# inst/OldDemo/FhNEx.R In CollocInfer: Collocation Inference for Dynamic Systems

```# An example file fitting the FitzHugh-Nagumo equations to data in the
# new R Profiling Code. This will eventually be interfaced with the new R
# "Partially Observed Markov Process (pomp)" class of objects.

library('fda')
library('odesolve')
library('maxLik')
library('MASS')
library('Matrix')
library('SparseM')
source('ProfileR.R')
source('sse.shortcut.R')
source('fhn.R')
source('findif.ode.R')
source('SSElik.R')
source('SSEproc.R')
source('makeid.R')
source('inneropt.R')

# First Create Some Data

t = seq(0,20,0.05)

pars = c(0.2,0.2,3)
names(pars) = c('a','b','c')

x0 = c(-1,1)
names(x0)= c('V','R')
y = lsoda(x0,times=t,func=make.fhn()\$fn.ode,pars)
y = y[,2:3]

data = y + matrix(rnorm(802),401,2)

# Now a basis object

knots = seq(0,20,0.2)
norder = 3
nbasis = length(knots) + norder - 2
range = c(0,20)

bbasis = create.bspline.basis(range=range,nbasis=nbasis,
norder=norder,breaks=knots)

# Initial values for coefficients will be obtained by smoothing

fd.data = array(data,c(dim(data)[1],1,dim(data)[2]))

DEfd = data2fd( fd.data,t,bbasis,fdnames=list(NULL,NULL,c('V','R')) )

coefs = matrix(DEfd\$coefs,dim(DEfd\$coefs)[1],dim(DEfd\$coefs)[3])
colnames(coefs) = DEfd\$fdnames[[3]]

# Usual meta-parameters; quadrature points, weights and knots

lambda = c(10000,10000)
qpts = knots
qwts = rep(1/length(knots),length(knots))

qwts = qwts%*%t(lambda)
weights = array(1,dim(data))

# Now I define a measurement process log likelihood along with some
# additional features: in this case it's squared error.

varnames = c('V','R')
parnames = c('a','b','c')

likmore = make.id()
likmore\$weights = weights

lik = make.SSElik()
lik\$more = likmore
#lik\$bvals = as.matrix.csr(eval.basis(t,bbasis))
lik\$bvals = Matrix(eval.basis(t,bbasis),sparse=TRUE)

# Proc is a process log likelihood -- in this case treated as squared
# discrepancy from the ODE definition.

procmore = make.fhn()
procmore\$names = varnames
procmore\$parnames = parnames

procmore\$weights = qwts
procmore\$qpts = qpts

proc = make.SSEproc()
proc\$more = procmore
#proc\$bvals = list(bvals=as.matrix.csr(eval.basis(procmore\$qpts,bbasis,0)),
#		dbvals = as.matrix.csr(eval.basis(procmore\$qpts,bbasis,1)))
proc\$bvals = list(bvals=Matrix(eval.basis(procmore\$qpts,bbasis,0),sparse=TRUE),
dbvals = Matrix(eval.basis(procmore\$qpts,bbasis,1),sparse=TRUE))

###Now lets try some optimization

spars = c(0.2,0.2,2)          # Perturbed parameters

control=list()                # Control parameters
control\$trace = 0
control\$maxit = 1000
control\$maxtry = 10
control\$reltol = 1e-6
control\$meth = "BFGS"

control.in = control
control.in\$reltol = 1e-12
control.out = control
control.out\$trace = 2

control.in\$print.level = 0
control.in\$iterlim = 1000

# We'll try a simple SSE setup:

res = sse.setup(pars=pars,coefs=coefs,fn=make.fhn(),basisvals=bbasis,lambda=lambda,times=t)

res = smooth.sse(make.fhn(),data,t,pars,coefs,bbasis,lambda=lambda,control.in=control.in)

res = profile.sse(make.fhn(),data,t,pars,coefs,bbasis,lambda=lambda,out.meth='nls',
control.in=control.in,control.out=control.out)

