Pendulum code error. How do I resolve unrecognized function or variable when it is clearly stated?

I have a code written out to simulate a pendulum, but there seems to be an error after the loop, and I can't seem to resolve it on my own. I would appreciate any advice on how to solve this issue. My professor can't seem to solve this issue either, and as a result, has told me that I must solve it without further assistance. I have everything written out with comment lines to help the user. I have also included the error message I get. Thanks!

Unrecognized function or variable 'period'.

Error in pendul (line 59)

AvePeriod = mean(period);

%pendul - Program to compute the motion of a simple pendulum 
%using either the Euler or Verlet methods

clear all; help pendul     %Clear the memory and print header

% Select the numerical method to use: Euler or Verlet
NumericalMethod = menu('Choose a numerical method:','Euler','Verlet');

%Set initial position and velocity of pendulum
theta0 = input('Enter initial angle (in degrees): ');
theta = theta0*pi/180; %Convert angle to radians
omega = 0; %Set the initial velocity

%Set the physical constants and other variables
g_over_L = 1;   %The constant g/L
time = 0;       %Initial time
irev = 0;       %Used to count the number of reversals
tau = input('Enter time step: ');

%Take one backward step to start Verlet
accel = -g_over_L*sin(theta); %Gravitational Acceleration
theta_old = theta - omega*tau + 0.5*tau^2*accel;

%Loop over desired number of steps with given time step and numerical method
nstep = input('Enter number of time steps: ');
for istep=1:nstep
    %Record angle and time for plotting
    t_plot(istep) = time;
    th_plot(istep) = theta*180/pi; %Convert angle to degrees
    time = time + tau;
    
    %Compute new position and velocity using Euler or Verlet method
    accel = -g_over_L*sin(theta); %Gravitational Acceleration
    if(NumericalMethod == 1)
        theta_old = theta;          %Save Previous Angle
        theta = theta + tau*omega;   %Euler Method
        omega = omega + tau*accel;
    else
        theta_new = 2*theta - theta_old + tau^2*accel;
        theta_old = theta;          %Verlet Method
        theta = theta_new;
    end
    
    %Test if the pendulum has passed through theta = 0;
    % if yes, use time to estimate period
    if( theta*theta_old < 0)        %Test position for sign change
        fprintf('Turning point at time t= %f \n',time);
        if(irev == 0)               %If this is the first change, just record the time
            time_old = time;
        else
            period(irev) = 2*(time - time_old);
            time_old = time;
        end
        irev = irev + 1; %Increment the number of reversals
    end
end

%Estimate period of oscillations, including error bar
AvePeriod = mean(period);
ErrorBar = std(period)/sqrt(irev);
fprintf('Average period = %g +/- %g\n', AvePeriod,ErrorBar);

%Graph the oscillations as theta versus time
clf; figure(gcf); %Clear and forward figure window
plot(t_plot,th_plot, '+');
xlabel('Time'); ylabel('\theta (degrees)');

Answer 1

[Walter Roberson]

for istep=1:nstep

if nstep is less than 1 then the loop will not be executed at all and period will not be assigned to.

If nstep is at least 1 then we need to investigate whether we can be certain that period is assigned to.

    if( theta*theta_old < 0)

If we have not executed enough steps for the angle to have crossed zero then period would not have been assigned to.

        if(irev == 0)

The first time we cross 0, we do not assign to period.

Putting these together: period will not be assigned to until you have executed enough steps to have crossed zero twice.

    if( theta*theta_old < 0)

No crossing will be detected if theta or theta_old are exactly 0 because then their multiple would be exactly 0 rather than less than 0.

You need to be careful about this case so that you do not accidentally detect the same crossing twice.

[Nicholas Davis]

Thank you for the prompt reply, Walter. Your insight is incredibly valuable. I've tried to alter things given your thoughts, but it seems I still have this error. What kind of addition should I include to the code to actually make it run enough to get a period? Thanks.

[Walter Roberson]

Increase the number of steps you allow. Each step only goes a fraction of a cycle.

But also before you output check that irev is at least 2, because if not then you have not found the period yet.