plotting scatter3 and surf plots from loop in matlab - matlab

I want to plot scatter3 and surf plots from a loop. Below is my code but it isn't working...not sure where I'm going wrong but clearly something is wrong with the z matrix?
for e = 1:10;
x = rand(1,3);
y = rand(1,3);
A = x+y;
subplot(2,2,1)
p = find(A(:,1) > 1.1 & A(:,1) < 1.6);
Result = A(p,:);
scatter3(Result(:,1), Result(:,2), Result(:,3))
hold on
z(e,:) = [Result(1) Result(2) Result(3)];
end
subplot(2,2,2)
surf(z)

I will reiterate what I said in my comment to you. I got this error message when trying to run your code: Attempted to access Result(1); index out of bounds because numel(Result)=0. This is because your p condition isn't satisfied - MATLAB could not find any elements in the first column that are between 1.1 and 1.6.
As such, what I would suggest you do is check to see if Result is empty before trying to access the value itself. However, I would suggest you don't write a loop and generate all of the random values at once, then do the filtering with the Boolean conditions. Therefore, the equivalent code without using a loop would be this:
x = rand(10,3);
y = rand(10,3);
A = x+y;
p = A(:,1) > 1.1 & A(:,1) < 1.6;
z = A(p,:);
figure;
subplot(2,1,1);
scatter3(z(:,1), z(:,2), z(:,3));
subplot(2,1,2);
surf(z);
We generate 10 3D points for x and y at the beginning, then add these and store this into A. Next, we find the rows in A that are between 1.1 and 1.6 in the first column and store this as a logical array. We then use this array to index into A and store the results into z. This is the recommended approach if you want to extract certain elements into an array rather than using find.
Once we obtain z, we plot these points with scatter, then also find a surface plot with surf for the same matrix. BTW, I've fixed your subplot as you are only creating two plots, yet you are allocating space for 4 plots.
If you're absolutely bent on using your code, you would simply do this:
z = []; %// Change
for e = 1:10
x = rand(1,3);
y = rand(1,3);
A = x+y;
subplot(2,1,1)
p = find(A(:,1) > 1.1 & A(:,1) < 1.6);
Result = A(p,:);
scatter3(Result(:,1), Result(:,2), Result(:,3))
hold on
if ~isempty(Result) %// Change here
z = [z; Result(1) Result(2) Result(3)]; %// Change
end
end
subplot(2,1,2)
surf(z)
What's important is the initialization of z. I made this empty, and we only add to z if Result is not empty - this will happen if you generate a number that is not between 1.1 and 1.6.

Related

Plot a surface only for coordinates that satisfy a specific equation in MATLAB

I have two grid coordinates matrices, X and Y, created by calling [X, Y] = meshgrid(x, y), so their elements represent coordinates. How can I plot a surface on the xy-plane, using heights from matrix V, only for coordinates that satisfy a specific equation? For example, my plot extends up to radius a, but I dont want to plot any data to the set of points that satisfy the equation sqrt(x^2 + (y-c)^2) < b, where b, c (a>b) are given constants and x=X(i,j), y=Y(i,j). Is there an easy way to do this, other than creating the two grid coordinates matrices (up to radius a) and then manually removing elements from X, Y, V, using nested for loops? I have not found any way to limit the plotting area I am interested in by changing x, y.
Using Logical Indexing
Just in case you're still looking for any implementation details. Referencing the comment by #Ander Biguri. I have to add that it might be easier to use mesh parameters X and Y directly in the logical indexing. Here is a little playground script that might help future readers. Below Region_Array is a logical array that specifies where the condition in this case sqrt(X.^2 + (Y-c).^2) < b is true. When true Region_Array is indexed with the value "1" and elsewhere with "0". I've split this into two steps just in case the complementary region is quickly wanted. The images/plots below show the resulting surf() and masks/regions. MATLAB has some thorough documentation and examples overviewing logical indexing: Find Array Elements That Meet a Condition
Trivial Surface Plot:
Masks/Regions Not to be Plotted:
Playground Script:
%Random test axes%
x = linspace(0,100,50);
y = linspace(0,100,50);
[X,Y] = meshgrid(x,y);
%Trivial plot of ones%
V = ones(length(x),length(y));
%Constant parameters%
b = 20;
c = 10;
%Eliminating within the curved region%
figure(1)
Region_Array = sqrt(X.^2 + (Y-c).^2) < b;
V(Region_Array) = NaN;
subplot(1,2,1); surf(X,Y,V);
axis([0 100 0 100]);
title("Eliminating Within the Curved Region");
%Eliminating outside the curved region%
V = ones(length(x),length(y));
V(~Region_Array) = NaN;
subplot(1,2,2); surf(X,Y,V);
axis([0 100 0 100]);
title("Eliminating Outside the Curved Region");
figure(2)
subplot(1,2,1); imshow(~Region_Array,'InitialMagnification',200);
title("Region Array Mask/Map (Inside)")
subplot(1,2,2); imshow(Region_Array,'InitialMagnification',200);
title("Region Array Mask/Map (Outside)")
Ran using MATLAB R2019b

Why can't I use 'scatter3' here?

