README.md

In astamm/fuse: Functions with Space Embedding

Overview of the fuse package

The fuse package (which stands for FU*nctions with Space E*mbedding) provides R6 classes for describing functional data with embedding in infinite-dimensional Hilbert spaces. Currently supported spaces are Sobolev spaces (including the popular (L^2) space of square-integrable functions) and Bayes spaces. In particular, addition, scalar multiplication, inner product and induced distance provide the vector space structure of each supported Hilbert space.

The R6 class implementation enables reference semantics which authorizes in-place operations, assigning only once the value in memory. The object is then accessed through its pointer which avoids repeatedly creating and deleting objects into memory. This has however to be manipulated with caution because methods accessed through the public members of the R6 class do modify on purpose the object. For users who would not want that extra level of reasoning or who would not need the computational speed-up provided by reference semantics, the package provides usual S3 methods for objects of class FunctionalData for all S3 generics in the Math, Ops, Summary and Complex groups.

Warning: The package currently supports only univariate functional data defined over univariate domains. Extensions to multivariate domains and multivariate functional data is currently under implementation.

Installation

You can install fuse from github with:

# install.packages("devtools")
devtools::install_github("astamm/fuse")

Example

library(fuse)

We can for example generate a FunctionalData version of the density of the standard normal distribution. If we create it embedded in Sobolev spaces and multiply it by 2, we obtain the following function:

f <- SobolevData$new(grid = c(-5, 5), value = dnorm, resolution = 100L)
(2 * f)$plot()

This is essentially the original density pointwise multiplied by a factor of 2 which does not result in a density anymore. If instead we embed the density of the standard normal distribution in Bayes space and again multiply it by 2, we get:

g <- BayesData$new(grid = c(-5, 5), value = dnorm, resolution = 100L)
(2 * g)$plot()

This shows a fundamental difference between Sobolev and Bayes spaces. In the latter, adding twice the information content in g provides additional information and thus has the effect of diminishing the variance of the resulting distribution which turns out to be another centered normal distribution with smaller variance.

astamm/fuse documentation built on May 3, 2019, 4:04 p.m.