Class of Euclidean random matrices.
Objects can be created by calls of the form new("EuclRandMatrix", ...)
.
More frequently they are created via the generating function
EuclRandMatrix
.
Dim
vector of positive integers: Dimensions of the random matrix.
Map
Object of class "list"
: list of functions.
Domain
Object of class "OptionalrSpace"
domain of the random matrix.
Range
Object of class "OptionalrSpace"
range of the random matrix.
Class "EuclRandVariable"
, directly.
Class "RandVariable"
, by class "EuclRandVariable"
.
signature(from = "EuclRandMatrix", to = "EuclRandVarList")
:
create a "EuclRandVarList"
object from a Euclidean random matrix.
signature(x = "EuclRandMatrix")
: generates
a new Euclidean random variable/matrix by extracting elements of
the slot Map
of x
.
signature(object = "EuclRandMatrix")
: accessor function
for slot Dim
.
signature(object = "EuclRandMatrix", )
: replacement
function for slot Dim
.
signature(x = "EuclRandMatrix")
: number of columns of x
.
signature(x = "EuclRandMatrix")
: number of rows of x
.
signature(object = "EuclRandMatrix")
: dimension
of the Euclidean random variable.
signature(RandVar = "EuclRandMatrix", x = "numeric")
:
evaluate the slot Map
of RandVar
at x
.
signature(RandVar = "EuclRandMatrix", x = "matrix")
:
evaluate the slot Map
of RandVar
at x
.
signature(RandVar = "EuclRandMatrix", x = "numeric", distr = "Distribution")
:
evaluate the slot Map
of RandVar
at x
assuming
a probability space with distribution distr
. In case x
does not lie in the support of distr
NA
is returned.
signature(RandVar = "EuclRandMatrix", x = "matrix", distr = "Distribution")
:
evaluate the slot Map
of RandVar
at rows of x
assuming a probability space with distribution distr
. For those
rows of x
which do not lie in the support of distr
NA
is returned.
signature(x = "EuclRandMatrix")
: transposes x
. In
addition, the results of the functions in the slot Map
of
x
are transposed.
signature(object = "EuclRandMatrix")
signature(x = "matrix", y = "EuclRandMatrix")
:
matrix multiplication of x
and y
. Generates
an object of class "EuclRandMatrix"
.
signature(x = "numeric", y = "EuclRandMatrix")
:
matrix multiplication of x
and y
. Generates
an object of class "EuclRandMatrix"
.
signature(x = "EuclRandVariable", y = "EuclRandMatrix")
:
matrix multiplication of x
and y
. Generates
an object of class "EuclRandMatrix"
.
signature(x = "EuclRandMatrix", y = "matrix")
:
matrix multiplication of x
and y
. Generates
an object of class "EuclRandMatrix"
.
signature(x = "EuclRandMatrix", y = "numeric")
:
matrix multiplication of x
and y
. Generates
an object of class "EuclRandMatrix"
.
signature(x = "EuclRandMatrix", y = "EuclRandMatrix")
:
matrix multiplication of x
and y
. Generates
an object of class "EuclRandMatrix"
.
signature(x = "EuclRandMatrix", y = "EuclRandVariable")
:
matrix multiplication of x
and y
. Generates
an object of class "EuclRandMatrix"
.
signature(e1 = "numeric", e2 = "EuclRandMatrix")
:
Given a numeric vector e1
, a Euclidean random matrix e2
and an arithmetic operator op
, the Euclidean random matrix
e1 op e2
is returned.
signature(e1 = "EuclRandMatrix", e2 = "numeric")
:
Given a Euclidean random matrix e1
, a numeric vector e2
,
and an arithmetic operator op
, the Euclidean random matrix
e1 op e2
is returned.
signature(e1 = "EuclRandMatrix", e2 = "EuclRandMatrix")
:
Given two Euclidean random matrices e1
and e2
,
and an arithmetic operator op
, the Euclidean random matrix
e1 op e2
is returned.
signature(x = "EuclRandMatrix")
:
Given a "Math"
group generic fct
, the Euclidean random
matrix fct(x)
is returned.
signature(object = "UnivariateDistribution", fun = "EuclRandMatrix", cond = "missing")
:
expectation of fun
under univariate distributions.
signature(object = "AbscontDistribution", fun = "EuclRandMatrix", cond = "missing")
:
expectation of fun
under absolutely continuous univariate distributions.
signature(object = "DiscreteDistribution", fun = "EuclRandMatrix", cond = "missing")
:
expectation of fun
under discrete univariate distributions.
signature(object = "MultivariateDistribution", fun = "EuclRandMatrix", cond = "missing")
:
expectation of fun
under multivariate distributions.
signature(object = "DiscreteMVDistribution", fun = "EuclRandMatrix", cond = "missing")
:
expectation of fun
under discrete multivariate distributions.
signature(object = "UnivariateCondDistribution", fun = "EuclRandMatrix", cond = "numeric")
:
conditional expectation of fun
under conditional univariate distributions.
signature(object = "AbscontCondDistribution", fun = "EuclRandMatrix", cond = "numeric")
:
conditional expectation of fun
under absolutely continuous conditional univariate distributions.
signature(object = "DiscreteCondDistribution", fun = "EuclRandMatrix", cond = "numeric")
:
conditional expectation of fun
under discrete conditional univariate distributions.
Matthias Kohl Matthias.Kohl@stamats.de
L1 <- list(function(x){x}, function(x){x^2}, function(x){x^3}, function(x){x^4},
function(x){x^5}, function(x){x^6})
L2 <- list(function(x){exp(x)}, function(x){abs(x)},
function(x){sin(x)}, function(x){floor(x)})
R1 <- new("EuclRandMatrix", Map = L1, Dim = as.integer(c(3,2)),
Domain = Reals(), Range = Reals())
dimension(R1)
R1[1:2, 2]
R1[1:2, 1:2]
Map(R1[1,2])
Map(t(R1)[2,1])
R2 <- EuclRandMatrix(Map = L2, ncol = 2, Domain = Reals(), dimension = 1)
dimension(R2)
(DL <- imageDistr(R2, Norm()))
plot(DL)
Map(gamma(R2)) # "Math" group
## "Arith" group
Map(2/R1)
Map(R2 * R2)
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