How to contour plot over large negative and positive values?

I'm trying to plot contour lines for a vorticity scalar field of a turbulent flow. However, since the values range from -1e6 to 1e6 approximately, ideally I would like a colorbar with "logarithmic" scale, however, negative values should not be logarithmic in the mathematical sense, instead they should be like a mirror of the positive values.

Consider the following contour lines

clines = [-logspace(6,1,6) 0 logspace(1,6,6)] %-1000000 -100000 ... -10 0 10 ... 1000000

If I plot them using contour, the colorbar will be linear.

Since Matlab 2018a the

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

command works, but obviously only for the logarithmic scale in the mathematical sense (negative values approach 0)

How can I create a colorbar for my needs?

Answer 1

[Chad Greene]

Can you simply do

contour(x,y,log(z),log(clines))