Where is the wrong in this code??

Because I trust the answers of all the Matlab experts in this group, and I thank all of them. The genius expert Torsten saw that there is some mistake in my code that used to plot cos(phase(f_b(1/z)), I used his notes but still there are some missing points in this work. I think this is because I did not write my question in the correct way.

So I ask again where is the wrong in this code??

I have two functions f_k(z) and f_b(1/z) where,

1-f_k(z) = (0.1000 + 0.3000i) + (0.4243 + 0.0017i)z + (0.9000- 0.0010i)z^2

we define p from f_k(z)as,

p=[ ( 0.9000 - 0.0010i) (0.4243 + 0.0017i) (0.1000 + 0.3000i) ];

2-f_b(1/z) = (0.1000 - 0.3000i)z^-1 + (0.2121 - 0.0008i)z^-2 + (0.9000 +0.0010i)z^-3

we define p1 from f_b(1/z)as,

p1=[ ( 0.9000 + 0.0010i) (0.2121 - 0.0008i) (0.1000 - 0.3000i) (0)];

The function f_b(1/z) is not defined at z = 0 which means the graph of this function must be undefined at z = 0

But when I use the code %f_of_1_over_z_result = polyval(p1, z); I found the graph for | f_b(1/z) | and | f_k (z) | are same

and | f_b(1/z) | defined at z = 0 (which must not happen in the myfunction |f_b(1/z)| because it is not defined at z = 0) , as you can see from the following figure:

But,

% Where as when I use the code % f_of_1_over_z_result = polyval(p1,1./z);

% the function |f_b(1/z)|does not define at z=0 (that what must happen in my case) as you can see in the following figure,

I used this code,

p=[ ( 0.9000 - 0.0010i) (0.4243 + 0.0017i) (0.1000 + 0.3000i) ];

p1=[ ( 0.9000 + 0.0010i) (0.2121 - 0.0008i) (0.1000 - 0.3000i) (0)];

re_z = -6.005:.01:6.005;

im_z= -6.005:.01:6.005;

[re_z,im_z] = meshgrid(re_z,im_z);

z = re_z + 1i*im_z;

f_of_z_result = polyval(p,z);

% %

f_of_1_over_z_result = polyval(p1,1./z); % I used this code in the first figure

% f_of_1_over_z_result = polyval(p1,z); % I used this code in the second figure

figure();

subplot(2,2,1)

surf(re_z,im_z,abs(f_of_z_result),'EdgeColor','none')

colorbar

title('|f_k(z)|')

xlabel('Z_R')

ylabel('Z_I')

zlim([0 15]) %adjust this value as needed

caxis([-6 6]) %adjust this value as needed

% grid on

subplot(2,2,2)

surf(re_z,im_z,cos(angle(f_of_z_result)),'EdgeColor','none')

colorbar

title('cos(phase of f_k(z))')

xlabel('Z_R')

ylabel('Z_I')

zlim([-5 5]) %adjust this value as needed

caxis([-1 1]) %adjust this value as needed

subplot(2,2,3)

surf(re_z,im_z,abs(f_of_1_over_z_result),'EdgeColor','none')

colorbar

title('|f_b(1/z)|')

xlabel('Z_R')

ylabel('Z_I')

zlim([0 15]) %adjust this value as needed

caxis([-0.15 0.15])

subplot(2,2,4)

surf(re_z,im_z, cos(angle(f_of_1_over_z_result)),'EdgeColor','none')

colorbar

title(('cos(phase of f_b(1/z))'))

xlabel('Z_R')

ylabel('Z_I')

caxis([-1 1]) %adjust this value as needed

zlim([-1 1]) %adjust this value as needed

grid on

Where is the wrong in this code??

Answer 1

[Torsten]

f_b(1/z) = (0.1000 - 0.3000i)z^-1 + (0.2121 - 0.0008i)z^-2 + (0.9000 +0.0010i)z^-3

I wrote it several times already, but this function is the same as

f(w) = (0.1000 - 0.3000i)w + (0.2121 - 0.0008i)w^2 + (0.9000 +0.0010i)w^3

except for 1/z=w=0.

But if we define f_b(0) = 0, we remove this singularity and the two functions are identical all over the complex plane.

This can be seen in the first 4 graphics where we get a value of 0 for abs(f_b(1/z)) at 1/z=0.

So summarizing: There is nothing wrong in your code, but you must decide whether you want to define

f_b(1/z) = (0.1000 - 0.3000i)z^-1 + (0.2121 - 0.0008i)z^-2 + (0.9000 +0.0010i)z^-3

or

f_b(z) = (0.1000 - 0.3000i)z^-1 + (0.2121 - 0.0008i)z^-2 + (0.9000 +0.0010i)z^-3

The first definition gives the 2 pictures in the first gallery, the second definition gives the 2 pictures in the second gallery.

[Torsten]

@Aisha Mohamed comment moved here:

Thanks Torsten so much.

As I study this function,

f_b(z) = (0.1000 - 0.3000i)z^-1 + (0.2121 - 0.0008i)z^-2 + (0.9000 +0.0010i)z^-3

which has singularity in z=0, so by using this defination the sutible code to plot this function is,

f_of_1_over_z_result = polyval(p1,1./z);

which give the second graph. Is this right please?

I always appreciate you efforts

[Torsten]

In order not to confuse people, the usual way to ask your question would have been

Given

f_b(z) = (0.1000 - 0.3000i)z + (0.2121 - 0.0008i)z^2 + (0.9000 +0.0010i)z^3

and setting

g(z) = f_b(1/z)

how to plot abs(g(z)) and cos(phase(g(z))) ?

?

p1=[ ( 0.9000 + 0.0010i)  (0.2121 - 0.0008i) (0.1000 - 0.3000i)  (0)]; 
re_z = -6.005:.01:6.005;
im_z= -6.005:.01:6.005;
[re_z,im_z] = meshgrid(re_z,im_z);
z = re_z + 1i*im_z;
f_of_1_over_z_result = polyval(p1,1./z);  % I used this code in the first figure
figure
subplot(2,2,1)
surf(re_z,im_z,abs(f_of_1_over_z_result),'EdgeColor','none')
colorbar
title('|f_b(1/z)|')
xlabel('Z_R')  
ylabel('Z_I')  
zlim([0 15])   %adjust this value as needed 
caxis([-0.15 0.15])
subplot(2,2,2)
surf(re_z,im_z, cos(angle(f_of_1_over_z_result)),'EdgeColor','none')
colorbar
title(('cos(phase of f_b(1/z))'))
xlabel('Z_R')  
ylabel('Z_I')
caxis([-1 1])    %adjust this value as needed 
zlim([-1 1])   %adjust this value as needed    
grid on

[Aisha Mohamed]

Thanks so much Torsten. your ways really helpful.