# 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.