Symmetric (Diverging) log color scale

I'm trying to figure out how to make a symmetric (diverging) logarithmic color map/scale. Does anyone have any solutions to go from something like the bottom graph (linear diverging color map) to the top one (logarithmic diverging colormap)? I'd normally start with a color map from cbrewer2 (great download, would highly recommend). But then if I use "set(gca,'ColorScale','log')" it only captures small vs big positive values, not small vs big for both positive vs negative values.

There is a matplotlib function that does exactly this, but having trouble turning it into MATLAB code

https://matplotlib.org/stable/api/_as_gen/matplotlib.colors.SymLogNorm.html?highlight=symlognorm#matplotlib.colors.SymLogNorm

Answer 1

[DGM]

Here's a shoddy example, but at least it does what's described.

% let A be your data
% note that the data is asymmetric and ends in the middle of a decade
A = linspace(-50, 500, 1000);

% plot A
% i'm going to plot xdata just for sake of giving some scale information
imagesc(signedlog10(A),'xdata',A) % represented in signed log10

% use a symmetric colormap
% MATLAB doesn't really have any good symmetric diverging colormaps
% but this will have to do
colormap(turbo(256))

% get the minimum and maximum value of A
% this needs to be symmetric unless you also make a 
% custom asymmetric divergent colormap
crange = [-1 1]*max(abs(imrange(A))); % make symmetric
crange = round(signedlog10(crange)); % you may choose to round to integer values

% set limits for the caxis 
caxis(crange); % represented in signed log10

% create ticks, ticklabels
% choose nticks as desired 
nticks = 4;
ticklabels = logspace(0,max(crange),nticks);
ticklabels = [-flip(ticklabels) 0 ticklabels]; % make symmetric

% set Ticks and TickLabels
colorbar('Ticks',signedlog10(ticklabels),'TickLabels',ticklabels)

function out = signedlog10(in)
    % naive signed-log
    %out = sign(in).*log10(abs(in));
    
    % modified continuous signed-log
    % see Measurement Science and Technology (Webber, 2012)
    C = 0; % controls smallest order of magnitude near zero
    out = sign(in).*(log10(1+abs(in)/(10^C)));
end

See also:

https://www.mathworks.com/matlabcentral/fileexchange/57902-symlog

and look at the link provided by OP for symlognorm

Note the different approach I used for solving this problem. I leveraged my eyeballs, fingers, and brain to read and comprehend the question and references. I then wrote some code using the aforementioned tools. It's not perfect, generalized, or timely, but it's enough to demonstrate a method similar to the one requested.

While I don't always have a satisfactory answer, I'm not in the habit of asking an AI to generate a code-like collage of text on my behalf and then insincerely pretending that it works without even spending a moment's glance to check that it does.

Providing actual value is less time-efficient than providing the illusion of value. It seems that there are a lot of very efficient users on the forum these days.

Answer 2

[Ishu]

Hi Danielle,

I understand you want symmetric logarithmic colorbar using "log" property of "ColorScale" but you are getting only positive values.

As the logarithm of a negative number or zero is undefined in the real number system so "set(gca, 'ColorScale', 'log')" only works with positive values. There is a manual approach that you can follow.

% data with both positive and negative values
data = linspace(-200, 100, 1000);

% Display the data
imagesc(data);
colormap('jet'); %set according to your data

% Create a symmetrical log scale for the colorbar
cb = colorbar;

% Set colorbar ticks and labels manually to simulate a symmetrical log scale
caxis([-max(abs(data(:))) max(abs(data(:)))]);
ticks = [-100 -10 -1 1 10 100 1000];
tickLabels = arrayfun(@num2str, ticks, 'UniformOutput', false);

% Apply the ticks and labels to the colorbar
set(cb, 'Ticks', log10(ticks(ticks > 0)), 'TickLabels', tickLabels);

% Adjust the color limits to the data
set(gca, 'CLim', log10([min(ticks(ticks > 0)) max(ticks)]));

For more information on "colorbar" you can follow below documentation:

https://www.mathworks.com/help/matlab/ref/colorbar.html

Hope it helps!

[DGM]

Yes, a manual approach is needed, but did you even look at the output of the code you pasted?