make.Fterm: Check each specification in list of forcing term...
In Data2LD: Functional Data Analysis with Linear Differential Equations

Description Usage Arguments Details Value References See Also Examples

A system of linear differential equations is defined by a list of length equal to the number of variables in the system. Each member of this list defines a single linear differential equation. Within each equation there may be one or more terms involving a coefficient function multiplying either a known fixed function, called a forcing function. Forcing terms often involve a fixed constant multiplier, which is frequently either 1 or -1. This function sets up a list object that specifies the structure of a single term.

1	make.Fterm(funobj, parvec, estimate, Ufd, factor=1)

`funobj`	A specification of the coefficient function. If `funobj` is of class `basisobj`, `fd` or `fdPar`, the coefficient function is a functional data object for a single function. If the class is `list`, its members define a function, its derivative, and other information that may be needed in the definition.
`parvec`	The vector of parameters defining coefficient function.
`estimate`	A vector of the same length as `parvec` containing logical values defining which parameteres are to be estimated (TRUE) or kept fixed (FALSE). If all values are the same, a single TRUE or FALSE is sufficient.
`Ufd`	A known forcing function. This may be specified as a functional data or functional parameter object, but may also be specified as a user-defined function. See function `make.coef` for more details.
`factor`	A real number that is treated as fixed. For example, it is frequently the case that a variable will appear in two or more places in a system of equations, and sometimes multipled by -1.

This function checks that all supplied terms conform to what is required.

A named list object defining a forcing term in a linear differential equation.

J. O. Ramsay and G. Hooker (2017) Dynamic Data Analysis. Springer.

checkModel, make.Variable, make.Xterm, printModel

#  Here is the code that sets up the single forcing term for the 
#  refinery data examnple:
TimeData <- RefineryData[,1]
TrayData <- RefineryData[,2]
ValvData <- RefineryData[,3]
conbasis <- create.constant.basis(c(0,193))
alphafdPar <- fdPar(conbasis)
Valvbreaks <- c(0,67,193)
Valvnbasis <- 2
Valvnorder <- 1
Valvbasis  <- create.bspline.basis(c(0,193), Valvnbasis, Valvnorder, Valvbreaks)
Valvfd     <- smooth.basis(TimeData, ValvData, Valvbasis)$fd
#  Fterm Fields:    funobj      parvec  estimate  Ufd      factor
FTerm <- make.Fterm(alphafdPar, 1.0,    TRUE,     Valvfd,  1)
FList <- vector("list", 1)
FList[[1]] <- FTerm
#
#  For other examples of the use of this function, 
#  see these examples in the description of the function \code{make.Variable}.
#
#  The single forcing term of the head impact data
#
#  The cosine and constant forcing terms for the average temperature in
#  Montreal.
#
#  The 20-step forcing function and its coefficient for the "fda" script data.
#
#  The set point forcing term for control variable of the cruise control data.
#