Find first row where the first 10 elements of that row are unique from each other

Hi,

I am plotting the Ricker map and trying to find at what point chaos in the map occurs. I have been trying to do so by searching for the row in matrix 'x' where the first 10 values are unique (non-repeating and converging to chaos). Can anyone help me in how to do this, or explain a better method.

Ntrans = 1024;                % Set a large value to eliminate transients later
NT = 256;                     % Total number of iterations
r_vec = linspace(0,4,1024);   % Set control parameter in an array using linspace
x_init = 0.15;                % Initial Population
c = zeros(1024,257);
% Setting array index K equal to # of elements in r_vec
% Assigning r to the element of r_vec each cycle through k
% Assigning x0 to value of initial population 
    for k = 1:length(r_vec)
        r = r_vec(k);
        x0 = x_init;
% Iterate the map Ntrans times to reach asymptotic solution.
    for jj = 1:Ntrans
 x0 = x0*exp(r*(1-x0));
    end
 % Assigning first entry in array to x0
        x(k,1) = x0;   
% Iterate the map NT times
    for j = 1:NT
        x(k,j+1) = x(k,j)*exp(r*(1-x(k,j))); 
end
    end
figure(1)
set(gcf,'name','Bifurcation diagram','numbertitle','off')
plot(r_vec,x,'r.','Markersize',1)
grid on; box on, xlabel('r'); ylabel('lim_{n\rightarrow\infty} x_n')
title('Bifurcation diagram of the Ricker map')
xticks(0:0.5:4), yticks(0:0.5:5)
axis([0 4 0 5])  

Answer 1

[Walter Roberson]

row_has_10_unique = all(diff(sort(x(:,1:10)),2) > 0,2);

[Reece]

Thanks for the response. This gives row 204 as the first true condition, yet the first 10 elements in this row are all equal.

[Walter Roberson]

I would suggest to you that if you use

format long g
x204 = x(204,1:10);
sx204 = sort(x204)
diff(sx204)

that you will see that the entries are not all exactly equal -- that instead they differ in digits that you were not examining before.

[Reece]

this shows sx204 as a 1x10 all with values 1, and gives false statements for all elements

[Walter Roberson]

What shows up for the diff() ?

Reminder:

format long g
p = 1

p = 
     1

q = p*(1+eps)

q = 
                         1

%those display as if they were the same, but
p == q     %does not compare equal

ans = logical
   0

q-p        %you can see the difference

ans = 
      2.22044604925031e-16

diff([p,q])

ans = 
      2.22044604925031e-16

[Reece]

format long g
x204 = x(204,1:10);
sx204 = sort(x204)
diff(sx204)
sx204 =
1     1     1     1     1     1     1     1     1     1
ans =
0     0     0     0     0     0     0     0     0

When I inspect x, the rows in question do not show any difference of value of any order.

Is there a way to impliment into the statement that the values must differ greater than 'epsilon' for the statement to be true?

Thanks again

[Walter Roberson]

row_has_10_unique = all(diff(sort(x(:,1:10)),[],2) > 0,2);

I tend to forget that the dimension is the third parameter to diff.