How do I measure density of random point with a fixed area in MATLAB?

There had a 9x9 area and I have generate a lot of point with this area in random.

How do I measure density of the red point (e.g. Bottom left).

Somebody can give something sample code to let me study with this topic? It is very helpful to my project research.

[Mathieu NOE]

hello

you can count the number of points by making this - assuming the data points coordinates are given in a 2 columns matrice (x coordinates = 1st column , y coordinates = 2ndt column

x = rand(1000,1);
y = rand(1000,1);

% area definition
xlow = 0.25;
xhigh = 0.5;
ylow = 0.25;
yhigh = 0.5;

area = (xhigh-xlow)*(yhigh-ylow);

indx = find(x >=xlow & x <=xhigh);
indy = find(y >=ylow & y <=yhigh);
ind = intersect(indx,indy);
plot(x,y,'*g',x(ind),y(ind),'or');

density = numel(ind)/area

[Chun Yin Lui]

As for the code "plot(x,y,'*g',x(ind),y(ind),'or');"

Sorry for what is the '*g' and 'or'?

Dose it is the funtion of matlab or something etc?

[Mathieu NOE]

hello

these are plot format option * = star, g = green, o = circle , r = red

Answer 1

[Adam Danz]

Use histogram2() or histcounts2() to compute 2D density.

Demo:

xy = randi(400,50,2); 
subplot(1,2,1)
plot(xy(:,1), xy(:,2), 'r.')
axis equal
grid on
xlim([1,400])
ylim([1,400])
title('raw data')
binEdges = linspace(1,400,4);
set(gca,'XTick',binEdges, 'YTick',binEdges)

% Compute density in 3X3 bins
subplot(1,2,2)
h = histogram2(xy(:,1), xy(:,2), binEdges,binEdges,...
    'DisplayStyle','tile','ShowEmptyBins','on');
axis equal
grid on
xlim([1,400])
ylim([1,400])
title('Density')
set(gca,'XTick',0:100:400, 'YTick',0:100:400)
cb = colorbar(); 
ylabel(cb,'Density')
% To label counts
[xTxt, yTxt] = ndgrid(h.XBinEdges(2:end)-h.BinWidth(1)/2, ...
    h.YBinEdges(2:end)-h.BinWidth(2)/2);
labels = compose('%.0f', h.Values);
hold on
text(xTxt(:), yTxt(:), labels(:), 'VerticalAlignment', 'Middle', 'HorizontalAlignment','Center')

[Chun Yin Lui]

That worked for me. Thanks Adam

[Chun Yin Lui]

Excuse me how can I exploit the number of density?

such as I want to put the bottom left to 'n' and display the number.

[Adam Danz]

Hi Chun, I don't fully understand your question.

The density values are in h.Values where h is the output to histogram2().

Are you asking how to move the text-numbers to the bottom/left of each grid square?

[Chun Yin Lui]

Thanks for help, actually I want to use the density substitute to the other equation by each area.

[Adam Danz]

I'm sorry, I still don't understand. Could you provide an example?

[Chun Yin Lui]

Sorry for I did not explain clearly, I need to define the number of density in different area and apply to the other equation.

For example the number of desity on bottom left is 5 and I want to put the 5 to "n". Then, substitute n to the equation "n = 2Y ". In the same way, the numer of upper right is 9 it will be put it in "n" and substitute n to the equation "n = 2Y "

[Chun Yin Lui]

Or you can say, I need to use the data of density in the 3X3 bins, but I don't know how to take the data

[Adam Danz]

I see. Take some time to look at the code. The density is stored in h.Values.

[Chun Yin Lui]

Thank you for your patient answers, I found the answer.

n = (h.Values(1));

n2 = (h.Values(2));

n3 = (h.Values(3));

.

.

.

n9 = (h.Values(9));

this is the number of density on 3x3 bins

[Chun Yin Lui]

Actually I am used n = label (1) in the beginning but it is wrong because "label()" does not a number, it just a word. So it can't put it in to any equation.

[ytu1990]

After calculating the density, how to return the density value to be linked to the coordinate of original point?

For example, return the value "9" to the points in the (1,1) grid...

[Adam Danz]

See h.Values