"MixComp" --- manipulation of MixAR time seriesClass "MixComp" represents components of mixture autoregressive
time series and their transformations obtained by arithmetic and
related operations. Methods are provided to allow convenient
computation with such time series.
Objects can be created by calls of the form new("MixComp", ...).
It is more usual however to obtain such objects initially
from functions such as mix_ek. Methods are defined to allow for
convenient and intuitive further manipulation of such objects.
Internally, an object of class MixComp is a matrix with one column
for each component. However, methods for arithmetic operations
involving MixComp objects are defined to perform natural
operations for mixture objects. For example, multiplication by
vectors is commutative and ``does the right thing''.
m:Object of class "matrix" with one column correponding to
each component of the mixture AR model.
Arithmetic operations involving MixComp objects are defined
to allow for convenient execution of computations for mixture
autoregressive models, see class "MixComp".
signature(e1 = "MixComp", e2 = "missing"):
unary minus for "MixComp" objects.
signature(e1 = "numeric", e2 = "MixComp"):
If e2 is thought of as a matrix, \(m\), then the number
of elements of e1 must be the same as the number of rows
of \(m\) and each column of \(m\) is subtracted from
e1, see also "mix_ek", "mix_hatk".
As a special case, if \(m\) has only one row, then it is
subtracted from each element of e1, i.e. that row is
replicated to obtain a matrix with as many rows as the length of
e1 and then subtracted from e1 as above.
The result is a MixComp object.
signature(e1 = "MixComp", e2 = "numeric"):
This is analogous to the above method. (FIXME: the code
of this function does not deal with the special case as in the
above method. Is this an omission or I have done it on purpose?)
signature(e1 = "function", e2 = "MixComp"):
This applies the function e1 to each element of
e2. Together with the arithmetic operations this allows for
easy computation with MixComp objects (e.g. pdfs, likelihoods).
signature(e1 = "character", e2 = "MixComp"):
signature(e1 = "list", e2 = "MixComp"):
If e1 is of length one it specifies a function to be
applied to each element of e2, otherwise it is a list of
functions, such that the \(i\)th function is applied to the
\(i\)th column of e2@m.
signature(e1 = "MixComp", e2 = "MixComp"): ...
signature(e1 = "MixComp", e2 = "numeric"):
see the following.
signature(e1 = "numeric", e2 = "MixComp"):
``Column'' \(i\) of the MixComp object is multiplied by
the \(i\)th element of the numeric vector, i.e. each ``row''
of the MixComp object is multiplied by the vector (or, the
vector is replicated to a matrix to be multiplied by the
MixComp object).
signature(e1 = "function", e2 = "MixComp"):
Multiplying a function by a MixComp object actually
applies the function to each element of the object.
This is a misuse of methods, prefer operator
%of% which does the same.
signature(e1 = "character", e2 = "MixComp"):
The first argument is a name of a function which is
applied to each element of the MixComp object. This is a
misuse of methods, see operator %of%
which does the same.
signature(e1 = "MixComp", e2 = "numeric"):
signature(e1 = "numeric", e2 = "MixComp"):
Division works analogously to "*".
signature(e1 = "MixComp", e2 = "numeric"):
If k is a scalar, raise each element of e1@m to
power k.
(For consistency this operation should have the semantics of "*" and "/" but this operator probably makes sense only for scalar 'e2', where the semantics doesn't matter. So, don't bother for now.)
signature(e1 = "numeric", e2 = "MixComp"):
signature(e1 = "MixComp", e2 = "numeric"):
Addition involving MixComp objects works analogously to subtraction.
signature(x = "MixComp", y = "missing", star = "missing", plus = "missing"):
With one argument inner computes the sum of the columns of
the argument. This is conceptually equivalent to y being a
vector of ones.
signature(x = "MixComp", y = "numeric", star = "missing", plus = "missing"):
signature(x = "numeric", y = "MixComp", star = "missing", plus = "missing"):
The number of elements of the numeric argument should be equal to
the number of rows of the MixComp object. Effectively,
computes the inner product of the two arguments. The order of the
arguments does not matter.
Returns a numeric vector.
signature(x = "MixComp", y = "numeric", star = "ANY", plus = "ANY"):
Computes a generalised inner product of x with y using the
specified functions in place of the usual "*" and "+"
operations. The defaults for star and + are
equivalent to multiplication and addition, respectively.
Note that "+" is a binary operation (not \(n\)-ary) in R. So
technically the correct way to specify the default operation here
is "sum" or sum. Since it is easy to make this mistake, if
plus == "+", it is replaced by "sum".
(In fact, plus is given a single argument, the vector of
values to work on. Since "+" works as a unary operator on one
argument, it would give surprising results if left as is.)
signature(x = "MixComp", y = "numeric", star = "ANY", plus = "missing"):
This is a more efficient implementation for the case when
plus = sum.
signature(x = "MixComp"):
Number of components.
signature(x = "MixComp")A "MixComp" object is essentially a matrix. This method
gives the dimension of the underlying matrix. This method
indirectly ensures that nrow() and ncol() work
naturally for "MixComp" objects.
Georgi N. Boshnakov
## dim, nrow, ncol
a <- new("MixComp", m = matrix(c(1:7, 11:17, 21:27), ncol = 3))
a
dim(a)
nrow(a)
ncol(a)
mix_ncomp(a)
-a
a - 1:7
1:7 + a
2*a
b <- new("MixComp", m = matrix(rnorm(18), ncol = 3))
## apply a function to the columns of a MixComp object
pnorm %of% b
## apply a separate function to to each column
flist <- list(function(x) pnorm(x),
function(x) pt(x, df = 5),
function(x) pt(x, df = 4) )
flist %of% b
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