Graphics from 2D data

Question

Weather502 2023-9-26

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https://ww2.mathworks.cn/matlabcentral/answers/2025982-graphics-from-2d-data

编辑： Star Strider 2023-9-29

采纳的回答： Star Strider

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

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Answer 1

Star Strider 2023-9-26

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https://ww2.mathworks.cn/matlabcentral/answers/2025982-graphics-from-2d-data#answer_1318877

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.

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Star Strider 2023-9-26

在 MATLAB Online 中打开

x y data.mat

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.

.

Star Strider 2023-9-26

在 MATLAB Online 中打开

x y data.mat

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 2023-9-29

Thank you @Star Strider

Star Strider 2023-9-29

编辑：Star Strider 2023-9-29

在 MATLAB Online 中打开

x y data.mat

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')

.

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Graphics from 2D data

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