How do I create a logarithmic scale colormap or colorbar?

I need to color 'surf' plots on a log scale and subsequently displace the log-based colorbar.

Answer 1

[MathWorks Support Team]

Please follow the steps below to create a log colorbar in a 'surf' plot:

 

% Plot the surface plot

[X, Y] = meshgrid(1:0.5:10,1:20);
Z = sin(X) + cos(Y);
figure;
surf(X, Y, Z)

% Show the colorbar

colorbar

% Set the log colobar

set(gca,'ColorScale','log')

Note: This feature was introduced in MATLAB R2018a.

For more information, refer to the "Color and Transparency Maps" section of the Axes Properties documentation:

https://www.mathworks.com/help/matlab/ref/matlab.graphics.axis.axes-properties.html#budumk7_sep_budumk7-ColorScale

[Wolfgang Schwanghart]

How does MATLAB determine the color axis limits when using log-transformed color axes? In the following code, both caxis limits will be the same.

A = random(makedist('Lognormal',5,1),100,100); 
subplot(1,2,1)
imagesc(A); set(gca,'colorscale','log'); colorbar
log10(caxis)
subplot(1,2,2)
imagesc(log10(A)); colorbar
caxis

However, if I run the following lines

A = random(makedist('Lognormal',5,1),100,100); 
subplot(1,2,1)
imagesc(A.^5); set(gca,'colorscale','log'); colorbar
log10(caxis)
subplot(1,2,2)
imagesc(log10(A.^5)); colorbar
caxis

both caxis are different.

[Walter Roberson]

As a demonstration...

Notice that the lower bounds of xaxis for the A.^5 case are 5e16 instead of 557, I do not currently have an explanation for this.

format long g

A = random(makedist('Lognormal',5,1),100,100); 
subplot(2,2,1)
imagesc(A); set(gca,'colorscale','log'); colorbar
log10(caxis)

ans = 1×2

0.549218064964577 4.14936014310785

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subplot(2,2,2)
imagesc(log10(A)); colorbar
caxis

ans = 1×2

0.549218064964577 4.14936014310785

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subplot(2,2,3)
B = A.^5;
imagesc(B); set(gca,'colorscale','log'); colorbar
[minB, maxB] = bounds(B,'all')

minB = 
          557.301644804751

maxB = 
      5.58213988624748e+20

caxis

ans = 1×2

1.0e+00 * 5.58213988624748e+16 5.58213988624748e+20

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log10(caxis)

ans = 1×2

16.7468007155392 20.7468007155392

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subplot(2,2,4)
imagesc(log10(B)); colorbar

caxis

ans = 1×2

2.74609032482288 20.7468007155392

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[Walter Roberson]

It looks like the algorithm for automatic caxis might be approximately:

Take the upper bound of the image. Divide the upper bound by 1e4 . If the lower bound of the data is above that, use the lower bound of the data as the lower bound of caxis; otherwise use the bound divided by 1e4 as the lower bound of the caxis.

The lower bound of the caxis does not come out as exactly 1e4 lower in all cases; I do not currently know what the adjustment is.

[Wolfgang Schwanghart]

Hi @Walter Roberson, thank you! That is very helpful. It'll be great if @MathWorks Support Team could comment on this, too.

[Walter Roberson]

@Wolfgang Schwanghart

@MathWorks Support Team does not (usually) read these posts.

[Guy]

Hi @Walter Roberson and @Wolfgang Schwanghart,

Thank you for pointing out this behavior of "colorbar" limits. A request has been made to the MathWorks development team to document specifically how the limits of a "colorbar" are determined.

Answer 2

[lvn]

set(gca,'ColorScale','log')

https://nl.mathworks.com/help/matlab/ref/matlab.graphics.axis.axes-properties.html#budumk7-ColorScale

[jonas]

I'm pretty sure it was introduced in 2018a

[Walter Roberson]

Another approach for R2018a is:

cb = colorbar();
cb.Ruler.Scale = 'log';
cb.Ruler.MinorTick = 'on';

In theory this should also work in R2017b (and perhaps other releases), but in R2017b you will get an warning message,

 Warning: Error updating ColorBar.
   DataSpace or ColorSpace transform method failed

[Walter Roberson]

You can tell by the wording of the official answer that it was written for an older version of MATLAB.

[Pat Williamson]

Hi Kristoffer Walker,

If you still need assistance with this issue, please create a MathWorks Technical Support Case. We would be happy to help you out.

https://www.mathworks.com/support/contact_us.html

Answer 3

[Berthold Reisz]

Try the following:

% let A be your data
A = 100*rand(100,100);

% plot log10 of A
pcolor(log10(A))

% get the minimum and maximum value of A
c1 = min(min(A));
c2 = max(max(A));

% set limits for the caxis
caxis([log10(c1) log10(c2)]);

% preallocate Ticks and TickLabels
num_of_ticks = 5;
Ticks      = zeros(1,num_of_ticks);
TickLabels = zeros(1,num_of_ticks);

% distribute Ticks and TickLabels
for n = 1:1:num_of_ticks
    
    Ticks(n)      = log10(round(c2)/num_of_ticks*n);
    TickLabels(n) = round(c2)/num_of_ticks*n;
end

% set Ticks and TickLabels
colorbar('Ticks',Ticks,'TickLabels',TickLabels)