I have 25 pairs of (x,y) co-ordinates. Each of these pairs corresponds to a country. I want to plot the 25 points on a scatter graph, and have the country name for each point directly next to the point on the scatter graph. I can't figure out how to do this in MATLAB or Octave (I have both MATLAB and Octave and don't mind which I use, which is why I'm asking about both).
Let's say I put the (x,y) co-ordinates and corresponding country labels in a matrix of 25 rows and 3 columns, with the labels in the first column. Does anyone know the command I can use for the desired graph?
Strings don't play well with matrices, so I'm adjusting your storage format slightly. Here's the test data: a 25x2 matrix of coordinates, and a 25x1 cell array of strings.
p = rand(25,2);
names = repmat({'name'}, 25, 1)
You'll have to play with the offsets slightly, but here's the idea:
scatter(p(:,1), p(:,2))
%# Compute some offsets for the lower-left of the text box, based
%# on overall size of the plot
offset_x = diff(xlim) * .01;
offset_y = diff(ylim) * .01;
text(p(:,1)+offset_x, p(:,2)+offset_y, names)
Related
So i have this code to obtain radial gravity on Earth in function of the latitude:
G=6.6e-11;
M=5.976e24;
N=1000;
r=6371000;
w=2*pi/(24*3600);
for i=1:1:360
Theta=i*pi/180;
x(i)=i;
Vi(i)=-G*M/(r*r);
Phii(i)=r*w*w*sin(Theta)*sin(Theta);
gr(i)=Vi(i)+Phii(i);
end
plot(x,gr)
And it runs well. I want to make a graph of a circle made of a border of points (representing angle (i)) that change colour according to the value of gr(I want to set ranges of values of gr so that if the value obtained falls in a specific category, the point will have a specific colour).
I'm really new to MATLAB. Is there any possible way to make this?
Thanks in advance.
Here is the basic algorithm that I would do:
Determine how many colours you want to represent in your plot.
Create a colour map that has this many points for what you want to compute.
Determine a linearly increasing vector that varies from the minimum value of gr to the maximum value of gr with as many points as you have determined in Step #2
For each point in gr:
a. Determine which point yields the closest distance of this point to the vector in Step #3
b. Use this to index which colour you want.
c. Convert your angle into Cartesian co-ordinates, then plot this point with the colour found in Step 4b.
Let's tackle each point in detail.
Step #1 - Determine how many colours you want
This is pretty simple. Just determine how many colours you want. For now, let's assume that you want 20 colours, so:
num_colours = 20;
Step #2 - Create a colour map
What we can do is create a 20 x 3 matrix where each row determines a RGB tuple that denotes the amount of red, green and blue that each colour will occupy. MATLAB has built-in colour maps that will help you facilitate this. Here are all of the available colour maps that MATLAB has:
Each colour map has a special variable where you can provide it an integer number, and it'll return this 2D matrix of as many rows as the number you have provided. Each row gives you an RGB triplet which denotes the proportion of red, green and blue respectively. This matrix varies from the beginning of the colour map (top row) to the end (bottom row). All you have to do is use any name seen in the figure I've shown you above to create a colour map of that type. For example, if you wanted to get a bones colour map of 15 points, simply do:
colour_map = bones(15);
If you wanted to get a jet colour map of 25 points, simply do:
colour_map = jet(25);
.... you get the idea right? I like hsv so let's use the HSV colour map. You can use any colour map you want, but let's just stick with HSV for the sake of this example.
As such:
colour_map = hsv(num_colours);
Step #3 - Get that linearly increasing vector
You want certain colours to map into certain ranges, which is why this step is important. Given a value in gr, we want to figure out which colour we want to choose, and all you have to do is determine which value in gr is the closest to a value in this vector in Step #3. Therefore, you can use linspace to do this for you:
bin_vector = linspace(min(gr), max(gr), num_colours);
This will create a num_colours 1D array where the beginning of this array starts at the minimum value of gr and varies up to the maximum value of gr and each value is equally spaced such that we generate a num_colours array.