# Alternative is simply to use the functional data object

res = sse.setup(pars=pars,fd.obj=DEfd,fn=make.fhn(),lambda=lambda,times=t)

res = smooth.sse(pars=pars,fd.obj=DEfd,fn=make.fhn(),lambda=lambda,times=t,data=fd.data,control.in=control.in)

res = profile.sse(fn=make.fhn(),data=fd.data,times=t,pars=pars,fd.obj=DEfd,lambda=lambda,out.meth='house',
control.in=control.in,control.out=control.out)

f = SplineCoefsErr(coefs,times=t,data=data,lik=lik,proc=proc,pars=spars)
g = SplineCoefsDC(coefs,times=t,data=data,lik=lik,proc=proc,pars=spars)
h = SplineCoefsDC2(coefs,times=t,data=data,lik=lik,proc=proc,pars=spars)
g2 = SplineCoefsDP(coefs,times=t,data=data,lik=lik,proc=proc,pars=spars)
h2 = SplineCoefsDCDP(coefs,times=t,data=data,lik=lik,proc=proc,pars=spars)

res = optim(coefs,SplineCoefsErr,gr=SplineCoefsDC,hessian=T,
method="BFGS",control=control.out,
times=t,data=data,lik=lik,proc=proc,pars=spars)

control=control.out,times=t,data=data,lik=lik,proc=proc,pars=spars)

res2 = maxNR(SplineCoefsErr,start=as.vector(coefs),times=t,data=data,lik=lik,proc=proc,pars=spars,sgn=-1,

res3 = SplineEst.NewtRaph(coefs,t,data,lik,proc,spars)

# record the coefficients for the sake of good starting values

ncoefs = array(res0\$par,c(bbasis\$nbasis,ncol(data)))

ProfileEnv = new.env()
assign('optcoef',ncoefs,3,ProfileEnv)
assign('curcoefs',ncoefs,3,ProfileEnv)

# Test outer objective criterion

f = ProfileErr(pars,pars,t,data,ncoefs,lik,proc,in.meth="nlminb",control.in=control.in)
g = ProfileDP(pars,pars,t,data,ncoefs,lik,proc,sum=FALSE)

# There are specific criteria for SSE so that a Gauss-Newton iteration can be used

res4 = ProfileSSE(pars,t,data,ncoefs,lik,proc,in.meth="nlminb",control.in)

# Gauss-Newton function coded in R.

res5 = Profile.GausNewt(spars,t,data,ncoefs,lik,proc,in.meth="nlminb",control.in)

# the alternative standard function is NLS

res6 = nls(~ProfileSSE(pars,times,data,coefs,lik,proc,in.meth,control.in),
data = list(times=t,data=data,coefs=ncoefs,lik=lik,proc=proc,
in.meth="nlminb",control.in=control.in),start = list(pars=pars),
trace=TRUE)

# for which we can try a Newey-West type covariance estimate

df = diag(res6\$m\$resid())%*%g
C6 = NeweyWest.Var(t(g)%*%g, df[1:401,]+df[402:802,],5)

# Try using a simple second-derivative optimizer for the inner optimization:

res7 = Profile.GausNewt(spars,t,data,ncoefs,lik,proc,in.meth='house',control.in)

# nls with a number of alternative inner optimizations: self defined:

res8 = nls(~ProfileSSE(pars,times,data,coefs,lik,proc,in.meth,control.in),
data = list(times=t,data=data,coefs=ncoefs,lik=lik,proc=proc,
in.meth='house',control.in=control.in),
start = list(pars=spars),trace=TRUE)

# nlminb:

res9 = nls(~ProfileSSE(pars,times,data,coefs,lik,proc,in.meth,control.in),
data = list(times=t,data=data,coefs=ncoefs,lik=lik,proc=proc,
in.meth='nlminb',control.in=control.in),
start = list(pars=spars),trace=TRUE)

# maxNR:

res10 = nls(~ProfileSSE(pars,times,data,coefs,lik,proc,in.meth,control.in),
data = list(times=t,data=data,coefs=ncoefs,lik=lik,proc=proc,
in.meth='maxNR',control.in=control.in),
start = list(pars=spars),trace=TRUE)

