Description Usage Arguments Details Value See Also Examples

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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | ```
make.id()
make.exp()
make.exptrans()
make.genlin()
make.fhn()
make.Henon()
make.SEIR()
make.NS()
chemo.fun(times,y,p,more=NULL)
``` |

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 |

`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.

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. |

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | ```
# 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()
``` |

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