Apply colormap coloring to a particular contour to indicate imaginary component

I have a set of data X, Y, Z, related via a function , where the data stored in Z are complex valued. I want to make a contour plot of this data at a precise value output value, i.e. the contour: all x and y such that . The typical part of the contour plot will just be contour(X,Y,real(Z),[z z]). However, I want the actually coloring of the contour line via a colormap for the imaginary part. So, for example, if the imaginary part is more negative the line will be blue in that region whereas if the imaginary part is more postive it will be more red.

[Walter Roberson]

That would require a line that does not have constant color, since you can have sections that have the same real(Z) value but which can vary completely in imaginary component.

[David Gillcrist]

Yes, that is what I'm trying to accomplish. The line color at a particular point in will depend on the imaginary value of the Z data, similar to what was done here: How to assign gradual color to a 3d line based on values of another vector.

Answer 1

[DGM]

It can be done, but not with contour() or plot().

% some fake data
x = linspace(-1,1,100);
y = x.';
z = x.*y + sqrt(x) - sqrt(y);

% get the level curves of real(z)
[cc,hh] = contour(x,y,real(z),20);

[~,allcontours] = getContourLineCoordinates(cc);

% redraw everything again 
figure
hold on;
zrange = [0 0];
for k = 1:numel(allcontours)
    % interpolate to find imag(z) along this level curve
    thisx = allcontours{k}(:,1);
    thisy = allcontours{k}(:,2);
    thisz = interp2(x,y,imag(z),thisx,thisy);
    
    % accumulate colorscale limits
    zrange(1) = min(zrange(1),min(imag(z(:))));
    zrange(2) = max(zrange(2),max(imag(z(:))));
    
    % draw the line using patch(), since line() can't do variable color
    patch([thisx;NaN],[thisy;NaN],[thisz;NaN],'EdgeColor','interp','LineWidth',1);
end
clim(zrange)

The rest will be setting up your preferred colormap and such.

This example uses Adam's contour extraction tool from the FEX (attached):

https://www.mathworks.com/matlabcentral/fileexchange/74010-getcontourlinecoordinates

[David Gillcrist]

This works great! I made a slight modification where I used cc = contourc(xx,yy,real(Z),[1 1]); instead of [cc,hh] = contour(x,y,real(z),20); as it allows me to get the contour info without plotting that contour plot and I'm only interested in a single contour. Additionally, immediately after

[~,allcontours] = getContourLineCoordinates(cc);

I wrote the lines

j = 1;
prelength = 1000;
removal_loc = nan(1,prelength);
counter = 0;
while j<=length(M)
    counter = counter + 1;
    removal_loc(counter) = j;
    j = j + M(2,j) + 1;
end

removal_loc(isnan(removal_loc)) = [];
M(:,removal_loc) = [];
imagZscale = imag(N(M(1,:),M(2,:),Ps(i)));

which gives me all the x and y points and allows me to get the outputs just from those points. I then modify two of your lines in your loop to be

% accumulate colorscale limits
zrange(1) = min(zrange(1),min(imagZscale));
zrange(2) = max(zrange(2),max(imagZscale));

Now the colorscale is only for values that exist on the contour(s) plotted and not other values in the output of the original function.

[DGM]

Good improvements.