Plotting brownian motion matlab - matlab

First of all, I just want to say that I'm not that used to using matlab, but I need for an assignment, I'm supposed to create a "brownian movement". My code is currently looking like this:
clf
hold on
prompt = 'Ge ett input';
size = input(prompt) ;
numParticles = input('Ange antal partiklar');
axis([-size size -size size]);
Part = [];
color = 'brkgmyco';
for i = drange(1:numParticles)
Part = [Part [0;0]];
end
for i = drange(1:200)
dxdy = randn(2,numParticles);
k = Part
Part = Part + dxdy;
My concern is how to print, I would even want like a small delay on every print, so you really can see what's happening for the assignment, is this possible to achieve from the code I've written for now or should anything be changed? Thanks in advance!

Here are some basic problems with your code, regardless of what you are trying to do:
You use size as a variable name. Doing so overrides MATLAB's function size.
The function zeros creates an array initialized by zeros, no need for a loop for that.
Instead of calculating randn for 200 times in a loop, you can do it once, with dxdy = randn(2,numParticles,200) and then simply refer to dxdy(:,:,i) within the loop.
The same holds for summation. Instead of summing within a loop to get the cumulative sum, use cumsum like Part = cumsum(randn(2,numParticles,200),3); and then refer to Part(:,:,i), within the loop.
Now to your task. You said you want to know how to print, but I believe you want to plot because you use some commands like axis, clf and hold, that refer to graphic objects. However, you never really do plot anything.
The basic and general function for plotting in 2D is plot, but there are many other more specific functions. One of them is scatter, and it has a sister function gscatter, that takes triples of x, y and groupand plot each (x(k),y(k)) colored by their group(k).
This code plots the particles on an axes, and animate their movement:
prompt = 'Ge ett input';
scope = input(prompt) ;
numParticles = input('Ange antal partiklar');
N = 500;
Part = cumsum(randn(2,numParticles,N)*scope/100,3);
h = gscatter(Part(1,:,1),Part(2,:,1),1:numParticles);
axis([-scope scope -scope scope]);
legend off
for k = 2:N
for p = 1:numParticles
h(p).XData = Part(1,p,k);
h(p).YData = Part(2,p,k);
end
drawnow
end
Is this what you look for?

Related

How can I store multiple point objects in an array or struct?

I am trying to use matlab's drawpoint to capture some points of interest in an image interactively.
The output of the argument is of images.roi.Point object type.
How can I store the selected points in an array or struct, so I can iterate over many points instead of defining a new variable for each point?
This is my code at the moment, it's functional, however I want to be able to loop over a certain number of points instead of defining different variables manually.
img = imread('test.jpg');
imshow(img)
p1 = drawpoint;
p2 = drawpoint;
p3 = drawpoint;
p4 = drawpoint;
disp('Press a key when selection is finalized!')
pause;
p = [p1.Position; p2.Position; p3.Position; p4.Position];
The reason I'm using drawpoint is that I want to select the points, adjust their position without loosing zooming capability and store all points once finalized.
How can I modify the code to enable iteration over a certain number of points?
Any help would be much appreciated
I don’t know if it is possible to create an array of these objects. I suspect it is possible, but I don’t know exactly what the syntax should look like. You can also use a cell array, as follows:
N = 4; % number of points
pts = cell(N,1);
for ii = 1:N
pts{ii} = drawpoint;
end
pause;
coords = zeros(N,2);
for ii = 1:N
coords(ii,:) = pts{ii}.Position;
end

Directional Derivatives of a Matrix

I have 40 structures in my Workspace. I Need to write a script to calculate the directional derivatives of all the elements. Here is the code :
[dx,dy] = gradient(Structure_element_1.value);
dxlb = min(min(dx));
dxub = max(max(dx));
dylb = min(min(dy));
dyub = max(max(dy));
[ddx,ddy] = gradient(gradient(Structure_element_1.value));
ddxlb = min(min(ddx));
ddxub = max(max(ddx));
ddylb = min(min(ddy));
ddyub = max(max(ddy));
This is the code for one element. I Need to find out the same for all the 40 elements and then use it later. Can anyone help with this.
To answer your literal question, you should store the variables in a structure array or at least a cell array. If all of your structures have the same fields, you can access all of them by indexing a single array variable, say Structure_element:
for i = 1:numel(Structure_element)
field = Structure_element(i).value
% compute gradients of field
end
Now to address the issue of the actual gradient computation. The gradient function computes an approximation for , where is your matrix of data. Normally, a MATLAB function is aware of how many output arguments are requested. When you call gradient(gradient(F)), the outer gradient is called on the first output of the inner gradient call. This means that you are currently getting an approximation for .
I suspect that you are really trying to get . To do this, you have to get both outputs from the inner call to gradient, pass them separately to the
outer call, and choose the correct output:
[dx,dy] = gradient(F);
[ddx, ~] = gradient(dx);
[~, ddy] = gradient(dy);
Note the separated calls. The tilde was introduced as a way to ignore function arguments in MATLAB Release 2009b. If you have an older version, just use an actual variable named junk or something like that.

