I used the folloing 2 codes from Davidgoodman and Torsten (Thank you very much for all of them) respectivally to plot this function
f(z) = (0.10 + 0.3i) + (0.4243 + 0.0017i)z + (0.9 − 0.001i)z^2
My question IS:
why always find dis continuity at Z_R (the real part of Z) in the phase of this function? and how to avoid this discontinuity?
this are the both codes
This code by Davidgoodman (Thank you very much)
re_z = -1:0.01:1;
im_z = -1:0.01:1;
[re_z,im_z] = meshgrid(re_z,im_z);
z = re_z + 1i*im_z;
caxis([-pi pi])
xlabel('x')
ylabel('y')
p=[(0.9-0.001i) (0.4243 + 0.0017i) (0.10 + 0.3i)];
f_of_z_result = polyval(p,z);
p1=[(0.9 + 0.001i) (0.2121 - 0.0008i) (0.10 -0.3i)];
f_of_1_over_z_result = polyval(p1,1./z);
figure();
subplot(2,2,1)
surf(re_z,im_z,abs(f_of_z_result),'EdgeColor','none')
title('|f(z)|')
xlabel('Z_R')
ylabel('Z_I')
% Zlabel('|f(z)|')
grid on
subplot(2,2,2)
surf(re_z,im_z,angle(f_of_z_result),'EdgeColor','none')
title('phase of f(z)')
xlabel('Z_R')
ylabel('Z_I')
subplot(2,2,3)
surf(re_z,im_z,abs(f_of_1_over_z_result),'EdgeColor','none')
title('|f(1/z)|')
xlabel('Z_R')
ylabel('Z_I')
subplot(2,2,4)
surf(re_z,im_z,angle(f_of_1_over_z_result),'EdgeColor','none')
title('phase of f(1/z)')
xlabel('Z_R')
ylabel('Z_I')
% Zlabel('phase of f(z)')
grid on
This code by Torsten (Thank you very much)
f = @(x,y) (0.3162).*exp(1i*((0.398)*pi))+((x+1i*y).*(0.4243).*exp(1i*((0.0013)*pi)) + (x+1i*y).^2*(0.9).*exp(-1i*(0.00035)*pi));
r = 0:0.01:0.9;
phi = 0:0.01:2*pi;
[R,PHI] = meshgrid(r,phi);
X = R.*cos(PHI);
Y = R.*sin(PHI);
F=f(X,Y);
figure
subplot(2,2,1)
surf(X,Y,abs(f(X,Y)),'EdgeColor','none')
view(2)
colorbar
title('|f(z)|')
xlabel('Z_R')
ylabel('Z_I')
% Zlabel('|f(z)|')
grid on
subplot(2,2,2)
surf(X,Y,angle(f(X,Y)),'EdgeColor','none')
view(2)
colorbar
title('phase of f(z)')
xlabel('Z_R')
ylabel('Z_I')
% Zlabel('|f(z)|')
grid on
subplot(2,2,3)
surf(X,Y,angle(f(X,Y)),'EdgeColor','none')
view(2)
colorbar
title('phase of f(z),view(2)')
xlabel('Z_R')
ylabel('Z_I')
% Zlabel('|f(z)|')
grid on
As we can see both codes work with |f(z)|, but not with the phase of the function.
I appriciate any help.
