I have three vectors of data; first column is axis x, second column axis y and third column is the measured data point value v:
x = [1 2 3 4 5];
y = [2 3 4 5 6];
v = [0 -1 +2 3 -5];
Is there a way to plot this in matlab and color the data points according to their value? I tried with scatter, but that doesn't give color coding.
Just use scatter, it can accept values for each point. Just set the size of each point, set it to be filled, turn on the colorbar and that's it. Just please don't use the jet colormap...
x = [1 2 3 4 5];
y = [2 3 4 5 6];
v = [0 -1 +2 3 -5];
pt_sz = 30;
colormap parula
scatter(x, y, pt_sz, v, 'filled');
colorbar;
grid on
You can try pcolor. It works like
z=rand(4,4);
pcolor(R,C,z);
Where z is a matrix storing the data (your v), R is the row (your x) and C is the column (your y).
Related
I have two (or more but if solved for two, it's solved for any number) 2-by-N matrices which represent points with an x (the first row) and y (the second row) coordinates. The points are always sorted in the increasing x coordinate. What I want to do is I want to merge these two matrices into one 3-by-N matrix so that if two points (one from each matrix) have the same x coordinate, they would form one column in the new matrix, the first row being the x coordinate and the second and third row being the two y coordinates. However, if there is a point in one matrix that has x coordinate different than all other points in the second matrix, I still want to have full 3-element column that is placed such that the x coordinates are still sorted and the missing value from the other matrix is replaced by the nearest value with lower x coordinate (or NaN if there is none).
Better to explain by example.
First matrix:
1 3 5 7 % x coordinate
1 2 3 4 % y coordinate
Second matrix:
2 3 4 7 8 % x coordinate
5 6 7 8 9 % y coordinate
Desired result:
1 2 3 4 5 7 8 % x coordinate
1 1 2 2 3 4 4 % y coordinate from first matrix
NaN 5 6 7 7 8 9 % y coordinate from second matrix
My question is, how can I do it effectively in matlab/octave and numpy? (Effectively because I can always do it "manually" with loops but that doesn't seem right.)
You can do it with interp1 and the keyword 'previous' for strategy (you can also choose 'nearest' if you do not care if it is larger or smaller) and 'extrap' for allowing extrapolation.
Define the matrices
a=[...
1 3 5 7;...
1 2 3 4];
b=[...
2 3 4 7 8;...
5 6 7 8 9];
Then find the interpolation points
x = unique([a(1,:),b(1,:)]);
And interpolate
[x ; interp1(a(1,:),a(2,:),x,'previous','extrap') ; interp1(b(1,:),b(2,:),x,'previous','extrap') ]
Timeit results:
I tested the algorithms on
n = 1e6;
a = cumsum(randi(3,2,n),2);
b = cumsum(randi(2,2,n),2);
and got:
Wolfie: 1.7473 s
Flawr: 0.4927 s
Mine: 0.2757 s
This verions uses set operations:
a=[...
1 3 5 7;...
1 2 3 4];
b=[...
2 3 4 7 8;...
5 6 7 8 9];
% compute union of x coordinates
c = union(a(1,:),b(1,:));
% find indices of x of a and b coordinates in c
[~,~,ia] = intersect(a(1,:),c);
[~,~,ib] = intersect(b(1,:),c);
% create output matrix
d = NaN(3,numel(c));
d(1,:) = c;
d(2,ia) = a(2,:);
d(3,ib) = b(2,:);
% fill NaNs
m = isnan(d);
m(:,1) = false;
i = find(m(:,[2:end,1])); %if you have multiple consecutive nans you have to repeat these two steps
d(m) = d(i);
disp(d);
Try it online!
Your example:
a = [1 3 5 7; 1 2 3 4];
b = [2 3 4 7 8; 5 6 7 8 9];
% Get the combined (unique, sorted) `x` coordinates
output(1,:) = unique([a(1,:), b(1,:)]);
% Initialise y values to NaN
output(2:3, :) = NaN;
% Add x coords from `a` and `b`
output(2, ismember(output(1,:),a(1,:))) = a(2,:);
output(3, ismember(output(1,:),b(1,:))) = b(2,:);
% Replace NaNs in columns `2:end` with the previous value.
% A simple loop has the advantage of capturing multiple consecutive NaNs.
for ii = 2:size(output,2)
colNaN = isnan(output(:, ii));
output(colNaN, ii) = output(colNaN, ii-1);
end
If you have more than 2 matrices (as suggested in your question) then I'd advise
Store them in a cell array, and loop over them to do the calls to ismember, instead of having one code line per matrix hardcoded.
The NaN replacement loop is already vectorised for any number of rows.
This is the generic solution for any number of matrices, demonstrated with a and b:
mats = {a, b};
cmats = horzcat(mats);
output(1, :) = unique(cmats(1,:));
output(2:numel(mats)+1, :) = NaN;
for ii = 1:size(mats)
output(ii+1, ismember(output(1,:), mats{ii}(1,:))) = mats{ii}(2,:);
end
for ii = 2:size(output,2)
colNaN = isnan(output(:,ii));
output(colNaN, ii) = output(colNaN, ii-1);
end
I have a vector of x-values at which I would like to add vertical lines to a graph, say a row vector: vec = [1 2 3 4 5]
I know that you can add single vertical lines like this:
plot([1 1],[0 1])
(gives a vertical line at x=1 from y=0 to y=1).