[X,Y] = meshgrid(-8:.5:8);
R = sqrt(X.^2 + Y.^2) + eps;
Z = sin(R)./R;
scatter3(X,Y,Z)
Error using scatter3 (line 64)
X, Y and Z must be vectors of the same length.
Matlab R2018b windows x64
As shown in the documentation, X, Y, Z must be vectors. (When you enter an article on mathworks from Googling, say, "matlab scatter3", you will first see the syntax for the function. Blue text means hyperlink. All the inputs are linked to the bottom of the page where their exact typing is defined.)
The reason is (probably) as follows.
As stated in the documentation, scatter3 puts circles (or other symbols of your choice if you modify the graphic object) on 3D coordinates of your choice. The coordinates are the ith element of X, Y, Z respectively. For example, the x-coordinate of the 10th point you wish to plot in 3D is X(10).
Thus it is not natural to input matrices into scatter3. If you know X(i), Y(i), Z(i) are indeed the coordinates you want to plot for all i, even though your X, Y, Z are not vectors for some reason, you need to reshape X, Y, Z.
In order to reshape, you can simply do scatter3(X(:), Y(:), Z(:)) which tells Matlab to read your arrays as a vectors. (You should look up in what order this is done. But it is in the intuitive way.) Or you can use reshape. Chances are: reshape is faster for large data set. But ofc (:) is more convenient.
The following should work:
[X,Y] = meshgrid(-8:.5:8);
R = sqrt(X.^2 + Y.^2) + eps;
Z = sin(R)./R;
X = X(:);
Y = Y(:);
Z = Z(:);
scatter3(X,Y,Z)
scatter3 needs vectors, not matrices as far as I can see here
this is my result:
If you want to use meshgrid without reshaping the matrices you have to use plot3 and the 'o' symbol. So you can get a similar result with:
plot3(X,Y,Z,'o')
EDIT:
A question that arose in association with this post was, which of the following methods is more efficient in terms of computation speed: The function reshape(X,[],1), suggested by me, or the simpler colon version X(:), suggested by #Argyll.
After timing the reshape function versus the : method, I have to admit that the latter is more efficient.
I added my results and the code I used to time both functions:
sizes = linspace(100,10000,100);
time_reshape = [];
time_col = [];
for i=1:length(sizes)
X = rand(sizes(i)); % Create random squared matrix
r = #() ResFcn(X);
c = #() ColFcn(X);
time_reshape = [time_reshape timeit(r)/1000] % Take average of 1000 measurements
time_col = [time_col timeit(c)/1000] % Take average of 1000 measurements
end
figure()
hold on
grid on
plot(sizes(2:end), time_col(2:end))
plot(sizes(2:end), time_reshape(2:end))
legend("Colon","Reshape","Location","northwest")
title("Comparison: Reshape vs. Colon Method")
xlabel("Length of squared matrix")
ylabel("Average execution time [s]")
hold off
function res = ResFcn(X)
for i = 1:1000 % Repeat 1000 times
res = reshape(X,[],1);
end
end
function res = ColFcn(X)
for i = 1:1000 % Repeat 1000 times
res = X(:);
end
end

Empty plot when using for loop

I want to use a for loop to plot a function. The code is
y = 0;
for k = 0:0.1:2
y = y + k;
plot(k, y);
hold on;
end
However, by running the code, the plot window is empty! How can I fix that in order to see a line on a 2D area?
Matlab automatically plots the linear interpolation between the points that are given to the plot function. Thus as you only give a single point, no interpolation can happen.
What you can do is to save the old y value and the old x value to ask Matlab to plot a linear interpolation between these two points. e.g.
yold = 0; %Init
kold=0; %Init
for k = 0:0.1:2
y = yold + k; %New y value
plot([kold,k], [yold,y]); %Plot a linear interpolation
kold = k; %Save the new values as old
yold = y; %Same
hold on;
end
EDIT/NOTE:
When adding new plots to the same window, MATLAB automatically changes color, thus the above will give you a rainbow, which is nice, but in case you want to keep it professional, you can add a color to the plot command, e.g.
plot([kold,k], [yold,y],'blue');

