How to create a plot with highlight (holes) based on Y value and colored density map based on X value

Hi Team,

can you please teach me how to plot the following

I start with 2 sin function addition.

>> t = [0:0.0001:0.4*pi];

y=cos(100*t) + cos(110*t);

plot (y)

Then can you please help me with

1. highlight the data points with bubble whose Y value is less than 0.5 but great than -0.5 (as in the pic below)
2. include a density heat map along the X axis with the relative density of the highlighted data points. (red means the highlighted data is very concentrated and blue means the highlighted data is very scarce)

The plot attached is more or less capture the requirement 1.

Thank you

Answer 1

[Voss]

To do #1, add the following lines of code after your plot(y) line:

hold on
idx = y>-0.5 & y<0.5;
plot(t(idx),y(idx),'o');

[Minghao Dong]

Thank you! It worked for #1

For #2, I found contourf, but not sure if it can apply to this case...

[Voss]

For #2, I think a patch object would be sufficient, but a surface may be more convenient; I don't think you will need a contour object. Regardless of the graphics object you use, it will be necessary to define "relative density" and calculate it.

So let's say relative density has been calculated and is stored in a row vector called d, which is the same size as t. Then you can make a surface representing your heat map like this:

surface(t,[-0.5; 0.5],[d; d],'EdgeColor','none');
colormap('jet');

[Minghao Dong]

Hi Benjamin

Thanks for your response!

I have tried some search and found something very close to the relative density but I can not extract it out as the vecter d with the same size as t for some reason.

//here are my code//

t = [0:0.0005:1.2];

y=cos(100*t) + cos(110*t);

plot(t,y)

hold on

idx = y>-0.5 & y<0.5;

plot(t(idx),y(idx),'o');

axis tight

h=scatterhist(t(idx),y(idx),'kernel','on');

delete (h(3))

% The original plot(t,y) was removed by h=scatterhist(t(idx),y(idx),'kernel','on');. So I re-plot it as following

hold on

plot (t,y)

% The axis can not capture all the plot I want to demonstrate. So i added

axis([0 1.2 -2 2])

%The plot is actually moving todards at the right direction but there is a error

Error in scatterhist/scatterhistXYLimCallback (line 527)

set(hYHist,'XLim',get(hScatter,'YLim'));

Q1: Do you know how should I debug above error or work around it?

Q2:

h=scatterhist(t(idx),y(idx),'kernel','on');

delete (h(3))

Shows the density on X axis, but h is just a 1X3 array.... Do you know anyway I can extract the array form here?

Thanks again!

[Voss]

You can use histcounts to calculate the histogram without creating any associated graphics objects. (The error you got is a result of deleting the y-histogram graphics object and then setting the YLim of the main axes.) But also, I think, for relative density of data, it should be a histogram based on t only (not y):

[N,edges] = histcounts(t(idx));

And then make a surface from the histogram counts (N) and edges (edges):

surface(edges,[-0.5; 0.5],N([1 1],[1:end end]),'EdgeColor','none');
colormap('jet');

But in order to make the lines show up on top of the heat-map surface, you can create the surface before the lines and set the axes 'SortMethod' property to 'childorder', so the whole code would be something like this:

t = 0:0.0005:1.2;
y=cos(100*t) + cos(110*t);

idx = y>-0.5 & y<0.5;

[N,edges] = histcounts(t(idx));

surface(edges,[-0.5; 0.5],N([1 1],[1:end end]),'EdgeColor','none');
colormap('jet');
hold on

plot(t,y);
plot(t(idx),y(idx),'o');

set(gca,'SortMethod','childorder');

[Minghao Dong]

Thanks great!

You are the man!

Thank you!

[Voss]

Great, glad it's working! Do you mind marking my answer as Accepted so that the question doesn't show up when other users browse unanswered questions (and also so I get credit for an accepted answer, of course)? Thanks!