But when I try something like
vec = [1 2 3 4 5];
lowLine = [0 0 0 0 0];
highLine = [1 1 1 1 1];
plot([vec vec],[lowLine highLine])
It does not give the required result, instead it gives a z-shape. Where am I going wrong?
In order to plot several lines in a single plot, you need to use the fact that MATLAB's plot function handles matrices as inputs, and that it sees each column of the inputs as different plots :
If X and Y are both matrices, then they must have equal size. The plot
function plots columns of Y versus columns of X.
Thus, in order to get the expected result, you need to write :
vec = [1 2 3 4 5];
lowLine = [0 0 0 0 0];
highLine = [1 1 1 1 1];
plot([vec;vec],[lowLine;highLine])
Result :
Say I have the following Time Series:
a = [1 3 1 5 1 3 5 1 5];
Now, on doing kmeans(a,3), I obtained:
b = kmeans(a,3); // [1 2 1 3 1 2 3 1 3]; based on the clusters.
I now wish to plot a, so that the color for a(i) corresponds to the cluster that is has been assigned in b. Can someone show me how to do that?
This plots each point with increasing x coordinates, y coordinate equal to a, and the color as given by b:
colors = hsv(max(b)); %// or use other color maps:
hold on
for ii = 1:length(a)
plot(ii,a(ii),'marker', 'o', 'color',colors(b(ii),:)) %// option 1
end
axis([0 length(a+1) min(a)-1 max(a)+1])
How can I set the x axis label as a vector? For example, if I do plot(1:5), the x axis label is [1, 2, 3, 4, 5]. I'd like to set it to a vector, e.g. [1 4 5 7 10]. Note that the vector's size may be huge, so doing it manually is not acceptable.
I believe this is what you want.
y = 1:5;
x = [1 4 5 7 10];
plot(y);
set(gca,'XTickLabel',x);
you can do this by sending plot two vectors: one for x and one for y.
plot([1 4 5 7 10], 1:5);
I have an intensity/greyscale image, and I have chosen a pixel inside this image. I want to send vectors starting from this pixel in all directions/angles, and I want to sum all the intensities of the pixels touching one vector, for all vectors.
After this step I would like to plot a histogram with the intensities on one axis and the angle on the other axis. I think I can do this last step on my own, but I don't know how to create these vectors inside my greyscale image and how to get the coordinates of the pixels a vector touches.
I previously did this in C++, which required a lot of code. I am sure this can be done with less effort in MATLAB, but I am quite new to MATLAB, so any help would be appreciated, since I haven't found anything helpful in the documentation.
It might not be the best way to solve it, but you can do it using a bit of algebra, heres how...
We know the Point-Slope formula of a line passing through point (a,b) with angle theta is:
y = tan(theta) * (x-a) + b
Therefore a simple idea is to compute the intersection of this line with y=const for all const, and read the intensity values at the intersection. You would repeat this for all angles...
A sample code to illustrate the concept:
%% input
point = [128 128]; % pixel location
I = imread('cameraman.tif'); % sample grayscale image
%% calculations
[r c] = size(I);
angles = linspace(0, 2*pi, 4) + rand;
angles(end) = [];
clr = lines( length(angles) ); % get some colors
figure(1), imshow(I), hold on
figure(2), hold on
for i=1:length(angles)
% line equation
f = #(x) tan(angles(i))*(x-point(1)) + point(2);
% get intensities along line
x = 1:c;
y = round(f(x));
idx = ( y<1 | y>r ); % indices of outside intersections
vals = diag(I(x(~idx), y(~idx)));
figure(1), plot(x, y, 'Color', clr(i,:)) % plot line
figure(2), plot(vals, 'Color', clr(i,:)) % plot profile
end
hold off
This example will be similar to Amro's, but it is a slightly different implementation that should work for an arbitrary coordinate system assigned to the image...
Let's assume that you have matrices of regularly-spaced x and y coordinates that are the same size as your image, such that the coordinates of pixel (i,j) are given by (x(i,j),y(i,j)). As an example, I'll create a sample 5-by-5 set of integer coordinates using MESHGRID:
>> [xGrid,yGrid] = meshgrid(1:5)
xGrid =
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
yGrid =
1 1 1 1 1
2 2 2 2 2
3 3 3 3 3
4 4 4 4 4
5 5 5 5 5
Next we can define a line y = m*(x - a) + b passing through the coordinate system by selecting some values for the constants and computing y using the x coordinates of the grid:
>> a = 0;
>> b = 1;
>> m = rand
m =
0.5469
>> y = m.*(xGrid(1,:)-a)+b
y =
1.5469 2.0938 2.6406 3.1875 3.7344
Finally, we find the y points in the grid that differ from the points computed above by less than the grid size:
>> index = abs(yGrid-repmat(y,size(yGrid,1),1)) <= yGrid(2,1)-yGrid(1,1)
index =
1 0 0 0 0
1 1 1 0 0
0 1 1 1 1
0 0 0 1 1
0 0 0 0 0
and use this index matrix to get the x and y coordinates for the pixels crossed by the line:
>> xCrossed = xGrid(index);
>> yCrossed = yGrid(index);