Draw matrix with circle points

Now I am working on some physics problem, and I need to obtaine scaled figure of dots as shown below:

This is 2D plot with dots of data scaled according to some parameter. Here is my try to calculate and build it:

clc
clear


Nx = 1024;
Ny = 1024;

L = 40;

x = linspace(-L/2,L/2, Nx); hx = x(3) - x(2);
x_int = x(2:end-1)';
y = linspace(-L/2, L/2, Ny); hy = y(3) - y(2);
y_int = y(2:end-1)';

% %1D second derivative in x
% ex = ones(length(x)-2, 1)/hx^2;
% d1d =  (spdiags([ex, -2*ex, ex], [-1, 0, 1], length(ex), length(ex)));
% ey = ones(length(y)-2, 1)/hy^2;
% d1d =  (spdiags([ey, -2*ey, ey], [-1, 0, 1], length(ey), length(ey)));


%1D second derivatives
ex = ones(length(x)-2, 1)/hx^2/12;
d1dx =  (spdiags([-ex, 16*ex, -30*ex, 16*ex, -ex], -2:2, length(ex), length(ex)));

ey = ones(length(x)-2, 1)/hy^2/12;
d1dy =  (spdiags([-ey, 16*ey, -30*ey, 16*ey, -ey], -2:2, length(ey), length(ey)));


%full second derivative matrix in 2D
Lxx = kron(eye(length(y)-2), d1dx);
Lyy = kron(d1dy, eye(length(x)-2));


[X,Y] = meshgrid(x(2:end-1), y(2:end-1));


N = 34; M = 55;   
[TH,R] = cart2pol(X,Y);
R0  = 10;
delta = 0.35;
gamma = 0.02;
array_r = [0.01 0.05 0.1 0.15 0.2 0.25]; n = 5; w = 1;
IPR = NaN(6,120);
for i = 1:1:6
    tic
    delta_r = array_r(1,i);
    V0 =  - 12*(exp(-(R-R0*(1+delta_r*cos(N*TH)+delta_r*cos(M*TH))).^2/w^2) + exp(-(R+R0*(1+delta_r*cos(N*TH)+delta_r*cos(M*TH))).^2/w^2));
    H = -0.5*(Lxx + Lyy) + spdiags(V0(:), 0, size(Lxx,1), size(Lxx, 2));
    [V, D] = eigs(H, 120, -14);
    D = diag(D);
    [D, ind] = sort(D);
    V = V(:,ind);
    for j = 1:1:120
        v = V(:,j);
        v = reshape(v, length(x)-2, length(x)-2);
        IPR(i,j) = trapz(x(2:end-1),trapz(x(2:end-1),(v.*conj(v)).^2,2))/(trapz(x(2:end-1),trapz(x(2:end-1),(v.*conj(v)),2))).^2;
    end
    toc

    if i == 1
        IPR_1 = IPR(i,:);
        D_1 = D;
    end

    if i == 2
        IPR_2 = IPR(i,:);
        D_2 = D;
    end

    if i == 3
        IPR_3 = IPR(i,:);
        D_3 = D;
    end

    if i == 4
        IPR_4 = IPR(i,:);
        D_4 = D;
    end

    if i == 5
        IPR_5 = IPR(i,:);
        D_5 = D;
    end

    if i == 6
        IPR_6 = IPR(i,:);
        D_6 = D;
    end

    load gong 
    sound(2*y,1*Fs);
end
f1 = figure;
plot(IPR')
f2 = figure;
imagesc(array_r,D,IPR)
% V0 =  - 12*(exp(-(R-R0*(1+delta_r*cos(N*TH)+delta_r*cos(M*TH))).^2/w^2) + exp(-(R+R0*(1+delta_r*cos(N*TH)+delta_r*cos(M*TH))).^2/w^2));
return

But as I read from documentation imagesc doesnt have parameter to make something in this manner. Also, my coding is awful, and using several if conditions hurts my eyes and limits me in changing number of i. Is there something I could do about it? Thanks in advance.

[Angelo Yeo]

I don't quite understand what you want. Do you want to draw circles with different colors? Do you data for their x, y positions and color indices (i.e., chi (IPR) in your case).

[Andrei]

Yes, I want to draw color scaled circles. Their x position is array_r, y position is from D1 to D6 and corresponding color scale is from IPR1 to IPR6. The situation is like:for array_r(1) == 0.01 I have D1, which contains 120 points of data, and I want these points to be scaled with IPR1. I hope now it is more clear to understand. Thanks for response anyway

[Mathieu NOE]

try with scatter , use z to tune your circle's color

use 'filled' option if you want filled circles

pointsize = 15;
x = linspace(0,3*pi,200);
y = cos(x) + rand(1,200);
c = linspace(1,10,length(x));
scatter(x,y,pointsize,c,"filled")