Description Usage Arguments Details Value References
A linear differential equation involves a set of terms consisting of the product
of a coefficient function that must be estimated and a derivative (including a
derivative order 0) of one of the variables in the system. We call this portion
of the equation the homogeneous part of the equation, as opposed to the part
consisting of forcing terms involving known forcing functions.
When both of the functions in a homogeneous term are defined by B-splines, the
product involves an inner product of two B-spline basis systems.
When a product of two homogeneous terms are required, as is usual in the
the use of the Data2LD package, a great improvement in efficiency of computation
can be acheived by an initial computation of the four-way array or tensor resulting
by taking the inner products of all possible quadruples of the B-spline basis
functions. Memoization is the process of storing these tensors in memory so that
they do not need to be re-computed each time the Data2LD.R function is called.
Memoization is taken care of automatically in the code using the R.cache package,
and is activated the first time a new modelList
object is encountered.
Normally the user does not have to worry about the memorization procedure. It is
possible, however, to manually re-activate the memoization.
However, users may also want to construct these four-way tensors
manually for debugging and other purposes, and this function is made available
for this reason.
1 | Btensorfn(XbasisList, modelList)
|
XbasisList |
A list object of length equal to the number of equations in the system. Each member of this list is a functional basis object used to approximate the values of the corresponding variable. |
modelList |
A list object containing the specification of a Data2LD model. Each member of this list contains a list object that defines a single linear differential equation. |
Variable specifications can be set by an invocation of function
make.Variable
for each linear differential equation in the system.
Functions Atensorfn
, BAtensorfn
and Btensorfn
will not
normally be required by users since they are invoked automatically with the
function checkModel
, which is required to be invoked before the
analysis of the data.
A list object of length equal to the number of variables in the system.
Each of the members of this list is a two-dimensional list object, and the members
of this list are the four-way tensors set up as vectors for each of the
possible pairs of forcing terms. All levels of the this list structure are designed
to be accessed numerically by a call like myBtensor[[ivar]][[ntermj]][[ntermk]]
.
J. O. Ramsay and G. Hooker (2017) Dynamic Data Analysis. Springer.
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