax.XAxis.MinorTickChild.VertexData(1,:)<0) = [];
ax.YAxis.MinorTickChild.VertexData(:,ax.YAxis.MinorTickChild.VertexData(2,:)<0) = [];
end
Note: this uses undocumented features -> so may only work in certain versions of Matlab (I have added the code for r2015a & r2015b) and Matlab may recreate the vertex data depending on what you do with the plots..
Here is a simple way for achieving that:
% some data:
x = 1:100;
f=#(x) 5.*x;
y=f(x)+rand(1,length(x))*50;
close all
% plotting:
f1 = figure('Color','white');
ax = axes;
plot(ax,x,y,'o');
% 'clean' the data area a little bit:
box off
ax.TickDir = 'out';
% pushing the axis a bit forward:
lims = axis;
pos = ax.Position;
axis([lims(1)-ax.XTick(2)/5 lims(2)+0.1 lims(3)-ax.YTick(2)/5 lims(4)+0.1])
% Create lines
firstXtick = 0.013; %this value need to be adjusted only once per figure
firstYtick = 0.023; %this value need to be adjusted only once per figure
lx = annotation(f1,'line',[pos(1) pos(1)+firstXtick],...
[pos(2) pos(2)],'Color',[1 1 1],'LineWidth',1);
ly = annotation(f1,'line',[pos(1) pos(1)],...
[pos(2) pos(2)+firstYtick],'Color',[1 1 1],'LineWidth',1);
Which yields this figure:
The only thing to adjust here, once per type of figure, is firstXtick and firstYtick values, that have to be fine tuned to the specific axis. After setting them to the correct value the figure can be resized with no problem. Zoom and pan require a little fixes.
You can start your axes from less than zero and then remove the less than zero ticks from your plot. e.g.
plot(0:3:30,0:3:30); %Some random data for plotting
h = gca;
axis([-1 30 -1 30]); %Setting the axis from less than zero
box off; %Removing box
h.TickDir = 'out'; %Setting Direction of ticks to outwards
h.XTickLabel(1)= {' '}; %Removing the first tick of X-axis
h.YTickLabel(1)= {' '}; %Removing the first tick of Y-axis
With this code, you'll get this result:
This may have a drawback, sometimes, that zero ticks may also get removed (as you can see in above figure). This is because the plot had set the first ticks of axes equal to zero. This can be avoided using if condition. So, the code can be modified as below:
plot(0:3:30,0:3:30);
h = gca;
axis([-1 30 -1 30]);
box off;
h.TickDir = 'out';
if str2num(cell2mat(h.XTickLabel(1))) <0
h.XTickLabel(1)= {' '};
end
if str2num(cell2mat(h.YTickLabel(1))) <0
h.YTickLabel(1)= {' '};
end
The above code will yield the following result:-
Also note that, for your case, since your axes ticks are very less, -1 may not be much suitable for the starting value of axes and you may need to use -0.1 instead i.e. axis([-0.1 30 -0.1 30]);
With a slight modification of #matlabgui's answer you can track the (major) tick limits:
ax = gca();
% Set the tick direction
ax.TickDir = 'out';
% Make sure this stays when saving, zooming, etc
addlistener ( ax, 'MarkedClean', #(obj,event) change_ticks(ax) );
% Draw the plot to generate the undocumented vertex data variable
% and call callback for the first time
drawnow();
The callback
function change_ticks( ax )
% Modify ruler
ax.XRuler.Axle.VertexData(1,1) = ax.XTick(1);
ax.XRuler.Axle.VertexData(1,2) = ax.XTick(end);
ax.YRuler.Axle.VertexData(2,1) = ax.YTick(1);
ax.YRuler.Axle.VertexData(2,2) = ax.YTick(end);
end
I haven't test extensively but seems to work for custom ticks too. This nicely cuts the rulers not only on zero but beyond the fist and last tick. This was tested in Matlab 2019a on Windows and ax.XRuler.Axle.VertexData works just fine. Note this is only for major ticks!
Generate a plot showing the graphs of
y=(2*a+1)*exp(-x)-(a+1)*exp(2*x)
in the range x ∈ <-2, 4> for all integer values of a between -3 and 3
I know how to make typical plot for 2 values and set a range on the axes, but how to draw the graph dependent on the parameter a?
To elaborate on Ben Voigt's comment: A more advanced technique would be to replace the for-loop with a call to bsxfun to generate a matrix of evaluations of M(i,j) = f(x(i),a(j)) and call plot with this matrix. Matlab will then use the columns of the matrix and plot each column with individual colors.
%%// Create a function handle of your function
f = #(x,a) (2*a+1)*exp(-x)-(a+1)*exp(2*x);
%%// Plot the data
x = linspace(-2, 4);
as = -3:3;
plot(x, bsxfun(f,x(:),as));
%%// Add a legend
legendTexts = arrayfun(#(a) sprintf('a == %d', a), as, 'uni', 0);
legend(legendTexts, 'Location', 'best');
You could also create the evaluation matrix using ndgrid, which explicitly returns all combinations of the values of x and as. Here you have to pay closer attention on properly vectorizing the code. (We were lucky that the bsxfun approach worked without having to change the original f.)
f = #(x,a) (2*a+1).*exp(-x)-(a+1).*exp(2*x); %// Note the added dots.
[X,As] = ndgrid(x,as);
plot(x, f(X,As))
However for starters, you should get familiar with loops.
You can do it using a simple for loop as follows. You basically loop through each value of a and plot the corresponding y function.
clear
clc
close all
x = -2:4;
%// Define a
a = -3:3;
%// Counter for legend
p = 1;
LegendText = cell(1,numel(a));
figure;
hold on %// Important to keep all the lines on the same plot.
for k = a
CurrColor = rand(1,3);
y= (2*k+1).*exp(-x)-(k+1).*exp(2.*x);
plot(x,y,'Color',CurrColor);
%// Text for legend
LegendText{p} = sprintf('a equals %d',k);
p = p+1;
end
legend(LegendText,'Location','best')
Which gives something like this:
You can customize the graph as you like. Hope that helps get you started!