How do I find out when a value first occurs?

My code is tracking a particle and its path, and I want to know how many 'steps' it takes to reach a distance greater than 10 from the origin. I have a matrix that I can look in and manually find out but I have an if statement that should find it for me but it's not working and I'm lost on how to make it work.

My code is:

close all; clear all; clc; format compact;

% m= particle
% dr = 1 %(delta)r = length of stride
% n = 1:1000 %n = number of steps
dr= 1;

%hold on             %Allow for multiple graphs to be drawn

%Zeroes function is an empty vector that stores data
m=zeros(1000,50);
y=zeros(1000,50);

out_of_bounds=zeros(1,50); %since there is only 1 row it should only 
    %record the fist time it crosses the boundary

dist=zeros(1000,50);

for n = 2:50000;                 %1000 steps, 50 runs
    a = 360 * rand;              % random angle in [0,360]

      %Each step taken at random from last position
      m(n) = m(n-1) + dr * cosd(a); 
      y(n) = y(n-1) + dr * sind(a);
      m(1,2:50) = 0;                 %Each particle starts at 0,0
      y(1,2:50) = 0;

      dist(n)=sqrt(((m(n)).^2)+((y(n)).^2)); %r is the radius equation

      B=10; %Boundary is 10

      if dist>= B && out_of_bounds(m)==0 %when the particle is greater than the distance of 10
      %then it should somehow record the number of steps into the out of
      %bounds array
      out_of_bounds(m)=n;
      end

end

Answer 1

[Star Strider]

You need to subscript ‘m’ both times in your if statement and change the && to &.

This works:

dr= 1;
%hold on             %Allow for multiple graphs to be drawn

%Zeroes function is an empty vector that stores data
m=zeros(1000,50);
y=zeros(1000,50);

out_of_bounds=zeros(1,50); %since there is only 1 row it should only 
    %record the fist time it crosses the boundary

dist=zeros(1000,50);

for n = 2:50000;                 %1000 steps, 50 runs
    a = 360 * rand;              % random angle in [0,360]

        %Each step taken at random from last position
        m(n) = m(n-1) + dr * cosd(a); 
        y(n) = y(n-1) + dr * sind(a);
        m(1,2:50) = 0;                 %Each particle starts at 0,0
        y(1,2:50) = 0;

        dist(n)=sqrt(((m(n)).^2)+((y(n)).^2)); %r is the radius equation

        B=10; %Boundary is 10

        if dist>= B & out_of_bounds(m(n))==0 %when the particle is greater than the distance of 10
        %then it should somehow record the number of steps into the out of
        %bounds array
        out_of_bounds(m(n))=n;
        end

end

figure(1)
plot(m, y)
grid

I leave it to you to determine if it produces the correct output.

The plot is optional. I added it because I wanted to see what your result looked like.

[Kathryn Jordan]

Thank you for your help and I appreciate it though it hasn't completely solved my problem.

[Star Strider]

My pleasure.

What isn’t yet solved?

[Kathryn Jordan]

The out_of_bounds matrix is still just zeros and it should have the value of how many steps it took for the particle to leave the boundary.

[Star Strider]

This was absolutely obvious but I didn’t see it before! (Chalk it up to a long day.)

Change your if statement to subscript ‘dist’:

if dist(n) >= B

I won't get into the full details, but it otherwise considered ‘dist’ as a vector. If you don’t tell your statement what element to test, it tests only the first element in the vector. There are ways around that, but you need to test only the current element, so subscripting it works in your code.

You might also consider changing your ‘out_of_bounds’ assignment to:

out_of_bounds=n;

but since I don’t know how you want to track it, I’ll leave to you to decide what you want to put into it.

[Kathryn Jordan]

I tried what you said but now that just gives me the final answer that when n=50000 it is bigger than 10, which is not what I need.

[Star Strider]

Change the ‘out_of_bounds’ assignment to:

out_of_bounds(n)=n;

That should work.

Or, you can create a separate counter (for instance, ‘k’) for ‘out_of_bounds’, intitialise it to 0 before the loop, and just increment it before the assignment. That would change your code inside your if block to:

k = k + 1;
out_of_bounds(k)=n;

[Kathryn Jordan]

Well the k works for the first particle but then it continues counting after that instead of moving onto the next particle.

