Question about taking fft of a set of real values, laying positive values of the vector, followed by 0, followed by negative values

I have the 1-dimensional FPU problem, and I have the following code:

YX(IT,1:N+1)=[0 Y(IT,1:N )]; 
sXF(IT,:)=imag(fft([YX(IT,1:N+1) 0 -YX(IT,N+1:-1:2)]))/sqrt(2*(N+1));

I am trying to understand why the positive values of YX, are laid with 0 and the negative values before taking the fft?

I tried to look in the matlab documentation for fft, and I see the following under "Compute the two-sided spectrum P2. Then compute the single-sided spectrum P1 based on P2 and the even-valued signal length L."

P2 = abs(Y/L);
P1 = P2(1:L/2+1);
P1(2:end-1) = 2*P1(2:end-1)

I see the signal is doubled here. Why is this done? And perhaps these two are unrelated questions.