How to do a loop for different values?

I am trying to find basin of attraction of the roots, and I want to run the code for different values of q ( where q=0:0.2:,0.99) . How to get the results for all the values of q ?

f = @(z) z.^4 - 5*z.^2+4; % Function with real roots

  % the roots

 r1 =-2;
 r2 =-1;
 r3 =1;
 r4=2;
  
%% range of basin 

nx = 1000;
ny = 1000;
xmin = -4; xmax = 4;
ymin = -2; ymax = 2;

x = linspace(xmin,xmax,nx); % Real space
y = linspace(ymin,ymax,ny); % Imaginary space
[X, Y] = meshgrid(x,y);
Z = X + 1i*Y;

%% Perform our method

  q=0.95;
  
nit = 100; % Maximum number of Newton iterations to be done
 for i = 1:nit 
     
    Z = Z - (f(Z).*Z.*(1-q))./ (f(Z)-f(q.*Z));
end

%% plotting
eps = 1e-10;   % Tolerance to determine closeness to 0.0


Z1 = abs(Z - r1) < eps; Z2 = abs(Z - r2) < eps;
Z3 = abs(Z - r3) < eps; Z4 = abs(Z - r4) < eps;
Z5 = ~(Z1 + Z2 + Z3+Z4);


figure;

map = [0.4660 0.6740 0.1880; 0.8500 0.3250 0.0980; 0 0.4470 0.7410; 0.9290 0.6940 0.1250; 0 0 0];
colormap(map);


Z = Z1 + 2*Z2 + 3*Z3 + 4*Z4 + 5*Z5;
image([xmin xmax],[ymin ymax], Z);
  set(gca,'YDir','normal');
axis equal; axis tight;
xlabel('$x$','Interpreter','latex','FontSize',14)
ylabel('$y$','Interpreter','latex','FontSize',14)
title('Basins of attraction for the root of $f(x)=z^4 - 5z^2+4$.','Interpreter','latex','FontSize',14)

[Dyuman Joshi]

Convert the script to a function that accepts "q" as an input and call it in a loop.

[Omar B.]

How can I do that?

[Dyuman Joshi]

Do you just want the plots as an output? or any other value/variable as well?

[Omar B.]

yes, I want to find different images for different values of q (q=0:0.2:0.99) when I run the code

Answer 1

[Dyuman Joshi]

The output images are not big/clear enough with subplot/tiledlayout.

So, this code generates a new figure for each image -

q = 0:0.2:0.99;

%Call the function
arrayfun(@myFun, q)

function myFun(q)

f = @(z) z.^4 - 5*z.^2+4; % Function with real roots

% the roots

 r1 =-2;
 r2 =-1;
 r3 =1;
 r4=2;
  
% range of basin 
nx = 1000;
ny = 1000;
xmin = -4; xmax = 4;
ymin = -2; ymax = 2;

x = linspace(xmin,xmax,nx); % Real space
y = linspace(ymin,ymax,ny); % Imaginary space
[X, Y] = meshgrid(x,y);

Z = X + 1i*Y;

%Perform our method
nit = 100; % Maximum number of Newton iterations to be done
for i = 1:nit
    %% Function evaluations are costly, especially for an array with 1000x1000 elements
    %% Calculate once and store the data in an array instead of calculating
    %% twice separately
    Z0 = f(Z);
    Z = Z.*(1 - (Z0.*(1-q))./(Z0-f(q.*Z)));
end

%% eps is a built-in function, better to not use it as a variable name
Eps = 1e-10;   % Tolerance to determine closeness to 0.0

Z1 = abs(Z - r1) < Eps; Z2 = abs(Z - r2) < Eps;
Z3 = abs(Z - r3) < Eps; Z4 = abs(Z - r4) < Eps;
Z5 = ~(Z1 + Z2 + Z3 + Z4);

map = [0.4660 0.6740 0.1880; 0.8500 0.3250 0.0980; 0 0.4470 0.7410; 0.9290 0.6940 0.1250; 0 0 0];
colormap(map);

%plotting
Z = Z1 + 2*Z2 + 3*Z3 + 4*Z4 + 5*Z5;
figure
image([xmin xmax],[ymin ymax], Z);
set(gca,'YDir','normal');
axis tight; axis equal;
xlabel('$x$','Interpreter','latex','FontSize',12)
ylabel('$y$','Interpreter','latex','FontSize',12)
title(sprintf('Basins of attraction for the root of $f(x)=z^4 - 5z^2+4$ for q = %g', q),'Interpreter','latex','FontSize',12)
end

[Omar B.]

Thank you so much