[Star Strider]

Try the full revised code:

dr= 1;
%hold on             %Allow for multiple graphs to be drawn

%Zeroes function is an empty vector that stores data
m=zeros(1000,50);
y=zeros(1000,50);

out_of_bounds=zeros(1,50); %since there is only 1 row it should only 
    %record the fist time it crosses the boundary

dist=zeros(1000,50);

for n = 2:50000;                 %1000 steps, 50 runs
    a = 360 * rand;              % random angle in [0,360]

          %Each step taken at random from last position
          m(n) = m(n-1) + dr * cosd(a); 
          y(n) = y(n-1) + dr * sind(a);
          m(1,2:50) = 0;                 %Each particle starts at 0,0
          y(1,2:50) = 0;

          dist(n)=sqrt(((m(n)).^2)+((y(n)).^2)); %r is the radius equation

          B=10; %Boundary is 10

          if dist(n)>= B  %when the particle is greater than the distance of 10
          %then it should somehow record the number of steps into the out of
          %bounds array
          out_of_bounds(n)=n;
          end

end  

idx_oob = find(out_of_bounds > 0);

Be sure to look at ‘idx_oob’.

[Kathryn Jordan]

Well that's closer but it looks for every time the value is grater than 10 and I'm trying to find it the first time it occurs for a particle, and then to find for the next particles.

[Star Strider]

I have to admit I’m having a difficult time understanding what you’re doing.

How many times are you iterating for each particle?

How many particles do you have?

I’m beginning to think it might be best to set up two nested loops, the outer one iterating over the particles and the inner one iterating each particle in turn. I doubt you can do all of them at once and get any useful information.

[Image Analyst]

I think so. That's exactly what I was working on when you were posting this. I've posted my code.

Answer 2

[Image Analyst]

Try this code. I think it's what you want to do but it's more robust and general.

% Monte Carlo experiment for random walk
clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 20;

% radius = length of one step.
radius = 1;
% Define Monte Carlo parameters
numExperiments = 50;
maxSteps = 1000;
% Initialize data.
x = zeros(maxSteps, numExperiments);
y = zeros(maxSteps, numExperiments);

% Since there is only 1 row it should only
%record the fist time it crosses the boundary
out_of_bounds=zeros(1, numExperiments);

dist=zeros(maxSteps, numExperiments);
B = 10; % Boundary is 10 = max allowed distance before we go to next particle

for experiment = 1 : numExperiments
  for stepNumber = 2: maxSteps
    angle = 360 * rand; % random angle in [0,360]
    
    % Find the location of the next point
    x(stepNumber, experiment) = x(stepNumber-1, experiment) + radius * cosd(angle);
    y(stepNumber, experiment) = y(stepNumber-1, experiment) + radius * sind(angle);

    % Find distance from origin (0,0)
    dist(stepNumber, experiment)=sqrt(x(stepNumber, experiment).^2 + y(stepNumber, experiment).^2);
    
    if dist(stepNumber, experiment) >= B
      % Then the particle is greater than the distance of 10
      % Record the number of steps 
      % it took to get out of bounds.
      out_of_bounds(experiment) = stepNumber;
      % All other points will be whatever this distance is.
      dist(stepNumber+1:end, experiment) = dist(stepNumber, experiment);
      break; % Quit tracking this particle.
    end  
  end
end
maxNumberOfSteps = max(out_of_bounds);
% Plot the number of steps to get out of bounds.
plot(out_of_bounds, 'b-', 'LineWidth', 2);
xlim([0, numExperiments]);
title('Steps until out of bounds', 'FontSize', fontSize);
xlabel('Experiment Number', 'FontSize', fontSize);
ylabel('Number of Steps Until Out of Bounds', 'FontSize', fontSize);
grid on;
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0 0 1 1]);
% Give a name to the title bar.
set(gcf, 'Name', 'Demo by ImageAnalyst', 'NumberTitle', 'Off') 

% Plot the distances as a function of step number.
figure
plot(dist, 'LineWidth', 2);
xlim([0, maxNumberOfSteps]);
grid on;
title('Distance vs. Step Number', 'FontSize', fontSize);
xlabel('Step Number', 'FontSize', fontSize);
ylabel('Distance', 'FontSize', fontSize);
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0 0 1 1]);
% Give a name to the title bar.
set(gcf, 'Name', 'Demo by ImageAnalyst', 'NumberTitle', 'Off')

Attached is the file, in case the formatting and line wrapping above is messed up.

I've also attached my earlier random walk code (not based on your code like this is). For extra bonus points, plot each path, take the histogram of distances and plot the distribution, and see how well your experiment matches up with the theoretical formula for distance vs. step.