# When squared error is not being employed, things proceed somewhat more slowly
# However, this allows the smoothing criteria to fit into the pomp framework

res11 = optim(pars,ProfileErr,allpars=pars,times=t,data=data,coef=ncoefs,lik=lik,proc=proc,hessian=T,
in.meth='nlminb',control.in=control.in,control=control.out,gr=ProfileDP,method="BFGS")

g = ProfileDP(res11\$par,res11\$par,t,data,ncoefs,lik,proc,sum=FALSE)

gg = apply(g,2,sum)

H = 0*res11\$hess

for(i in 1:length(pars)){
tpars = res11\$par
tpars[i] = tpars[i] + 1e-4

tf = ProfileErr(tpars,tpars,t,data,ncoefs,lik,proc,in.meth="nlminb",control.in=control.in)
tg = ProfileDP(tpars,tpars,t,data,ncoefs,lik,proc,sum=TRUE)

H[,i] = (tg-gg)*1e4
}

C11 = NeweyWest.Var(H,g,5)

# optim searches a much larger space, which can be a problem, but it finds a better
# minimum than

res12 = nlminb(pars,ProfileErr,allpars=pars,times=t,data=data,coef=ncoefs,lik=lik,proc=proc,
in.meth='nlminb',control.in=control.in,control=control.out,gr=ProfileDP)

# Now lets see what happens for a finite-difference approximation

proc2more = make.findif.ode()
proc2more\$more = list()
proc2more\$more\$fn = fhn.fun
proc2more\$names = varnames
proc2more\$parnames = parnames

proc2more\$more\$eps = 1e-6

proc2more\$weights = qwts
proc2more\$qpts = qpts

proc2 = make.SSEproc()
proc2\$more = proc2more
proc2\$bvals = list(bvals=eval.basis(procmore\$qpts,bbasis,0),
dbvals = eval.basis(procmore\$qpts,bbasis,1))

res13 = Profile.GausNewt(pars,t,data,ncoefs,lik,proc2,in.meth='nlminb',control.in)

res14 = nls(~ProfileSSE(pars,times,data,coefs,lik,proc2,in.meth,control.in),
data = list(times=t,data=data,coefs=ncoefs,lik=lik,proc=proc,
in.meth='nlminb',control.in=control.in),
start = list(pars=spars),trace=TRUE)

# Now we'll only observe the first component

data2 = data
data2[,2] = NA

res15 = Profile.GausNewt(pars,t,data2,ncoefs,lik,proc,in.meth='nlminb',control.in)

res16 = nls(~ProfileSSE(pars,times,data,coefs,lik,proc2,in.meth,control.in),
data = list(times=t,data=data2,coefs=ncoefs,lik=lik,proc=proc,
in.meth='nlminb',control.in=control.in),
start = list(pars=spars),trace=TRUE)

# Lets suppose that I've measured a linear combination

source('genlin.R')

lik2more = make.genlin()
lik2more\$more = list()
lik2more\$weights = weights[,1]

lik2more\$more = list()
lik2more\$more\$mat = matrix(c(1,0),1,2)
lik2more\$more\$sub = matrix(0,0,3)

lik2 = lik;
lik2\$more = lik2more;

data3 = as.matrix(data[,1],nrow(data),1)

res17 = Profile.GausNewt(pars,t,data3,ncoefs,lik2,proc,in.meth='house',control.in)

# Now lets add estimating a set of parameters in lik to the mix

lik3more = lik2more
lik3more\$more\$mat = matrix(0,1,2)
lik3more\$more\$sub = matrix(c(1,1,4,1,2,5),2,3,byrow=T)

lik3 = lik2
lik3\$more = lik3more

proc2 = proc
proc2\$more\$parnames = c(proc\$more\$parnames,'l1','l2')

pars2 = c(pars,1,0)
names(pars2) = proc2\$more\$parnames

res18 = Profile.GausNewt(pars2,t,data3,ncoefs,lik3,proc2,in.meth='nlminb',control.in)

res19 = optim(pars2,ProfileErr,allpars=pars2,times=t,data=data3,ncoefs,lik=lik3,proc=proc2,
in.meth='nlminb',control.in=control.in,control=control.out,gr=ProfileDP,method="BFGS")