Step #4 - Bring it all home
Now, for each point in gr, we need to figure out which point is the closest to that vector in Step #3, we then use this to figure out the colour we want, then we need to convert our angle into Cartesian co-ordinates, then plot this point.
For illustration purposes, I'm going to assume your radius is 1. You can figure out how to get the x and y co-ordinates by simply doing cos(theta) and sin(theta), where theta is the angle you are examining. Since your gr array has 360 slots, I'm going to assume a resolution of 1 degree per slot. Therefore, you can easily do this in a for loop. Make sure you use hold on because we are going to call plot multiple times, and we don't want to overwrite the plot each time we call plot. You want all of the points to stay in the plot.
Without further ado:
figure; %// Create blank figure
hold on; %// Remember all points
%// For each point in our array...
for idx = 1 : 360
%// Find the closest slot between gr and our vector in Step #3
[~,min_idx] = min(abs(gr(idx) - bin_vector));
%// Grab this colour
clr = colour_map(min_idx,:);
%// Plot the point with this colour
plot(cosd(idx), sind(idx), '.', 'Color', clr, 'MarkerSize', 10);
end
Take notice that cosd and sind take in degrees as the input argument while cos and sin take in radians. Also, take note that I also changed the size of the point so that it's bigger. With the above logic, and your array in gr, this is what I get:
If you want the radius to get larger, all you have to do is multiply each cosd and sind term with your radius. Therefore, you can do something like this:
radius = 2;
for idx = 1 : 360
... %// Insert colour code here
...
...
%// Now plot
plot(radius*cosd(idx), radius*sind(idx), '.', 'Color', clr, 'MarkerSize', 10);
end
Just leave the code the same, but for the plot command, just multiply each x and y value by the radius.
Minor note in efficiency
The way you're calculating your gr array is using an inefficient for loop. There are some situations (like mine above) where you need to use a for loop, but for simple computations there is no need. It's better if you vectorize its creation. Therefore, you can get rid of the for loop to calculate your gr array like so:
x = 1 : 360;
Theta = x*pi/180;
Phii = r*w*w*sin(Theta).*sin(Theta);
Vi = -G*M/(r*r);
gr = Vi + Phii;
x is simply a vector going from 1 to 360, and that's done in the first line. Also, Vi is just an array which contains a single value and if you know how operations work between a scalar and an array, you can just do an addition with this single value and it'll add every value in your array by this much. As such, there's no need to create an array for Vi. Also, take a look at how I calculated Phii. I'm using element-by-element operations as Theta is now an array. You want to create an array Phii that takes corresponding values of Theta, and applies that formula to each value in Theta to produce Phii.
Hope this helps. Good luck!
I have 11 1x50 matrices that contain densities. The first looks like [20, 20, 20... 20] and represents time=0. The second looks like [20, 19, 22,..], etc. and represents time=100. These continue to vary until t=1000.
What I'm hoping to do is to create a plot with the elements' position on the x-axis (50 positions for the 50 pieces of data in each) and time (0-1000) on the y-axis. Ideally, I'd like the plot to be completely filled in with color densities, and a colorbar on the side that shows what densities the color range represents.
Any help would be greatly appreciated!
Sort of inspired by: http://www.chrisstucchio.com/blog/2012/dont_use_scatterplots.html
Assuming you have (or can arrange to have) all those vectors as columns of a 11x50 matrix:
A = randi(100, 11,50); %//example data
you can just use
imagesc(1:50, 0:100:1000, A)
colorbar
axis xy %// y axis increasing, not decreasing
Example:
Looking at the comments, it will be easier to stack these vectors into a 2D matrix. You have 11 individually named vectors. Assuming that your vectors are named vec1, vec2, vec3, etc., create a 2D matrix A that stacks these vectors on top of each other. Also, you'll need to include an extra row and column at the end of this matrix that contains the minimum over all of your vectors. The reason why this is will be apparent later, but for now take my word for it as this is what you need.
