Breaking Vector into Subvectors

How can I evenly split a vector into subvectors. My problem is, in my code I am using dde23 with some randomness involved. I am trying to obtain the coordinates of the numerical solution in intervals of 1 second. The randomness I include however changes the length of the time vector and hence the coordinates of the numerical solution everytime I rund the code. Is there a nice way where I can split the solution vector into subvectors that correspond to 1 second time intervals whilst including this randomness? My current code is as seen below.

Here sol.y corresponds to the coordinates at each time which is in the sol.x vector. I am wanting to split the Car1, Car2 and Car3 vector into intervals corresponding to 1 second.

%3 Cars
%Defines the time delay for each x
lags = [1 1 1];
%Creates a vector of times
tspan = [0 10];
rng('shuffle')
sol = dde23(@ddefun, lags, @history, tspan);
hold on
plot(sol.x,sol.y,'-')
grid on
xlabel('Time (s)');
ylabel('Velocity (m/s)');
legend('Car 1','Car 2','Car 3','Location','NorthWest');

Car1=sol.y(1,:);
Car2=sol.y(2,:);
Car3=sol.y(3,:);

function dydt = ddefun(t,x,Z)
a = -1;
b = 1;
alpha =0.5;
s=rng;
R=rand(1,1);
rng(s);
%Generates a random number between -1 and 1
omega= (b-a).*R + a;
%Calculates a value slowing down/speeding up car 1
gamma=-1/2+mod(t+pi*omega*t,1);
  ylag1 = Z(:,1);
  ylag2 = Z(:,2);
  ylag3 = Z(:,3);  
  %Specifies system of equations
  dydt = zeros(3,1);
  dydt=[gamma*x(1);alpha*(ylag1(1)-ylag2(2));alpha*(ylag2(2)-ylag3(3))];
end  

%Gives initial velocity profiles
function s = history(t)
  s = [20 20 20];
end

[Joshua Peters]

Note: I have attempted using mat2cell but I am finding that this has issues when the vecors change length every time the code is run. This is because it is not guaranteed that the vectors can be split evenly.

Answer 1

[Prahlad Gowtham Katte]

Hello,

As per my understanding of the query, you are trying to split the vector into sub vectors. For this you can first get the index array of vector where index (i) corresponds to indices in X axis where elements lie in between i-1 and i. Then using those indices you can create a cell array for “Car 1”, “Car2” and “Car 3“.

The following modified code will help in achieving the desired functionality.

%3 Cars
%Defines the time delay for each x
lags = [1 1 1];
%Creates a vector of times
tspan = [0 10];
rng("shuffle")
sol = dde23(@ddefun, lags, @history, tspan);
hold on
plot(sol.x,sol.y,'-')
grid on
xlabel("Time (s)");
ylabel("Velocity (m/s)");
legend("Car 1","Car 2","Car 3","Location","NorthWest");

Car1=sol.y(1,:);
Car2=sol.y(2,:);
Car3=sol.y(3,:);

%%%  Here is the code I've added
maximum=max(sol.x); %Find the maximum value of X axis
Car1_split={};
Car2_split={};
Car3_split={};

for j=1:maximum
    if j==1
        l=sol.x>=j-1; %Including 0 in the 1st sub array
    else
        l=sol.x>j-1; 
    end
    m=sol.x<=j;
    n=l&m;
    idx=find(n);%Finding Indices of the elements satisfying above conditions

    %Appending selected Car1,2,3 coressponding indices to the split cell array.
    Car1_split=[Car1_split Car1(idx)];
    Car2_split=[Car2_split Car2(idx)];
    Car3_split=[Car3_split Car3(idx)];
end

function dydt = ddefun(t,x,Z)
a = -1;
b = 1;
alpha =0.5;
s=rng;
R=rand(1,1);
rng(s);
%Generates a random number between -1 and 1
omega= (b-a).*R + a;
%Calculates a value slowing down/speeding up car 1
gamma=-1/2+mod(t+pi*omega*t,1);
  ylag1 = Z(:,1);
  ylag2 = Z(:,2);
  ylag3 = Z(:,3);  
  %Specifies system of equations
  dydt = zeros(3,1);
  dydt=[gamma*x(1);alpha*(ylag1(1)-ylag2(2));alpha*(ylag2(2)-ylag3(3))];
end  

%Gives initial velocity profiles
function s = history(t)
  s = [20 20 20];
end   

For better understanding of the used functions please refer to the following links.

1.Find Array Elements That Meet a Condition - MATLAB & Simulink (mathworks.com)

2.Find indices and values of nonzero elements - MATLAB find (mathworks.com)

Hope it helps.