res20 = nlminb(pars2,ProfileErr,allpars=pars2,times=t,data=data3,coef=ncoefs,lik=lik3,proc=proc2,
in.meth='nlminb',control.in=control.in,control=control.out,gr=ProfileDP)

f = ProfileErr(res20\$par,res20\$par,t,data3,ncoefs,lik3,proc2,in.meth="nlminb",control.in=control.in)
g = ProfileDP(res20\$par,res20\$par,t,data3,ncoefs,lik3,proc2,sum=FALSE)

gg = apply(g,2,sum)

H = matrix(0,5,5)

for(i in 1:5){
tpars = res20\$par
tpars[i] = tpars[i] + 1e-4

tf = ProfileErr(tpars,tpars,t,data3,ncoefs,lik3,proc2,in.meth="nlminb",control.in=control.in)
tg = ProfileDP(tpars,tpars,t,data3,ncoefs,lik3,proc2,sum=TRUE)

H[,i] = (tg-gg)*1e4
}

C20 = NeweyWest.Var(0.5*(H+t(H)),g,5)

res21 = nls(~ProfileSSE(pars,times,data,coefs,lik,proc,in.meth,control.in),
data = list(times=t,data=data3,coefs=ncoefs,lik=lik3,proc=proc2,
in.meth='nlminb',control.in=control.in),
start = list(pars=pars2),trace=TRUE)

ff =  ProfileSSE(res20\$par,t,data3,ncoefs,lik3,proc2,in.meth="nlminb",control.in)

res22 = maxNR(ProfileErr,start=pars2,allpars=pars2,times=t,data=data3,coef=ncoefs,lik=lik3,proc=proc2,

# Now we'll set up some repeat experiments

x02 = c(1,-1)
names(x02)= c('V','R')
y2 = lsoda(x02,times=t,func=fhn.fun.ode,pars)
y2 = y2[,2:3]

data2 = y2 + matrix(rnorm(802),401,2)

replik = lik
replik\$bvals = diag(rep(1,2))%x%lik\$bvals
replik\$more\$weights = rbind(lik\$more\$weights,lik\$more\$weights)

repproc = proc
repproc\$bvals = list(bvals = diag(rep(1,2))%x%proc\$bvals\$bvals,
dbvals=diag(rep(1,2))%x%proc\$bvals\$dbvals)
repproc\$more\$weights = rbind(proc\$more\$weights,proc\$more\$weights)

reptimes = c(t,t+max(t))

repdata = rbind(data,data2)

coefs3 = solve( t(replik\$bvals)%*%replik\$bvals )%*%( t(replik\$bvals)%*%repdata )

control=control.out,times=reptimes,data=repdata,lik=replik,proc=repproc,pars=spars)

ncoefs = array(res23\$par,dim(coefs3))

ProfileEnv = new.env()
assign('optcoef',ncoefs,3,ProfileEnv)
assign('curcoefs',ncoefs,3,ProfileEnv)

res24 = Profile.GausNewt(spars,reptimes,repdata,ncoefs,replik,repproc,in.meth="nlminb",control.in)

# Lets try this assuming we have functional data

fd.data2 = array(0,c(nrow(data2),2,2))

fd.data2[,2,] = data2
fd.data2[,1,] = data

DEfd2 = data2fd(fd.data2,t,bbasis,fdnames=list(NULL,NULL,c('V','R')) )

res = sse.setup(pars=pars,fd.obj=DEfd2,fn=make.fhn(),lambda=100,times=t)

res = smooth.sse(pars=pars,fd.obj=DEfd2,fn=make.fhn(),lambda=100,times=t,data=fd.data2,control.in=control.in)

res = profile.sse(fn=make.fhn(),data=fd.data2,times=t,pars=pars,fd.obj=DEfd2,,lambda=100,out.meth='nls',
control.in=control.in,control.out=control.out)

# Alternatively, we can just do the sse setup thing

coefs2 = DEfd2\$coefs

dimnames(coefs2) = list(NULL,NULL,c('V','R'))

res = sse.setup(pars=pars,coefs=coefs,fn=make.fhn(),basisvals=bbasis,lambda=100,times=t)

res = smooth.sse(make.fhn(),data,t,pars,coefs,bbasis,lambda=100,control.in=control.in)

res = profile.sse(make.fhn(),data,t,pars,coefs,bbasis,lambda=100,out.meth='nls',
control.in=control.in,control.out=control.out)

# Alternative is simply to use the functional data object

res = sse.setup(pars=pars,fd.obj=DEfd,fn=make.fhn(),lambda=100,times=t)