In other words:
A = [vec1; vec2; vec3; vec4; vec5; vec6; vec7; vec8; ...
vec9; vec10; vec11];
minA = min(A(:));
A = [A minA*ones(11,1); minA*ones(1,51)];
As such, the first row contains the information at time 0, the next row contains information at time 100, etc. up to time 1000.
Now that we have that finished, we can use the pcolor function to plot this data for you. pcolor stands for pseudo-coloured checkerboard plot. You call this by doing:
pcolor(A);
This will take a matrix stored in A and produce a checkerboard plot of your data. Each point in your matrix gets assigned a colour. The colours get automatically mapped so that the least value gets mapped to the lowest colour while the highest value gets mapped to the highest colour. pcolor does not plot the last row and last column of the matrix, but pcolor does use all of the data in the matrix. In order to ensure that the colours get properly mapped, we need to pad your matrix so that the last row and last column get assigned to the smallest value over all of your vectors. As you want to plot all values in the matrix, that's why we did what we did above.
Once we do this, we'll need to modify the X and Y ticks so that it conforms to your data. As such:
pcolor(A);
set(gca, 'XTick', 0.5:5:51.5);
set(gca, 'XTickLabel', 0:5:50);
set(gca, 'YTick', 1.5:11.5);
set(gca, 'YTickLabel', 0:100:1000);
xlabel('Sample Number');
ylabel('Time');
colorbar;
What the code does above is that it generates a checkerboard pattern like what we talked about. This labels the Sample Number on the x axis while time is on the y axis. You'll see with the two set commands that I did, this is a bit of a hack. The y axis by default labeled the ticks going from 1 - 12. What I did was that I changed these labels so that they go from 0 to 1000 in steps of 100 instead and I also removed the tick of 12. In addition, I have made sure that these labels go in the middle of each row. I do this by setting the YTick property so that I add 0.5 to each value going from 1 - 11. Once I do this, I then change the labels so that they go from 0 - 1000 in steps of 100. I also do the same for the x axis in a similar fashion to the y axis. I then add a colorbar to the side as per your request.
Following the above code, and generating random integer data that is between 13 and 27 as per your comments:
A = randi([13,27], 11, 50);
minA = min(A(:));
A = [A minA*ones(11,1); minA*ones(1,51)];
We get:
Obviously, the limits of the colour bar will change depending on the dynamic range of your data. I used randi and generated random integers within the range of 13 to 27. When you use this code for your purposes, the range of the colour bar will change depending on the dynamic range of your data, but the colours will be adjusted accordingly.
Good luck!
G'day
I'm trying to program a smart way to find the closest grid points to the points along a contour.
The grid is a 2-dimensional grid, stored in x and y (which contain the x and y kilometre positions of the grid cells).
The contour is a line, made up of x and y locations, not necessarily regularly spaced.
This is shown below - the red dots are the grid, and the blue dots are the points on the contour. How do I find the indices of the red dot closest to each blue dot?
Edit - I should mention that the grid is a latitude/longitude grid, of an area fairly close to the south pole. So, the points (the red dots) are the position in metres from the south pole (using a polar stereographic representation). Since the grid is a geographic grid there is unequal grid spacing - with slightly different shaped cells (where the red dots define the vertices of the cells) due to the distortion at high latitudes.
The result is that I can't just find which row/column of the x and y matrix corresponds closest to the input point coordinates - unlike a regular grid from meshgrid, the values in the rows and columns vary...
Cheers
Dave
The usual method is to go:
for every blue point {
for every red point {
is this the closest so far
}
}
But a better way is to put the red data into a kd tree. This is a tree that splits the data along its mean, then splits the two data sets along their means etc until you have them separated into a tree structure.
This will change your searching effeciancy from O(n*m) to O(log(n)*m)
Here is a library:
http://www.mathworks.com.au/matlabcentral/fileexchange/4586-k-d-tree
This library will provide you the means to easily make a kd tree out of the data and to search for the closest point in it.
Alternatively you can use a quadtree, not as simple but the same idea. (you may have to write your own library for that)
Make sure the largest data set (in this case your red points) go into the tree as this will provide the greatest time reduction.
