4.6.1: MATLAB/Octave program

Here is a program that runs in MATLAB or OCTAVE that performs the iteration of a linear function — where we are given the coefficients of the function and the starting value. The program outputs the iteration sequence.

Needs to be debugged the olympic rings on the blue bar select the Jupyter hub

function x=iterlin(a, b, x0, N)
%function x=iterlin(a, b, x0, N)
%
%Iterates f(x)=ax+b
%
%Inputs
% a - slope of function
% b -intercept of function
% x0 - initial condition
% N - number of iterations
%Output
% x - vector of iterates
x=zeros(1, N); %ititialize x as a vector of zeros
x(1)=x0; %set initial condition
for i=1:(N-1)
x(i+1)=a*x(i)+b;
print a %iterate
end
x=iterlin(0.5, 2, 1, 10)

parse error:

  syntax error

>>> plot(x, ’k-o’) %plot
            ^

parse error:

  syntax error

>>> xlabel(’i’) %label axes
           ^

parse error:

  syntax error

>>> ylabel(’x_i’)
           ^

This code is a function that will work in \(M A T L A B\) or its free open source alternative Octave. It should be saved as iterlin.m and placed in a directory accessible to MATLAB/Octave. To do this make the directory your current directory or add it to your path in MATLAB/Octave.

We can get information about the function by entering the following at the MATLAB/Octaveprompt.

> help iterlin

To run the function with \(\left(a, b, x_0, n\right)=(0.5,2,5,10)\) and save the output to \(x\) type:

\(>x=i t e r l i n(0.5,2,5,10)\)
We can plot the result and label the axes using:

\(>\) plot \((\mathrm{x}\), ' \(\mathrm{k}-\mathrm{o}\) ') \(\%\) plot
\(>\) xlabel('i') \%label axes
> ylabel('x_i')

While we have not done it for this lab, by altering the program line that calculates \(x(i+1)=a * x(i)+b\), you could use a modified form of your program to compute iterates of any reasonable function. (With functions that do not involve parameters \(a\) and \(b\), you can simply ignore the inputs for \(a\), and \(b\) - giving them any values you wish - or you can modify the first line of the program.)