res = smooth.sse(pars=pars,fd.obj=DEfd,fn=make.fhn(),lambda=100,times=t,data=fd.data,control.in=control.in)

res = profile.sse(fn=make.fhn(),data=fd.data,times=t,pars=pars,fd.obj=DEfd,,lambda=100,out.meth='nls',
control.in=control.in,control.out=control.out)

f = SplineCoefsErr(coefs,times=t,data=data,lik=lik,proc=proc,pars=spars)
g = SplineCoefsDC(coefs,times=t,data=data,lik=lik,proc=proc,pars=spars)
h = SplineCoefsDC2(coefs,times=t,data=data,lik=lik,proc=proc,pars=spars)
g2 = SplineCoefsDP(coefs,times=t,data=data,lik=lik,proc=proc,pars=spars)
h2 = SplineCoefsDCDP(coefs,times=t,data=data,lik=lik,proc=proc,pars=spars)

res = optim(coefs,SplineCoefsErr,gr=SplineCoefsDC,hessian=T,
method="BFGS",control=control.out,
times=t,data=data,lik=lik,proc=proc,pars=spars)

control=control.out,times=t,data=data,lik=lik,proc=proc,pars=spars)

res2 = maxNR(SplineCoefsErr,start=as.vector(coefs),times=t,data=data,lik=lik,proc=proc,pars=spars,sgn=-1,

res3 = SplineEst.NewtRaph(coefs,t,data,lik,proc,spars)

# record the coefficients for the sake of good starting values

ncoefs = array(res0\$par,c(bbasis\$nbasis,ncol(data)))

ProfileEnv = new.env()
assign('optcoef',ncoefs,3,ProfileEnv)
assign('curcoefs',ncoefs,3,ProfileEnv)

# Test outer objective criterion

f = ProfileErr(pars,pars,t,data,ncoefs,lik,proc,in.meth="nlminb",control.in=control.in)
g = ProfileDP(pars,pars,t,data,ncoefs,lik,proc,sum=FALSE)

# There are specific criteria for SSE so that a Gauss-Newton iteration can be used

res4 = ProfileSSE(pars,t,data,ncoefs,lik,proc,in.meth="nlminb",control.in)

# Gauss-Newton function coded in R.

res5 = Profile.GausNewt(spars,t,data,ncoefs,lik,proc,in.meth="nlminb",control.in)

# the alternative standard function is NLS

res6 = nls(~ProfileSSE(pars,times,data,coefs,lik,proc,in.meth,control.in),
data = list(times=t,data=data,coefs=ncoefs,lik=lik,proc=proc,
in.meth="nlminb",control.in=control.in),start = list(pars=pars),
trace=TRUE)

# for which we can try a Newey-West type covariance estimate

df = diag(res6\$m\$resid())%*%g
C6 = NeweyWest.Var(t(g)%*%g, df[1:401,]+df[402:802,],5)

# Try using a simple second-derivative optimizer for the inner optimization:

res7 = Profile.GausNewt(spars,t,data,ncoefs,lik,proc,in.meth='house',control.in)

# nls with a number of alternative inner optimizations: self defined:

res8 = nls(~ProfileSSE(pars,times,data,coefs,lik,proc,in.meth,control.in),
data = list(times=t,data=data,coefs=ncoefs,lik=lik,proc=proc,
in.meth='house',control.in=control.in),
start = list(pars=spars),trace=TRUE)

# nlminb:

res9 = nls(~ProfileSSE(pars,times,data,coefs,lik,proc,in.meth,control.in),
data = list(times=t,data=data,coefs=ncoefs,lik=lik,proc=proc,
in.meth='nlminb',control.in=control.in),
start = list(pars=spars),trace=TRUE)

# maxNR:

res10 = nls(~ProfileSSE(pars,times,data,coefs,lik,proc,in.meth,control.in),
data = list(times=t,data=data,coefs=ncoefs,lik=lik,proc=proc,
in.meth='maxNR',control.in=control.in),
start = list(pars=spars),trace=TRUE)

