Atensorfn: Compute the four-way tensors corresponding to pairs of...
In Data2LD: Functional Data Analysis with Linear Differential Equations
Description
Usage
Arguments
Details
Value
References
Description
Forcing terms consist of the product of a coefficient function that must be estimated
and a known forcing function that does not. When both of these functions in a forcing
term are defined by B-splines, the product involves an inner product of two B-spline
basis systems. When a product of two forcing 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.
Usage
1
Atensorfn(modelList)
Arguments
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.
Details
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.
Value
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 myAtensor[[ivar]][[ntermj]][[ntermk]].
References
J. O. Ramsay and G. Hooker (2017) Dynamic Data Analysis. Springer.
Data2LD documentation built on Aug. 6, 2020, 1:08 a.m.
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Description Usage Arguments Details Value References
Description
Forcing terms consist of the product of a coefficient function that must be estimated
and a known forcing function that does not. When both of these functions in a forcing
term are defined by B-splines, the product involves an inner product of two B-spline
basis systems. When a product of two forcing 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.
Usage
1 | Atensorfn(modelList)
|
Arguments
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. |
Details
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.
Value
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 myAtensor[[ivar]][[ntermj]][[ntermk]].
References
J. O. Ramsay and G. Hooker (2017) Dynamic Data Analysis. Springer.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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