Graphics from 2D data

Hi there,

I have a matrix x of size 39505X2 and i was wondering how can i plot graphics as shown below from my data

Answer 1

[Star Strider]

It would be nice to have ‘x’ since I suspect that ‘x(:,1)’ cycliically repeats. Using reshape to use the cyclic repeat information to create a matrix from ‘x(:,2)’ could be the solution.

[Weather502]

xy = load("x y data.mat")

xy = struct with fields:
    all_data: [39505×2 double]

xy.all_data

ans = 39505×2

0.4534 0.5567 0.4534 0.6945 0.3485 0.6043 0.3591 0.6032 0.4371 0.5032 0.4418 0.5032 0.4418 0.4861 0.3958 0.4764 0.3873 0.4693 0.3873 0.4764

My data is very random and i have attached in

[Torsten]

So you have x/y data. And where are the z-data your colour plot is based on: z = f(x,y) ?

[Star Strider]

Oh well. So much for that idea.

There are duplicated values, however they are in no regular pattern. It is likely not possible to construct anything of significance from these data. I have no idea where the matrix in the plot came from, however it was not from these data.

LD = load('x y data.mat')

LD = struct with fields:
    all_data: [39505×2 double]

Data = LD.all_data

Data = 39505×2

0.4534 0.5567 0.4534 0.6945 0.3485 0.6043 0.3591 0.6032 0.4371 0.5032 0.4418 0.5032 0.4418 0.4861 0.3958 0.4764 0.3873 0.4693 0.3873 0.4764

x = Data(:,1);
y = Data(:,2);

[Ux,~,ixx] = unique(x,'stable');
Xcounts = accumarray(ixx, (1:numel(ixx)).', [], @(x){x});
% [MaxSizeX,idxx] = maxk(cellfun(@numel, Xcounts),5)

[Uy,~,ixy] = unique(y,'stable');
Ycounts = accumarray(ixy, (1:numel(ixy)).', [], @(x){x});
% [MaxSizeY,idxy] = maxk(cellfun(@numel, Ycounts),5)

figure
scatter(x, y, 5, exp(-(x-mean(x)).^2 .* (y-mean(y)).^2), '.')
colormap(turbo)
colorbar
axis('equal')

I can get this far, however I cannot figure out how to get what appears to be an imagesc plot from it.

.

[Walter Roberson]

I wonder if it is a density plot?

xy = load("x y data.mat")

xy = struct with fields:
    all_data: [39505×2 double]

x = xy.all_data(:,1);
y = xy.all_data(:,2);
scatter(x, y)

No. density doesn't seem to match example plot.

[Weather502]

probably i am looking some kind of density plot ot contour map to visualize my data.

Thanks

[Star Strider]

I experimented a bit more with this.

Here are some options —

LD = load('x y data.mat');
Data = LD.all_data

Data = 39505×2

0.4534 0.5567 0.4534 0.6945 0.3485 0.6043 0.3591 0.6032 0.4371 0.5032 0.4418 0.5032 0.4418 0.4861 0.3958 0.4764 0.3873 0.4693 0.3873 0.4764

x = Data(:,1);
y = Data(:,2);

[Ux,~,ixx] = unique(x,'stable');
Xcounts = accumarray(ixx, (1:numel(ixx)).', [], @(x){x});
% [MaxSizeX,idxx] = maxk(cellfun(@numel, Xcounts),5)

[Uy,~,ixy] = unique(y,'stable');
Ycounts = accumarray(ixy, (1:numel(ixy)).', [], @(x){x});
% [MaxSizeY,idxy] = maxk(cellfun(@numel, Ycounts),5)

SF = 3E+2;                                                      % Scalle Factor (For Gaussian Approximation)
z = exp(-(x-mean(x)).^2*SF) .* exp(-(y-mean(y)).^2*SF);

% figure
% plot(x, exp(-(x-mean(x)).^2*SF))
% hold on
% plot(y, exp(-(y-mean(y)).^2*SF))
% hold off

figure
scatter(x, y, 5, z, '.')
colormap(turbo)
colorbar
axis('equal')

figure
% stem3(x, y, z, '.')
hold on
scatter3(x, y, z, 2.5, z, 'o', 'filled')
hold off
colormap(turbo)
colorbar
xlabel('X')
ylabel('Y')
zlabel('Density')
grid on
view(-37.5,30)

% axis('equal')

xv = linspace(min(x), max(x), fix(sqrt(numel(x))));
yv = linspace(min(y), max(y), fix(sqrt(numel(y))));

F = scatteredInterpolant(x, y, z);

Warning: Duplicate data points have been detected and removed - corresponding values have been averaged.

[X,Y] = ndgrid(xv, yv);

Z = F(X,Y);

figure
surfc(X, Y, Z, 'EdgeColor','interp')
colormap(turbo)
colorbar
xlabel('X')
ylabel('Y')
zlabel('Density')

% [az,el] = view

[Uxy,~,ix] = unique(Data,'rows','stable');

Tally = accumarray(ix, (1:numel(ix)), [], @(x){Data(x,:)});
Density = cellfun(@(x)size(x,1), Tally);

figure
scatter3(Uxy(:,1), Uxy(:,2), Density, 5, Density, 'o', 'filled')
colormap(turbo)
colorbar
xlabel('X')
ylabel('Y')
zlabel('Density')
title('Empirical Density Plot')

figure
hist3(Data,[250 250],'CDataMode','auto','FaceColor','interp')
colormap(turbo)
colorbar
xlabel('X')
ylabel('Y')
zlabel('Density')
title('Empirical Density Histogram Plot')

[N,C] = hist3(Data,[250 250]);

figure
imagesc(C{1}, C{2}, N)
colormap(turbo)
colorbar
set(gca, 'YDir','normal')
xlabel('X')
ylabel('Y')
title('Image Plot Of Density Data')

The accumarray call that produced the density data for the final plot is the best I can do with an empirical approximation of the density. It counts the numbers of (x,y) pairs with the same coordinates, as determined by the last unique call. It might be possible to do a nonlinear fit of the hist3 results to a bivariate Gaussian distribution.

.

[Weather502]

Thank you @Star Strider

[Star Strider]

As always, my pleasure!

EDIT — (29 Sep 2023 at 17:48)

Just out of interest —

LD = load('x y data.mat');
Data = LD.all_data;
x = Data(:,1);
y = Data(:,2);

zfcn = @(b,xy) b(1).*exp(-(xy(:,:,1)-b(2)).^2*b(3)) .* exp(-(xy(:,:,2)-b(4)).^2*b(5));

[N,C] = hist3(Data,[250 250]);

xv = linspace(min(x), max(x), size(N,1));
yv = linspace(min(y), max(y), size(N,2));

[X,Y] = ndgrid(xv, yv);
XY = cat(3, X, Y);

B = lsqcurvefit(zfcn,[50,mean(x),300,mean(y),300],XY,N)

Local minimum possible.

lsqcurvefit stopped because the final change in the sum of squares relative to 
its initial value is less than the value of the function tolerance.

B = 1×5

31.5122 0.3762 771.2200 0.5087 335.3531

ZZ = zfcn(B,XY);

figure
surf(X, Y, N, 'EdgeColor',[1 1 1]*0.5, 'FaceAlpha',0.25, 'EdgeAlpha',0.25)
hold on
surf(X,Y,ZZ, 'EdgeColor','interp')
hold off
colormap(turbo)
colorbar
xlabel('X')
ylabel('Y')

.