# When squared error is not being employed, things proceed somewhat more slowly
# However, this allows the smoothing criteria to fit into the pomp framework

res11 = optim(pars,ProfileErr,allpars=pars,times=t,data=data,coef=ncoefs,lik=lik,proc=proc,hessian=T,
in.meth='nlminb',control.in=control.in,control=control.out,gr=ProfileDP,method="BFGS")

g = ProfileDP(res11\$par,res11\$par,t,data,ncoefs,lik,proc,sum=FALSE)

gg = apply(g,2,sum)

H = 0*res11\$hess

for(i in 1:length(pars)){
tpars = res11\$par
tpars[i] = tpars[i] + 1e-4

tf = ProfileErr(tpars,tpars,t,data,ncoefs,lik,proc,in.meth="nlminb",control.in=control.in)
tg = ProfileDP(tpars,tpars,t,data,ncoefs,lik,proc,sum=TRUE)

H[,i] = (tg-gg)*1e4
}

C11 = NeweyWest.Var(H,g,5)

# optim searches a much larger space, which can be a problem, but it finds a better
# minimum than

res12 = nlminb(pars,ProfileErr,allpars=pars,times=t,data=data,coef=ncoefs,lik=lik,proc=proc,
in.meth='nlminb',control.in=control.in,control=control.out,gr=ProfileDP)

# Now lets see what happens for a finite-difference approximation

proc2more = make.findif.ode()
proc2more\$more = list()
proc2more\$more\$fn = fhn.fun
proc2more\$names = varnames
proc2more\$parnames = parnames

proc2more\$more\$eps = 1e-6

proc2more\$weights = qwts
proc2more\$qpts = qpts

proc2 = make.SSEproc()
proc2\$more = proc2more
proc2\$bvals = list(bvals=eval.basis(procmore\$qpts,bbasis,0),
dbvals = eval.basis(procmore\$qpts,bbasis,1))

res13 = Profile.GausNewt(pars,t,data,ncoefs,lik,proc2,in.meth='nlminb',control.in)

res14 = nls(~ProfileSSE(pars,times,data,coefs,lik,proc2,in.meth,control.in),
data = list(times=t,data=data,coefs=ncoefs,lik=lik,proc=proc,
in.meth='nlminb',control.in=control.in),
start = list(pars=spars),trace=TRUE)

# Now we'll only observe the first component

data2 = data
data2[,2] = NA

res15 = Profile.GausNewt(pars,t,data2,ncoefs,lik,proc,in.meth='nlminb',control.in)

res16 = nls(~ProfileSSE(pars,times,data,coefs,lik,proc2,in.meth,control.in),
data = list(times=t,data=data2,coefs=ncoefs,lik=lik,proc=proc,
in.meth='nlminb',control.in=control.in),
start = list(pars=spars),trace=TRUE)

# Lets suppose that I've measured a linear combination

source('genlin.R')

lik2more = make.genlin()
lik2more\$more = list()
lik2more\$weights = weights[,1]

lik2more\$more = list()
lik2more\$more\$mat = matrix(c(1,0),1,2)
lik2more\$more\$sub = matrix(0,0,3)

lik2 = lik;
lik2\$more = lik2more;

data3 = as.matrix(data[,1],nrow(data),1)

res17 = Profile.GausNewt(pars,t,data3,ncoefs,lik2,proc,in.meth='house',control.in)

# Now lets add estimating a set of parameters in lik to the mix

lik3more = lik2more
lik3more\$more\$mat = matrix(0,1,2)
lik3more\$more\$sub = matrix(c(1,1,4,1,2,5),2,3,byrow=T)

lik3 = lik2
lik3\$more = lik3more

proc2 = proc
proc2\$more\$parnames = c(proc\$more\$parnames,'l1','l2')

pars2 = c(pars,1,0)
names(pars2) = proc2\$more\$parnames

res18 = Profile.GausNewt(pars2,t,data3,ncoefs,lik3,proc2,in.meth='nlminb',control.in)

res19 = optim(pars2,ProfileErr,allpars=pars2,times=t,data=data3,ncoefs,lik=lik3,proc=proc2,
in.meth='nlminb',control.in=control.in,control=control.out,gr=ProfileDP,method="BFGS")

res20 = nlminb(pars2,ProfileErr,allpars=pars2,times=t,data=data3,coef=ncoefs,lik=lik3,proc=proc2,
