# How to correctly use contourf with logarithmic color scale?

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Sebastian on 5 Sep 2023
Commented: Sebastian on 6 Sep 2023
Dear Matlab Community,
I have a 1372 x 4118 (double) matrix I want to plot using contourf() function. The data entries of the matrix vary from 1 to 1e-9.In order to see changes throughout the whole scale I want to use a log scale fo caxis. The following code sets the Colorbar to log scale but the color representation in the plot is not in agreement with the colorbar: ( Due to memory constraints I reduce the matrix to 600 x 600 )
matrix = matrix.a;
x= linspace(1,600,600);
y=linspace(-1,-600,600);
contourf(x,y,matrix);
set(gca,'ColorScale','log');
c = colorbar;
c.Label.String = 'energy [keV]';
xlim([0 100]);
ylim([-200,0]);
clim([1e-7,1e0]);
Please find attached an image of the wrong plot with the full matrix, a subset of the matrix , and the matrix itself.
Best Regards
sethi
Walter Roberson on 5 Sep 2023
I do not see any problem. With your sample data, the left edge (near x == 0) has a sharp peak to 1, but most of the rest of the data is around roughly 5e-4
Sebastian on 5 Sep 2023
Dear Mr. Roberson,
thank you for the fast reply. I would expect a more pronounced color gradient than this shown in the attached image (contourf_logscale_2.jpg). In this image, values of 1e-5 have the same greenish color as values of 1e-2. But according to the scale bar there should be a bluish or orange color, respectively
.

Voss on 5 Sep 2023
The problem is that contourf picks the levels in a linear fashion, so the levels in your contour plot are [0 0.1 0.2 0.3 ... 0.9 1], which obviously don't work very well when the color scale is logarithmic.
One way around this is to use use the log of your data in contourf and then adjust the colorbar tick labels appropriately:
matrix = matrix.a;
x = linspace(1,600,600);
y = linspace(-1,-600,600);
figure
contourf(x,y,log10(matrix));
c = colorbar;
c.Label.String = 'energy [keV]';
c.Ticks = -7:0;
c.TickLabels = compose('10^{%d}',c.Ticks);
xlim([0,100]);
ylim([-200,0]);
clim([-7,0]);
Another way is to specify the contour levels yourself:
figure
n_levels = 8;
contourf(x,y,matrix,logspace(-7,0,n_levels));
set(gca,'ColorScale','log');
c = colorbar;
c.Label.String = 'energy [keV]';
xlim([0 100]);
ylim([-200,0]);
clim([1e-7,1e0]);
Surface plot (no contours), for reference:
figure
p = pcolor(x,y,matrix);
p.EdgeColor = 'none';
set(gca,'ColorScale','log');
c = colorbar;
c.Label.String = 'energy [keV]';
xlim([0,100]);
ylim([-200,0]);
clim([1e-7,1e0]);
Sebastian on 6 Sep 2023
Hello, thank you so much this is exactly what i wanted! This issue is finally solved :)

Nathan Hardenberg on 5 Sep 2023
There are two ways I know of:
1. Define your own (manual) values on which contours should be drawn, or
2. just plot the logarithmic values instead of the linear ones
matrix = matrix.a;
x = linspace( 1, 600, 600);
y = linspace(-1,-600, 600);
figure(1);
% using contourf with manual lines
contourf(x, y, matrix, [1 0.1 0.01 0.001 0.0001 0.00001 0]);
set(gca,'ColorScale','log');
c = colorbar;
c.Label.String = 'energy [keV]';
xlim([0 100]); ylim([-200,0]);
figure(2);
contourf(x, y, log10(matrix)); % draw logarithmic values
c = colorbar;
c.Label.String = 'log10(energy) [keV]';
xlim([0 100]); ylim([-200,0]);
Sebastian on 6 Sep 2023

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