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 are typically one or more terms involving a coefficient function multiplying either a derivative of one of the variables in the system. These 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.Xterm(funobj, parvec, estimate, variable, derivative=0, factor=1)
|
funobj |
A specification of the coefficient function. If |
parvec |
The vector of parameters defining coefficient function. |
estimate |
A vector of the same length as |
variable |
An integer specifying the variable within which this is a term. |
derivative |
The order of the derivative of the variable. |
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 homogeous term in a linear differential equation.
J. O. Ramsay and G. Hooker (2017) Dynamic Data Analysis. Springer.
make.Fterm
,
make.Variable
,
printModel
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 28 29 30 31 32 33 34 35 36 37 38 | # Here is the code that sets up the single homogeneous term for the
# refinery data examnple:
conbasis <- create.constant.basis(c(0,193))
betafdPar <- fdPar(conbasis)
# Xterm Fields: funobj parvec estimate variable deriv. factor
XTerm <- make.Xterm(betafdPar, 0.04, TRUE, 1, 0, -1)
# Enter this list object in a list of length one.
XList <- vector("list", 1)
XList[[1]] <- XTerm
# Here is the code that sets up the single homogeneous term involving a
# non-functional data function for the average temperature for Montreal.
# Functions \code{fun.explinear} and \code{fun.Dexplinear} are in the
# package, and compute the positive value of the exponential transform
# of a functional data object and its derivative. The basis object
# Set up the list object for the positive coefficient for
# the homogeneous term.
# \code{Wbasisobj} is also supplied in the list object \code{linfun}.
nWbasis <- 7
Wbasisobj <- create.fourier.basis(c(0,365), nWbasis)
linfun <- list(fd=fun.explinear, Dfd=fun.Dexplinear, more=Wbasisobj)
estimate = rep(TRUE,7)
estimate[7] <- FALSE
parvec <- matrix(0,7,1)
Xterm <- make.Xterm(funobj=linfun, parvec=parvec, estimate=estimate,
variable=1, derivative=0, factor= -1)
XList <- vector("list", 1)
XList[[1]] <- Xterm
#
# For other examples of the use of this function,
# see these examples in the description of the function \code{make.Variable}.
#
# The single homogeneous term of the head impact data
#
# The single zero derivative terms in the two second order equations
# for the "fda" script model.
#
# The speed and control terms of the cruise control data
#
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