in.meth='nlminb',control.in=control.in,control=control.out,gr=ProfileDP)

f = ProfileErr(res20\$par,res20\$par,t,data3,ncoefs,lik3,proc2,in.meth="nlminb",control.in=control.in)
g = ProfileDP(res20\$par,res20\$par,t,data3,ncoefs,lik3,proc2,sum=FALSE)

gg = apply(g,2,sum)

H = matrix(0,5,5)

for(i in 1:5){
tpars = res20\$par
tpars[i] = tpars[i] + 1e-4

tf = ProfileErr(tpars,tpars,t,data3,ncoefs,lik3,proc2,in.meth="nlminb",control.in=control.in)
tg = ProfileDP(tpars,tpars,t,data3,ncoefs,lik3,proc2,sum=TRUE)

H[,i] = (tg-gg)*1e4
}

C20 = NeweyWest.Var(0.5*(H+t(H)),g,5)

res21 = nls(~ProfileSSE(pars,times,data,coefs,lik,proc,in.meth,control.in),
data = list(times=t,data=data3,coefs=ncoefs,lik=lik3,proc=proc2,
in.meth='nlminb',control.in=control.in),
start = list(pars=pars2),trace=TRUE)

ff =  ProfileSSE(res20\$par,t,data3,ncoefs,lik3,proc2,in.meth="nlminb",control.in)

res22 = maxNR(ProfileErr,start=pars2,allpars=pars2,times=t,data=data3,coef=ncoefs,lik=lik3,proc=proc2,

# Now we'll set up some repeat experiments

x02 = c(1,-1)
names(x02)= c('V','R')
y2 = lsoda(x02,times=t,func=fhn.fun.ode,pars)
y2 = y2[,2:3]

data2 = y2 + matrix(rnorm(802),401,2)

replik = lik
replik\$bvals = diag(rep(1,2))%x%lik\$bvals
replik\$more\$weights = rbind(lik\$more\$weights,lik\$more\$weights)

repproc = proc
repproc\$bvals = list(bvals = diag(rep(1,2))%x%proc\$bvals\$bvals,
dbvals=diag(rep(1,2))%x%proc\$bvals\$dbvals)
repproc\$more\$weights = rbind(proc\$more\$weights,proc\$more\$weights)

reptimes = c(t,t+max(t))

repdata = rbind(data,data2)

coefs3 = solve( t(replik\$bvals)%*%replik\$bvals )%*%( t(replik\$bvals)%*%repdata )

control=control.out,times=reptimes,data=repdata,lik=replik,proc=repproc,pars=spars)

ncoefs = array(res23\$par,dim(coefs3))

ProfileEnv = new.env()
assign('optcoef',ncoefs,3,ProfileEnv)
assign('curcoefs',ncoefs,3,ProfileEnv)

res24 = Profile.GausNewt(spars,reptimes,repdata,ncoefs,replik,repproc,in.meth="nlminb",control.in)

# Lets try this assuming we have functional data

fd.data2 = array(0,c(nrow(data2),2,2))

fd.data2[,2,] = data2
fd.data2[,1,] = data

DEfd2 = data2fd(fd.data2,t,bbasis,fdnames=list(NULL,NULL,c('V','R')) )

res = sse.setup(pars=pars,fd.obj=DEfd2,fn=make.fhn(),lambda=lambda,times=t)

res = smooth.sse(pars=pars,fd.obj=DEfd2,fn=make.fhn(),lambda=lambda,times=t,data=fd.data2,control.in=control.in,in.meth='house')

res = profile.sse(fn=make.fhn(),data=fd.data2,times=t,pars=pars,fd.obj=DEfd2,,lambda=lambda,out.meth='nls',
control.in=control.in,control.out=control.out)

# Alternatively, we can just do the sse setup thing

coefs2 = DEfd2\$coefs
dimnames(coefs2) = list(NULL,NULL,c('V','R'))

res = sse.setup(pars=pars,coefs=coefs2,fn=make.fhn(),basisvals=bbasis,lambda=10000,times=t)

res = smooth.sse(fn=make.fhn(),data=fd.data2,times=t,pars=pars,coefs=coefs2,basisvals=bbasis,
lambda=10000,control.in=control.in)

res = profile.sse(fn=make.fhn(),data=fd.data2,times=t,pars=pars,coefs=coefs2,basisvals=bbasis,
lambda=1e8,out.meth='nls',control.in=control.in,control.out=control.out,in.meth='house')
```

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CollocInfer documentation built on May 2, 2019, 4:03 a.m.