make.transform: Transfer Functions

In CollocInfer: Collocation Inference for Dynamic Systems

Transfer Functions

Description

Returns a list of functions that calculate the transform and its derivatives.

Usage

make.id()

make.exp()

make.genlin()

make.fhn()

make.Henon()

make.SEIR()

make.NS()

chemo.fun(times,y,p,more=NULL)

Arguments

All the functions created by make... functions, require the arguments needed by chemo.fun

times	Evaluation times
y	Values of the state at the evaluation times
p	Parameters to be used
more	A list of additional arguments, in this case NULL, for pomp.sekelton and pomp.dmeasure, more should be a list containing a pomp object in the element pomp.obj.

Details

make.genlin requires the specification of further elements in the list. In particular the element more should be a list containing

mat

a matrix defining the linear transform before any parameters are added. This may be all zero, but it may also specify fixed elements, if desired.

sub

a k-by-3 matrix indicating which parameters should be entered into which elements of mat. Each row is a triple giving the row and colum of mat to be specified and the element of the parameter vector that should be substituted. sub over-rides any values in mat.

force

if input functions are given, these are given as a list.

force.mat

specifying the influence of the elements of force on the state variables. Defined as in mat.

force.sub

defined as in sub, over-rides the elements of force.mat with parameter values.

make.diagnostics estimates forcing-function diagnostics as in Hooker, 2009 for goodness-of-fit assessment. It requires

psi

Values of a basis expansion for forcing functions at the quadrature points.

which

Which states are to be forced?

fn, dfdx, d2fdx2

Functions and derivatives as would be used to estimate parameters for the original equations.

pars

Parameters to go into more$fn.

make.SEIR estimates parameters and a seasonal variation in the infection rate in an SEIR model. It requires the specification of the seasonal change rate in more by a list with objects

beta.fun

A function to calculate beta, it should have arguments t, p and betadef and return a matrix giving the value of beta at times t with parameters p.

beta.dfdp

Should calculate the derivative of beta.fun with respect to p, at times t returning a matrix. The matrix should be of size length(t) by length(p) where p is the entire parameter vector.

betadef

Additional inputs (eg bases) to beta.fun and beta.dfdp.

make.NS provides functions for the North Shore example. This is a possibly time-varying forced linear system of one dimension. It requires more to specify betabasis to describe the autoregressive coefficient, and alphabasis to provide a contant in front of the functional data object rainfd.

chemo.fun Is a five-state predator-prey-resources model used as an example. It stands alone as a function and should be used with the findif.ode functions.

Value

A list of functions that calculate the transform and its derivatives, in a form compatible with the collocation inference functions.

make.id	returns the identity transform.
make.exp	returns the exponential transform.
make.genlin	returns a linear combination transform – see details section below.
make.fhn	returns the FitzHugh-Nagumo equations.
make.Henon	reutrns the Henon map.
make.SEIR	returns SEIR equations for estimating the shape of a seasonal forcing component.
make.diagnostics	functions to perform forcing function diagnostics.

See Also

LS.setup, multinorm.setup

Examples

# Observe the FitzHugh-Nagumo equations

proc = make.SSEproc()
proc$more = make.fhn()

lik = make.SSElik()
lik$more = make.id()

# Observe an unknown scalar transform of each component of a Henon map, given
# in the first two elements of the parameter vector:

proc = make.Dproc()
proc$more = make.multinorm()
proc$more$more = c(make.Henon,make.cvar)

lik = make.multinorm()
lik$more = c(make.genlin,make.cvar)
lik$more$more = list(mat = matrix(0,2,2),sub=matrix(c(1,1,1,2,2,2),2,3,byrow=TRUE))

# Model SEIR equations on the log scale and then exponentiate

lik = make.SSElik()
lik$more = make.exp()

proc = make.SSEproc()
proc$more = make.logtrans()
proc$more$more = make.SEIR()

CollocInfer documentation built on April 4, 2025, 2:21 a.m.