I have several 4 x 4 matrices with data that I would like to represent in a 2-D plot. The plot is supposed to show how the results of a simulation change with varying parameters.
On the y-axis I would like to have the possible values of parameter A (in this case, [10,20,30,40]) and on the x-axis I want to have the possible values of parameter B (in this case, [2,3,4,5]). C is a 4 x 4 matrix with the evaluation value for running the simulation with the corresponding parameter combination.
Example: The evaluation value for the parameter combination A = 10, B = 2 equals 12 dB. I would like to plot it at the cross section A and B (I hope you understand what I mean by this) and code the value by a fat colored dot (e.g. red means high values, blue means low values).
How can I do this? I would basically like to have something like mesh without lines.
I'm sorry for my imperfect English! I hope you understood what I would like to achieve, thank you in advance!
You can do this with the mesh command (and the built-in colormaps you can choose from can be found here, or you could even make your own):
[A, B] = meshgrid(10:10:40, 2:5); % Grids of parameter values
C = rand(4); % Random sample data
hMesh = mesh(A, B, C); % Plot a mesh
set(hMesh, 'Marker', '.', ... % Circular marker
'MarkerSize', 60, ... % Make marker bigger
'FaceColor', 'none', ... % Don't color the faces
'LineStyle', 'none'); % Don't render lines
colormap(jet); % Change the color map
view(0, 90); % Change the view to look from above
axis([5 45 1.5 5.5]); % Expand the axes limits a bit
colorbar; % Add colorbar
And here's the plot:
Related
This question already has answers here:
Change color of 2D plot line depending on 3rd value
(5 answers)
Closed 6 months ago.
I'm looking to do something similar to the below image (source) in Matlab. Ignore the vectors and the shaded cone; I just want to
plot a trajectory on the unit sphere, given by a function m(x) (whose values are points on the sphere),
color it according to parameter x (running from -inf to +inf),
display a color bar which explains the mapping from x-value to color.
I can plot the sphere easily with the help of built-in functions sphere and mesh, and I can draw the trajectory with plot3. To generate the x-values I can use something like
x = tan((-1:0.01:1)*pi/2);
which gives a distribution of points fitting for the types of functions m(x) will be (most of the action will be around x = 0).
The tricky part is the color. I have looked at the colormap and colorbar built-ins, but both seem to pertain to meshes and surfaces rather than curves, so I don't see an obvious way to adapt it to my use case.
Does anyone have any ideas for how I might proceed?
When using plot it is not possible for one line to be multicoloured. In order to make one line multicoloured, you must plot each individual segment and then colour them individually. For example:
% make some dummy data
% note that this is in the form of 1 x N row vectors
t = -.99:0.01:0.99;
x = cos(t * pi/2);
y = sin(t * pi/2);
z = t;
% reorder data in order to plot individual line segments
indices = [1:length(x) - 1; 2:length(x)];
figure;
p = plot3(x(indices), y(indices), z(indices), 'LineWidth', 2);
set(p, {'Color'}, num2cell(parula(length(x) - 1), 2)); % see what happens when you comment out this line
You can change the colormap you want by changing the parula keyword above. You can use any of the supplied colormaps, or create your own (in the form of an M x 3 RGB triple matrix).
You can then add the colorbar (note that these are dummy values).
c = colorbar;
caxis([-6 6]);
set(c, 'Ticks', [-6, -4, -2, -1, 0, 1, 2, 4, 6]);
set(c, 'TickLabels', {'-\infty', '-4', '-2', '-1', '0', '1', '2', '4', '\infty'});
You can achieve a somewhat similar, but different, effect using scatter3(). It is similar to plot3() but will allow you to set color (and size, if you wish) for each data point that it plots. If the aesthetics suit you, it is a simple and versatile approach.
I produced a plot that contains 50 curves and each of them corresponds to a specific value of a parameter called "Jacobi constant", so I have 50 values of jacobi constant stored in array called jacobi_cst_L1:
3.000900891023230
3.000894276927840
3.000887643313580
3.000881028967010
3.000874419173230
3.000867791975870
3.000861196034850
3.000854592397690
3.000847948043080
3.000841330136040
3.000834723697250
3.000828099771820
3.000821489088600
3.000814922863360
3.000808265737810
3.000801695858850
3.000795067776960
3.000788475204760
3.000781845363950
3.000775192199620
3.000768609354090
3.000761928862980
3.000755335851910
3.000748750854930
3.000742084743060
3.000735532899990
3.000728906460450
3.000722309400740
3.000715644446600
3.000709016645110
3.000702431180730
3.000695791284050
3.000689196186970
3.000682547292110
3.000675958537960
3.000669315388860
3.000662738391370
3.000656116141060
3.000649560630930
3.000642857256680
3.000636330415510
3.000629657944820
3.000623060310100
3.000616425935580
3.000609870077710
3.000603171772120
3.000596554947660
3.000590018845460
3.000583342259840
3.000576748353570
I want to use a colormap to color my curves and then show in a lateral bar the legend that show the numerical values corresponding to each color of orbit.
