Custom colormap for a contourf plot?

I am working on a contourf plot and my Z matrix contains heights between -2 and 2e+15 and the entries for which Z is undefined contain (-3).

1. I want a custom colormap for the Z filled contours such that:

The (-3) value contours will be colored in white.

The contours in the range (-2,0] will be colored in different shades of black linearly dependent on the heights.

The contours in the range [0,2) will be colored in different shades of magenta linearly dependent on the heights.

The contours in the range [2,10) will be colored in different shades of blue linearly dependent on the heights.

[10,1e+2) :different shades of cyan linearly dependent on the heights.

[1e+2,1e+4) :different shades of green linearly dependent on the heights.

[1e+4,1e+8) :different shades of yellow linearly dependent on the heights.

[1e+8,1e+16) :different shades of red linearly dependent on the heights.

.

2. I want a custom colorbar with all the ranges boundaries (and only them) mentioned on it and with different areas allocated to each range to illustrate their different magnitudes.

3. Only if possible: to allocate a small area to the white color at the bottom of this colorbar and instead of (-3), to write there: 'outside of the function domain'.

[dpb]

On a linear scale with values from ~0 to 10^15, only the top of the axis values will be anything visually but a plane at the origin.

Answer 1

[Ganesh Regoti]

See the following code which may help you

%% Colorbar ranges 
crange = [-3 -2; -2 0; 0 2; 2 10; 10 100;100 10^4;10^4 10^8; 10^8 10^16];
cmap = rand(size(crange,1),3);  %Specify your customized colors in RGB format
 
%% Data
[X, Y] = meshgrid(linspace(1,2^15,1000),linspace(0,2^15,1000));
A = X + Y;  % I have used random data set.
 
 
%% Arrange the colors range
colors = zeros(size(A));         
for i = 1:size(crange,1) % Categorizing the values which fall into specified range
    colors(A > crange(i,1) & A<=crange(i,2)) = crange(i,2);           
end
 
contourf(X,Y,colors,8); 
 
%% Color bar
h = colorbar;
h.Ticks = -3:((10^8 +3)/8):10^8; % Set ticks for all ranges. 
h.TickLabels = {'outside of function domain','-2','0','2','10','100','10^4','10^8','10^16'}; % Set tick labels.
caxis([-3 10^8]); % Set colormap limits
colormap(cmap);