Generating a random list of (x, y) points that satisfy a condition?

Question

So I need to generate a matrix of x and y points given that they meet the condition that at these (x,y) points concentration is greater than 10. Note that I first run a code that gives me concentration at each location, and now I need Matlab to "randomly" pick (x,y) points with the above condition.

Would appreciate any suggestions on how to go about this.

Answer 1

assuming your data looks something like this :

data= [...  x  y  concentration
            1, 1, 1; ...
            2, 1, 11; ...
            1, 2, 12; ...
            2, 2, 1 ...
    ]

You could find all concentrations bigger than 10 with:

data_cbigger10=data(data(:,3)>10,:) % using logical indexing 

and choose a random point from there with:

randomPoint=data_cbigger10(ceil(size(data_cbigger10,2)*rand),:) % pick a random index

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If the dimensions are as follows:

the dimension of concentration is 52x61x61 as concentration is c(x,y,time), that of x is 1x61 and 1x52 for y. @PetrH – s2015

this should do the trick:

This is your data, I just make something up:

x=linspace(0,1,61);
y=linspace(0,1,52);
con=20*rand(61,52);

Now I find all positions in con which are bigger than 10. This results in a logical matrix. By multipling it with an random matrix the same size I get a matrix with random values where 'con' is bigger than 10, but everywhere else equals zero.

data_cbigger10=rand(size(con)).*(con>10);

by finding the max, or min, Value a random point is choosen:

for n=1:1:10
    data_cbigger10=rand(size(con)).*(con>10);

    [vals,xind]=max(data_cbigger10);
    xind=squeeze(xind);
    [vals,yind]=max(squeeze(vals));
    [~,time_ind]=max(squeeze(vals));

    yind=yind(time_ind);
    xind=xind(yind,time_ind);
    x_res(n)=x(xind)
    y_res(n)=y(yind)
    time_res(n)=time(time_ind)
    con_res(n)=con(xind,yind,time_ind)
    con(xind,yind,time_ind)=0; % setting the choosen point to zero, so it will not be choosen again.
end

Hope this works now for you.

Answer 2

Assuming you have the concentration for each point (x,y) stored in an array concentration you can use the find() and randsample() functions like so:

conGT10 = find(concentration>10);    % find where concentration is greater than 10 (gives you indices)
randomPoints = randsample(conGT10,nn);    % choose nn random numbers from those that satisfy the condition
x1 = x(randomPoints);     % given the randomly drawn indices pull the corresponding numbers for x and y
y1 = y(randomPoints);

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EDIT: The above assumes that arrays x , y , and concentration are 1d and of the same length. Apparently this is not true for your problem.

You have a grid of points on a (x,y) plane and you measure concentration on this grid in different time periods. So the length of x is nx , the length of y is ny and the size of concentration is nx by ny by nt . For simplicity I will assume that you measure concentration only once, ie nt=1 and concentration is only 2d array.

The modified version of my previous answer would then be as follows:

[rows,cols] = find(concentration>10);    % find where concentration is greater than 10 (gives you indices)
randomIndices = randsample(length(rows),nn);    % choose nn random integers from 1 to n, where n is the number of observations that satisfy the condition 'concentration>10'
randomX = x(rows(randomIndices));
randomY = y(cols(randomIndices));