By considering my example image, I would want to add the array of constants in the lateral bar and then to color each curve according the lateral bar.
% Family of 50 planar Lyapunov orbits around L1 in dimensionless unit
fig = figure;
for k1 = 1:(numel(files_L1_L2_Ly_prop)-2)
plot([Ly_orb_filt(1).prop(k1).orbits.x],[Ly_orb_filt(1).prop(k1).orbits.y],...
"Color",my_green*1.1); hold on %"Color",my_green*1.1
colorbar()
end
axis equal
% Plot L1 point
plot(Ly_orb_filt_sys_data(1).x,Ly_orb_filt_sys_data(1).y,'.',...
'color',[0,0,0],'MarkerFaceColor',my_green,'MarkerSize',10);
text(Ly_orb_filt_sys_data(1).x-0.00015,Ly_orb_filt_sys_data(1).y-0.0008,'L_{1}');
%Primary bodies plots
plot(AstroData.mu_SEM_sys -1,0,'.',...
'color',my_blue,'MarkerFaceColor',my_blue,'MarkerSize',20);
text(AstroData.mu_SEM_sys-1,0-0.001,'$Earth + Moon$','Interpreter',"latex");
grid on;
xlabel('$x$','interpreter','latex','fontsize',12);
ylabel('$y$','interpreter','latex','FontSize',12);
How can I color each line based on its Jacobi constant value?
You can use any colour map to produce a series of RGB-triplets for the plotting routines to read (Or create an m-by-3 matrix with elements between 0 and 1 yourself):
n = 10; % Plot 10 lines
x = 1:15;
colour_map = jet(n); % Get colours. parula, hsv, hot etc.
figure;
hold on
for ii = 1:n
% Plot each line individually
plot(x, x+ii, 'Color', colour_map(ii, :))
end
colorbar % Show the colour bar.
Which on R2007b produces:
Note that indexing into a colour map will produce linearly spaced colours, thus you'll need to either interpolate or calculate a lot to get the specific ones you need. Then you can (need to?) modify the resulting colour bar's labels by hand to reflect your input values. I'd simply use parula(50), treat its indices as linspace(jacobi(1), jacobi(end), 50) and then my_colour = interp1(linspace(jacobi(1), jacobi(end), 50), parula(50), jacobi).
So in your code, rather than using "Color",my_green*1.1 for each line, use "Color",my_colour(kl,:), where my_colour is whatever series of RGB triplets you have defined.
This question already has answers here:
Change color of 2D plot line depending on 3rd value
(5 answers)
Closed 5 years ago.
How do you create a color gradient in Matlab such that you plot a 2D line plot of y=y(x), and you color it using another variable that also depends on x such that z=z(x). A scatter or point plot is also fine by me.
I would also like to have a colormap legend kind of thing showing the color gradient and it's actual representation of z. This stuff is quite common in visualisation tools such as VisIt and ParaView but I could not yet FIGURE it out in Matlab.
If a scatter plot is fine, you can use the 4th input to scatter:
x = -10:0.01:10;
y = sinc(x);
z = sin(x);
scatter(x,y,[],z,'fill')
where z is the color.
The only way I know of to do this is with a little trick using surf:
% Create some sample data:
x = cumsum(rand(1,20)); % X data
y = cumsum(rand(1,20)); % Y data
z = 1:20; % "Color" data
% Plot data:
surf([x(:) x(:)], [y(:) y(:)], [z(:) z(:)], ... % Reshape and replicate data
'FaceColor', 'none', ... % Don't bother filling faces with color
'EdgeColor', 'interp', ... % Use interpolated color for edges
'LineWidth', 2); % Make a thicker line
view(2); % Default 2-D view
colorbar; % Add a colorbar
And the plot:
To manipulate the color of the line continuously, you'll want to use surface.
