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

```## Example Diagnostics -- Learning the FitzHugh-Nagumo Equations
#
# Demonstration estimation of function functions. This also provides
# a template for random-effects treatment within profiling.

library(fda)
library(odesolve)
library(MASS)
library('CollocInfer')

source('../Devel/Diagnostics.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,t,make.fhn()\$fn.ode,pars)
y = y[,2:3]

data = y + 0.2*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

DEfd = data2fd(data,t,bbasis)
coefs = DEfd\$coefs

names(coefs) = c('V','R')

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

lambda = c(100,100)
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 = eval.basis(t,bbasis)

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

procmore = make.genlin()
procmore\$names = varnames
procmore\$parnames = parnames
procmore\$more = list(mat=matrix(0,2,2),sub= matrix(c(1,1,1,1,2,2,2,1,3,2,2,4),4,3,byrow=TRUE))

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

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

spars = c(0,1,-1,0)

Ires = inneropt(data,times=t,spars,coefs,lik,proc,in.meth='nlminb')

Ores = outeropt(data=data,times=t,pars=spars,coefs=Ires\$coefs,lik=lik,proc=proc,
in.meth="nlminb",out.meth="nlminb")

traj = as.matrix(proc\$bvals\$bvals %*% Ores\$coefs)
dtraj = as.matrix(proc\$bvals\$dbvals %*% Ores\$coefs)
ftraj = dtraj - proc\$more\$fn(proc\$more\$qpts,dtraj,Ores\$pars,proc\$more\$more)

par(mfrow=c(2,2))
for(i in 1:2){
for(j in 1:2){
plot(traj[,i],ftraj[,j],type='l')
}
}

## Now we estimate some forcing functions

fbasis = create.bspline.basis(range=range,nbasis=23,norder=4)

dproc = make.SSEproc()
dproc\$more = make.diagnostics()
dproc\$more\$qpts = procmore\$qpts
dproc\$more\$weights = procmore\$weights
dproc\$more\$more = procmore
dproc\$more\$more\$p = Ores\$pars
dproc\$more\$more\$which = 1:2
dproc\$more\$more\$psi = eval.basis(procmore\$qpts,fbasis)
dproc\$bvals = list(bvals=eval.basis(procmore\$qpts,bbasis,0),
dbvals = eval.basis(procmore\$qpts,bbasis,1))

dpars = rep(0,2*fbasis\$nbasis)

dOres = outeropt(data=data,times=t,pars=dpars,coefs=Ires\$coefs,lik=lik,proc=dproc,
in.meth="nlminb",out.meth="nlminb")

# Trajectories

force = dproc\$more\$more\$psi %*% matrix(dOres\$par,fbasis\$nbasis,2)
traj = dproc\$bvals\$bvals %*% dOres\$coefs

plot(traj[,1],force[,1],type='l')
```

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