Problem With Graph In Function

Hi , I have a problem. The question is as follows:

Below you will find a Matlab script that simulates the customers' shopping model . In this model it is assumed there are two types of customers. We now want this model to be more general. Transform this script into a function that simulates this model for the case with n types of customers. Call this function convcustomers

%%define our customer transition matrix
C = [0.4 0.1; 0.6 0.95];
%%set our maximum time frame
t = 50;
%%we'll store the populations as the columns of the matrix X
X = zeros(2,t+1);
%%set the initial populations
% remember X(:,1) means 'column 1, all rows of matrix X'
X(:,1) = [200;100];
%%iterate over time
for j = 1:t
X(:,j+1) = C * X(:,j);
end
%%plot the results
figure(1);
plot(1:1:t+1, X(1,:),'r-',1:1:t+1,X(2,:),'b-');
xlabel('Time');
ylabel('Customers');
title('Customer populations over time');
legend('One-time','Repeat');

This function should do the following few things:

It takes as inputs:

1.) the matrix C that characterises our system of dynamic equations (notice: the size of C implicitly determines n),

the length of the simulation t (i.e. the total number of periods for which we simulate the model), and

a vector of initial conditions for the system (call it initdistr)

2. It spits out the following output:

an n x (t+1) matrix containing the simulated values of the different types (it's called X in the script I provide for guidance)

The function also produces a graph of the simulated series, and the graph has a legend, with types numbered from 1 to n.

This is my code so far :

function [X, G ] = convcustomers( C, t, initdistr )
%CONVCUSTOMERS This function calculates the ratio
%   of one time to repeat customers in a n time period.

X(:,1) = initdistr;

for j = 1:t
X(:,j+1) = C * X(:,j);

end

figure(1);
G = plot(1:1:t+1, X(1,:) ,'r-',1:1:t+1, X(2,:) ,'b-');
xlabel('Time');
ylabel('Customers');
title('Customer populations over time');
legend('One-time','Repeat');

end

I am unsure how to produce a graph for this with a legend with types numbered 1 to n.

Thanks

Answer 1

[James Tursa]

E.g., something like this to get you started

T = 1:1:t+1;
m = size(X,1);
figure(1);
G = plot(T',X');
legend([repmat('type',m,1) num2str((1:m)')]);