While at first look, this function looks most useful for plotting 3d surfaces, it provides more flexibility for line coloring than the basic plot function. We can use the edges of the mesh to plot our line, and take advantage of the vertex colors, C, to render interpolated color along the edge.
You can check out the full list of rendering properties, but the ones you are most likely to want are
'FaceColor', 'none', do not draw the faces
'EdgeColor', 'interp', interpolate between vertices
Here's an example adapted from MATLAB Answers post
x = 0:.05:2*pi;
y = sin(x);
z = zeros(size(x)); % We don't need a z-coordinate since we are plotting a 2d function
C = cos(x); % This is the color, vary with x in this case.
surface([x;x],[y;y],[z;z],[C;C],...
'FaceColor','none',...
'EdgeColor','interp');
Generate a colormap, e.g. jet(10). The example would generate a 10*3 matrix.
Use interp1 to interpolate between the values in the RGB space using your data by setting the first color as the lowest value and the last color as the highest value. This would generate a n*3 matrix where n is the number of data points.
Use scatter with the optional parameter c to plot the points with the interpolated colors.
activate colorbar to show the colorbar.
Environment: Windows 7 64 bit, Matlab 2014a
Objective:
To draw a heatmap of errors for two parameters to be optimized.
To put proper tick marks and tick values
Draw the grid lines in the correct place
Problem: Arranging the X and Y tick positions and values. When the last ("end") value of the vectors in x and y axes are the same, the code I use puts the ticks and values properly. However, when the end values are different it does not, and produces something really weird.
Below I have included the code which I have modified so that you can run it without the need of adding anything. Of course in my case the error vector are the error values, not random numbers. To see the problem of "end value" use the second b vector.
fontsize = 20
k = [2^-5, 2^-3, 2^-1, 2^0, 2^1, 2^3, 2^5, 2^7, 2^9, 2^11, 2^13, 2^15]
b = [2^-5, 2^-3, 2^-1, 2^0, 2^1, 2^3, 2^5, 2^7, 2^8, 2^9, 2^10, 2^11, 2^13, 2^15]
% b = [2^-5, 2^-3, 2^-1, 2^0, 2^1, 2^3, 2^5, 2^7, 2^8, 2^9, 2^10, 2^11, 2^13, 2^19]
errorVector = randi(20, 1, length(b)*length(k))'
figure
% Create a matrix from error vector (size of error vector is [length(k)*length(b),1])
B = reshape(errorVector, [length(b), length(k)])
B = flipud(B)
% imagesc(x,y,C)
imagesc(b, k, B)
title('Heatmap Parameters Percent Error', 'FontSize', fontsize);
% Set colorbar limits
caxis([0 15])
colorbar;
ax1 = gca;
xTickLabel = (k)'
xTick = linspace(k(1), k(end), numel(xTickLabel))';
set(ax1, 'XTick', xTick, 'XTickLabel', xTickLabel)
xlabel('k parameter', 'FontSize', fontsize)
yTickLabel = (b)'
yTick = linspace(b(1), b(end), numel(yTickLabel))';
set(ax1, 'YTick', yTick, 'YTickLabel', flipud(yTickLabel(:)))
ylabel('b parameter', 'FontSize', fontsize)
set(ax1,'FontSize', fontsize)
Here, change any of the end values of b or k vectors, and the program will output a graph where the X and Y ticks are totally wrong.
Also, I would like to draw grid lines. When I use "grid on" it draws grid lines right on the tick marks which is not correct in the case of heatmap. Because tick marks will be in the center of the columns -or rows- but the grid lines should be at the boundaries between the columns -or rows.
By the way if you know a better way to plot a heatmap in Matlab, please do tell.
Please help me solve this problem. Any help is appreciated,
Ilyas
First of all - you don't need to flipud the B matrix - by default imagesc plots the y-data inversed, but you can fix this with the following statement:
set(gca,'ydir','normal');
This also means you don't have to mess around with flipping the tick-labels. You can get the labels right by doing the following:
% replace the imagesc call with:
imagesc(B);
set(gca,'ydir','normal');
% formatting stuff
...
% replace the set commands with:
set(ax1, 'XTick', 1:length(k), 'XTickLabel', k)
set(ax1, 'YTick', 1:length(b), 'YTickLabel', b)
By default, if you don't provide x and y data to the imagesc command, it will number them linearly (1,2,3...). Basically what we've done here is make sure that it has ticks for each of the elements of b and k, and then set the labels to the values of the respective vectors.
