Does anybody know how to "plot" an area in the complex plane? For example
{z:|f(z)|<1} where f(z)=(1+z)/(1-z).
Or more generally, f(z) is a complex function.
P.S. Shaded area may be preferable.
MATLAB: Area plotting in the complex plane
MATLABplotting
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Your âTâ matrix must become a cell array. See my sample of âTâ for an example.
Once you do that, I would do something like this:
Y = [12.004 13.1573 11.1665 11.8082 12.2129 12.8075 12.4167 11.5708 12.5798 13.7489];T={'cluster2'; 'cluster1'; 'cluster3'; 'cluster9'; 'cluster0'; 'cluster7'; 'cluster4'}; % Sample Of Cell Array
[UnqClust,~,idx] = unique(T); % Unique Values & Locations
Out = Y(idx); % Mapped Output
for k1 = 1:length(idx) fprintf(1, '\t%s\t%.4f\n', T{k1}, Out(k1)) % Demonstration Output (Delete Loop)
end cluster2 11.1665 cluster1 13.1573 cluster3 11.8082 cluster9 12.4167 cluster0 12.0040 cluster7 12.8075 cluster4 12.2129clear; clc;% entire z-plane
x=-3:0.01:3;y=-3:0.01:3 ;% our z region
zregion=[];for n=1:length(x) for k=1:length(y) z=x(n)+y(k)*1i; if abs(z-2)<1 zregion=[zregion z]; end endend% mapping
fzRegion=[];for n=1:length(zregion) z=zregion(n); fz=2/(z-1); fzRegion=[fzRegion fz];end% plot these two regions
figure;subplot(1,2,1);plot(real(zregion), imag(zregion), 'b.'); zoom on; grid on; hold on; plot( [-5 5],[0 0 ], '-k', 'LineWidth', 2 );plot( [0 0],[-5 5 ], '-k', 'LineWidth', 2 );axis square; xlabel('x'); ylabel('y'); title('abs(z-2)<1')subplot(1,2,2);plot(real(fzRegion), imag(fzRegion), 'r.'); zoom on; grid on; hold on; plot( [-200 200],[0 0 ], '-k', 'LineWidth', 2 );plot( [0 0],[-200 200 ], '-k', 'LineWidth', 2 );axis square; xlabel('u'); ylabel('v'); title('f(z)');But be careful... Point z1=1+j0 is a boundary point of your z-region. As z is approaching z1, f(z) going to infinity.
If you run the above script, you will receive the following graph:
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