Plotting multiple lines within a FOR loopin MATLAB

Okay so this sounds easy but no matter how many times I have tried I still cannot get it to plot correctly. I need only 3 lines on the same graph however still have an issue with it.
iO = 2.0e-6;
k = 1.38e-23;
q = 1.602e-19;
for temp_f = [75 100 125]
T = ((5/9)*temp_f-32)+273.15;
vd = -1.0:0.01:0.6;
Id = iO*(exp((q*vd)/(k*T))-1);
plot(vd,Id,'r',vd,Id,'y',vd,Id,'g');
legend('amps at 75 F', 'amps at 100 F','amps at 125 F');
end;
ylabel('Amps');
xlabel('Volts');
title('Current through diode');
Now I know the plot function that is currently in their isn't working and that some kind of variable needs setup like (vd,Id1,'r',vd,Id2,'y',vd,Id3,'g'); however I really can't grasp the concept of changing it and am seeking help.
You can use the "hold on" function to make it so each plot command plots on the same window as the last.
It would be better to skip the for loop and just do this all in one step though.
iO = 2.0e-6;
k = 1.38e-23;
q = 1.602e-19;
temp_f = [75 100 125];
T = ((5/9)*temp_f-32)+273.15;
vd = -1.0:0.01:0.6;
% Convert this 1xlength(vd) vector to a 3xlength(vd) vector by copying it down two rows.
vd = repmat(vd,3,1);
% Convert this 1x3 array to a 3x1 array.
T=T';
% and then copy it accross to length(vd) so each row is all the same value from the original T
T=repmat(T,1,length(vd));
%Now we can calculate Id all at once.
Id = iO*(exp((q*vd)./(k*T))-1);
%Then plot each row of the Id matrix as a seperate line. Id(1,:) means 1st row, all columns.
plot(vd,Id(1,:),'r',vd,Id(2,:),'y',vd,Id(3,:),'g');
ylabel('Amps');
xlabel('Volts');
title('Current through diode');
And that should get what you want.