Generate heatmap with coordinates and data stored in vectors

Let A be an n by 3 matrix, such that the first two columns are all ordered pairs of the form (5*i,5*i) for i from 1 to 200. The third column contains values from 0 to 1, which I will call intensities. I want to make a 1000 by 1000 plot so that the rectangle at (5*i,5*i) is shaded with intensity described by the third column entry.
I'm familiar with the heatmap function and imshow, but I don't see a way to include this "scaling by 5" to make a nice plot. And of course in general the x and y coordinates may not be scaled by the same amount.
Is there a nice way to do this in Matlab?
With imagesc it's actually pretty simple:
First some example data:
%// generate example data
ii = 1:200;
[xx,yy] = meshgrid(ii);
A(:,1) = 5*xx(:);
A(:,2) = 5*yy(:);
A(:,3) = randi([0,1],1,40000);
Actual answer
n = 200;
%// reshape data
D = reshape( A(:,3),n,n );
%// heatmap
imagesc(A(:,1),A(:,2),D)
colormap(gray)
caxis([0,1])
gives:
Important notice
If your coordinates are not sorted as required for imagesc you can sort them with:
A = sortrows(A,[2,1]);
Clown Example
%// original image
load clown
I = reshape(1:numel(X),size(X));
[R,C] = ind2sub(size(X),I);
A(:,1) = R(:);
A(:,2) = C(:);
A(:,3) = X(:);
D = reshape( A(:,3),200,320 );
figure(1)
subplot(1,3,1)
imagesc(A(:,1),A(:,2),D)
%// shuffled image -> shuffled data
shuffle = randperm(320*200);
A = A(shuffle,:);
D = reshape( A(:,3),200,320 );
subplot(1,3,2)
imagesc(A(:,1),A(:,2),D)
%// sorted image
A = sortrows(A,[2,1]);
D = reshape( A(:,3),200,320 );
subplot(1,3,3)
imagesc(A(:,1),A(:,2),D)
You see, even if your coordinates are sorted like a mess, you can rebuild the image with sortrows.
See this
function DrawHeatmap(X,Y,Z)
%DRAWHEATMAP Draw a 2D heatmap for (X,Y) coordinates whose values are in Z
% X, Y , Z must be columns
% By: Eng. Osama Talaat Abdel-Hafiz - PhD Student
% Egypt - Sept 2017
if size(X,2)==1 && size(Y,2)==1 && size(Z,2)==1
F = scatteredInterpolant(X,Y,Z); % create a function from interpolation
[X,Y] = meshgrid(min(X):0.1:max(X),min(Y):0.1:max(Y));
Z = F(X,Y);
contourf(X, Y, Z, linspace(floor(min(min(Z))),ceil(max(max(Z))),400), 'LineColor','none')
colorbar;
else
error('X, Y , Z must be columns')
end
end

Plotting histogram side by side in Matlab

I have two vectors, c and d, whose histogram I need to plot side by side in the same figure in matlab. when i do
hist(c);
hold on;
hist(d)
the scale changes and I cant see the histogram of c vector. Where am i going wrong? Any help will be appreciated.
If you want the two to be in the same figure, you could try adjusting the X and Y limits to suit your needs (try help xlim and help ylim). However plotting them in the same figure might not always suit your needs, as a particular plot has to of course maintain a certain limit for X and Y.
If displaying them side by side in different figures would suffice however, you could consider using subplot():
>> A=[1 1 1 2 2];
>> B=[1 2 2 2 2];
>> figure(1);
>> hold on;
>> subplot(1,2,1);
>> hist(A);
>> subplot(1,2,2);
>> hist(B);
Resultant figure:
Notice how the different axis limits are maintained.
You can use axis([xmin xmax ymin ymax]) to control the x and y axis and select a range that will display both histograms. Depending on what you want your plot to look like, you may also want to try using nelements = hist(___) to get the number of elements in each bin and then plot them using bar(x,nelements) to control the location of each bar.
hist assumes you want to divide the range into 10 equal sized bins by default. If you want to use the same bins for both histograms, first find the range of your values and make a set of bin centers (e.g. binCenters = linspace(min(x), max(x), 15)'), then callhist(x, binCenters)`.
I use MATLAB histograms quite frequently and have wrote this small matlab script to plot two histograms (first one red and second blue) in one figure. The script is quite simple but the important thing is that the histograms should be comparable (i.e. equally spaced frequency bins).
function myhist(varargin)
% myhist function to plot the histograms of x1 and x2 in a single figure.
% This function uses the same xvalue range and same bins to plot the
% histograms, which makes comparison possible.
if nargin<2
x1 = cell2mat(varargin(1));
x2 = x1;
res = 100;
elseif nargin==2
x1 = cell2mat(varargin(1));
if length(cell2mat(varargin(2)))==1
res = cell2mat(varargin(2));
x2 = x1;
else
x2 = cell2mat(varargin(2));
res = 100;
end
elseif nargin>2
x1 = cell2mat(varargin(1));
x2 = cell2mat(varargin(2));
res = cell2mat(varargin(3));
end
if numel(x1)~=length(x1) || numel(x2)~=length(x2)
error('Inputs must be vectors.')
return
end
xrangel = max(min(x1),min(x2));
xrangeh = min(max(x1),max(x2));
x1_tmp = x1(x1>=xrangel & x1<=xrangeh);
x2_tmp = x2(x2>=xrangel & x2<=xrangeh);
xbins = xrangel:(xrangeh - xrangel)/res:xrangeh;
hist(x1_tmp,xbins)
hold on
h = findobj(gca,'Type','patch');
set(h,'FaceColor','r','EdgeColor','w');
hist(x2_tmp,xbins)