Matlab - I am having problems with iteration (loops)

[rad0786]

Homework Statement

Hi. I sort of doubt that anyone will reply to this post since it is a MATLAB problem, but ill give it a shot.

I am trying to write a MATLAB function that will graph the logistic map.

Homework Equations

x(n+1) = r*xn*(1-xn) (1)

The inputs are r, x0 and N.

I want the function to store the sequence x1, x2, . . . , xN given by (1) as the components of a vector x and plots them with respect to n.

The Attempt at a Solution

function [x_i+1]=logistic_map(r,x0,N)
% [x]=logistic_map(r,x0,N)
% the initial condition is x0
% x depends on scalars r, x0, N
% the function computes xn+1 = r*xn(1-xn)

for i = 1:N
x_i+1 = r*x0*(1-x0)
end

plot(1:N,x_i+1)

 

[trajan22]

where is (1), and what exactly is the program not doing that you want it to? I have some MATLAB experience so i might be able to help. What are the test numbers you are using?
One problem i noticed is that you have an operator in the output value you might want to rename the output variable to something more simple. (without +=-/*...) that is the first problem that appears out of it.

also from what i can see the for loop is Unnecessary because your values are never changing. your graph will just be a line.

 

[marcusl]

You need to define x as an array variable and then use an index for it. Since your notation is non-standard it's hard for me to determine what you are trying to accomplish; the following is my best guess.

function [x_i+1]=logistic_map(r,x0,N)
% [x]=logistic_map(r,x0,N)
% the initial condition is x0
% x depends on scalars r, x0, N
% the function computes x(n+1) = r*x(n)*(1-x(n))

x = zeros(1,N); % Not necessary but it shows you the dimensionality of x
x(1) = x0;
for i = 1:N-1
x(i+1) = r*x(i)*(1-x(i));
end
plot(1:N,x)

This is unlikely to be very satisfactory to you because it resembles a factorial function and will overflow any computer for fairly small values of N.

Also it looks like you have a lot to learn about programming and Matlab syntax. I highly recommend you do the online tutorials, and pick up one of the many books on Matlab for engineering and physics available in college bookstores or Amazon.

 

[rad0786]

marcusl;

I tried your code, but it din't seem to work...

Ill look at it a bit closer in the morning and see if i could untangle is problem.

 

[LeBrad]

marcusl;

I tried your code, but it din't seem to work...

Ill look at it a bit closer in the morning and see if i could untangle is problem.

It would be helpful is you posted the errors you are getting.

But I would guess the problems are:
1.) Change xi+1 to x in the function definition line, because you can't use +-/* in variable names for obvious reasons
2.) change plot(1:N,x) to plot([1:N],x)

 

[J77]

yeah - just change the function line.

plot(1:N,x) will work fine, as will simply plot(x)

 

[rad0786]

It would be helpful is you posted the errors you are getting.

But I would guess the problems are:
1.) Change xi+1 to x in the function definition line, because you can't use +-/* in variable names for obvious reasons
2.) change plot(1:N,x) to plot([1:N],x)

Thank you LeBrad for your help.
I should have posted my errors and problems as I went along...i'll make sure I do so in the future.

yeah - just change the function line.

plot(1:N,x) will work fine, as will simply plot(x)

Thank you J77 for your help.


So this is what I had in my editor window:



function [x]=logistic_map1(r,x0,N)
% [x]=logistic_map(r,x0,N)
% the initial condition is x0
% x depends on scalars r, x0, N
% the function computes x(n+1) = r*x(n)*(1-x(n))

x = zeros(1,N); % Not necessary but it shows you the dimensionality of x
x(1) = x0;
for i = 1:N-1
x(i+1) = r*x(i)*(1-x(i));
end
plot(1:N,x)



Then in my command window:

I simply defined my variables x0, r and N.

Then i typed in function [x]=logistic_map1(r,x0,N)

and got a graph

Thanks guys, I apprecaite your help

 

[rad0786]

Hi... I am back for more...

Homework Statement

I would like to creat a loop in MATLAB for a messy equation and plot it.

Homework Equations

x(n+1) = (6*2^n)*(sqrt(x^2(n) + 1) -1)/(xn) where n = 1,2,...

(NOTE: x^2n mean the nth x^2)

I know the above equation is kind of messy...but i just can't seem to get latex to work - so please bear with me.

the initial condition is x(1) = 1/sqrt(3)

The Attempt at a Solution

I followed the outline for what we did above.

Thus, in my editor window, I had:


function [p]=circle(x1)


x(2) = x1;

for i = 2:10
p(i+1) = (6*2^i)*(sqrt(x(i)^2+1)-1)/x(i);
end

plot(x)



Then in the command window, I would define x1 = sqrt(3)

and when I ran [p]=circle(x1) , I got an error.



>> [p]=circle(x1)
? Attempted to access x(3); index out of bounds because numel(x)=2.

Error in ==> circle at 7
p(i+1) = (6*2^i)*(sqrt(x(i)^2+1)-1)/x(i);



Believe me, I can't find anything wrong with my equation? I looked at it a million times.

Could someone help me please?

 

[J77]

The Attempt at a Solution

function [p]=circle(x1)

x(2) = x1;

for i = 2:10
p(i+1) = (6*2^i)*(sqrt(x(i)^2+1)-1)/x(i);
end

plot(x)

Then in the command window, I would define x1 = sqrt(3)

and when I ran [p]=circle(x1) , I got an error.

>> [p]=circle(x1)
? Attempted to access x(3); index out of bounds because numel(x)=2.

Error in ==> circle at 7
p(i+1) = (6*2^i)*(sqrt(x(i)^2+1)-1)/x(i);

Why start at x(2)?

