# Glossary of Common Terms#

This glossary contains concepts and API elements specific to the functional data analysis setting or for the package scikit-fda. If the term you are looking is not listed here, it may be a more generally applicable term listed in the scikit-learn Glossary of Common Terms and API Elements.

## General Concepts#

codomain#

The set of allowed output values of a function. Note that the set of actual output values, called the image, can be a strict subset of the codomain.

curve#
trajectory#

A functional data object whose domain and codomain are both the set of real numbers ($$\mathbb{R}$$). Thus, its dim_domain and dim_codomain attributes shall both be 1.

domain#

The set of possible input values of a function.

domain range#

The valid range where a function can be evaluated. It is a Python sequence that contains, for each dimension of the domain, a tuple with the minimum and maximum values for that dimension. Usually used in plotting functions and as the domain of integration for this function.

FDA#
Functional Data Analysis#

The branch of statistics that deals with curves, surfaces or other objects varying over a a continuum (functional data objects).

functional data#

A collection of functional data objects. Represented by a FData object.

functional data object#
functional data objects#
functional object#
functional objects#

An object of study of Functional Data Analysis. It is a function between $$\mathbb{R}^p$$ and $$\mathbb{R}^q$$. Usually represented by a FData object of length 1, but in some cases regular Python callables are also accepted.

functional observation#
functional observations#

An observed functional data object, represented as a FData object of length 1.

image#

The set of actual ouput values that a function takes. It must be a (non necessarily strict) subset of the codomain.

multivariate functional data#

Often used for functional data where each functional data object is a vector-valued function.

multivariate object#
multivariate objects#

An object of study of multivariate statistics. It is a vector of possibly related variables, represented as a 1d array.

operator#
operators#

Function whose domain is a set of functions.

vector-valued function#

A functional data object that outputs vectors, that is, its codomain has dimension greater than 1.