I think I've found a way to do it using the nearest flag of griddata.
I make a matrix that is the same size as the grid x and y matrices, but is filled with the linear indices of the corresponding matrix element. This is formed by reshaping a vector (which is 1:size(x,1)*size(x,2)) to the same dimensions as x.
I then use griddata and the nearest flag to find the linear index of the point closest to each point on my contour (blue dots). Then, simply converting back to subscript notation with ind2sub leaves me with a 2 row vectors describing the matrix subscripts for the points closest to each point on the blue-dotted contour.
This plot below shows the contour (blue dots), the grid (red dots) and the closest grid points (green dots).
This is the code snippet I used:
index_matrix1 = 1:size(x,1)*size(x,2);
index_matrix1 = reshape(index_matrix1,size(x));
lin_ind = griddata(x,y,index_matrix1,CX,CY,'nearest'); % where CX and CY are the coords of the contour
[sub_ind(1,:),sub_ind(2,:)] = ind2sub(size(x),lin_ind);
I suppose that in the stereographic representation, your points form a neat grid in r-theta coordinates. (I'm not too familiar with this, so correct me if I'm wrong. My suggestion may still apply).
For plotting you convert from the stereographic to latitude-longitude, which distorts the grid. However, for finding the nearest point, consider converting the latitude-longitude of the blue contour points into stereographic coordinates, where it is easy to determine the cell for each point using its r and theta values.
If you can index the cell in the stereographic representation, the index will be the same when you transform to another representation.
The main requirement is that under some transformation, the grid points are defined by two vectors, X and Y, so that for any x in X and y in Y, (x, y) is a grid point. Next transform both the grid and the contour points by that transformation. Then given an arbitrary point (x1, y1), we can find the appropriate grid cell by finding the closest x to x1 and the closest y to y1. Transform back to get the points in the desired coordinate system.
dsearchn: N-D nearest point search.
[k, d] = dsearchn(A,B) : returns the distances, d, to the closest points. d is a column vector of length p.
http://au.mathworks.com/help/matlab/ref/dsearchn.html?s_tid=gn_loc_drop
Im faced with a problem where i need to plot a two dimensional data with different colors and markers.
We are given with 2 array, namely points (n x 2 dimension) and Label (n x 1 dimension). Im not sure about the number of unique values in the Label array but maximum could be 10. I would like to plot the points with different color and markers based on its corresponding Label value.
Can any one help me in this regard
Use gscatter, which does a scatter plot, using a group (Label in your case) to plot in different colours/makers.
GSCATTER(X,Y,G,CLR,SYM,SIZ) specifies the colors, markers, and
size to use. CLR is either a string of color specifications or
a three-column matrix of color specifications. SYM is a string
of marker specifications. Type "help plot" for more information.
For example, if SYM='o+x', the first group will be plotted with a
circle, the second with plus, and the third with x. SIZ is a
marker size to use for all plots. By default, the marker is '.'.
So you can specify colours like 'rgcmykwb' to do red for the first group, green for the second, etc or [] just to have Matlab sort it out.
By default Matlab uses the same marker for each group, so you need to specify what markers you want to be used for each group. If you do '.ox+*sdv^<>ph' you'll just cycle along all the markers that Matlab has.
n=50;
% make nx2 matrix of random points.
points = random('unif',0,1,n,2);
% make nx1 matrix of random labels from {1,2,...,5}
labels=round(random('unif',1,5,n,1));
% plot. Let Matlab sort out the colours and we will specify markers.
gscatter(points(:,1),points(:,2),labels,[],'ox+*sdv^<>ph.')
It looks a bit like this:
I've got a series of XY point pairs in MATLAB. These pairs describe points around a shape in an image; they're not a function, meaning that two or more y points may exist for each x value.
I can plot these points individually using something like
plot(B(:,1),B(:,2),'b+');
I can also use plot to connect the points:
plot(B(:,1),B(:,2),'r');
What I'm trying to retrieve are my own point values I can use to connect the points so that I can use them for further analysis. I don't want a fully connected graph and I need something data-based, not just the graphic that plot() produces. I'd love to just have plot() generate these points (as it seems to do behind the scenes), but I've tried using the linseries returned by plot() and it either doesn't work as I understand it or just doesn't give me what I want.
