EuclRandMatrix-class: Euclidean random matrix

Description

Class of Euclidean random matrices.

Arguments

Objects from the Class

Objects can be created by calls of the form new("EuclRandMatrix", ...). More frequently they are created via the generating function EuclRandMatrix.

Slots

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.

Extends

Class "EuclRandVariable", directly.
Class "RandVariable", by class "EuclRandVariable".

Methods

coerce: 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.
Dim: signature(object = "EuclRandMatrix"): accessor function for slot Dim.
Dim<-: signature(object = "EuclRandMatrix", ): replacement function for slot Dim.
ncol: signature(x = "EuclRandMatrix"): number of columns of x.
nrow: signature(x = "EuclRandMatrix"): number of rows of x.
dimension: signature(object = "EuclRandMatrix"): dimension of the Euclidean random variable.
evalRandVar: signature(RandVar = "EuclRandMatrix", x = "numeric"): evaluate the slot Map of RandVar at x.
evalRandVar: signature(RandVar = "EuclRandMatrix", x = "matrix"): evaluate the slot Map of RandVar at x.
evalRandVar: 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.
evalRandVar: 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.
t: signature(x = "EuclRandMatrix"): transposes x. In addition, the results of the functions in the slot Map of x are transposed.
show: 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".
Arith: 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.
Arith: 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.
Arith: 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.
Math: signature(x = "EuclRandMatrix"): Given a "Math" group generic fct, the Euclidean random matrix fct(x) is returned.
E: signature(object = "UnivariateDistribution", fun = "EuclRandMatrix", cond = "missing"): expectation of fun under univariate distributions.
E: signature(object = "AbscontDistribution", fun = "EuclRandMatrix", cond = "missing"): expectation of fun under absolutely continuous univariate distributions.
E: signature(object = "DiscreteDistribution", fun = "EuclRandMatrix", cond = "missing"): expectation of fun under discrete univariate distributions.
E: signature(object = "MultivariateDistribution", fun = "EuclRandMatrix", cond = "missing"): expectation of fun under multivariate distributions.
E: signature(object = "DiscreteMVDistribution", fun = "EuclRandMatrix", cond = "missing"): expectation of fun under discrete multivariate distributions.
E: signature(object = "UnivariateCondDistribution", fun = "EuclRandMatrix", cond = "numeric"): conditional expectation of fun under conditional univariate distributions.
E: signature(object = "AbscontCondDistribution", fun = "EuclRandMatrix", cond = "numeric"): conditional expectation of fun under absolutely continuous conditional univariate distributions.
E: signature(object = "DiscreteCondDistribution", fun = "EuclRandMatrix", cond = "numeric"): conditional expectation of fun under discrete conditional univariate distributions.

Author

Matthias Kohl Matthias.Kohl@stamats.de

Examples

Run this code

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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