matrix indexation and loops over a specific set within a vector

I have the following definitions

long  = 1000;
init  = 500;      
N  = init+long;        
T  = init+1:N-1;   
T1  = init+2:N;

I then fill the vectors that I want according to this loop,

       for t=1:N+1
         Rk(t)=1+A(t)*alpha*kh(t).^(alpha-1)-delta;  
         Yi(t)=A(t)*(1-alpha)*kh(t).^alpha - A(t)*alpha*kh(t).^(alpha-1)+eta(t);
         Rap(t)=Rk(t).^(1-gamma)+(1-gamma)*Rk(t).^(-gamma)*theta(t)*Yi(t)-0.5*gamma*(1-gamma)*(theta(t)*Yi(t)).^2;  
       end

Finally, I compute some new vectors according to this loop

for t=T1
         fi1(t)=(v(t).^(1-gamma))*(Rk(t))*(Yi(t)');  % Expectations 1 
         fi2(t)=((v(t).^(1-gamma))*(Yi(t)).^2);   
         fi3(t)=(((v(t).^(1-gamma))*Rap(t)).^(1/(1-gamma)));
     end

So, from the last loop I aim into getting a vector of size T1, but instead I receive a 1x1500 vector.

My scope is essentially to take all the numbers in vectors, v, Rk, Yi, from exactly the region that T1 specifies (i.e 502:1500), so I should get the 1x999, and not the 1x1500 vector.

So I suppose even if someone stars with an index 502 to count the loop, Matlab still understand this as 1, and loops until N, which is the end point of T1.

Can somebody tell me how should amend the code in order to get what I described above.

Answer 1

[Guillaume]

If you start with an index with an index 502 to count the loop, Matlab understands this as 502.

The issue is with your assignment. You assign the result to indices 502 to 1500, so matlab automatically fills up indices 1 to 501 with zeros. Hence you end up with vectors of size max(T1). To fix this, offset your assignment indices back to 1:

for t = T1
   fi1(t-T1(1)+1)=(v(t).^(1-gamma))*(Rk(t))*(Yi(t)'); %why is there a conjugate transpose here?
   fi2(t-T1(1)+1)=((v(t).^(1-gamma))*(Yi(t)).^2);
   fi3(t)=(((v(t).^(1-gamma))*Rap(t)).^(1/(1-gamma)));
end

If gamma is scalar though, the above is simply:

fi1 = (v(T1).^(1-gamma)).*(Rk(T1)).*(Yi(T1)'); %no loop!
fi2 = ((v(T1).^(1-gamma)).*(Yi(T1)).^2);   
fi3 = (((v(T1).^(1-gamma)).*Rap(T1)).^(1/(1-gamma)))

[msh]

I see your point, I now understand what was wrong. In the first case, there is a typo about the conjugate. Indeed I initially tried to implement want to are suggesting in the bottom. However, I am not sure whether there are indeed equivalent. For instance v and Yi are both Fx1 matrices, so their product will be a FxF matrix which is clrearly not the same as in the first case, where essentially I want an element by element multiplication.

[Guillaume]

Sorry, I made a mistake (and edited my original answer). I should have replaced your matrix multiplications *, but element by element multiplication .*, in my simplification.

If all you want is element by element operation, then use dots on every operator. It will be a lot faster than loops.