% The function ilv_dec.m resamples Qlu for implementation
% of the direct neural coupling mechanism between Qlu
% and F.
%
%
% Function arguments:
% ilv - vector of Qlu at original sampling period
% Ogran - original granularity (deltaT/2)
% Sgran - desired granularity
%
% Function output:
% ilvn - vector of Qlu at desired granularity
%
function ilvn = ilv_dec(ilv,Ogran,Sgran)
% Creating time vector which corresponds to Qlu at the original granularity.
t = (0:length(ilv))*Ogran;
% Pre-allocating memory for function output.
N = floor(((length(ilv)-1)*Ogran)/Sgran)-1;
ilvn = zeros(1,N);
% Initializing variables.
m = 1;
start = m;
% Calculating the samples of the function output at Sgran intervals
% by averaging the originally sampled Qlu from the start of the
% previous Sgran interval to the end of the next Sgran interval.
for i = 1:N
% Integrating over precisely over the desired interval
% according to the trapezoidal rule.
ts = i*Sgran;
ti = (i-1)*Sgran;
tf = (i+1)*Sgran;
m = start;
scale = (ti-t(m))/(t(m+1)-t(m));
sumilv = 0.5*(t(m+1)-ti)*(scale*(ilv(:,m+1)-ilv(:,m))+ilv(:,m)+ilv(:,m+1));
m = m+1;
mbrealscalar(t(m+1) < ts);
while (t(m+1) < ts)
sumilv = sumilv + 0.5*(t(m+1)-t(m))*(ilv(:,m+1)+ilv(:,m));
m = m+1;
end
start = m;
mbrealscalar(t(m+1) < tf);
while (t(m+1) < tf)
sumilv = sumilv + 0.5*(t(m+1)-t(m))*(ilv(:,m+1)+ilv(:,m));
m = m+1;
end
scale = (tf-t(m))/(t(m+1)-t(m));
sumilv = sumilv+0.5*(tf-t(m))*(scale*(ilv(:,m+1)-ilv(:,m))+ilv(:,m)+ilv(:,m));
% Averaging over the integration interval.
ilvn(:,i) = sumilv/(2*Sgran);
end