MATLAB - Labeling Curves During Iteration

I want to show the p value that was used to generate each curve next to each of the curves plotted. Note that since there is a plot of E and -E, the same p value should be next to both. I've been attempting this for a while and I have not come across anything super useful.
t = -3.1;%coupling
a = 1;%distance between r1 and r3
n = 5;%latice vector span in a1 direction
m = 1;%latice vector span in a2 direction
i = -7;%unique axial vector t_hat direction
j = 11;%unique axial vector c_hat direction
max_p = abs((n*(i+j/2)-j*(m+n/2)));%# of unique p values
La = sqrt(3)*sqrt(m^2+n*m+n^2)*a/gcd(2*n+m,2*m+n);%unit cell length
C = sqrt(n^2+n*m+m^2);%circumference of the nanotube
hold on;
for p=0:1:max_p
kt = -pi/La:.05:pi/La;
kc = 2*pi*p/C;
ka1 = kc*a*.5*(2*n+m)/C + kt*a*sqrt(3)*.5*m/C;
ka2 = kc*a*.5*(n+2*m)/C - kt*a*sqrt(3)*.5*n/C;
E = abs(t+t*exp(1i*ka2)+t*exp(1i*ka1));
title_ = sprintf('(%d,%d) Carbon Nanotube Dispersion Diagram',n,m);
title(title_);
xlabel('k_{t}a');
ylabel('Energy (eV)');
plot(kt,E);
plot(kt,-E);
end
There is a command named text that writes comments into the figures,
http://www.mathworks.se/help/techdoc/ref/text.html
with if you can't solve it with that and the to string operation i misunderstood the question
First, do you need to plot both E and -E? Since these are the same except for their sign you don't really add any information to the plot by having -E there as well. However, if you do need both lines, then just construct an array of strings for the legend, during the loop, which has each string included twice (once for E and once for -E).
... Initial calculations ...
hold on;
for p=0:1:max_p
kt = -pi/La:.05:pi/La;
kc = 2*pi*p/C;
ka1 = kc*a*.5*(2*n+m)/C + kt*a*sqrt(3)*.5*m/C;
ka2 = kc*a*.5*(n+2*m)/C - kt*a*sqrt(3)*.5*n/C;
E = abs(t+t*exp(1i*ka2)+t*exp(1i*ka1));
plot(kt,E);
plot(kt,-E);
% Construct array containing legend text
legend_text{2*(p+1)-1} = strcat('p=', num2str(p));
legend_text{2*(p+1)} = strcat('p=', num2str(p));
end
title_ = sprintf('(%d,%d) Carbon Nanotube Dispersion Diagram',n,m);
title(title_);
xlabel('k_{t}a');
ylabel('Energy (eV)');
legend(legend_text)
I am sure there is a more elegant way of constructing the legend text, but the above code works. Also, notice that I moved the calls to xlabel, ylabel and title to outside of the loop. This way they are only called once and not for each iteration of the loop.
Finally, you need to take care to ensure that each iteration of the loop plots with a different line colour or line style (see edit below). You could colour/style each pair of E and -E lines the same for a given iteration of the loop and just display the legend for E (or -E), which would obviously halve the number of legend entries. To do this you will need to hide one of line's handle visibility - this prevents it from getting an item in the legend. To do this use the following in your loop:
plot(kt, E);
plot(kt,-E, 'HandleVisibility', 'off');
% Construct array containing legend text
legend_text{p+1} = strcat('p=', num2str(p));
Finally, it is best to include clear all at the top of your Matlab scripts.
Edit: To have each plotted line use a different colour for each iteration of your loop use something like the following
... initial calculations ...
cmap = hsv(max_p); % Create a max_p-by-3 set of colors from the HSV colormap
hold on;
for p = 0:1:max_p
plot(kt, E, 'Color', cmap(p,:)); % Plot each pair of lines with a different color
plot(kt, -E, 'Color', cmap(p,:));
end

How to write this in an elegant way (cell arrays and structs in MATLAB)

I would like to plot connected points in MATLAB.
My connected points come from connecting objects of "stats", where each "stat" comes from a BW regionprops struct.
The code I have written works, but it suffers from a lot of "ugliness", which I couldnt fix even after trying various ways.
function plot_line( line )
a = cell2mat(line);
b = {a.Centroid};
matx = {};
maty = {};
for i = 1:size(b,2)
matx{end+1} = b{i}(1);
maty{end+1} = b{i}(2);
end
plot ( cell2mat(matx), cell2mat(maty) );
end
Can you help me make this code nicer? It's not critical, as my code works fine and as the lines are short (<100 points) the performance is not an issue.
It is just that it would be really nice to know how this tiny function should be written in the proper way, without for loops and 3 calls of cell2mat.
In my example:
line is a <1xn cell>,
line{1} has a property 'Centroid' and
line{i}.Centroid(1) are the x coordinates and
line{i}.Centroid(2) are the y coordinates.
Actually, all I need is plotting line{i}.Centroid(1), line{i}.Centroid(2) for i = 1:size(line,2), but I don't know how.
Instead of creating a cell array b, you can create a numerical array directly, by catenating using CAT:
tmp = cat(1,line{:});
coordinates = cat(1,tmp.Centroid);
plot(coordinates(:,1),coordinates(:,2))
EDIT
If you want to keep it really short (i.e. even shorter than #Amro's solution you can use CELLFUN like this in order get a one-liner:
plot(cellfun(#(x)x.Centroid(1),line),cellfun(#(x)x.Centroid(2),line))
Example:
line = repmat({struct('Centroid',[1 2])},1,5); %# similar to the data you have
%# extract x/y coordinates
x = cellfun(#(s)s.Centroid(1),line)
y = cellfun(#(s)s.Centroid(2),line)
%# plot
plot(x,y)
You could also do it as:
xy = cell2mat(cellfun(#(s)s.Centroid, line, 'UniformOutput',false)');
plot(xy(:,1),xy(:,2))