Unfortunately, I'm not sure if there is a way to get the grid spacing right with imagesc or not. You could try using pcolor instead, which has it's own set of issues, but allows you to get grid lines (of sorts) between the elements. It also allows you to use an interpolated shading mode, which will make your plot look more like a typical heat map.
To use pcolor instead, you just have to replace imagesc:
% imagesc(B);
% set(gca,'ydir','normal');
pcolor(B);
% this uses a smoother shading method, for a more 'heatmap' like output
% shading interp
Everything else should work as intended, I believe.
I'm trying to do something similar to what's outlined in this post:
MATLAB, Filling in the area between two sets of data, lines in one figure
but running into a roadblock. I'm trying to shade the area of a graph that represents the mean +/- standard deviation. The variable definitions are a bit complicated but it boils down to this code, and when plotted without shading, I get the screenshot below:
x = linspace(0, 100, 101)';
mean = torqueRnormMean(:,1);
meanPlusSTD = torqueRnormMean(:,1) + torqueRnormStd(:,1);
meanMinusSTD = torqueRnormMean(:,1) - torqueRnormStd(:,1);
plot(x, mean, 'k', 'LineWidth', 2)
plot(x, meanPlusSTD, 'k--')
plot(x, meanMinusSTD, 'k--')
But when I try to implement shading just on the lower half of the graph (between mean and meanMinusSTD) by adding the code below, I get a plot that looks like this:
fill( [x fliplr(x)], [mean fliplr(meanMinusSTD)], 'y', 'LineStyle','--');
It's obviously not shading the correct area of the graph, and new near-horizontal lines are being created close to 0 that are messing with the shading.
Any thoughts? I'm stumped.
You may be getting a problem with using mean as a variable, since it's also a reserved MATLAB command. Try clearing the variable space and then using a unique variable name.
As for the second problem, you want
fill( [x fliplr(x)], [meanUniqueName fliplr(meanMinusSTD)], 'y', 'LineStyle','--');
You also don't need to do this in two steps, but can do it all at once. A code snippet from a script I'm currently working on does the exact same thing and contains the lines:
avar = allan(DATA, tau);
xFill = [avar.tau1 fliplr(avar.tau1)];
yFill = [avar.sig2+avar.sig2err fliplr(avar.sig2-avar.sig2err)];
figure(2);
fill(xFill,yFill,'y','LineStyle','--')
line(avar.tau1,avar.sig2);
So I fill the area between the two error lines, and then draw the data line on top.
It turned out to be a column vs row vector issue. For some reason using the fill method above with flipud with the original column vectors doesn't work, but transposing the original variables then using fliplr does. Go figure. Here's the code in case it helps someone else:
x = linspace(0,100, 101);
mean = torqueRnormMean(:,DOF)';
meanPlusSTD = torqueRnormMean(:,DOF)' + torqueRnormStd(:,DOF)';
meanMinusSTD = torqueRnormMean(:,DOF)' - torqueRnormStd(:,DOF)';
fill( [x fliplr(x)], [meanPlusSTD fliplr(meanMinusSTD)], 'k');
alpha(.25);
plot(x, mean, 'k', 'LineWidth', 2)
plot(x, meanPlusSTD, 'k')
plot(x, meanMinusSTD, 'k')
Note that I removed the dotted line and just used thin vs. thick lines to denote standard deviation and mean. I did this because the line style was inconsistent. This code is in a loop where DOF runs from 1:9, and in some of the subplots both std curves would be dashed and in some just the top or bottom. It didn't matter enough to me to have them dashed so I kept it simple. Now this is an example of the graph I get:
One thing that you appear to be doing wrong is that you're applying fliplr to column vectors. That will have no effect. The example you cited uses row vectors. You also concatenate them into a matrix instead of into a single vector like the example. I think that the equivalent with column vectors would be:
fill( [x;flipud(x)], [mean;flipud(meanMinusSTD)], 'y');
Another possibility:
x = 1:1000; % example x values
y_upper = 5+sin(2*pi/200*x); % example upper curve
y_lower = 2+sin(2*pi/230*x); % example lower curve
bar(x, y_upper, 1, 'b', 'edgecolor', 'b');
hold on
bar(x, y_lower, 1, 'w', 'edgecolor', 'w');
axis([0 1000 0 7])
It uses bar (with unit width and same-color edges) to fill the upper curve, and then a second bar to "remove" (plot in white) the lower part.