You need to initialise at x(1).

Also the output of the map should be x, not p (also in function output it should be x), and the loop should run from 1 to N-1 as in previous example.

 

[rad0786]

Why start at x(2)?

You need to initialise at x(1).

Also the output of the map should be x, not p (also in function output it should be x), and the loop should run from 1 to N-1 as in previous example.

Thank you.

It worksmuch more better now, however, I still keep getting an error.

I made new changes according to what you said:





function [x]=circle(x1)


x(2) = x1;

for i = 1:36
x(i+1) = (6*2^i)*(sqrt((x(i))^2+1)-1)/x(i);
end

plot(x)





I define x1=1/qurt(3) in the command window.

Thn when I run the programme, I get :

>> [x]=circle(x1)
Warning: Divide by zero.
> In circle at 7
x =

0 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN

And a blank graph.


Is their something wrong with my equation?

 

[J77]

function [x]=circle(x1)

x(2) = x1;

for i = 1:36
x(i+1) = (6*2^i)*(sqrt((x(i))^2+1)-1)/x(i);
end

plot(x)

I define x1=1/qurt(3) in the command window.

Thn when I run the programme, I get :

>> [x]=circle(x1)
Warning: Divide by zero.
> In circle at 7
x =

0 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN

And a blank graph.Is their something wrong with my equation?

You still have initialised at x(2) - what you want is x(1)=x1;

Also, the error comes from x being 0 - the x(1)=x1 should fix this. The only way for this is if x(1)=0 - which gives x(2)=NAN (ie. divide by x(1)=0) - ie. a correct initialisation should fix it

 

[neurocomp2003]

why would you initialise x2 and then start your counter at i=1? your essentially overwriteing x2..
2 ways to fix that solution...one posted above.

if you are new to matlab...two things you should at least learn to do ...(1) fprintf(1,...) or disp(...) or leave out the semi-colon.
like in any programming environment...if you get an error trace your steps on PAPER & PEN...its always your friend.

 

[rad0786]

You still have initialised at x(2) - what you want is x(1)=x1;

Also, the error comes from x being 0 - the x(1)=x1 should fix this. The only way for this is if x(1)=0 - which gives x(2)=NAN (ie. divide by x(1)=0) - ie. a correct initialisation should fix it

Thank you once again, that helped.

why would you initialise x2 and then start your counter at i=1? your essentially overwriteing x2..
2 ways to fix that solution...one posted above.

if you are new to matlab...two things you should at least learn to do ...(1) fprintf(1,...) or disp(...) or leave out the semi-colon.
like in any programming environment...if you get an error trace your steps on PAPER & PEN...its always your friend.

I initialised at x2 because i didn't think the counter was supposed to include x1. Now i see it does...

I will take your advice. I allready did a bit of disp(...) and it is a very good tool...i have never heard of fprint(1...) yet.

Thank you all for taking the time to help me...i appreciate it.

 

[neurocomp2003]

matlab is like linux...u can type help functionname...and the function name that I'm speaking of is fprintf...it allows you to format easier than disp(...) and the one without the ";" eg...you can write everything on one line ...
fprintf("x: %d",x); rather than having it display on multiple lines..though it depends on the of your matrix.

 

[rad0786]

matlab is like linux...u can type help functionname...and the function name that I'm speaking of is fprintf...it allows you to format easier than disp(...) and the one without the ";" eg...you can write everything on one line ...
fprintf("x: %d",x); rather than having it display on multiple lines..though it depends on the of your matrix.

That sounds more complicated...but you know more than me. I will definitley invest some time into learning fprint.


For my last question, is their a way that I can store my results for x in a vector instead of plotting it?

Or simply just get the resluts of each x(i)...hence

x1= 1/sqrt(3)
x2=...
x3=...
x4=...
x5=...
x6=...

and so on?

 

[rad0786]

Nevermind...I see it...the more i fool arond with this...the better i get.

 

[neurocomp2003]

not sure what you mean...but MATLAB is made to control martices/vectors... if your talking abotu allocating memory just do x=size(n,m); and it will preallocate this size for you to use. If you do x(i)=x(i-1)...without preallocating MATLAB will keep rebuilding the size of the matrix which will slow donw your computer.

lastly if your asking if you can return a vector x from your function (which is probalby what you mean) then yes you can...

the line "function x=fx(...)" will allow you to do so
set which ever vector you want inside your function...
then at the very end just say x = vector.
However it looks like you were preallocating the x which is better...it will automatically return x.

when you want x outside this function simply type (say in command prompt)
"x=function(...)"

 

[rad0786]

Oh...

I meant...I wanted to return my function in a row vecotr...

but yea...like you said...everything in MATLAB is in vectors...

I got confused because it kept returning something like this:

Colume 1 - 8

blah blah blah

Colume 9 - 16

Blah blah blah


So i just hit the " ' " after my function and got

blah
blah
blah
Blah
blah
blah

And now i am satisfied :)

 

[J77]

Just a follow-up:

If you don't assign values to the start of an array, Matlab puts them at zero.

Specifically, when you wrote:

x(2)=1/sqrt(3);

Matlab created the array [0 1/sqrt(3)].

Also, you may like to put the command keyboard in your code, when you reach this point you go into debugging mode, ie. you get a command line, plus access to all variables up to that point, you can then check their values to make sure they're as you want them; type return to continue running the code.

 

[mikaili]

I have also found a silly problem with Matlab loop
try the following simple program :
clear all
for s=0:0.1:1
V(10*s+1)=s;
end
it will get into trouble when s reaches 0.6

would anybody please check and let me know the result