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prediction_multiL_ff_norm <-
function(times,reg,ksb,ks1,ks21,ks22,kd1,kd2,delta1,delta2,noise)
{
time2=c(-max(delta1,delta2),times)
h1=splinefun(time2,c(as.numeric(reg)[1],as.numeric(reg)))
p=c(ksb=ksb,ks1=ks1,ks21=ks21,ks22=ks22,kd1=kd1,kd2=kd2,delta1=delta1,delta2=delta2)
sys<-function(t,z,p)
{ gp=p["ksb"]+p["ks1"]*h1(t-p["delta1"])-p["kd1"]*z
list(gp,c())}
targ0=(p["ksb"]+p["ks1"]*h1(times[1]))/p["kd1"]
S1=deSolve::lsoda(targ0,times,sys,p,rtol=1e-4,atol=1e-6)
time2=c(-max(delta1,delta2),times)
reg2= S1[,2]
reg2= norm.data(reg2)+rnorm(n=length(times),mean=0,sd=abs(norm.data(reg2)*noise))
h2=splinefun(time2,c(as.numeric(reg2)[1],reg2))
sys<-function(t,z,p)
{ gp=p["ksb"]+p["ks21"]*h1(t-p["delta1"])+p["ks22"]*h2(t-p["delta2"])-p["kd2"]*z
list(gp,c())}
targ0=(p["ksb"]+p["ks21"]*h1(times[1])+p["ks22"]*h2(times[1]))/p["kd2"]
S2=deSolve::lsoda(targ0,times,sys,p,rtol=1e-4,atol=1e-6)
tar2 = S2[,2]
tar2 = norm.data(tar2)+rnorm(n=length(times),mean=0,sd=abs(norm.data(tar2)*noise))
output=list(tar1=reg2,tar2=tar2)
return(output)}
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