Generate a geographical heat map

Hello,

I am trying to generate a heat map on mapping toolbox.

Here I have the coordinates of the centers in my grid:

Lat = 54.2 + 0.1/6 * [11 9 7 5 3 1]' * ones(1,3) ;  
Lon = 9.15 + 0.025 * ones(6,1) * [1 3 5]   ;
coord = [ [Lat(:,1) , Lon(:,1)] ; [Lat(:,2) , Lon(:,2)] ; [Lat(:,3) , Lon(:,3)] ]  ;

So coord is a 18 by 2 matrix, referring to the coordinates of 18 points.

Let us assume I want to assign a random value to each point, then I can define

values = rand(18, 1) .

How can I generate a heat map with such values in such locations?

How can I make each 'pixel' of the heat map like a sqare with size 0.05 by 0.033 degrees in longitude and latitude?

Thank you in advance for your help :)

[Adam Danz]

A heatmap is a deptiction of 3D data in a 2D plane. Your Lat and Lon coordinates define the 2D plane but the 3rd dimension is missing in your description. The "values" vector is 1D so it's unclear how it should map onto the 2D surface of the heatmap.

[Maurilio Matracia]

The idea is to convert the numbers present in "values" into the colors of the heatmap and assign them to the respective points defined by the coordinates. So you have 2D coordinates to which you assign a 1D set of values and you get a 3D heatmap

Answer 1

[Adam Danz]

I think this is what you're looking for.

heatmap

Note the change in inputs from matrix to vector of unique values.

rng('default') % for reproducibility
Lat = 54.2 + 0.1/6 * [11 9 7 5 3 1]';  
Lon = 9.15 + 0.025 * [1 3 5]' ;
values = rand(18, 1);
valuesMatrix = reshape(values(:),numel(Lat),numel(Lon));  
hm = heatmap(Lon,Lat,valuesMatrix);

imagesc with text labels

rng('default') % for reproducibility
Lat = 54.2 + 0.1/6 * [11 9 7 5 3 1]';  
Lon = 9.15 + 0.025 * [1 3 5]' ;
values = rand(18, 1);
valuesMatrix = reshape(values(:),numel(Lat),numel(Lon));  
figure()
h = imagesc(Lon, Lat, valuesMatrix);

% reproduce heatmap's colormap
n=256;
cmap = [linspace(.9,0,n)', linspace(.9447,.447,n)', linspace(.9741,.741,n)'];
% Or
% cmap = sky(n);  % R2023a or later

colormap(cmap); 
axis xy
colorbar()
hold on
% Add text labels 
[xTxt, yTxt] = ndgrid(h.XData, h.YData); 
labels = compose('%.4f', h.CData');
th = text(xTxt(:), yTxt(:), labels(:), ...
    'VerticalAlignment', 'middle','HorizontalAlignment','Center');

geodensityplot & geoscatter for geoaxes

The types of graphics objects that can be plotted to geographic axes are limited. Some options are geobubble | geodensityplot | geoplot | geoscatter | geodensityplot; see the documentation for an updated list. The first two examples below use geodensityplot where each coordinate influences a radius of 3000 meters and the third demo uses geoscatter.

rng('default') % for reproducibility
Lat = 54.2 + 0.1/6 * [11 9 7 5 3 1]';  
Lon = 9.15 + 0.025 * [1 3 5]' ;
values = rand(18, 1);
valuesMatrix = reshape(values(:),numel(Lat),numel(Lon));  
[LatMatix, LonMatrix] = ndgrid(Lat,Lon);
figure()
tiledlayout(2,2)
nexttile
h = geodensityplot(LatMatix(:), LonMatrix(:), valuesMatrix(:),'Radius',3000);
nexttile
h = geodensityplot(LatMatix(:), LonMatrix(:), valuesMatrix(:),'Radius',3000,'FaceColor','interp');
nexttile
 h = geoscatter(LatMatix(:), LonMatrix(:), 600, valuesMatrix(:), 'filled','Marker','s','MarkerFaceAlpha',.4);
 [latlim, lonlim] = geolimits();
 geolimits(latlim+(range(latlim)*.1),lonlim) % 10% lat axis increase

[Maurilio Matracia]

This is the idea I got in mind, but my problem is how to put this heatmap into an existing map of the mapping toolbox, so that I can see these colors inside the geographical area of interest.

[Adam Danz]

That's an entirely different question.

Heatmaps are notoriously difficult to customize and coexist with other plots.

You can use imagesc instead. Just adjust my updated answer to add an axis handle.

[Maurilio Matracia]

Thank you very much for your answer.

However, it seems that MATLAB does not allow me to plot the image on top of my existing geomap:

hold on
Lat = 54.2 + 0.1/6 * [11 9 7 5 3 1]';  
Lon = 9.15 + 0.025 * [1 3 5]' ;
values = rand(18, 1);
valuesMatrix = reshape(values(:),numel(Lat),numel(Lon));  
h = imagesc(Lon, Lat, valuesMatrix);
axis xy
colorbar()
hold on
% Add text labels 
[xTxt, yTxt] = ndgrid(h.XData, h.YData); 
labels = compose('%.4f', h.CData');
th = text(xTxt(:), yTxt(:), labels(:), ...
    'VerticalAlignment', 'middle','HorizontalAlignment','Center');

And I get this error:

Error using newplot (line 81)
Adding Cartesian plot to geoaxes is not supported.

Error in matlab.graphics.internal.newplotimagewrapper (line 7)
axReturn = newplot(varargin{:});

Error in imagesc (line 52)
    hh = image(varargin{:}, 'CDataMapping', 'scaled');

[Adam Danz]

Didn't know you were using geoaxes. There are multiple axis types that support maps. I've updated my answer to include geoaxes.

It would be wise to include that info in future questions to get an answer faster and more efficiently.

[Maurilio Matracia]

Thanks for the update! Do you know if it is possible to change the shape of the spots in geodensityplot? Like making them rectangles instead of circles

[Adam Danz]

This is actually the first time I'm using geodensityplot and maybe the second time I've used geoscatter. The documentation I linked to contains lots of examples to follow. geodensityplot does not currently have an option to change the shape of the markers. But geoscatter does.

I've update the answer to suggest some solutions.

Answer 2

[Sami]

if true
  % code
end% Define circuit parameters
L = 1;   % Inductor (H)
C = 1;   % Capacitor (F)
R = 1;   % Resistor (Ohm)

% Define the transfer function num = [1]; % Numerator den = [L*C, R*C, 1]; % Denominator

H1 = tf(num, den);

% Display the transfer function disp('Transfer Function of RLC Circuit:'); H1

% Plot Bode plot to analyze frequency response bode(H1); grid on; title('Bode Plot of RLC Circuit');