I want to find particular values of t at which y becomes 2 (by writing some commands in code itself). Can I extract such values of t as a vector?

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Dharma 2018-4-23

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/396848-i-want-to-find-particular-values-of-t-at-which-y-becomes-2-by-writing-some-commands-in-code-itself

评论： Star Strider 2018-5-30

clear
clc;
N=2000;  % Number of time stpes
dt=0.05;  %Time step
%Initialize
 y=zeros(N,1); 
 t=zeros(N,1);
%Initial values
t(1)=0;
y(1)=1;
      for j=2:N
            t(j)=t(j-1)+dt;
      y(j)=y(j-1)+dt*sin(t(j-1));
      end
      plot(t,y)

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Star Strider 2018-4-23

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/396848-i-want-to-find-particular-values-of-t-at-which-y-becomes-2-by-writing-some-commands-in-code-itself#answer_316743

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Try this:

N=2000;  % Number of time stpes
dt=0.05;  %Time step
%Initialize
y=zeros(N,1);
t=zeros(N,1);
%Initial values
t(1)=0;
y(1)=1;
for j=2:N
    t(j)=t(j-1)+dt;
    y(j)=y(j-1)+dt*sin(t(j-1));
end
zci = @(v) find(v(:).*circshift(v(:), [-1 0]) <= 0);                                    % Returns Approximate Zero-Crossing Indices Of Argument Vector
idx_2 = zci(y - 2);                                                                     % Vector Of Approximate Indices Where ‘y=2’
for k = 1:numel(idx_2)
    t2(k) = interp1(y(idx_2(k)+[-1 1]), t(idx_2(k)+[-1 1]), 2, 'linear','extrap');      % Interopolate: ‘t’ Where ‘y=2’
end
figure
plot(t,y)
hold on
plot(t2, 2*ones(size(t2)), 'pg')
hold off

This uses the ‘zci’ utility function to find the approximate indices where ‘t=2’, then uses the ‘idx_2’ index vector to loop through your data to find the closest values of ‘t’ that the interp1 function can calculate where ‘y=2’.

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Dharma 2018-5-30

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Hi Star,

I am requesting you for your suggestion on the following code which uses your previous suggestion for extrapolation. My question is why does code give error message (in the line of t2 calculation i.e. inside for loop of m) when I change number of oscillators (N) from 50 to 60? Lets just ignore other parameters and loop. Thank you!

Dharma

N=60;   % number of oscillators
dt=0.05;  %time step
J=2000;  %number of time steps
%Initialize matrices
t=zeros(1,J);
theta=zeros(N,J);
r=zeros(1,J);
sigN=0.2; %standard deviation of natural frequencies distribution
rng default
 theta(:,1)=2*pi*rand(N,1);%random initial values of theta
 W = random('Normal',0,sigN,N,1);% random values drawn from Gaussian
 K=zeros(1,J);
 r(1)=1;
    K(1)=0.3;         
    for j=2:J
        t(j)=t(j-1)+dt;
        K(j)=0.3;
        kura = @(x,N) W+(K(j)/N)*...
        sum(sin(meshgrid(x)-meshgrid(x)'),2);
        %4th order Runge-Kutta method
        k1=kura(theta(:,j-1),N);
        k2=kura(theta(:,j-1)+0.5*dt*k1,N);
        k3=kura(theta(:,j-1)+0.5*dt*k2,N);
        k4=kura(theta(:,j-1)+dt*k3,N);
          theta(:, j)=theta(:,j-1)+(dt/6)*(k1+2*k2+2*k3+k4);
          r(j)=1/N*sqrt((sum(cos(theta(:,j))))^2+(sum(sin(theta(:,j))))^2);
      end
          zci = @(v) find(v(:).*circshift(v(:), [-1 0]) <= 0);  
          idx_2 = zci(r - 0.2);                                                                   
      for m = 1:numel(idx_2)
          t2(m) = interp1(r(idx_2(m)+[-1 1]), t(idx_2(m)+[-1 1]), 0.2, 'linear','extrap'); 
       % Interpolate t where r=0.4
      end

Dharma 2018-5-30

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Thanks. Actually I was using the same as you suggested (Except in comment where I wrote r=0.4). I found solution as well. If I choose value of r smaller than 0.2 then I will be able to increase N. Do you have any suggestion for this?

   zci = @(v) find(v(:).*circshift(v(:), [-1 0]) <= 0);  
            idx_2 = zci(r - 0.2);                                                                   
        for m = 1:numel(idx_2)
            t2(m) = interp1(r(idx_2(m)+[-1 1]), t(idx_2(m)+[-1 1]), 0.2, 'linear','extrap'); 
         % Interpolate t where r=0.4
        end
Also in the line interp1(r(idx_2(m))+[-1 1], what does [-1 1] represent?
Thank you again!

Star Strider 2018-5-30

My pleasure.

‘If I choose value of r smaller than 0.2 then I will be able to increase N. Do you have any suggestion for this?’

I have no idea what you are doing, so I cannot answer that.

‘Also in the line interp1(r(idx_2(m))+[-1 1], what does [-1 1] represent?’

That vector creates a region ±1 indices around the chosen point, creating a region over which interp1 can interpolate. It is designed to create a strictly monotonic region in a function that may not otherwise be monotonic.

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