How can I color a (circle) area in a scatterplot?

In my task, I should draw n samples from a two dimensional random variable U=(U1,U2), where U1 and U2 are independent and both uniformly distributed on [-1,1].

Afterwards, I should plot the sample and mark all the samples which fulfill (U1^2 + U2^2)<1. (I already know that the outcome will be a circle with radius r=1.)

To plot the sample I used scatter(U1,U2). How can I color the samples which fulfill the condition (U1^2 + U2^2)<1?

Answer 1

[Adam]

doc scatter

shows a 4-argument syntax which allows you to include a vector of colours of equal length to the x and y. So you can use whatever logic you wish to make some of those colours different and the rest a standard colour. In your case just a simple logical mask can be used to insert your chosen colour into an array of your chosen default colour.

You can pass in [] as the 3rd argument if you don't care about explicitly setting the marker size.

Answer 2

[jonas]

You could do something like,

id=(U1.^2+U2.^2)<1;
plot(U1(id),U2(id),'.r',U1(~id),U2(~id),'.k')

Answer 3

[JohnGalt]

I don't have access to the scatterplot function but the technique you're looking for is called logical indexing... where you set up an index for each co-ordinate which is either true or false. if it's true plot it one colour, if it's false plot it another colour.

samples  = rand(10000,2)*2 -1;  % create data
x = samples(:,1); 
y = samples(:,2);
mask = (x.^2 + y.^2) <1;  % create logical mask (true/false)
figure; hold on;  % new figure window. enable overlaying of plots
plot(x,y,'b.');   % plot a blue dot for all points
plot(x(mask),y(mask),'r.') % overwrite all points where mask==true with a red dot

Answer 4

[Anna Boehm]

Thanks to all, it works perfectly!