I'd think this was an interpolation problem, but the points don't comprise a function; they describe a shape. Essentially, all I need are the points that plot() seems to calculate; straight lines connecting a series of points. A curve would be a bonus and would save me grief downstream.
How can I do this in MATLAB?
Thanks!
Edit: Yes, a picture would help :)
The blue points are the actual point values (x,y), plotted using the first plot() call above. The red outline is the result of calling plot() using the second approach above. I'm trying to get the point data of the red outline; in other words, the points connecting the blue points.
Adrien definitely has the right idea: define a parametric coordinate then perform linear interpolation on the x and y coordinates separately.
One thing I'd like to add is another way to define your parametric coordinate so you can create evenly-spaced interpolation points around the entire shape in one pass. The first thing you want to do, if you haven't already, is make sure the last coordinate point reconnects to the first by replicating the first point and adding it to the end:
B = [B; B(1,:)];
Next, by computing the total distance between subsequent points then taking the cumulative sum, you can get a parametric coordinate that makes small steps for points close together and larger steps for points far apart:
distance = sqrt(sum(diff(B,1,1).^2,2)); %# Distance between subsequent points
s = [0; cumsum(distance)]; %# Parametric coordinate
Now, you can interpolate a new set of points that are evenly spaced around the edge along the straight lines joining your points using the function INTERP1Q:
sNew = linspace(0,s(end),100).'; %'# 100 evenly spaced points from 0 to s(end)
xNew = interp1q(s,B(:,1),sNew); %# Interpolate new x values
yNew = interp1q(s,B(:,2),sNew); %# Interpolate new y values
These new sets of points won't necessarily include the original points, so if you want to be sure the original points also appear in the new set, you can do the following:
[sAll,sortIndex] = sort([s; sNew]); %# Sort all the parametric coordinates
xAll = [B(:,1); xNew]; %# Collect the x coordinates
xAll = xAll(sortIndex); %# Sort the x coordinates
yAll = [B(:,2); yNew]; %# Collect the y coordinate
yAll = yAll(sortIndex); %# Sort the y coordinates
EXAMPLE:
Here's an example to show how the above code performs (I use 11 pairs of x and y coordinates, one of which is repeated for the sake of a complete example):
B = [0.1371 0.1301; ... %# Sample data
0.0541 0.5687; ...
0.0541 0.5687; ... %# Repeated point
0.0588 0.5863; ...
0.3652 0.8670; ...
0.3906 0.8640; ...
0.4090 0.8640; ...
0.8283 0.7939; ...
0.7661 0.3874; ...
0.4804 0.1418; ...
0.4551 0.1418];
%# Run the above code...
plot(B(:,1),B(:,2),'b-*'); %# Plot the original points
hold on; %# Add to the plot
plot(xNew,yNew,'ro'); %# Plot xNew and yNew
I'd first define some parametric coordinate along the different segments (i.e. between the data points)
s = 1:size(B,1);
Then, just use interp1 to interpolate in s space. e.g. If you want to generate 10 values on the line between data point 5 and 6 :
s_interp = linspace(5,6,10); % parametric coordinate interpolation values
x_coord = interp1(s,B(:,1),s_interp,'linear');
y_coord = interp1(s,B(:,2),s_interp,'linear');
This should do the trick.
A.
Actually there is a MATLAB function "improfile", which might help you in your problem. Lets say these are the 4 coordinates which you want to find the locations between these coordinates.
xi=[15 30 20 10];
yi=[5 25 30 50];
figure;
plot(xi,yi,'r^-','MarkerSize',12)
grid on
Just generate a random image and run the function
n=50; % total number of points between initial coordinates
I=ones(max([xi(:);yi(:)]));
[cx,cy,c] = improfile(I,xi,yi,n);
hold on, plot(cx,cy,'bs-','MarkerSize',4)
Hope it helps