# I used different codes to plot the phase of this function f(z) = (0.10 + 0.3i) + (0.4243 + 0.0017i)z + (0.9 − 0.001i)z^2 why I always find discontinuity at Z_R =0

조회 수: 10 (최근 30일)
Aisha Mohamed . 2022년 6월 19일
댓글: Jeffrey Clark . 2022년 8월 7일
이 질문에 Cris LaPierre 님이 플래그를 지정함
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.
##### 댓글 수: 2표시 이전 댓글 수: 1숨기기 이전 댓글 수: 1
Jeffrey Clark 2022년 8월 7일
@Aisha Mohamed, when looking at phase (angle) over some extent of a function it is visually easier to see relationships when unwrap is used to make it linear continuous: Shift phase angles - MATLAB unwrap (mathworks.com) 댓글을 달려면 로그인하십시오.

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